From bba29382e307cd5f8028769964fe2ebd64883167 Mon Sep 17 00:00:00 2001
From: Riccardo Giuntoli <taglio@gmail.com>
Date: Sun, 16 Jan 2022 19:12:02 +0100
Subject: [PATCH] s

s
---
 .../radio_aficion/Documentos/Resumen IEM.pdf  | Bin 0 -> 1020506 bytes
 es.telecomlobby.com/radio_aficion/URE_1.html  | 301 ++++++++++++-----
 es.telecomlobby.com/radio_aficion/URE_1.md    | 303 +++++-------------
 3 files changed, 311 insertions(+), 293 deletions(-)
 create mode 100644 es.telecomlobby.com/radio_aficion/Documentos/Resumen IEM.pdf

diff --git a/es.telecomlobby.com/radio_aficion/Documentos/Resumen IEM.pdf b/es.telecomlobby.com/radio_aficion/Documentos/Resumen IEM.pdf
new file mode 100644
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diff --git a/es.telecomlobby.com/radio_aficion/URE_1.html b/es.telecomlobby.com/radio_aficion/URE_1.html
index e944e5bd..8797e65b 100644
--- a/es.telecomlobby.com/radio_aficion/URE_1.html
+++ b/es.telecomlobby.com/radio_aficion/URE_1.html
@@ -2,14 +2,16 @@
 <html>
 <head>
 <meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>
-<title>URE_1</title><link href='https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text/css' /><style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; }
+
+<link href='https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text/css' /><style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; --title-bar-height:20px; }
+.mac-os-11 { --title-bar-height:28px; }
 html { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }
-body { margin: 0px; padding: 0px; height: auto; bottom: 0px; top: 0px; left: 0px; right: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
+body { margin: 0px; padding: 0px; height: auto; inset: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
 iframe { margin: auto; }
 a.url { word-break: break-all; }
 a:active, a:hover { outline: 0px; }
 .in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }
-#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 40px; }
+#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }
 #write.first-line-indent p { text-indent: 2em; }
 #write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }
 #write.first-line-indent li { margin-left: 2em; }
@@ -65,7 +67,7 @@ div.hr:focus { cursor: none; }
 #write pre.ty-contain-cm { white-space: normal; }
 .CodeMirror-gutters { margin-right: 4px; }
 .md-fences { font-size: 0.9rem; display: block; break-inside: avoid; text-align: left; overflow: visible; white-space: pre; background: inherit; position: relative !important; }
-.md-diagram-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }
+.md-fences-adv-panel { width: 100%; margin-top: 10px; text-align: center; padding-top: 0px; padding-bottom: 8px; overflow-x: auto; }
 #write .md-fences.mock-cm { white-space: pre-wrap; }
 .md-fences.md-fences-with-lineno { padding-left: 0px; }
 #write.fences-no-line-wrapping .md-fences.mock-cm { white-space: pre; overflow-x: auto; }
@@ -77,6 +79,7 @@ div.hr:focus { cursor: none; }
 li div { padding-top: 0px; }
 blockquote { margin: 1rem 0px; }
 li .mathjax-block, li p { margin: 0.5rem 0px; }
+li blockquote { margin: 1rem 0px; }
 li { margin: 0px; position: relative; }
 blockquote > :last-child { margin-bottom: 0px; }
 blockquote > :first-child, li > :first-child { margin-top: 0px; }
@@ -86,10 +89,10 @@ blockquote > :first-child, li > :first-child { margin-top: 0px; }
   body, html { border: 1px solid transparent; height: 99%; break-after: avoid; break-before: avoid; font-variant-ligatures: no-common-ligatures; }
   #write { margin-top: 0px; padding-top: 0px; border-color: transparent !important; }
   .typora-export * { -webkit-print-color-adjust: exact; }
-  html.blink-to-pdf { font-size: 13px; }
   .typora-export #write { break-after: avoid; }
   .typora-export #write::after { height: 0px; }
   .is-mac table { break-inside: avoid; }
+  .typora-export-show-outline .typora-export-sidebar { display: none; }
 }
 .footnote-line { margin-top: 0.714em; font-size: 0.7em; }
 a img, img a { cursor: pointer; }
@@ -100,6 +103,7 @@ p > .md-image:only-child { display: inline-block; width: 100%; }
 #write .MathJax_Display { margin: 0.8em 0px 0px; }
 .md-math-block { width: 100%; }
 .md-math-block:not(:empty)::after { display: none; }
+.MathJax_ref { fill: currentcolor; }
 [contenteditable="true"]:active, [contenteditable="true"]:focus, [contenteditable="false"]:active, [contenteditable="false"]:focus { outline: 0px; box-shadow: none; }
 .md-task-list-item { position: relative; list-style-type: none; }
 .task-list-item.md-task-list-item { padding-left: 0px; }
@@ -130,18 +134,9 @@ a.md-toc-inner { font-size: inherit; font-style: inherit; font-weight: inherit;
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-<div id='write'  class=''><h1><a name="teoría-eléctrica-y-electromagnética-y-apuntes-sobre-la-«la-maquina»" class="md-header-anchor"></a><span>Teoría eléctrica y electromagnética y apuntes sobre la «La Maquina»</span></h1><p><img src="http://telecomlobby.com/Images/felipe_vi_ure_riccardo_giuntoli_radioham_notes.webp" referrerpolicy="no-referrer" alt="Felipe VI URE"></p><p><span>Subiendo una montaña Genovesa, allí fue la primera vez que cargaba con una radio en 27Mhz y banda lateral en mi mochila, soñaba con conectarme con países lejanos y gente desconocida. Allí fue, cerca del 1992. Desde aquella fecha mucha vida ha pasado delante de mis ojos, felicidad, trabajos, amores y muertes. Ahora en el 2020, debajo de esta QSL donde se representa rey Felipe VI de España y su identificación en la radio afición empiezo a estudiar y apuntar mis notas en esta parte de mi pagina web. Pagina donde se subraya que estoy estudiando esta arte con el fin de salir del control neuronal vía radio que ha sido activado sobre mi organismo en Noviembre 2017. Estudio también para juntarme a ti, Saray. Mujer que amo.</span></p><h4><a name="11-estructura-de-la-materia" class="md-header-anchor"></a><span>1.1 Estructura de la materia</span></h4><p><span>Tanto los cuerpos sólidos como los líquidos y gases están compuestos de pequeñas partículas cuyas propiedades son idénticas al cuerpo al cual pertenecen. Se llaman </span><strong><span>moléculas</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Mol%C3%A9cula'><span>[1]</span></a><span> y presentan espacios entra ellos.río*</span></p><h4><a name="111-molécula" class="md-header-anchor"></a><span>1.1.1 Molécula</span></h4><p><span>Están en continuo movimiento y entre ellas existen fuerzas atractivas y repulsivas según el estado en que se encuentre la materia:</span></p><ul><li><strong><span>Sólidos</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/S%C3%B3lido'><span>[2]</span></a><span>, atractivas.</span></li><li><strong><span>Líquidos</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/L%C3%ADquido'><span>[3]</span></a><span>, equilibradas.</span></li><li><strong><span>Gases</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Gas'><span>[4]</span></a><span>, repulsivas.</span></li></ul><p><span>Mediante </span><strong><span>calor</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Calor'><span>[5]</span></a><span> podemos pasar de estado sólido a líquido y de líquido a gaseoso. Mediante el </span><strong><span>frío</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Fr%C3%ADo'><span>[6]</span></a><span> el revés. </span></p><blockquote><p><span>En la red de neuroestimuladores inalámbricos que ven individuos objetivo como clientes del complejo sistema de radio que la compone muchas veces se puede apreciar algo parecido a humo sobresalir de nuestro cuerpo. Es muy posible que los ingenieros que hayan programado este magnifico sistema de radio quieran representar un flujo de calor desde el interior del cuerpo humano hacía fuera. Por esto en red neuronal mensajería subliminal se habla de «maquina a vapor».</span></p></blockquote><p><span>Cada molécula está compuesta por distintos átomos según el </span><strong><span>elemento químico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico'><span>[7]</span></a><span> que constituyan.</span></p><h4><a name="112-átomo" class="md-header-anchor"></a><span>1.1.2 Átomo</span></h4><p><img src="https://telecomlobby.com/Images/tabla_elementos.webp" referrerpolicy="no-referrer" alt="Tabla elementos"></p><p><span>Una molécula la podemos descomponer en partículas muchos menores llamadas </span><strong><span>átomos</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/%C3%81tomo'><span>[8]</span></a><span>. Toda la materia que existe en la naturaleza está formada por cuerpos simples denominados elementos. El átomo es la parte más pequeña de estos cuerpos que conserva las características originales de un elemento cualquiera.</span></p><p><span>Para entender la </span><strong><span>electricidad</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Electricidad'><span>[9]</span></a><span> hay que estudiar átomo y componentes.</span></p><p><span>Cada átomo consta de dos partes el núcleo y la corteza, el núcleo está cargado con carga eléctrica positiva y se compone básicamente de </span><strong><span>protones</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Prot%C3%B3n'><span>[10]</span></a><span>, partículas con carga positiva, y </span><strong><span>neutrones</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Neutr%C3%B3n'><span>[11]</span></a><span>, partículas con </span><strong><span>masa</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Masa'><span>[12]</span></a><span> pero sin </span><strong><span>carga</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica'><span>[13]</span></a><span>. Alrededor del núcleo, existen una o más capas, cuyo conjunto se denomina corteza, donde describen órbitas a gran velocidad los </span><strong><span>electrones</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Electr%C3%B3n'><span>[14]</span></a><span>, partículas de carga negativa fuertemente atraídos por la carga positiva de este y resulta extremadamente difícil cambiarlos de órbita; los de las órbitas exteriores pueden llegar a abandonar un átomo para pasar a otro, o bien quedar como electrones libres.</span></p><h4><a name="113-ionización-o-electrización-carga-eléctrica" class="md-header-anchor"></a><span>1.1.3 Ionización o electrización. Carga eléctrica.</span></h4><p><img src="https://telecomlobby.com/Images/tabla_ionizacion.webp" referrerpolicy="no-referrer" alt="Ionización"></p><p><span>Si no sometidos a la acción de ninguna fuerza externa el átomo es neutro del punto de vista eléctrico. Si perdiese electrones, quedaría cargado positivamente y se denominaría </span><strong><span>ion</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Ion'><span>[15]</span></a><span> positivo, al revés o sea con un exceso de electrones tiene carga negativa y tendremos un ion negativo.</span></p><p><span>La carga eléctrica es un estado de desequilibrio entre el número de electrones y protones; los cuerpos con cargas de distinto signo se atraen entre sí mientras que los que poseen el mismo tipo de carga se repelen. </span></p><h4><a name="114-conductores-semiconductores-y-aislantes" class="md-header-anchor"></a><span>1.1.4 Conductores, semiconductores y aislantes.</span></h4><p><span>Las capas más externas de la corteza del átomo si no están semillenas o sea a tener menos del 50% de su capacidad de electrones existe el peligro de abandono de estos en dichas capas; toman el nombre de electrones libres. Un cuerpo conductor de electricidad es una sustancia compuesta por átomos cuya capa más externa no llega a estar semillena de electrones asegurando así el paso de la </span><strong><span>corriente</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica'><span>[16]</span></a><span> que otra cosa no es que un flujo de electrones libres desde un cuerpo con carga negativa a otro con carga positiva.</span></p><p><span>Los metales tienen una pequeña energía de ionización, tienden a tener un gran número de electrones libres y por ello son buenos conductores de la electricidad. Un aislador o aislante lo forma sustancias que presentan gran resistencia a que las cargas que las forman se desplacen y por tanto no conducen, en condiciones normales, la electricidad.</span></p><blockquote><p><span>Los productos necesarios a cubrir nuestro cuerpo humano del ser receptores y clientes finales de la red de monitorio neuronal son sin duda ninguna aislantes.</span></p></blockquote><p><span>Un </span><strong><span>semiconductor</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Semiconductor'><span>[17]</span></a><span> es un elemento que cambia comportamiento dependiendo donde en que campo eléctrico se encuentre. </span></p><h4><a name="115-conductividad" class="md-header-anchor"></a><span>1.1.5 Conductividad.</span></h4><p><span>Propiedad que tienen los cuerpos o las sustancias de transmitir de un punto a otro de su masa el calor o la electricidad.</span></p><p><span>La </span><strong><span>Comisión Electrotécnica Internacional</span></strong><span> </span><a href='https://www.iec.ch/'><span>[18]</span></a><span> definió como patrón de la conductividad eléctrica la de un hilo de cobre de 1 metro de longitud y un gramo de masa, que da una resistencia de 0,15388 Ω a 20 °C a lo cual asignó una </span><strong><span>conductividad eléctrica</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica'><span>[19]</span></a><span> de 100% IACS, a toda </span><strong><span>aleación</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Aleaci%C3%B3n'><span>[20]</span></a><span> de cobre con una conductividad mayor se le denomina de alta conductividad.</span></p><p><strong><span>Conductancia</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica'><span>[21]</span></a><span> es la medida de la facilidad con que la electricidad fluye a través de un circuito o de un objeto. La unidad de medida de conductancia es el </span><strong><span>Siemens</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Siemens_(unidad)'><span>[22]</span></a><span> y de la conductividad el Siemens/m.</span></p><p><span>Siendo lambda λ un coeficiente de conductividad propio de cada materia podemos expresar la conductancia como </span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n39" cid="n39" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="38.277ex" height="6.196ex" viewBox="0 -1560 16480.2 2667.7" role="img" focusable="false" style="vertical-align: -2.573ex; max-width: 100%;"><defs><path stroke-width="0" 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-Conductancia = \frac{λxsuperficie(cm^2)}{longitud(cm)}\\
-\end{align*}</script></div></div><p><span>La inversa de la conductividad es la </span><strong><span>resistividad</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Resistividad'><span>[23]</span></a><span> que expresa la </span><strong><span>resistencia</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica'><span>[24]</span></a><span> de un conductor de las medidas antes mencionadas, que es la inversa de la conductancia, la temperatura del conductor influye en la resistencia, si aumenta la resistencia también lo hará y viceversa; ocurre en los cuerpos conductores; en los semiconductores el fenómeno es inverso.</span></p><h4><a name="116-campo-eléctrico-intensidad-de-campo-unidad-de-campo-voltiosmetro-potencial-apantallamiento-de-campos-eléctricos" class="md-header-anchor"></a><span>1.1.6 campo eléctrico: intensidad de campo. Unidad de campo: voltios/metro. Potencial. Apantallamiento de campos eléctricos.</span></h4><p><span>Una carga eléctrica es la cantidad de electricidad acumulada en un cuerpo y se mide en una unidad denominada </span><strong><span>Culombio</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Culombio'><span>[25]</span></a><span> que equivale a:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n43" cid="n43" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.086ex" height="2.811ex" viewBox="0 -856.4 11231.4 1210.2" role="img" focusable="false" style="vertical-align: -0.822ex; max-width: 100%;"><defs><path stroke-width="0" id="E21-MJMATHI-43" d="M50 252Q50 367 117 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id="MathJax-Element-2">\begin{align*}
-C = 6,24x10^{18} electrones\\
-\end{align*}</script></div></div><p><span>En cualquier punto del espacio en donde exista una carga eléctrica se origina un </span><strong><span>campo eléctrico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico'><span>[26]</span></a><span> que se manifiesta, experimentalmente, por la fuerza de origen eléctrico a que se halla sometida cualquier carga que se sitúe en el otro punto de su alrededor.</span></p><p><span>La </span><strong><span>ley de Coulomb</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Ley_de_Coulomb'><span>[27]</span></a><span> dice que el valor de la fuerza con que se atraen o se repelen dos cargas puntuales en reposo es directamente proporcional al producto de dichas cargas e inversamente proporcional al cuadrado de la distancia que las separa:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n46" cid="n46" 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y="0"></use><use transform="scale(0.707)" xlink:href="#E22-MJMAIN-31" x="630" y="-213"></use><g transform="translate(899,0)"><use xlink:href="#E22-MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E22-MJMAIN-32" x="630" y="-213"></use></g></g><g transform="translate(470,-726)"><use xlink:href="#E22-MJMATHI-64" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E22-MJMAIN-32" x="740" y="408"></use></g></g></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-3">\begin{align*}
-F = k\frac{q_1q_2}{d^2}\\
-\end{align*}</script></div></div><p><span>estando la carga q1 situada en un punto P a una distancia d de otra carga puntual q2. La intensidad del </span><strong><span>campo eléctrico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico'><span>[28]</span></a><span> en un punto se define como la fuerza ejercida sobre la unidad de carga eléctrica positiva colocada en el citado punto, y viene dada por la expresión:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n48" cid="n48" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.771ex" height="5.612ex" viewBox="0 -1459.5 6790.3 2416.4" role="img" focusable="false" style="vertical-align: -2.017ex; margin-bottom: -0.206ex; max-width: 100%;"><defs><path stroke-width="0" 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0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,11)"><use xlink:href="#E23-MJMATHI-45" x="0" y="0"></use><use xlink:href="#E23-MJMAIN-3D" x="1041" y="0"></use><g transform="translate(1819,0)"><g transform="translate(397,0)"><rect stroke="none" width="1019" height="60" x="0" y="220"></rect><use xlink:href="#E23-MJMATHI-46" x="135" y="676"></use><g transform="translate(60,-686)"><use xlink:href="#E23-MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E23-MJMAIN-32" x="630" y="-213"></use></g></g></g><use xlink:href="#E23-MJMAIN-3D" x="3634" y="0"></use><use xlink:href="#E23-MJMATHI-6B" x="4690" y="0"></use><g transform="translate(5211,0)"><g transform="translate(120,0)"><rect stroke="none" width="1019" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#E23-MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E23-MJMAIN-31" x="630" y="-213"></use></g><g transform="translate(60,-686)"><use xlink:href="#E23-MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E23-MJMAIN-32" x="630" y="-213"></use></g></g></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-4">\begin{align*}
-E = \frac{F}{q_2}=k\frac{q_1}{q_2}\\
-\end{align*}</script></div></div><p><span>La intensidad del campo eléctrico, en un punto dado, se mide en </span><strong><span>voltios</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Voltio'><span>[29]</span></a><span> partido por metro.</span></p><p><span>Si interponemos entre un campo eléctrico y un punto dado una pantalla de material conductor, el citado punto no recibe la influencia del campo eléctrico. Este efecto se conoce como </span><strong><span>apantallamiento</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico'><span>[30]</span></a><span> o blindaje. El </span><strong><span>potencial eléctrico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico'><span>[31]</span></a><span> en un punto es el trabajo que debe realizar una fuerza eléctrica para mover una carga positiva q desde el infinito con potencial cero hasta ese punto, dividido por dicha carga. Es el trabajo que debe realizar una fuerza externa para traer una carga unitaria q desde el infinito hasta el punto considerado en contra de la fuerza eléctrica dividido por esa carga:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n51" cid="n51" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.2ex" height="5.612ex" viewBox="0 -1459.5 3530.6 2416.4" role="img" focusable="false" style="vertical-align: -2.017ex; margin-bottom: -0.206ex; max-width: 100%;"><defs><path stroke-width="0" id="E24-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path><path stroke-width="0" id="E24-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E24-MJMATHI-46" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path><path stroke-width="0" id="E24-MJMATHI-71" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,11)"><use xlink:href="#E24-MJMATHI-56" x="0" y="0"></use><use xlink:href="#E24-MJMAIN-3D" x="1046" y="0"></use><g transform="translate(1824,0)"><g transform="translate(397,0)"><rect stroke="none" width="869" height="60" x="0" y="220"></rect><use xlink:href="#E24-MJMATHI-46" x="60" y="676"></use><use xlink:href="#E24-MJMATHI-71" x="204" y="-686"></use></g></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-5">\begin{align*}
-V = \frac{F}{q}\\
-\end{align*}</script></div></div><p><span>Se puede representar el potencial eléctrico mediante las denominadas </span><strong><span>superficies equipotenciales</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Superficie_equipotencial'><span>[32]</span></a><span>, que son el lugar geométrico de los puntos del espacio en los que el potencial tiene un mismo valor o, dicho de otra manera, las superficies en las que todos sus puntos de un campo de fuerza que tienen el mismo potencial.</span></p><h4><a name="12-teoría-eléctrica" class="md-header-anchor"></a><span>1.2 Teoría eléctrica. </span></h4><h4><a name="121-corriente-eléctrica-voltaje-y-resistencia-circuito-eléctrico" class="md-header-anchor"></a><span>1.2.1 Corriente eléctrica, voltaje y resistencia. Circuito eléctrico.</span></h4><p><img src="https://telecomlobby.com/Images/circuito_simbolos.webp" referrerpolicy="no-referrer" alt="circuito simbolos"></p><p><span>Se denomina corriente eléctrica al paso de electrones a lo largo de un conductor que une dos puntos con distinta carga eléctrica. </span></p><p><span>La </span><strong><span>corriente continua</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Corriente_continua'><span>[33]</span></a><span> es un flujo continuo de electrones a través de un conductor entre dos puntos de distinto potencial y sus valores son constantes, las cargas eléctricas circulan siempre en la misma dirección; es continua toda corriente que mantenga la misma </span><strong><span>polaridad</span></strong><span> </span><a href='https://bit.ly/3nqudHw'><span>[34]</span></a><span>.</span></p><p><span>La </span><strong><span>corriente alterna</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Corriente_alterna'><span>[35]</span></a><span> a la corriente eléctrica en la que la magnitud y dirección varían cíclicamente.</span></p><p><span>Para que circule la corriente eléctrica deben desplazarse los electrones, lo que precisa una fuerza que los empuje la llamada </span><strong><span>fuerza electromotriz</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Fuerza_electromotriz'><span>[36]</span></a><span> que es producida por una diferencia de potencial o </span><strong><span>voltaje</span></strong><span> </span><a href='https://bit.ly/36B9Hgz'><span>[37]</span></a><span>.</span></p><p><span>La intensidad de una corriente eléctrica depende, para una misma diferencia de potencial, del diámetro del </span><strong><span>conductor</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico'><span>[38]</span></a><span>, que opone siempre una </span><strong><span>resistencia</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica'><span>[39]</span></a><span>.</span></p><p><span>Podemos hacer una comparación de términos entre </span><strong><span>hidráulica</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Hidr%C3%A1ulica'><span>[40]</span></a><span> y electricidad:</span></p><ul><li><span>Desnivel; diferencia de potencial.</span></li><li><strong><span>Fuerza hidráulica</span></strong><span> </span><a href='https://bit.ly/2IxeKX7'><span>[41]</span></a><span>; fuerza electromotriz.</span></li><li><span>Tubería; conductor.</span></li><li><span>Caudal de agua; intensidad de corriente</span></li><li><span>Partículas de agua; electrones. </span></li></ul><p><span>Existen seis formas elementales de producción de corriente eléctrica. </span></p><p><span>Un </span><strong><span>circuito eléctrico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Circuito'><span>[42]</span></a><span> es un conjunto de conductores por el que circula la corriente eléctrica y en el cual hay intercalados, generalmente, elementos productores y consumidores de la misma.</span></p><h4><a name="122-unidades-eléctricas-fundamentales-voltios-amperios-y-ohmios" class="md-header-anchor"></a><span>1.2.2 Unidades eléctricas fundamentales: voltios, amperios y ohmios</span></h4><p><span>El voltaje es la presión eléctrica o diferencia del nivel de cargas que existe entre dos puntos como resultado de la presencia de una </span><strong><span>fuerza electromotriz</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Fuerza_electromotriz'><span>[43]</span></a><span> entra ellos. Para medirla se utiliza el </span><strong><span>Voltio</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Voltio'><span>[44]</span></a><span>; 1 V es la fuerza electromotriz necesaria para producir una corriente de 1 </span><strong><span>amperio</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Amperio'><span>[45]</span></a><span> en un circuito cuya resistencia sea de 1 </span><strong><span>ohmio</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Ohmio'><span>[46]</span></a><span>:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n77" cid="n77" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" 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-Voltios = amperios x ohmios
-\end{align*}</script></div></div><p><span>Un </span><strong><span>kilovoltio</span></strong><span> son 1000 voltios. Un </span><strong><span>milivoltio</span></strong><span> es la milésima parte de un voltio y el </span><strong><span>microvoltio μV</span></strong><span> es la millonésima parte del voltio.</span></p><p><span>La corriente eléctrica es el flujo o movimiento de los electrones a través de un conductor como consecuencia de la aplicación de una tensión o diferencia de potencial, la intensidad de corriente es el amperio que corresponde al paso de una carga de un culombio durante un segundo:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n80" cid="n80" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="23.557ex" height="13.55ex" viewBox="0 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-I = \frac{q}{t}\\\\
-Amperio = \frac{Culombio}{segundo}
-\end{align*}</script></div></div><p><span>La resistencia es la dificultad o facilidad que encuentra la corriente eléctrica para circular a través de un material.</span></p><p><span>La unidad de resistencia es el ohmio Ω. representa la resistencia de un conductor en el que, con una diferencia de potencial aplicada en sus extremos de 1 V circula una corriente de 1 A de intensidad.</span></p><h4><a name="123-ley-de-ohm" class="md-header-anchor"></a><span>1.2.3 Ley de Ohm</span></h4><p><span>Al pasar una corriente I por una resistencia R se produce una caída de tensión o ddp que se expresa con la fórmula:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n85" cid="n85" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.875ex" height="2.577ex" viewBox="0 -806.1 4251.6 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex; max-width: 100%;"><defs><path stroke-width="0" id="E27-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path stroke-width="0" id="E27-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E27-MJMATHI-49" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path stroke-width="0" id="E27-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E27-MJMATHI-52" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,-50)"><use xlink:href="#E27-MJMATHI-45" x="0" y="0"></use><use xlink:href="#E27-MJMAIN-3D" x="1041" y="0"></use><use xlink:href="#E27-MJMATHI-49" x="2097" y="0"></use><use xlink:href="#E27-MJMATHI-78" x="2601" y="0"></use><use xlink:href="#E27-MJMATHI-52" x="3173" y="0"></use></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-8">\begin{align*}
-E = IxR
-\end{align*}</script></div></div><p><span>Si aumenta la resistencia disminuye la intensidad y viceversa.</span></p><h4><a name="124-aplicación-de-la-ley-de-ohm-resistencias-agrupación-de-resistencias" class="md-header-anchor"></a><span>1.2.4 Aplicación de la Ley de Ohm. Resistencias. Agrupación de resistencias.</span></h4><p><span>Si tomamos dos conductores de la misma forma y tamaño pero de distintos materiales y les aplicamos una misma fem, las corrientes que circularán serán distintas, porque cada material, al tener una conductividad distinta, tiene una resistencia al paso de la corriente diferente.</span></p><p><span>Una resistencia es un elemento o componente de un circuito eléctrico formado por un encapsulado de material que una cierta cantidad de resistencia y con dos rabillos o puntos para su conexión a un circuito.</span></p><p><span>Las resistencias pueden agruparse en serie, en paralelo o combinando ambas formas. El cálculo de la resistencia resultante se realiza aplicando la Ley de Ohm. En el caso de resistencia conectadas en serie la resistencia del conjunto es la suma de los valores de cada una de ellas</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n91" cid="n91" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.728ex" height="2.577ex" viewBox="0 -806.1 8494.2 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex; max-width: 100%;"><defs><path stroke-width="0" id="E28-MJMATHI-52" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path><path stroke-width="0" id="E28-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E28-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E28-MJMAIN-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path stroke-width="0" id="E28-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E28-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,-50)"><use xlink:href="#E28-MJMATHI-52" x="0" y="0"></use><use xlink:href="#E28-MJMAIN-3D" x="1036" y="0"></use><g transform="translate(2092,0)"><use xlink:href="#E28-MJMATHI-52" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E28-MJMAIN-31" x="1073" y="-213"></use></g><use xlink:href="#E28-MJMAIN-2B" x="3527" y="0"></use><g transform="translate(4527,0)"><use xlink:href="#E28-MJMATHI-52" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E28-MJMAIN-32" x="1073" y="-213"></use></g><use xlink:href="#E28-MJMAIN-2B" x="5962" y="0"></use><g transform="translate(6962,0)"><use xlink:href="#E28-MJMATHI-52" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E28-MJMAIN-33" x="1073" y="-213"></use></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-9">\begin{align*}
-R = R_1+R_2+R_3
-\end{align*}</script></div></div><p><span>La intensidad que pasa por cada una de ellas es igual a la del conjunto:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n93" cid="n93" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="17.43ex" height="2.577ex" viewBox="0 -806.1 7504.4 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex; max-width: 100%;"><defs><path stroke-width="0" id="E29-MJMATHI-49" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path stroke-width="0" id="E29-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E29-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E29-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E29-MJMAIN-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,-50)"><use xlink:href="#E29-MJMATHI-49" x="0" y="0"></use><use xlink:href="#E29-MJMAIN-3D" x="781" y="0"></use><g transform="translate(1837,0)"><use xlink:href="#E29-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E29-MJMAIN-31" x="622" y="-213"></use></g><use xlink:href="#E29-MJMAIN-3D" x="3008" y="0"></use><g transform="translate(4064,0)"><use xlink:href="#E29-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E29-MJMAIN-32" x="622" y="-213"></use></g><use xlink:href="#E29-MJMAIN-3D" x="5235" y="0"></use><g transform="translate(6291,0)"><use xlink:href="#E29-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E29-MJMAIN-33" x="622" y="-213"></use></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-10">\begin{align*}
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y="0"></use><use xlink:href="#E30-MJMAIN-3D" x="781" y="0"></use><g transform="translate(1837,0)"><use xlink:href="#E30-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E30-MJMAIN-31" x="622" y="-213"></use></g><use xlink:href="#E30-MJMAIN-2B" x="2953" y="0"></use><g transform="translate(3953,0)"><use xlink:href="#E30-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E30-MJMAIN-32" x="622" y="-213"></use></g><use xlink:href="#E30-MJMAIN-2B" x="5069" y="0"></use><g transform="translate(6069,0)"><use xlink:href="#E30-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E30-MJMAIN-33" x="622" y="-213"></use></g></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-11">\begin{align*}
-R = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}\\\\
-I = I_1+I_2+I_3
-\end{align*}</script></div></div><p><span>Un </span><strong><span>shunt</span></strong><span> </span><a href='https://bit.ly/3eZMHfb'><span>[47]</span></a><span> es una resistencia acoplada en paralelo con cualquier elemento de un circuito para derivar corriente por ella. Una aplicación típica son los aparatos de medida que soportan poca intensidad de corriente, </span><strong><span>galvanómetro</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Galvan%C3%B3metro'><span>[48]</span></a><span> G, por lo que es preciso limitar ésta adoptando una resistencia en paralelo Rs. </span></p><h4><a name="125-código-de-colores-de-las-resistencias" class="md-header-anchor"></a><span>1.2.5 Código de colores de las resistencias.</span></h4><p><img src="https://telecomlobby.com/Images/banda_colores_resistencias.webp" referrerpolicy="no-referrer" alt="resistencias"></p><p><span>Permite indicar su valor en ohmios mediante bandas de colores.</span></p><p><span>El conjunto de dichos anillos nos da la lectura del número de ohmios de la resistencia. La tolerancia de una resistencia expresa los márgenes alrededor de los cuales puede variar su valor. A mayor precisión, menor tolerancia.</span></p><h4><a name="126-disipación-de-potencia-en-las-resistencias" class="md-header-anchor"></a><span>1.2.6 Disipación de potencia en las resistencias</span></h4><p><span>Una resistencia se intercala en un circuito para obstaculizar el paso de la corriente y transformar en calor el voltaje que no necesitamos ne un punto dado. Se conoce como </span><strong><span>efecto Joule</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Efecto_Joule'><span>[49]</span></a><span>. Todo conducto por lo que circula una corriente experimenta un aumento de su temperatura. La ley de joule enuncia que la cantidad de calor desprendida en un conductor por el paso de una corriente constante es proporcional al cuadrado de la intensidad de la corriente, a la resistencia del conductor y al tiempo que dure el paso. se llama potencia de disipación, medidas en vatios, al producto del votake por la intensidad que ha de circular por la resistencia:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n103" cid="n103" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.868ex" height="2.577ex" viewBox="0 -806.1 4248.6 1109.7" role="img" focusable="false" style="vertical-align: -0.705ex; max-width: 100%;"><defs><path stroke-width="0" id="E31-MJMATHI-50" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path stroke-width="0" id="E31-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E31-MJMATHI-56" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path><path stroke-width="0" id="E31-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E31-MJMATHI-49" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,-50)"><use xlink:href="#E31-MJMATHI-50" x="0" y="0"></use><use xlink:href="#E31-MJMAIN-3D" x="1028" y="0"></use><use xlink:href="#E31-MJMATHI-56" x="2084" y="0"></use><use xlink:href="#E31-MJMATHI-78" x="2853" y="0"></use><use xlink:href="#E31-MJMATHI-49" x="3425" y="0"></use></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-12">\begin{align*}
-P = V xI
-\end{align*}</script></div></div><p><span>Si la resistencia disipa una potencia mayor que aquélla para la que está preparada, se quema, cortándose el hilo del que está hecha o fundiéndose el material resistivo. Disipación máxima es la potencia calorífica que podemos suministrar a un resistencia sin que la temperatura se eleve peligrosamente.</span></p><p><span>Los valores de disipación de potencia más frecuentes de las resistencias son los de 0,125W, 0,25W, 0,5W y 1 W.</span></p><h4><a name="127-coeficientes-negativos-y-positivos-de-temperatura-ntp-y-ptc" class="md-header-anchor"></a><span>1.2.7 Coeficientes negativos y positivos de temperatura NTP y PTC</span></h4><p><span>Un </span><strong><span>termistor</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Termistor'><span>[50]</span></a><span> NTC es una resistencia cuyo valor se va reduciendo a medida que aumenta la temperatura. Análogamente a un NTC un termistor PTC es una resistencia cuyo valor va aumentando a medida que aumenta la temperatura.</span></p><h4><a name="128-otros-tipos-de-resistencias" class="md-header-anchor"></a><span>1.2.8 Otros tipos de resistencias.</span></h4><p><span>Una resistencia ajustable permite fijar su valor dentro de un rango mediante una abrazadera móvil en contacto con el elemento resistivo. Un </span><strong><span>reóstato</span></strong><span> </span><a href=''><span>[51]</span></a><span> es una resistencia variable que se usa en los circuitos de gran consumo, empleándose para regular la corriente en máquinas y motores. Un </span><strong><span>potenciómetro</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Potenci%C3%B3metro'><span>[52]</span></a><span> es una resistencia variable que puede ser variada por el usuario para realizar cualquier función. Es lineal cuando su resistencia es proporcional al desplazamiento del cursor ya que se desliza por una pista uniforme. En el no lineal al ser la pista de diferente grosor, la respuesta, la resistencia, no corresponde al desplazamiento del cursor. Estos últimos suelen tener una respuesta que se aproxima a la función logaritmo.</span></p><h4><a name="129-leyes-de-kirchhoff" class="md-header-anchor"></a><span>1.2.9 Leyes de Kirchhoff</span></h4><p><span>Las leyes de </span><strong><span>Kirchhoff</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Gustav_Kirchhoff'><span>[53]</span></a><span> son útiles al análisis de múltiples tipos de circuitos:</span></p><ol start='' ><li><span>La suma de las intensidades de corriente que llegan a un nudo de un circuito es igual a la suma de las intensidades que salen de él. </span></li><li><span>En un circuito cerrado o malla la suma de todas las caídas de tensión es igual a la suma de todas las subidas de tensión, la suma algebraica de las tensiones en todo circuito cerrado es cero.</span></li></ol><h4><a name="1210-potencia-eléctrica-unidad-de-potencia-el-vatio" class="md-header-anchor"></a><span>1.2.10 Potencia eléctrica. Unidad de potencia: el vatio.</span></h4><p><span>La corriente eléctrica puede desarrollar un trabajo, la relación que hay entre un trabajo y tiempo de la </span><strong><span>potencia</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica'><span>[54]</span></a><span> que es la expresión de la cantidad del trabajo producido en la unidad de tiempo. 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299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E32-MJMATHI-64" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path stroke-width="0" id="E32-MJMATHI-45" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 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y="0"></use><use xlink:href="#E32-MJMATHI-6E" x="2063" y="0"></use><use xlink:href="#E32-MJMATHI-63" x="2663" y="0"></use><use xlink:href="#E32-MJMATHI-69" x="3096" y="0"></use><use xlink:href="#E32-MJMATHI-61" x="3441" y="0"></use><use xlink:href="#E32-MJMAIN-3D" x="4247" y="0"></use><use xlink:href="#E32-MJMATHI-74" x="5303" y="0"></use><use xlink:href="#E32-MJMATHI-65" x="5664" y="0"></use><use xlink:href="#E32-MJMATHI-6E" x="6130" y="0"></use><use xlink:href="#E32-MJMATHI-73" x="6730" y="0"></use><use xlink:href="#E32-MJMATHI-69" x="7199" y="0"></use><g transform="translate(7544,0)"><text font-family="STIXGeneral, 'PingFang SC', serif" stroke="none" transform="scale(50.259) matrix(1 0 0 -1 0 0)">ó</text></g><use xlink:href="#E32-MJMATHI-6E" x="8047" y="0"></use><use xlink:href="#E32-MJMATHI-78" x="8647" y="0"></use><use xlink:href="#E32-MJMATHI-69" x="9219" y="0"></use><use xlink:href="#E32-MJMATHI-6E" x="9564" y="0"></use><use xlink:href="#E32-MJMATHI-74" x="10164" y="0"></use><use xlink:href="#E32-MJMATHI-65" x="10525" y="0"></use><use xlink:href="#E32-MJMATHI-6E" x="10991" y="0"></use><use xlink:href="#E32-MJMATHI-73" x="11591" y="0"></use><use xlink:href="#E32-MJMATHI-69" x="12060" y="0"></use><use xlink:href="#E32-MJMATHI-64" x="12405" y="0"></use><use xlink:href="#E32-MJMATHI-61" x="12928" y="0"></use><use xlink:href="#E32-MJMATHI-64" x="13457" y="0"></use></g><g transform="translate(10056,-1350)"><use xlink:href="#E32-MJMATHI-50" x="0" y="0"></use><use xlink:href="#E32-MJMAIN-3D" x="1028" y="0"></use><use xlink:href="#E32-MJMATHI-45" x="2084" y="0"></use><use xlink:href="#E32-MJMATHI-78" x="2848" y="0"></use><use xlink:href="#E32-MJMATHI-49" x="3420" y="0"></use></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-13">\begin{align*}
-Potencia = tensiónxintensidad\\\\
-P=ExI
-\end{align*}</script></div></div><p><span>Donde P es expresada en vatios, la tensión en voltios, y la intensidad en amperios. Aplicando la ley de Ohm sabemos que la tensión es igual a la intensidad por la resistencia. O sea obtenemos:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n121" cid="n121" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.943ex" height="2.811ex" viewBox="0 -856.4 4711.4 1210.2" role="img" focusable="false" style="vertical-align: -0.822ex; max-width: 100%;"><defs><path stroke-width="0" id="E33-MJMATHI-50" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path stroke-width="0" id="E33-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E33-MJMATHI-49" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path stroke-width="0" id="E33-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path stroke-width="0" id="E33-MJMATHI-78" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E33-MJMATHI-52" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,-92)"><use xlink:href="#E33-MJMATHI-50" x="0" y="0"></use><use xlink:href="#E33-MJMAIN-3D" x="1028" y="0"></use><g transform="translate(2084,0)"><use xlink:href="#E33-MJMATHI-49" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#E33-MJMAIN-32" x="739" y="583"></use></g><use xlink:href="#E33-MJMATHI-78" x="3061" y="0"></use><use xlink:href="#E33-MJMATHI-52" x="3633" y="0"></use></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-14">\begin{align*}
-P = I^{2}xR
-\end{align*}</script></div></div><p><span>Si por ejemplo en un circuito circulan 20 amperios y la resistencia es de 100 ohmios la potencia será:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n123" cid="n123" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.173ex" height="2.811ex" viewBox="0 -856.4 14713.3 1210.2" role="img" focusable="false" style="vertical-align: -0.822ex; max-width: 100%;"><defs><path stroke-width="0" id="E34-MJMATHI-50" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path stroke-width="0" id="E34-MJMAIN-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path stroke-width="0" id="E34-MJMAIN-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 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103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path stroke-width="0" id="E34-MJMAIN-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path stroke-width="0" id="E34-MJMAIN-34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path><path stroke-width="0" id="E34-MJMATHI-57" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 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694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-15,0)"><g transform="translate(0,-92)"><use xlink:href="#E34-MJMATHI-50" x="0" y="0"></use><use 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-P = 20^{2}x100=40000W=40kW
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-\end{align*}</script></div></div><h4><a name="13-almacenamiento-de-cargas-eléctricas-condensadores" class="md-header-anchor"></a><span>1.3 Almacenamiento de cargas eléctricas: condensadores</span></h4><p><img src="https://telecomlobby.com/Images/condensadores.webp" referrerpolicy="no-referrer" alt="Condensadores"></p><p><span>Constan de dos placas conductoras separadas por un cuerpo no conductor llamado </span><strong><span>dieléctrico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Diel%C3%A9ctrico'><span>[57]</span></a><span>:</span></p><ul><li><span>aire</span></li><li><span>aceite</span></li><li><span>vidrio (por esto el jefe de la banda de actores no estatales de Barcelona lo he encontrado viviendo en una nave industrial abandonada ya que el techo y las paredes están lleno de </span><strong><span>fibra de vidrio</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Fibra_de_vidrio'><span>[58]</span></a><span>)</span></li><li><strong><span>mica</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Mica'><span>[59]</span></a></li><li><strong><span>polietileno</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Polietileno'><span>[60]</span></a></li></ul><p><span>Las placas suelen ser láminas de </span><strong><span>estaño</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Esta%C3%B1o'><span>[61]</span></a><span> alternando con láminas del dieléctrico usado; los </span><strong><span>condensadores</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico'><span>[62]</span></a><span> tienen la capacidad de acumular una determinada carga eléctrica a un voltaje determinado, la acumula en carga y la restituye en descarga al resto del circuito. Al cerrarlo una placa queda asociada al polo positivo y otra al negativo de la pila o fuente que la alimente, la armadura conectada al polo positivo va cediendo electrones a éste, mientras que la otra armadura recoge electrones del polo negativo, se puede apreciar el flujo de corriente intercalando un </span><strong><span>amperímetro</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Amper%C3%ADmetro'><span>[63]</span></a><span>. Se pueden recargar hasta que entre las placas de éstos se llega a alcanzar un voltaje igual al existente en los bornes de la batería o fuente que los alimente. Si se abre el interruptor desconectando la alimentación de las armaduras estas quedan cargadas el circuito queda abierto y se mantiene la diferencia de potencia entre las armaduras; aparece un campo eléctrico desde la placa positiva a la negativa en el que habrá más dispersión de líneas de fuerza cuanto más alejadas estén. El condensador se descarga  instantáneamente si se unen o cortocircuitan las placas del mismo pero si se añade una resistencia de un valor dado la descarga durará un tiempo determinado. </span></p><p><span>Tanto descarga como carga no son instantáneas y además tampoco tienen forma lineal sino </span><strong><span>exponencial</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial'><span>[64]</span></a><span>, su capacidad eléctrica es:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n143" cid="n143" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="38.638ex" height="14.251ex" viewBox="0 -3319.1 16635.9 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-Capacidad eléctrica=\frac{carga eléctrica}{voltaje}\\\\
-V=\frac{Q}{V}
-\end{align*}</script></div></div><p><span>Un </span><strong><span>faradio</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Faradio'><span>[65]</span></a><span> es la capacidad de un condensador al que aplicada una fem de 1 voltio adquiere una carga de 1 culombio. El microfaradio μF equivale a 10-6 F y el nanofaradio nF a 10-9F, el picofaradio a 10-12F.</span></p><p><span>La energía almacenada en condensador se expresa por la fórmula:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n146" cid="n146" mdtype="math_block"><div class="md-rawblock-container md-math-container" tabindex="-1"><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="-1" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.491ex" height="3.044ex" viewBox="0 -906.7 6239 1310.7" role="img" focusable="false" style="vertical-align: -0.938ex; max-width: 100%;"><defs><path stroke-width="0" id="E37-MJMATHI-57" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 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type="math/tex; mode=display" id="MathJax-Element-18">\begin{align*}
-W = \mbox{1/2}CV^{2}
-\end{align*}</script></div></div><p><span>O sea que depende de su capacidad y del voltaje aplicado.</span></p><p><span>Se llama </span><strong><span>constante dieléctrica</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica'><span>[66]</span></a><span> a la relación que hay entre la capacidad de un condensador formado por un determinado dieléctrico y su capacidad de un condensador formado por un determinado dieléctrico y su capacidad en el vacío. Se denomina </span><strong><span>rigidez dieléctrica</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica'><span>[67]</span></a><span> o tensión de trabajo de un condensador a aquella que puede soportar sin que se perfore su dieléctrico. La tensión de prueba es aquella a la que el fabricante somete al condensador sin que se haya producido la perforación y es siempre mayor que la tensión de trabajo.</span></p><p><span>Los condensadores como otros componentes varían de valor con la temperatura, el parámetro se denomina </span><strong><span>coeficiente de temperatura</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Coeficiente_de_temperatura'><span>[68]</span></a><span> que puede ser positivo o negativo. Los cerámicos o de mica son muy estables en frente de la temperatura. </span></p><h4><a name="131-relación-entre-capacidad-dimensiones-y-dieléctrico" class="md-header-anchor"></a><span>1.3.1 Relación entre capacidad, dimensiones y dieléctrico</span></h4><p><span>La capacidad de un condensador depende de dos magnitudes:</span></p><ul><li><span>la distancia entre las placas inversamente proporcional a mayor superficie de las placas, mayor capacidad y a mayor distancia menor capacidad.</span></li><li><span>constante dieléctrica del material, directamente proporcional.</span></li></ul><h4><a name="132-condensadores-diversos-tipos-tabla-de-colores" class="md-header-anchor"></a><span>1.3.2 Condensadores: diversos tipos. Tabla de colores.</span></h4><p><img src="https://telecomlobby.com/Images/tabla_colores_condensadores.webp" referrerpolicy="no-referrer" alt="Tabla colores condesadores"></p><p><span>Los variables cambian su capacidad variando la superficie de sus placas. Se usan para sintonizar circuitos </span><strong><span>oscilantes</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Oscilaci%C3%B3n'><span>[69]</span></a><span>. </span></p><p><span>Los ajustables o trimmer utilizados para ajustar la capacidad.</span></p><p><span>Los fijos que pueden ser </span><strong><span>polarizados</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica'><span>[70]</span></a><span> o no. Los non polarizados se clasifican según el tipo de dieléctrico que utilizan como hemos visto. Los </span><strong><span>electrolíticos</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico'><span>[71]</span></a><span> tienen dieléctrico líquido o en papel impregnado.</span></p><p><span>Al ser pequeños los condensadores se emplean, generalmente, códigos de bandas de colores para indicar su capacidad expresada en picofaradios. Las bandas indican su capacidad, su tolerancia y su tensión máxima. </span></p><p><span>La forma de expresar la tolerancia depende de si tiene más o menos de 10 picofaradios de capacidad, si mayor se expresa un porcentaje de incremento o disminución de la misma o si es menor de dicho valor expresa la fracción di picofaradio a sumar o restar. 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y="0"></use><use xlink:href="#E38-MJMATHI-72" x="1858" y="0"></use><g transform="translate(2309,0)"><text font-family="STIXGeneral, 'PingFang SC', serif" stroke="none" transform="scale(50.259) matrix(1 0 0 -1 0 0)">ó</text></g><use xlink:href="#E38-MJMATHI-6E" x="2812" y="0"></use><use xlink:href="#E38-MJMAIN-2212" x="3634" y="0"></use><use xlink:href="#E38-MJMATHI-76" x="4634" y="0"></use><use xlink:href="#E38-MJMATHI-65" x="5119" y="0"></use><use xlink:href="#E38-MJMATHI-72" x="5585" y="0"></use><use xlink:href="#E38-MJMATHI-64" x="6036" y="0"></use><use xlink:href="#E38-MJMATHI-65" x="6559" y="0"></use><use xlink:href="#E38-MJMAIN-2212" x="7248" y="0"></use><use xlink:href="#E38-MJMATHI-72" x="8248" y="0"></use><use xlink:href="#E38-MJMATHI-6F" x="8699" y="0"></use><use xlink:href="#E38-MJMATHI-6A" x="9184" y="0"></use><use xlink:href="#E38-MJMATHI-6F" x="9596" y="0"></use><use xlink:href="#E38-MJMAIN-2212" x="10303" y="0"></use><use xlink:href="#E38-MJMATHI-6E" x="11303" y="0"></use><use xlink:href="#E38-MJMATHI-65" x="11903" y="0"></use><use xlink:href="#E38-MJMATHI-67" x="12369" y="0"></use><use xlink:href="#E38-MJMATHI-72" x="12849" y="0"></use><use xlink:href="#E38-MJMATHI-6F" x="13300" y="0"></use><use xlink:href="#E38-MJMAIN-2212" x="14007" y="0"></use><use xlink:href="#E38-MJMATHI-72" x="15008" y="0"></use><use xlink:href="#E38-MJMATHI-6F" x="15459" y="0"></use><use xlink:href="#E38-MJMATHI-6A" x="15944" y="0"></use><use xlink:href="#E38-MJMATHI-6F" x="16356" y="0"></use></g></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-19">\begin{align*}
-marrón-verde-rojo-negro-rojo 
-\end{align*}</script></div></div><p><span>1500 pF de capacidad, 20% de tolerancia, 250V de tensión máxima de trabajo.</span></p><h4><a name="133-asociación-de-condensadores" class="md-header-anchor"></a><span>1.3.3 Asociación de condensadores</span></h4><p><span>Los condensadores pueden agruparse en serie o en paralelo.</span></p><p><span>En serie la capacidad resultante se obtiene dividiendo la unidad por la suma de las inversas de todas las capacidades; las armaduras externas actúan de terminales de conexión. Al quedare tan distanciadas estás, la capacidad total resulta mucho menor que la de uno de los condensadores.</span></p><p><span>En paralelo la capacidad total es la suma de las capacidades de todos ellos.</span></p><h4><a name="14-campo-magnético" class="md-header-anchor"></a><span>1.4 Campo magnético</span></h4><p><img src="https://telecomlobby.com/Images/iman.webp" referrerpolicy="no-referrer" alt="Iman"></p><p><span>Un </span><strong><span>imán</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Im%C3%A1n'><span>[72]</span></a><span> crea a su alrededor un campo de atracción de sustancias tales como el hierro y que se denomina </span><strong><span>campo magnético</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico'><span>[73]</span></a><span> y es el espacio en que un imán ejerce su influencia.</span></p><p><span>Se crea un campo magnético en los alrededores de un conductor recorrido por una corriente eléctrica, si no hay corriente no hay campo cosa que no ocurre con los imanes. </span></p><h4><a name="141-magnetismo" class="md-header-anchor"></a><span>1.4.1 magnetismo.</span></h4><p><span>Se llama </span><strong><span>magnetismo</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Magnetismo'><span>[74]</span></a><span> al conjunto de fenómenos originados por los campos magnéticos. Un imán puede ser </span><strong><span>magnetita</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Magnetita'><span>[75]</span></a><span>, </span><strong><span>acero</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Acero'><span>[76]</span></a><span> o bien alguna aleación. Los extremos se llaman polos, norte y sur. Al centro la línea neutra. El magnetismo es formado por las líneas ovales de fuerza entra los dos polos.</span></p><p><span>Una aguja imantada que gire libremente siempre se orientará en la dirección norte-sur. La tierra produce un campo magnético y llamamos a los dos polos </span><strong><span>norte geográfico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Polo_norte'><span>[77]</span></a><span> y </span><strong><span>sur geográfico</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Polo_sur'><span>[78]</span></a><span>. Polos de mismo nombre se repelen y los de nombre contrario se atraen. </span></p><h4><a name="142-características-de-un-campo-magnético" class="md-header-anchor"></a><span>1.4.2 Características de un campo magnético.</span></h4><p><span>El total de las líneas de fuerza se denomina </span><strong><span>flujo magnético</span></strong><span> </span><a href='https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico'><span>[79]</span></a><span>. El numero de líneas que salen es igual al que entran de la superficie. La unidad de flujo magnético es el </span><strong><span>Weber</span></strong><span> </span><a href='https://bit.ly/36XehpI'><span>[80]</span></a><span>. Un Wb es el flujo magnético que al atravesar un circuito de una sola espira produce en ella una fuerza electromotriz de un voltio si se anula dicho flujo en un segundo por decrecimiento uniforme.</span></p><h3><a name="external-links" class="md-header-anchor"></a><span>External links</span></h3><ol start='' ><li><p><a href='https://es.wikipedia.org/wiki/Mol%C3%A9cula' target='_blank' class='url'>https://es.wikipedia.org/wiki/Mol%C3%A9cula</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/S%C3%B3lido' target='_blank' class='url'>https://es.wikipedia.org/wiki/S%C3%B3lido</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/L%C3%ADquido' target='_blank' class='url'>https://es.wikipedia.org/wiki/L%C3%ADquido</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Gas' target='_blank' class='url'>https://es.wikipedia.org/wiki/Gas</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Calor' target='_blank' class='url'>https://es.wikipedia.org/wiki/Calor</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Fr%C3%ADo' target='_blank' class='url'>https://es.wikipedia.org/wiki/Fr%C3%ADo</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/%C3%81tomo' target='_blank' class='url'>https://es.wikipedia.org/wiki/%C3%81tomo</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Electricidad' target='_blank' class='url'>https://es.wikipedia.org/wiki/Electricidad</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Prot%C3%B3n' target='_blank' class='url'>https://es.wikipedia.org/wiki/Prot%C3%B3n</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Neutr%C3%B3n' target='_blank' class='url'>https://es.wikipedia.org/wiki/Neutr%C3%B3n</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Masa' target='_blank' class='url'>https://es.wikipedia.org/wiki/Masa</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Electr%C3%B3n' target='_blank' class='url'>https://es.wikipedia.org/wiki/Electr%C3%B3n</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Ion' target='_blank' class='url'>https://es.wikipedia.org/wiki/Ion</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Semiconductor' target='_blank' class='url'>https://es.wikipedia.org/wiki/Semiconductor</a></p></li><li><p><a href='https://www.iec.ch/' target='_blank' class='url'>https://www.iec.ch/</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Aleaci%C3%B3n' target='_blank' class='url'>https://es.wikipedia.org/wiki/Aleaci%C3%B3n</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Siemens_(unidad)' target='_blank' class='url'>https://es.wikipedia.org/wiki/Siemens_(unidad)</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Resistividad' target='_blank' class='url'>https://es.wikipedia.org/wiki/Resistividad</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Culombio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Culombio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Ley_de_Coulomb' target='_blank' class='url'>https://es.wikipedia.org/wiki/Ley_de_Coulomb</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Voltio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Voltio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Superficie_equipotencial' target='_blank' class='url'>https://es.wikipedia.org/wiki/Superficie_equipotencial</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Corriente_continua' target='_blank' class='url'>https://es.wikipedia.org/wiki/Corriente_continua</a></p></li><li><p><a href='https://bit.ly/3nqudHw' target='_blank' class='url'>https://bit.ly/3nqudHw</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Corriente_alterna' target='_blank' class='url'>https://es.wikipedia.org/wiki/Corriente_alterna</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Fuerza_electromotriz' target='_blank' class='url'>https://es.wikipedia.org/wiki/Fuerza_electromotriz</a></p></li><li><p><a href='https://bit.ly/36B9Hgz' target='_blank' class='url'>https://bit.ly/36B9Hgz</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Hidr%C3%A1ulica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Hidr%C3%A1ulica</a></p></li><li><p><a href='https://bit.ly/2IxeKX7' target='_blank' class='url'>https://bit.ly/2IxeKX7</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Circuito' target='_blank' class='url'>https://es.wikipedia.org/wiki/Circuito</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Fuerza_electromotriz' target='_blank' class='url'>https://es.wikipedia.org/wiki/Fuerza_electromotriz</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Voltio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Voltio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Amperio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Amperio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Ohmio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Ohmio</a></p></li><li><p><a href='https://bit.ly/3eZMHfb' target='_blank' class='url'>https://bit.ly/3eZMHfb</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Galvan%C3%B3metro' target='_blank' class='url'>https://es.wikipedia.org/wiki/Galvan%C3%B3metro</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Efecto_Joule' target='_blank' class='url'>https://es.wikipedia.org/wiki/Efecto_Joule</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Termistor' target='_blank' class='url'>https://es.wikipedia.org/wiki/Termistor</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Reostato' target='_blank' class='url'>https://es.wikipedia.org/wiki/Reostato</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Potenci%C3%B3metro' target='_blank' class='url'>https://es.wikipedia.org/wiki/Potenci%C3%B3metro</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Gustav_Kirchhoff' target='_blank' class='url'>https://es.wikipedia.org/wiki/Gustav_Kirchhoff</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Vatio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Vatio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Caballo_de_vapor' target='_blank' class='url'>https://es.wikipedia.org/wiki/Caballo_de_vapor</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Diel%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Diel%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Fibra_de_vidrio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Fibra_de_vidrio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Mica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Mica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Polietileno' target='_blank' class='url'>https://es.wikipedia.org/wiki/Polietileno</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Esta%C3%B1o' target='_blank' class='url'>https://es.wikipedia.org/wiki/Esta%C3%B1o</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Amper%C3%ADmetro' target='_blank' class='url'>https://es.wikipedia.org/wiki/Amper%C3%ADmetro</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial' target='_blank' class='url'>https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Faradio' target='_blank' class='url'>https://es.wikipedia.org/wiki/Faradio</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Coeficiente_de_temperatura' target='_blank' class='url'>https://es.wikipedia.org/wiki/Coeficiente_de_temperatura</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Oscilaci%C3%B3n' target='_blank' class='url'>https://es.wikipedia.org/wiki/Oscilaci%C3%B3n</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica' target='_blank' class='url'>https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Im%C3%A1n' target='_blank' class='url'>https://es.wikipedia.org/wiki/Im%C3%A1n</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Magnetismo' target='_blank' class='url'>https://es.wikipedia.org/wiki/Magnetismo</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Magnetita' target='_blank' class='url'>https://es.wikipedia.org/wiki/Magnetita</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Acero' target='_blank' class='url'>https://es.wikipedia.org/wiki/Acero</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Polo_norte' target='_blank' class='url'>https://es.wikipedia.org/wiki/Polo_norte</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Polo_sur' target='_blank' class='url'>https://es.wikipedia.org/wiki/Polo_sur</a></p></li><li><p><a href='https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico' target='_blank' class='url'>https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico</a></p></li><li><p><a href='https://bit.ly/36XehpI' target='_blank' class='url'>https://bit.ly/36XehpI</a></p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p></li></ol></div>
+<body class='typora-export'><div class='typora-export-content'>
+<div id='write'  class=''><h1 id='teoría-eléctrica-y-electromagnética'><span>Teoría eléctrica y electromagnética</span></h1><p><img src="http://telecomlobby.com/Images/felipe_vi_ure_riccardo_giuntoli_radioham_notes.webp" referrerpolicy="no-referrer" alt="Felipe VI URE"></p><p><span>Subiendo una </span><strong><a href='https://it.wikipedia.org/wiki/Monte_Fasce'><span>montaña Genovesa</span></a></strong><span>, allí fue la primera vez que cargaba con una radio en 27Mhz AM, FM y banda lateral en mi mochila, soñaba con conectarme con países lejanos y gente desconocida. Allí fue, cerca del 1992. Desde aquella fecha mucha vida ha pasado delante de mis ojos, felicidad, trabajos, amores y muertes. Ahora en el 2022, con la conciencia de ser victima de trata de pesonas, debajo de esta QSL donde se representa rey Felipe VI de España y su identificación en la radio afición empiezo a estudiar y apuntar mis notas en este apartado de mi pagina web. Pagina donde se subraya que estoy estudiando esta arte con el fin de salir del control neuronal vía radio que ha sido activado de forma continua sobre mi organismo en Noviembre 2017, que seguramente me ve como individuo obyectivo, como victima de trata, desde finales de los noventa, y que se encuentra físicamente en la ciudad donde vivo, Barcelona.</span></p><h4 id='11-estructura-de-la-materia'><span>1.1 Estructura de la materia</span></h4><p><span>Tanto los cuerpos sólidos como los líquidos y gases están compuestos de pequeñas partículas cuyas propiedades son idénticas al cuerpo al cual pertenecen. Se llaman </span><strong><a href='https://es.wikipedia.org/wiki/Mol%C3%A9cula'><span>moléculas</span></a></strong><span> y presentan espacios entra ellos.</span></p><h4 id='111-molécula'><span>1.1.1 Molécula</span></h4><p><span>Están en continuo movimiento y entre ellas existen fuerzas atractivas y repulsivas según el estado en que se encuentre la materia:</span></p><ul><li><strong><a href='https://es.wikipedia.org/wiki/S%C3%B3lido'><span>Sólidos</span></a></strong><span>, atractivas.</span></li><li><strong><a href='https://es.wikipedia.org/wiki/L%C3%ADquido'><span>Líquidos</span></a></strong><span>, equilibradas.</span></li><li><strong><a href='https://es.wikipedia.org/wiki/Gas'><span>Gases</span></a></strong><span>, repulsivas.</span></li></ul><p><span>Mediante </span><strong><a href='https://es.wikipedia.org/wiki/Calor'><span>calor</span></a></strong><span> podemos pasar de estado sólido a líquido y de líquido a gaseoso. Mediante el </span><strong><a href='https://es.wikipedia.org/wiki/Fr%C3%ADo'><span>frío</span></a></strong><span> el revés. </span></p><p><span>Cada molécula está compuesta por distintos átomos según el </span><strong><a href='https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico'><span>elemento químico</span></a></strong><span> que constituyan.</span></p><h4 id='112-átomo'><span>1.1.2 Átomo</span></h4><p><img src="https://telecomlobby.com/Images/tabla_elementos.webp" referrerpolicy="no-referrer" alt="Tabla elementos"></p><p><span>Una molécula la podemos descomponer en partículas muchos menores llamadas </span><strong><a href='https://es.wikipedia.org/wiki/%C3%81tomo'><span>átomos</span></a></strong><span>. Toda la materia que existe en la naturaleza está formada por cuerpos simples denominados elementos. El átomo es la parte más pequeña de estos cuerpos que conserva las características originales de un elemento cualquiera.</span></p><p><span>Para entender la </span><strong><a href='https://es.wikipedia.org/wiki/Electricidad'><span>electricidad</span></a></strong><span> hay que estudiar átomo y componentes.</span></p><p><span>Cada átomo consta de dos partes el núcleo y la corteza, el núcleo está cargado con carga eléctrica positiva y se compone básicamente de </span><strong><a href='https://es.wikipedia.org/wiki/Prot%C3%B3n'><span>protones</span></a></strong><span>  partículas con carga positiva, y </span><strong><a href='https://es.wikipedia.org/wiki/Neutr%C3%B3n'><span>neutrones</span></a></strong><span>, partículas con </span><strong><a href='https://es.wikipedia.org/wiki/Masa'><span>masa</span></a></strong><span> pero sin </span><strong><a href='https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica'><span>carga</span></a></strong><span>. Alrededor del núcleo, existen una o más capas, cuyo conjunto se denomina corteza, donde describen órbitas a gran velocidad los </span><strong><a href='https://es.wikipedia.org/wiki/Electr%C3%B3n'><span>electrones</span></a></strong><span>, partículas de carga negativa fuertemente atraídos por la carga positiva de este y resulta extremadamente difícil cambiarlos de órbita; los de las órbitas exteriores pueden llegar a abandonar un átomo para pasar a otro, o bien quedar como electrones libres.</span></p><h4 id='113-ionización-o-electrización-carga-eléctrica'><span>1.1.3 Ionización o electrización. Carga eléctrica.</span></h4><p><img src="https://telecomlobby.com/Images/tabla_ionizacion.webp" referrerpolicy="no-referrer" alt="Ionización"></p><p><span>Si no sometidos a la acción de ninguna fuerza externa el átomo es neutro del punto de vista eléctrico. Si perdiese electrones, quedaría cargado positivamente y se denominaría </span><strong><a href='https://es.wikipedia.org/wiki/Ion'><span>ion</span></a></strong><span> positivo, al revés o sea con un exceso de electrones tiene carga negativa y tendremos un ion negativo.</span></p><p><span>La carga eléctrica es un estado de desequilibrio entre el número de electrones y protones; los cuerpos con cargas de distinto signo se atraen entre sí mientras que los que poseen el mismo tipo de carga se repelen. </span></p><h4 id='114-conductores-semiconductores-y-aislantes'><span>1.1.4 Conductores, semiconductores y aislantes.</span></h4><p><span>Las capas más externas de la corteza del átomo si no están semillenas o sea a tener menos del 50% de su capacidad de electrones existe el peligro de abandono de estos en dichas capas; toman el nombre de electrones libres. Un cuerpo conductor de electricidad es una sustancia compuesta por átomos cuya capa más externa no llega a estar semillena de electrones asegurando así el paso de la </span><strong><a href='https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica'><span>corriente</span></a></strong><span> que otra cosa no es que un flujo de electrones libres desde un cuerpo con carga negativa a otro con carga positiva.</span></p><p><span>Los metales tienen una pequeña energía de ionización, tienden a tener un gran número de electrones libres y por ello son buenos conductores de la electricidad. Un aislador o aislante lo forma sustancias que presentan gran resistencia a que las cargas que las forman se desplacen y por tanto no conducen, en condiciones normales, la electricidad.</span></p><p><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Semiconductor'><span>semiconductor</span></a></strong><span> es un elemento que cambia comportamiento dependiendo donde en que campo eléctrico se encuentre. </span></p><h4 id='115-conductividad'><span>1.1.5 Conductividad.</span></h4><p><span>Propiedad que tienen los cuerpos o las sustancias de transmitir de un punto a otro de su masa el calor o la electricidad.</span></p><p><span>La </span><strong><a href='https://www.iec.ch/'><span>Comisión Electrotécnica Internacional</span></a></strong><span> definió como patrón de la conductividad eléctrica la de un hilo de cobre de 1 metro de longitud y un gramo de masa, que da una resistencia de 0,15388 Ω a 20 °C a lo cual asignó una </span><strong><a href='https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica'><span>conductividad eléctrica</span></a></strong><span> de 100% IACS, a toda </span><strong><a href='https://es.wikipedia.org/wiki/Aleaci%C3%B3n'><span>aleación</span></a></strong><span> de cobre con una conductividad mayor se le denomina de alta conductividad.</span></p><p><strong><a href='https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica'><span>Conductancia</span></a></strong><span> es la medida de la facilidad con que la electricidad fluye a través de un circuito o de un objeto. La unidad de medida de conductancia es el </span><strong><a href='https://es.wikipedia.org/wiki/Siemens_(unidad)'><span>Siemens</span></a></strong><span> y de la conductividad el Siemens/m.</span></p><p><span>Siendo lambda λ un coeficiente de conductividad propio de cada materia podemos expresar la conductancia como </span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n39" cid="n39" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" contenteditable="false" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="36.699ex" height="5.665ex" role="img" focusable="false" viewBox="0 -1502 16221.1 2503.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -2.267ex;"><defs><path id="MJX-46-TEX-I-1D436" 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data-c="28" xlink:href="#MJX-46-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(4047,0)"><use data-c="1D450" xlink:href="#MJX-46-TEX-I-1D450"></use></g><g data-mml-node="mi" transform="translate(4480,0)"><use data-c="1D45A" xlink:href="#MJX-46-TEX-I-1D45A"></use></g><g data-mml-node="mo" transform="translate(5358,0)"><use data-c="29" xlink:href="#MJX-46-TEX-N-29"></use></g></g><rect width="8480.6" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>C</mi><mi>o</mi><mi>n</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>i</mi><mi>a</mi><mo>=</mo><mfrac><mrow><mi>λ</mi><mi>x</mi><mi>s</mi><mi>u</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>f</mi><mi>i</mi><mi>c</mi><mi>i</mi><mi>e</mi><mo stretchy="false">(</mo><mi>c</mi><msup><mi>m</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><mrow><mi>l</mi><mi>o</mi><mi>n</mi><mi>g</mi><mi>i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo stretchy="false">(</mo><mi>c</mi><mi>m</mi><mo stretchy="false">)</mo></mrow></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>La inversa de la conductividad es la </span><strong><a href='https://es.wikipedia.org/wiki/Resistividad'><span>resistividad</span></a></strong><span> que expresa la </span><strong><a href='https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica'><span>resistencia</span></a></strong><span> de un conductor de las medidas antes mencionadas, que es la inversa de la conductancia, la temperatura del conductor influye en la resistencia, si aumenta la resistencia también lo hará y viceversa; ocurre en los cuerpos conductores; en los semiconductores el fenómeno es inverso.</span></p><h4 id='116-campo-eléctrico-intensidad-de-campo-unidad-de-campo-voltiosmetro-potencial-apantallamiento-de-campos-eléctricos'><span>1.1.6 campo eléctrico: intensidad de campo. Unidad de campo: voltios/metro. Potencial. Apantallamiento de campos eléctricos.</span></h4><p><span>Una carga eléctrica es la cantidad de electricidad acumulada en un cuerpo y se mide en una unidad denominada </span><strong><a href='https://es.wikipedia.org/wiki/Culombio'><span>Culombio</span></a></strong><span> que equivale a:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n43" cid="n43" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" contenteditable="false" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="24.65ex" height="2.565ex" role="img" focusable="false" viewBox="0 -817 10895.3 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.717ex;"><defs><path id="MJX-48-TEX-I-1D436" d="M50 252Q50 367 117 473T286 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columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>C</mi><mo>=</mo><mn>6</mn><mo>,</mo><mn>24</mn><mi>x</mi><msup><mn>10</mn><mrow data-mjx-texclass="ORD"><mn>18</mn></mrow></msup><mi>e</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>s</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>En cualquier punto del espacio en donde exista una carga eléctrica se origina un </span><strong><a href='https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico'><span>campo eléctrico</span></a></strong><span> que se manifiesta, experimentalmente, por la fuerza de origen eléctrico a que se halla sometida cualquier carga que se sitúe en el otro punto de su alrededor.</span></p><p><span>La </span><strong><a href='https://es.wikipedia.org/wiki/Ley_de_Coulomb'><span>ley de Coulomb</span></a></strong><span> dice que el valor de la fuerza con que se atraen o se repelen dos cargas puntuales en reposo es directamente proporcional al producto de dichas cargas e inversamente proporcional al cuadrado de la distancia que las separa:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n46" cid="n46" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="10.879ex" height="4.181ex" role="img" focusable="false" viewBox="0 -1174 4808.7 1847.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.525ex;"><defs><path id="MJX-22-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 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xlink:href="#MJX-22-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(2082.6,0)"><use data-c="1D458" xlink:href="#MJX-22-TEX-I-1D458"></use></g><g data-mml-node="mfrac" transform="translate(2603.6,0)"><g data-mml-node="mrow" transform="translate(220,676)"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-22-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-22-TEX-N-31"></use></g></g><g data-mml-node="msub" transform="translate(882.6,0)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-22-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-22-TEX-N-32"></use></g></g></g><g data-mml-node="msup" transform="translate(624.3,-719.9)"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-22-TEX-I-1D451"></use></g><g data-mml-node="mn" transform="translate(553,289) scale(0.707)"><use data-c="32" xlink:href="#MJX-22-TEX-N-32"></use></g></g><rect width="1965.1" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>F</mi><mo>=</mo><mi>k</mi><mfrac><mrow><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub></mrow><msup><mi>d</mi><mn>2</mn></msup></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>estando la carga q1 situada en un punto P a una distancia d de otra carga puntual q2. La intensidad del </span><strong><a href='https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico'><span>campo eléctrico</span></a></strong><span> en un punto se define como la fuerza ejercida sobre la unidad de carga eléctrica positiva colocada en el citado punto, y viene dada por la expresión:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n48" cid="n48" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="14.926ex" height="5.059ex" role="img" focusable="false" viewBox="0 -1368 6597.2 2236" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.964ex;"><defs><path id="MJX-23-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 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-193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-23-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-23-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-23-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,12)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D438" xlink:href="#MJX-23-TEX-I-1D438"></use></g><g data-mml-node="mo" transform="translate(1041.8,0)"><use data-c="3D" xlink:href="#MJX-23-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(2097.6,0)"><g data-mml-node="mi" transform="translate(286.8,676)"><use data-c="1D439" xlink:href="#MJX-23-TEX-I-1D439"></use></g><g data-mml-node="msub" transform="translate(220,-686)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-23-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-23-TEX-N-32"></use></g></g><rect width="1082.6" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(3697.9,0)"><use data-c="3D" xlink:href="#MJX-23-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(4753.7,0)"><use data-c="1D458" xlink:href="#MJX-23-TEX-I-1D458"></use></g><g data-mml-node="mfrac" transform="translate(5274.7,0)"><g data-mml-node="msub" transform="translate(220,676)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-23-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-23-TEX-N-31"></use></g></g><g data-mml-node="msub" transform="translate(220,-686)"><g data-mml-node="mi"><use data-c="1D45E" xlink:href="#MJX-23-TEX-I-1D45E"></use></g><g data-mml-node="mn" transform="translate(479,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-23-TEX-N-32"></use></g></g><rect width="1082.6" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>E</mi><mo>=</mo><mfrac><mi>F</mi><msub><mi>q</mi><mn>2</mn></msub></mfrac><mo>=</mo><mi>k</mi><mfrac><msub><mi>q</mi><mn>1</mn></msub><msub><mi>q</mi><mn>2</mn></msub></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>La intensidad del campo eléctrico, en un punto dado, se mide en </span><strong><a href='https://es.wikipedia.org/wiki/Voltio'><span>voltios</span></a></strong><span> partido por metro.</span></p><p><span>Si interponemos entre un campo eléctrico y un punto dado una pantalla de material conductor, el citado punto no recibe la influencia del campo eléctrico. Este efecto se conoce como </span><strong><a href='https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico'><span>apantallamiento</span></a></strong><span> o blindaje. El </span><strong><a href='https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico'><span>potencial eléctrico</span></a></strong><span> en un punto es el trabajo que debe realizar una fuerza eléctrica para mover una carga positiva </span><code>q</code><span> desde el infinito con potencial cero hasta ese punto, dividido por dicha carga. Es el trabajo que debe realizar una fuerza externa para traer una carga unitaria q desde el infinito hasta el punto considerado en contra de la fuerza eléctrica dividido por esa carga:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n51" cid="n51" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" contenteditable="false" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="7.447ex" height="5.059ex" role="img" focusable="false" viewBox="0 -1368 3291.6 2236" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.964ex;"><defs><path id="MJX-50-TEX-I-1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path><path id="MJX-50-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-50-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path><path id="MJX-50-TEX-I-1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,12)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D449" xlink:href="#MJX-50-TEX-I-1D449"></use></g><g data-mml-node="mo" transform="translate(1046.8,0)"><use data-c="3D" xlink:href="#MJX-50-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(2102.6,0)"><g data-mml-node="mi" transform="translate(220,676)"><use data-c="1D439" xlink:href="#MJX-50-TEX-I-1D439"></use></g><g data-mml-node="mi" transform="translate(364.5,-686)"><use data-c="1D45E" xlink:href="#MJX-50-TEX-I-1D45E"></use></g><rect width="949" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>V</mi><mo>=</mo><mfrac><mi>F</mi><mi>q</mi></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Se puede representar el potencial eléctrico mediante las denominadas </span><strong><a href='https://es.wikipedia.org/wiki/Superficie_equipotencial'><span>superficies equipotenciales</span></a></strong><span>, que son el lugar geométrico de los puntos del espacio en los que el potencial tiene un mismo valor o, dicho de otra manera, las superficies en las que todos sus puntos de un campo de fuerza que tienen el mismo potencial.</span></p><h4 id='12-teoría-eléctrica'><span>1.2 Teoría eléctrica. </span></h4><h4 id='121-corriente-eléctrica-voltaje-y-resistencia-circuito-eléctrico'><span>1.2.1 Corriente eléctrica, voltaje y resistencia. Circuito eléctrico.</span></h4><p><img src="https://telecomlobby.com/Images/circuito_simbolos.webp" referrerpolicy="no-referrer" alt="circuito simbolos"></p><p><span>Se denomina corriente eléctrica al paso de electrones a lo largo de un conductor que une dos puntos con distinta carga eléctrica. </span></p><p><span>La </span><strong><a href='https://es.wikipedia.org/wiki/Corriente_continua'><span>corriente continua</span></a></strong><span> es un flujo continuo de electrones a través de un conductor entre dos puntos de distinto potencial y sus valores son constantes, las cargas eléctricas circulan siempre en la misma dirección; es continua toda corriente que mantenga la misma </span><strong><a href='https://bit.ly/3nqudHw'><span>polaridad</span></a></strong><span>.</span></p><p><span>La </span><strong><a href='https://es.wikipedia.org/wiki/Corriente_alterna'><span>corriente alterna</span></a></strong><span> a la corriente eléctrica en la que la magnitud y dirección varían cíclicamente.</span></p><p><span>Para que circule la corriente eléctrica deben desplazarse los electrones, lo que precisa una fuerza que los empuje la llamada </span><strong><a href='https://es.wikipedia.org/wiki/Fuerza_electromotriz'><span>fuerza electromotriz</span></a></strong><span> que es producida por una diferencia de potencial o </span><strong><a href='https://bit.ly/36B9Hgz'><span>voltaje</span></a></strong><span>.</span></p><p><span>La intensidad de una corriente eléctrica depende, para una misma diferencia de potencial, del diámetro del </span><strong><a href='https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico'><span>conductor</span></a></strong><span>, que opone siempre una </span><strong><a href='https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica'><span>resistencia</span></a></strong><span>.</span></p><p><span>Podemos hacer una comparación de términos entre </span><strong><a href='https://es.wikipedia.org/wiki/Hidr%C3%A1ulica'><span>hidráulica</span></a></strong><span> y electricidad:</span></p><ul><li><span>Desnivel; diferencia de potencial.</span></li><li><strong><a href='https://bit.ly/2IxeKX7'><span>Fuerza hidráulica</span></a></strong><span>; fuerza electromotriz.</span></li><li><span>Tubería; conductor.</span></li><li><span>Caudal de agua; intensidad de corriente</span></li><li><span>Partículas de agua; electrones. </span></li></ul><p><span>Existen seis formas elementales de producción de corriente eléctrica. </span></p><p><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Circuito'><span>circuito eléctrico</span></a></strong><span> es un conjunto de conductores por el que circula la corriente eléctrica y en el cual hay intercalados, generalmente, elementos productores y consumidores de la misma.</span></p><h4 id='122-unidades-eléctricas-fundamentales-voltios-amperios-y-ohmios'><span>1.2.2 Unidades eléctricas fundamentales: voltios, amperios y ohmios</span></h4><p><span>El voltaje es la presión eléctrica o diferencia del nivel de cargas que existe entre dos puntos como resultado de la presencia de una </span><strong><a href='https://es.wikipedia.org/wiki/Fuerza_electromotriz'><span>fuerza electromotriz</span></a></strong><span> entra ellos. Para medirla se utiliza el </span><strong><a href='https://es.wikipedia.org/wiki/Voltio'><span>Voltio</span></a></strong><span>: 1 V es la fuerza electromotriz necesaria para producir una corriente de 1 </span><strong><a href='https://es.wikipedia.org/wiki/Amperio'><span>amperio</span></a></strong><span> en un circuito cuya resistencia sea de 1 </span><strong><a href='https://es.wikipedia.org/wiki/Ohmio'><span>ohmio</span></a></strong><span>:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n77" cid="n77" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="28.239ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 12481.6 1000" 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rowspacing="3pt"><mtr><mtd><mi>V</mi><mi>o</mi><mi>l</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>s</mi><mo>=</mo><mi>a</mi><mi>m</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>o</mi><mi>s</mi><mi>x</mi><mi>o</mi><mi>h</mi><mi>m</mi><mi>i</mi><mi>o</mi><mi>s</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Un </span><strong><span>kilovoltio</span></strong><span> son 1000 voltios. Un </span><strong><span>milivoltio</span></strong><span> es la milésima parte de un voltio y el </span><strong><span>microvoltio μV</span></strong><span> es la millonésima parte del voltio.</span></p><p><span>La corriente eléctrica es el flujo o movimiento de los electrones a través de un conductor como consecuencia de la aplicación de una tensión o diferencia de potencial, la intensidad de corriente es el amperio que corresponde al paso de una carga de un culombio durante un segundo:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n80" cid="n80" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="22.406ex" height="12.867ex" role="img" focusable="false" viewBox="0 -3093.5 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xlink:href="#MJX-26-TEX-I-1D454"></use></g><g data-mml-node="mi" transform="translate(1412,0)"><use data-c="1D462" xlink:href="#MJX-26-TEX-I-1D462"></use></g><g data-mml-node="mi" transform="translate(1984,0)"><use data-c="1D45B" xlink:href="#MJX-26-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(2584,0)"><use data-c="1D451" xlink:href="#MJX-26-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(3104,0)"><use data-c="1D45C" xlink:href="#MJX-26-TEX-I-1D45C"></use></g></g><rect width="4452" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>I</mi><mo>=</mo><mfrac><mi>q</mi><mi>t</mi></mfrac></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>A</mi><mi>m</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>o</mi><mo>=</mo><mfrac><mrow><mi>C</mi><mi>u</mi><mi>l</mi><mi>o</mi><mi>m</mi><mi>b</mi><mi>i</mi><mi>o</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>g</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>o</mi></mrow></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>La resistencia es la dificultad o facilidad que encuentra la corriente eléctrica para circular a través de un material.</span></p><p><span>La unidad de resistencia es el ohmio Ω. representa la resistencia de un conductor en el que, con una diferencia de potencial aplicada en sus extremos de 1 V circula una corriente de 1 </span><code>A</code><span> de intensidad.</span></p><h4 id='123-ley-de-ohm'><span>1.2.3 Ley de Ohm</span></h4><p><span>Al pasar una corriente </span><code>I</code><span> por una resistencia </span><code>R</code><span> se produce una caída de tensión o ddp que se expresa con la fórmula:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n85" cid="n85" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.897ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3932.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-27-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-27-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-27-TEX-I-1D43C" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path id="MJX-27-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-27-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D438" xlink:href="#MJX-27-TEX-I-1D438"></use></g><g data-mml-node="mo" transform="translate(1041.8,0)"><use data-c="3D" xlink:href="#MJX-27-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(2097.6,0)"><use data-c="1D43C" xlink:href="#MJX-27-TEX-I-1D43C"></use></g><g data-mml-node="mi" transform="translate(2601.6,0)"><use data-c="1D465" xlink:href="#MJX-27-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(3173.6,0)"><use data-c="1D445" xlink:href="#MJX-27-TEX-I-1D445"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>E</mi><mo>=</mo><mi>I</mi><mi>x</mi><mi>R</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Si aumenta la resistencia disminuye la intensidad y viceversa.</span></p><h4 id='124-aplicación-de-la-ley-de-ohm-resistencias-agrupación-de-resistencias'><span>1.2.4 Aplicación de la Ley de Ohm. Resistencias. Agrupación de resistencias.</span></h4><p><span>Si tomamos dos conductores de la misma forma y tamaño pero de distintos materiales y les aplicamos una misma </span><code>fem</code><span>, las corrientes que circularán serán distintas, porque cada material, al tener una conductividad distinta, tiene una resistencia al paso de la corriente diferente.</span></p><p><span>Una resistencia es un elemento o componente de un circuito eléctrico formado por un encapsulado de material que una cierta cantidad de resistencia y con dos rabillos o puntos para su conexión a un circuito.</span></p><p><span>Las resistencias pueden agruparse en serie, en paralelo o combinando ambas formas. El cálculo de la resistencia resultante se realiza aplicando la Ley de Ohm. En el caso de resistencia conectadas en serie la resistencia del conjunto es la suma de los valores de cada una de ellas</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n91" cid="n91" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="18.38ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 8124.1 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-28-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path><path id="MJX-28-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-28-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-28-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-28-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-28-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D445" xlink:href="#MJX-28-TEX-I-1D445"></use></g><g data-mml-node="mo" transform="translate(1036.8,0)"><use data-c="3D" xlink:href="#MJX-28-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(2092.6,0)"><g data-mml-node="mi"><use data-c="1D445" xlink:href="#MJX-28-TEX-I-1D445"></use></g><g data-mml-node="mn" transform="translate(792,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-28-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(3510.3,0)"><use data-c="2B" xlink:href="#MJX-28-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(4510.6,0)"><g data-mml-node="mi"><use data-c="1D445" xlink:href="#MJX-28-TEX-I-1D445"></use></g><g data-mml-node="mn" transform="translate(792,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-28-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(5928.3,0)"><use data-c="2B" xlink:href="#MJX-28-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(6928.6,0)"><g data-mml-node="mi"><use data-c="1D445" xlink:href="#MJX-28-TEX-I-1D445"></use></g><g data-mml-node="mn" transform="translate(792,-150) scale(0.707)"><use data-c="33" xlink:href="#MJX-28-TEX-N-33"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>R</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub><mo>+</mo><msub><mi>R</mi><mn>2</mn></msub><mo>+</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>La intensidad que pasa por cada una de ellas es igual a la del conjunto:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n93" cid="n93" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="16.141ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 7134.3 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-29-TEX-I-1D43C" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path><path id="MJX-29-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-29-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-29-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-29-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-29-TEX-I-1D43C"></use></g><g data-mml-node="mo" transform="translate(781.8,0)"><use data-c="3D" xlink:href="#MJX-29-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(1837.6,0)"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-29-TEX-I-1D43C"></use></g><g data-mml-node="mn" transform="translate(473,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-29-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(2991.9,0)"><use data-c="3D" xlink:href="#MJX-29-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(4047.7,0)"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-29-TEX-I-1D43C"></use></g><g data-mml-node="mn" transform="translate(473,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-29-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(5202,0)"><use data-c="3D" xlink:href="#MJX-29-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(6257.8,0)"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-29-TEX-I-1D43C"></use></g><g data-mml-node="mn" transform="translate(473,-150) scale(0.707)"><use data-c="33" xlink:href="#MJX-29-TEX-N-33"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>I</mi><mo>=</mo><msub><mi>I</mi><mn>1</mn></msub><mo>=</mo><msub><mi>I</mi><mn>2</mn></msub><mo>=</mo><msub><mi>I</mi><mn>3</mn></msub></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>En el caso de resistencias conectadas en paralelo, la del conjunto es menor que la de cada una de ellas. La intensidad es inversamente proporcional a su valor.</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n95" cid="n95" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="19.986ex" height="11.83ex" role="img" focusable="false" viewBox="0 -2864.5 8833.6 5229" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -5.35ex;"><defs><path id="MJX-30-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 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xlink:href="#MJX-30-TEX-I-1D43C"></use></g><g data-mml-node="mn" transform="translate(473,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-30-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(2936.3,0)"><use data-c="2B" xlink:href="#MJX-30-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(3936.6,0)"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-30-TEX-I-1D43C"></use></g><g data-mml-node="mn" transform="translate(473,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-30-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(5035.3,0)"><use data-c="2B" xlink:href="#MJX-30-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(6035.6,0)"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-30-TEX-I-1D43C"></use></g><g data-mml-node="mn" transform="translate(473,-150) scale(0.707)"><use data-c="33" xlink:href="#MJX-30-TEX-N-33"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>R</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mfrac><mn>1</mn><msub><mi>R</mi><mn>1</mn></msub></mfrac><mo>+</mo><mfrac><mn>1</mn><msub><mi>R</mi><mn>2</mn></msub></mfrac><mo>+</mo><mfrac><mn>1</mn><msub><mi>R</mi><mn>3</mn></msub></mfrac></mrow></mfrac></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>I</mi><mo>=</mo><msub><mi>I</mi><mn>1</mn></msub><mo>+</mo><msub><mi>I</mi><mn>2</mn></msub><mo>+</mo><msub><mi>I</mi><mn>3</mn></msub></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Un </span><strong><a href='https://bit.ly/3eZMHfb'><span>shunt</span></a></strong><span> es una resistencia acoplada en paralelo con cualquier elemento de un circuito para derivar corriente por ella. Una aplicación típica son los aparatos de medida que soportan poca intensidad de corriente, </span><strong><a href='https://es.wikipedia.org/wiki/Galvan%C3%B3metro'><span>galvanómetro</span></a></strong><span> </span><code>G</code><span>, por lo que es preciso limitar ésta adoptando una resistencia en paralelo </span><code>Rs</code><span>. </span></p><h4 id='125-código-de-colores-de-las-resistencias'><span>1.2.5 Código de colores de las resistencias.</span></h4><p><img src="https://telecomlobby.com/Images/banda_colores_resistencias.webp" referrerpolicy="no-referrer" alt="resistencias"></p><p><span>Permite indicar su valor en ohmios mediante bandas de colores.</span></p><p><span>El conjunto de dichos anillos nos da la lectura del número de ohmios de la resistencia. La tolerancia de una resistencia expresa los márgenes alrededor de los cuales puede variar su valor. A mayor precisión, menor tolerancia.</span></p><h4 id='126-disipación-de-potencia-en-las-resistencias'><span>1.2.6 Disipación de potencia en las resistencias</span></h4><p><span>Una resistencia se intercala en un circuito para obstaculizar el paso de la corriente y transformar en calor el voltaje que no necesitamos ne un punto dado. Se conoce como </span><strong><a href='https://es.wikipedia.org/wiki/Efecto_Joule'><span>efecto Joule</span></a></strong><span>. Todo conducto por lo que circula una corriente experimenta un aumento de su temperatura. La ley de joule enuncia que la cantidad de calor desprendida en un conductor por el paso de una corriente constante es proporcional al cuadrado de la intensidad de la corriente, a la resistencia del conductor y al tiempo que dure el paso. Se llama potencia de disipación, medidas en vatios, al producto del voltaje por la intensidad que ha de circular por la resistencia:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n103" cid="n103" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.89ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3929.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-31-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path id="MJX-31-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-31-TEX-I-1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path><path id="MJX-31-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-31-TEX-I-1D43C" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 2T43 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D443" xlink:href="#MJX-31-TEX-I-1D443"></use></g><g data-mml-node="mo" transform="translate(1028.8,0)"><use data-c="3D" xlink:href="#MJX-31-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(2084.6,0)"><use data-c="1D449" xlink:href="#MJX-31-TEX-I-1D449"></use></g><g data-mml-node="mi" transform="translate(2853.6,0)"><use data-c="1D465" xlink:href="#MJX-31-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(3425.6,0)"><use data-c="1D43C" xlink:href="#MJX-31-TEX-I-1D43C"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>P</mi><mo>=</mo><mi>V</mi><mi>x</mi><mi>I</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Si la resistencia disipa una potencia mayor que aquélla para la que está preparada, se quema, cortándose el hilo del que está hecha o fundiéndose el material resistivo. Disipación máxima es la potencia calorífica que podemos suministrar a un resistencia sin que la temperatura se eleve peligrosamente.</span></p><p><span>Los valores de disipación de potencia más frecuentes de las resistencias son los de </span><code>0,125W</code><span>, </span><code>0,25W</code><span>, </span><code>0,5W</code><span> y </span><code>1W</code><span>.</span></p><h4 id='127-coeficientes-negativos-y-positivos-de-temperatura-ntp-y-ptc'><span>1.2.7 Coeficientes negativos y positivos de temperatura NTP y PTC</span></h4><p><img src="https://upload.wikimedia.org/wikipedia/commons/1/10/Thermistor.svg" referrerpolicy="no-referrer" alt="Simbolo electronico generico CEI"></p><p><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Termistor'><span>termistor</span></a></strong><span> </span><code>NTC</code><span> es una resistencia cuyo valor se va reduciendo a medida que aumenta la temperatura. Análogamente a un </span><code>NTC</code><span> un termistor </span><code>PTC</code><span> es una resistencia cuyo valor va aumentando a medida que aumenta la temperatura.</span></p><h4 id='128-otros-tipos-de-resistencias'><span>1.2.8 Otros tipos de resistencias.</span></h4><p><span>Una resistencia ajustable permite fijar su valor dentro de un rango mediante una abrazadera móvil en contacto con el elemento resistivo. Un </span><strong><a href='https://es.wikipedia.org/wiki/Reostato'><span>reóstato</span></a></strong><span> es una resistencia variable que se usa en los circuitos de gran consumo, empleándose para regular la corriente en máquinas y motores. </span></p><p><img src="https://upload.wikimedia.org/wikipedia/commons/1/1c/Potentiometer_symbol_Europe.svg" referrerpolicy="no-referrer" alt="Simbolo electronico europeo"></p><p><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Potenci%C3%B3metro'><span>potenciómetro</span></a></strong><span> es una resistencia variable que puede ser variada por el usuario para realizar cualquier función. Es lineal cuando su resistencia es proporcional al desplazamiento del cursor ya que se desliza por una pista uniforme. En el no lineal al ser la pista de diferente grosor, la respuesta, la resistencia, no corresponde al desplazamiento del cursor. Estos últimos suelen tener una respuesta que se aproxima a la función logaritmo.</span></p><h4 id='129-leyes-de-kirchhoff'><span>1.2.9 Leyes de Kirchhoff</span></h4><p><span>Las leyes de </span><strong><a href='https://es.wikipedia.org/wiki/Gustav_Kirchhoff'><span>Kirchhoff</span></a></strong><span> son útiles al análisis de múltiples tipos de circuitos:</span></p><ol start='' ><li><span>La suma de las intensidades de corriente que llegan a un nudo de un circuito es igual a la suma de las intensidades que salen de él. </span></li><li><span>En un circuito cerrado o malla la suma de todas las caídas de tensión es igual a la suma de todas las subidas de tensión, la suma algebraica de las tensiones en todo circuito cerrado es cero.</span></li></ol><h4 id='1210-potencia-eléctrica-unidad-de-potencia-el-vatio'><span>1.2.10 Potencia eléctrica. Unidad de potencia: el vatio.</span></h4><p><span>La corriente eléctrica puede desarrollar un trabajo, la relación que hay entre un trabajo y tiempo de la </span><strong><a href='https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica'><span>potencia</span></a></strong><span> que es la expresión de la cantidad del trabajo producido en la unidad de tiempo. La unidad de potencia es el </span><strong><a href='https://es.wikipedia.org/wiki/Vatio'><span>vatio</span></a></strong><span>:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n119" cid="n119" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="31.413ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 13884.5 3600" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -3.507ex;"><defs><path id="MJX-32-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 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xlink:href="#MJX-32-TEX-I-1D452"></use></g><g data-mml-node="mi" transform="translate(2063,0)"><use data-c="1D45B" xlink:href="#MJX-32-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(2663,0)"><use data-c="1D450" xlink:href="#MJX-32-TEX-I-1D450"></use></g><g data-mml-node="mi" transform="translate(3096,0)"><use data-c="1D456" xlink:href="#MJX-32-TEX-I-1D456"></use></g><g data-mml-node="mi" transform="translate(3441,0)"><use data-c="1D44E" xlink:href="#MJX-32-TEX-I-1D44E"></use></g><g data-mml-node="mo" transform="translate(4247.8,0)"><use data-c="3D" xlink:href="#MJX-32-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(5303.6,0)"><use data-c="1D461" xlink:href="#MJX-32-TEX-I-1D461"></use></g><g data-mml-node="mi" transform="translate(5664.6,0)"><use data-c="1D452" xlink:href="#MJX-32-TEX-I-1D452"></use></g><g data-mml-node="mi" transform="translate(6130.6,0)"><use data-c="1D45B" xlink:href="#MJX-32-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(6730.6,0)"><use data-c="1D460" xlink:href="#MJX-32-TEX-I-1D460"></use></g><g data-mml-node="mi" transform="translate(7199.6,0)"><use data-c="1D456" xlink:href="#MJX-32-TEX-I-1D456"></use></g><g data-mml-node="mi" transform="translate(7544.6,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="825.5px" font-family="serif" font-style="italic">ó</text></g><g data-mml-node="mi" transform="translate(7957.5,0)"><use data-c="1D45B" xlink:href="#MJX-32-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(8557.5,0)"><use data-c="1D465" xlink:href="#MJX-32-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(9129.5,0)"><use data-c="1D456" xlink:href="#MJX-32-TEX-I-1D456"></use></g><g data-mml-node="mi" transform="translate(9474.5,0)"><use data-c="1D45B" xlink:href="#MJX-32-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(10074.5,0)"><use data-c="1D461" xlink:href="#MJX-32-TEX-I-1D461"></use></g><g data-mml-node="mi" transform="translate(10435.5,0)"><use data-c="1D452" xlink:href="#MJX-32-TEX-I-1D452"></use></g><g data-mml-node="mi" transform="translate(10901.5,0)"><use data-c="1D45B" xlink:href="#MJX-32-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(11501.5,0)"><use data-c="1D460" xlink:href="#MJX-32-TEX-I-1D460"></use></g><g data-mml-node="mi" transform="translate(11970.5,0)"><use data-c="1D456" xlink:href="#MJX-32-TEX-I-1D456"></use></g><g data-mml-node="mi" transform="translate(12315.5,0)"><use data-c="1D451" xlink:href="#MJX-32-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(12835.5,0)"><use data-c="1D44E" xlink:href="#MJX-32-TEX-I-1D44E"></use></g><g data-mml-node="mi" transform="translate(13364.5,0)"><use data-c="1D451" xlink:href="#MJX-32-TEX-I-1D451"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,0)"><g data-mml-node="mtd" transform="translate(13884.5,0)"></g></g><g data-mml-node="mtr" transform="translate(0,-1300)"><g data-mml-node="mtd" transform="translate(9960,0)"><g data-mml-node="mi"><use data-c="1D443" xlink:href="#MJX-32-TEX-I-1D443"></use></g><g data-mml-node="mo" transform="translate(1028.8,0)"><use data-c="3D" xlink:href="#MJX-32-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(2084.6,0)"><use data-c="1D438" xlink:href="#MJX-32-TEX-I-1D438"></use></g><g data-mml-node="mi" transform="translate(2848.6,0)"><use data-c="1D465" xlink:href="#MJX-32-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(3420.6,0)"><use data-c="1D43C" xlink:href="#MJX-32-TEX-I-1D43C"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>P</mi><mi>o</mi><mi>t</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>i</mi><mi>a</mi><mo>=</mo><mi>t</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>i</mi><mi>ó</mi><mi>n</mi><mi>x</mi><mi>i</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>d</mi></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>E</mi><mi>x</mi><mi>I</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Donde </span><code>P</code><span> es expresada en vatios, la tensión en voltios, y la intensidad en amperios. Aplicando la ley de Ohm sabemos que la tensión es igual a la intensidad por la resistencia. O sea obtenemos:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n121" cid="n121" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="9.976ex" height="2.565ex" role="img" focusable="false" viewBox="0 -817 4409.3 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.717ex;"><defs><path id="MJX-33-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path id="MJX-33-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-33-TEX-I-1D43C" d="M43 1Q26 1 26 10Q26 12 29 24Q34 43 39 45Q42 46 54 46H60Q120 46 136 53Q137 53 138 54Q143 56 149 77T198 273Q210 318 216 344Q286 624 286 626Q284 630 284 631Q274 637 213 637H193Q184 643 189 662Q193 677 195 680T209 683H213Q285 681 359 681Q481 681 487 683H497Q504 676 504 672T501 655T494 639Q491 637 471 637Q440 637 407 634Q393 631 388 623Q381 609 337 432Q326 385 315 341Q245 65 245 59Q245 52 255 50T307 46H339Q345 38 345 37T342 19Q338 6 332 0H316Q279 2 179 2Q143 2 113 2T65 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66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-33-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,-67)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D443" xlink:href="#MJX-33-TEX-I-1D443"></use></g><g data-mml-node="mo" transform="translate(1028.8,0)"><use data-c="3D" xlink:href="#MJX-33-TEX-N-3D"></use></g><g data-mml-node="msup" transform="translate(2084.6,0)"><g data-mml-node="mi"><use data-c="1D43C" xlink:href="#MJX-33-TEX-I-1D43C"></use></g><g data-mml-node="TeXAtom" transform="translate(590.2,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-33-TEX-N-32"></use></g></g></g><g data-mml-node="mi" transform="translate(3078.3,0)"><use data-c="1D465" xlink:href="#MJX-33-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(3650.3,0)"><use data-c="1D445" xlink:href="#MJX-33-TEX-I-1D445"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>P</mi><mo>=</mo><msup><mi>I</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>x</mi><mi>R</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Si por ejemplo en un circuito circulan 20 amperios y la resistencia es de 100 ohmios la potencia será:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n123" cid="n123" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="32.528ex" height="2.565ex" role="img" focusable="false" viewBox="0 -817 14377.2 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.717ex;"><defs><path id="MJX-34-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z"></path><path id="MJX-34-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 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data-c="1D465" xlink:href="#MJX-34-TEX-I-1D465"></use></g><g data-mml-node="mn" transform="translate(4093.1,0)"><use data-c="31" xlink:href="#MJX-34-TEX-N-31"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mo" transform="translate(5870.9,0)"><use data-c="3D" xlink:href="#MJX-34-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(6926.7,0)"><use data-c="34" xlink:href="#MJX-34-TEX-N-34"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(1000,0)"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(1500,0)"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(2000,0)"></use></g><g data-mml-node="mi" transform="translate(9426.7,0)"><use data-c="1D44A" xlink:href="#MJX-34-TEX-I-1D44A"></use></g><g data-mml-node="mo" transform="translate(10752.4,0)"><use data-c="3D" xlink:href="#MJX-34-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(11808.2,0)"><use data-c="34" xlink:href="#MJX-34-TEX-N-34"></use><use data-c="30" xlink:href="#MJX-34-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mi" transform="translate(12808.2,0)"><use data-c="1D458" xlink:href="#MJX-34-TEX-I-1D458"></use></g><g data-mml-node="mi" transform="translate(13329.2,0)"><use data-c="1D44A" xlink:href="#MJX-34-TEX-I-1D44A"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>P</mi><mo>=</mo><msup><mn>20</mn><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>x</mi><mn>100</mn><mo>=</mo><mn>40000</mn><mi>W</mi><mo>=</mo><mn>40</mn><mi>k</mi><mi>W</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Los múltiplos del vatio son el kilowatio y el </span><strong><a href='https://es.wikipedia.org/wiki/Caballo_de_vapor'><span>caballo de vapor</span></a></strong><span> equivalente a 1kW o el </span><strong><a href='https://es.wikipedia.org/wiki/Caballo_de_fuerza'><span>caballo de fuerza</span></a></strong><span> </span><code>HP</code><span> a 736W. </span></p><p><span>La energía eléctrica se expresa como la potencia consumida durante una unidad de tiempo, como unidad se emplea el </span><strong><a href='https://es.wikipedia.org/wiki/Kilovatio_hora'><span>kilovatio hora</span></a></strong><span> </span><code>kWh</code><span> que equivale a la energía eléctrica consumida por un aparato al ser atravesado por una corriente de 1 amperio, a una tensión de 1000 V y durante una hora, puede corresponder a cualquier otra combinación de los tres valores cuyo producto total sea 1kW:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n126" cid="n126" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" contenteditable="false" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="41.319ex" height="8.145ex" role="img" focusable="false" viewBox="0 -2050 18263 3600" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -3.507ex;"><defs><path id="MJX-52-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 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src="https://telecomlobby.com/Images/condensadores.webp" referrerpolicy="no-referrer" alt="Condensadores"></p><p><span>Constan de dos placas conductoras separadas por un cuerpo no conductor llamado </span><strong><a href='https://es.wikipedia.org/wiki/Diel%C3%A9ctrico'><span>dieléctrico</span></a></strong><span>:</span></p><ul><li><span>aire</span></li><li><span>aceite</span></li><li><span>vidrio</span></li><li><strong><a href='https://es.wikipedia.org/wiki/Mica'><span>mica</span></a></strong></li><li><strong><a href='https://es.wikipedia.org/wiki/Polietileno'><span>polietileno</span></a></strong></li></ul><p><img src="https://upload.wikimedia.org/wikipedia/commons/9/9e/Condensator_tekening.png" referrerpolicy="no-referrer"></p><p><span>Las placas suelen ser láminas de </span><strong><a href='https://es.wikipedia.org/wiki/Esta%C3%B1o'><span>estaño</span></a></strong><span> alternando con láminas del dieléctrico usado; los </span><strong><a href='https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico'><span>condensadores</span></a></strong><span> tienen la capacidad de acumular una determinada carga eléctrica a un voltaje determinado, la acumula en carga y la restituye en descarga al resto del circuito. Al cerrarlo una placa queda asociada al polo positivo y otra al negativo de la pila o fuente que la alimente, la armadura conectada al polo positivo va cediendo electrones a éste, mientras que la otra armadura recoge electrones del polo negativo, se puede apreciar el flujo de corriente intercalando un </span><strong><a href='https://es.wikipedia.org/wiki/Amper%C3%ADmetro'><span>amperímetro</span></a></strong><span>. Se pueden recargar hasta que entre las placas de éstos se llega a alcanzar un voltaje igual al existente en los bornes de la batería o fuente que los alimente. Si se abre el interruptor desconectando la alimentación de las armaduras estas quedan cargadas el circuito queda abierto y se mantiene la diferencia de potencia entre las armaduras; aparece un campo eléctrico desde la placa positiva a la negativa en el que habrá más dispersión de líneas de fuerza cuanto más alejadas estén. El condensador se descarga  instantáneamente si se unen o cortocircuitan las placas del mismo pero si se añade una resistencia de un valor dado la descarga durará un tiempo determinado. </span></p><p><span>Tanto descarga como carga no son instantáneas y además tampoco tienen forma lineal sino </span><strong><a href='https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial'><span>exponencial</span></a></strong><span>, su capacidad eléctrica es:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n143" cid="n143" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="36.708ex" height="13.584ex" role="img" focusable="false" viewBox="0 -3252 16225 6004" 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rowspacing="3pt"><mtr><mtd><mi>C</mi><mi>a</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mi>e</mi><mi>l</mi><mi>é</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>c</mi><mi>a</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>a</mi><mi>e</mi><mi>l</mi><mi>é</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>c</mi><mi>a</mi></mrow><mrow><mi>v</mi><mi>o</mi><mi>l</mi><mi>t</mi><mi>a</mi><mi>j</mi><mi>e</mi></mrow></mfrac></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><mi>V</mi><mo>=</mo><mfrac><mi>Q</mi><mi>V</mi></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Faradio'><span>faradio</span></a></strong><span> es la capacidad de un condensador al que aplicada una fem de 1 voltio adquiere una carga de 1 culombio. El microfaradio μF equivale a 10-6 F y el nanofaradio nF a 10-9F, el picofaradio a 10-12F.</span></p><p><span>La energía almacenada en condensador se expresa por la fórmula:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n146" cid="n146" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="13.363ex" height="2.565ex" role="img" focusable="false" viewBox="0 -817 5906.4 1133.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.717ex;"><defs><path id="MJX-37-TEX-I-1D44A" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 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id="MJX-37-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path><path id="MJX-37-TEX-I-1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,-67)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D44A" xlink:href="#MJX-37-TEX-I-1D44A"></use></g><g data-mml-node="mo" transform="translate(1325.8,0)"><use data-c="3D" xlink:href="#MJX-37-TEX-N-3D"></use></g><g data-mml-node="mstyle" transform="translate(2381.6,0)"><g data-mml-node="mtext"><use data-c="31" xlink:href="#MJX-37-TEX-N-31"></use><use data-c="2F" xlink:href="#MJX-37-TEX-N-2F" transform="translate(500,0)"></use><use data-c="32" xlink:href="#MJX-37-TEX-N-32" transform="translate(1000,0)"></use></g></g><g data-mml-node="mi" transform="translate(3881.6,0)"><use data-c="1D436" xlink:href="#MJX-37-TEX-I-1D436"></use></g><g data-mml-node="msup" transform="translate(4641.6,0)"><g data-mml-node="mi"><use data-c="1D449" xlink:href="#MJX-37-TEX-I-1D449"></use></g><g data-mml-node="TeXAtom" transform="translate(861.3,413) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-37-TEX-N-32"></use></g></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>W</mi><mo>=</mo><mstyle displaystyle="false" scriptlevel="0"><mtext>1/2</mtext></mstyle><mi>C</mi><msup><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>O sea que depende de su capacidad y del voltaje aplicado.</span></p><p><span>Se llama </span><strong><a href='https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica'><span>constante dieléctrica</span></a></strong><span> a la relación que hay entre la capacidad de un condensador formado por un determinado dieléctrico y su capacidad de un condensador formado por un determinado dieléctrico y su capacidad en el vacío. Se denomina </span><strong><a href='https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica'><span>rigidez dieléctrica</span></a></strong><span> o tensión de trabajo de un condensador a aquella que puede soportar sin que se perfore su dieléctrico. La tensión de prueba es aquella a la que el fabricante somete al condensador sin que se haya producido la perforación y es siempre mayor que la tensión de trabajo.</span></p><p><span>Los condensadores como otros componentes varían de valor con la temperatura, el parámetro se denomina </span><strong><a href='https://es.wikipedia.org/wiki/Coeficiente_de_temperatura'><span>coeficiente de temperatura</span></a></strong><span> que puede ser positivo o negativo. Los cerámicos o de mica son muy estables en frente de la temperatura. </span></p><h4 id='131-relación-entre-capacidad-dimensiones-y-dieléctrico'><span>1.3.1 Relación entre capacidad, dimensiones y dieléctrico</span></h4><p><span>La capacidad de un condensador depende de dos magnitudes:</span></p><ul><li><span>la distancia entre las placas inversamente proporcional a mayor superficie de las placas, mayor capacidad y a mayor distancia menor capacidad.</span></li><li><span>constante dieléctrica del material, directamente proporcional.</span></li></ul><h4 id='132-condensadores-diversos-tipos-tabla-de-colores'><span>1.3.2 Condensadores: diversos tipos. Tabla de colores.</span></h4><p><img src="https://telecomlobby.com/Images/tabla_colores_condensadores.webp" referrerpolicy="no-referrer" alt="Tabla colores condesadores"></p><p><span>Los </span><strong><a href='https://es.wikipedia.org/wiki/Condensador_variable'><span>variables</span></a></strong><span> cambian su capacidad variando la superficie de sus placas. Se usan para sintonizar circuitos </span><strong><a href='https://es.wikipedia.org/wiki/Oscilaci%C3%B3n'><span>oscilantes</span></a></strong><span>. </span></p><p><span>Los ajustables o trimmer utilizados para ajustar la capacidad.</span></p><p><span>Los fijos que pueden ser </span><strong><a href='https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica'><span>polarizados</span></a></strong><span> o no. Los non polarizados se clasifican según el tipo de dieléctrico que utilizan como hemos visto. Los </span><strong><a href='https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico'><span>electrolíticos</span></a></strong><span> tienen dieléctrico líquido o en papel impregnado.</span></p><p><span>Al ser pequeños los condensadores se emplean, generalmente, códigos de bandas de colores para indicar su capacidad expresada en picofaradios. Las bandas indican su capacidad, su tolerancia y su tensión máxima. </span></p><p><span>La forma de expresar la tolerancia depende de si tiene más o menos de 10 picofaradios de capacidad, si mayor se expresa un porcentaje de incremento o disminución de la misma o si es menor de dicho valor expresa la fracción di picofaradio a sumar o restar. Por ejemplo</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n164" cid="n164" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="37.884ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 16744.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-38-TEX-I-1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 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xlink:href="#MJX-38-TEX-I-1D45C"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>m</mi><mi>a</mi><mi>r</mi><mi>r</mi><mi>ó</mi><mi>n</mi><mo>−</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>d</mi><mi>e</mi><mo>−</mo><mi>r</mi><mi>o</mi><mi>j</mi><mi>o</mi><mo>−</mo><mi>n</mi><mi>e</mi><mi>g</mi><mi>r</mi><mi>o</mi><mo>−</mo><mi>r</mi><mi>o</mi><mi>j</mi><mi>o</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>1500 pF de capacidad, 20% de tolerancia, 250V de tensión máxima de trabajo.</span></p><h4 id='133-asociación-de-condensadores'><span>1.3.3 Asociación de condensadores</span></h4><p><span>Los condensadores pueden agruparse en serie o en paralelo.</span></p><p><span>En serie la capacidad resultante se obtiene dividiendo la unidad por la suma de las inversas de todas las capacidades; las armaduras externas actúan de terminales de conexión. Al quedare tan distanciadas estás, la capacidad total resulta mucho menor que la de uno de los condensadores.</span></p><p><span>En paralelo la capacidad total es la suma de las capacidades de todos ellos.</span></p><h4 id='14-campo-magnético'><span>1.4 Campo magnético</span></h4><p><img src="https://telecomlobby.com/Images/iman.webp" referrerpolicy="no-referrer" alt="Iman"></p><p><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Im%C3%A1n'><span>imán</span></a></strong><span> crea a su alrededor un campo de atracción de sustancias tales como el hierro y que se denomina </span><strong><a href='https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico'><span>campo magnético</span></a></strong><span> y es el espacio en que un imán ejerce su influencia.</span></p><p><span>Se crea un campo magnético en los alrededores de un conductor recorrido por una corriente eléctrica, si no hay corriente no hay campo cosa que no ocurre con los imanes. </span></p><h4 id='141-magnetismo'><span>1.4.1 magnetismo.</span></h4><p><span>Se llama </span><strong><a href='https://es.wikipedia.org/wiki/Magnetismo'><span>magnetismo</span></a></strong><span> al conjunto de fenómenos originados por los campos magnéticos. Un imán puede ser </span><strong><a href='https://es.wikipedia.org/wiki/Magnetita'><span>magnetita</span></a></strong><span>, </span><strong><a href='https://es.wikipedia.org/wiki/Acero'><span>acero</span></a></strong><span> o bien alguna aleación. Los extremos se llaman polos, norte y sur. Al centro la línea neutra. El magnetismo es formado por las líneas ovales de fuerza entra los dos polos.</span></p><p><span>Una aguja imantada que gire libremente siempre se orientará en la dirección norte-sur. La tierra produce un campo magnético y llamamos a los dos polos </span><strong><a href='https://es.wikipedia.org/wiki/Polo_norte'><span>norte geográfico</span></a></strong><span> y </span><strong><a href='https://es.wikipedia.org/wiki/Polo_sur'><span>sur geográfico</span></a></strong><span>. Polos de mismo nombre se repelen y los de nombre contrario se atraen. </span></p><h4 id='142-características-de-un-campo-magnético'><span>1.4.2 Características de un campo magnético.</span></h4><p><span>El total de las líneas de fuerza se denomina </span><strong><a href='https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico'><span>flujo magnético</span></a></strong><span>. El numero de líneas que salen es igual al que entran de la superficie. La unidad de flujo magnético es el </span><strong><a href='https://bit.ly/36XehpI'><span>Weber</span></a></strong><span>. Un </span><code>Wb</code><span> es el flujo magnético que al atravesar un circuito de una sola espira produce en ella una fuerza electromotriz de un voltio si se anula dicho flujo en un segundo por decrecimiento uniforme.</span></p><p><span>La </span><strong><a href='https://es.wikipedia.org/wiki/Inducci%C3%B3n_magn%C3%A9tica'><span>densidad de flujo</span></a></strong><span> es el </span><strong><a href='https://es.wikipedia.org/wiki/Tesla_(unidad)'><span>Tesla</span></a></strong><span> </span><code>T</code><span> que es la inducción magnética uniforme que repartida sobre una superificie de un metro cuadrado, produce a través de esa superficie un flujo magnetico de un </span><code>Wb</code><span>.</span></p><p><span>La </span><strong><a href='https://es.wikipedia.org/wiki/Reluctancia_magn%C3%A9tica'><span>reluctancia</span></a></strong><span> es la propiedad de los cuerpos de oponerse a la creación de un flujo magnético. Menos el hierro y sus aleaciones los demás cuerpos tienen un reluctancia muy parecida a la del vacío, concepto análogo a la resistencia eléctrica. </span></p><p><span>La </span><strong><a href='https://es.wikipedia.org/wiki/Permeabilidad_magn%C3%A9tica'><span>permeabilidad</span></a></strong><span> es el inverso de la reluctacia, mejor dicho es la mayor facilidad con que puede crearse un campo magnético en un cuerpo frente al esfuerzo necesario para crearlo en el aire.</span></p><h4 id='15-electromagnetismo'><span>1.5 Electromagnetismo</span></h4><p><img src="https://live.staticflickr.com/2448/4074152433_abe5f9210e_n.jpg" referrerpolicy="no-referrer"></p><p><span>Conjunto de acciones y reacciones producidas por los campos eléctricos y magnéticos sobre la materia. Todo conductor por ser recorrido por una corriente eléctrica genera a su alrededor un campo magnético. Se demuestra colocando una aguja imantada móvil cerca del conductor. El campo creado por un conductor recto, un hilo, es débil, se puede reforzar enrollándolo en forma de bucle o espira. Cuanto más lo enrollemos, más reforzaremos el campo magnético creado, siendo máximo al formar múltiples bucles hasta conseguir:</span></p><p><img src="https://upload.wikimedia.org/wikipedia/commons/4/4b/Inductor.svg" referrerpolicy="no-referrer"></p><ul><li><span>Un inductor o </span><strong><a href='https://es.wikipedia.org/wiki/Inductor'><span>bobina</span></a></strong><span>.</span></li><li><span>Un </span><strong><a href='https://es.wikipedia.org/wiki/Solenoide'><span>solenoide</span></a></strong><span>.</span></li></ul><p><span>Si colocamos un conductor dentro de un campo magnético de flujo variable, el campo induce en el conductor una </span><code>fem</code><span>; si el campo fuera constante no haría falta nada más que mover el conductor. Se produce así un fenómeno denominado </span><strong><a href='https://es.wikipedia.org/wiki/Inducci%C3%B3n_electromagn%C3%A9tica'><span>inducción electromagnética</span></a></strong><span>, la corriente inducida será tanto mayor cuanto mayor sea la rapidez con que varíe el campo magnético o la corriente que lo genera. </span></p><p><span>Para conocer la dirección del campo creado por el paso de la corriente pro un conductor basta con observar la </span><strong><a href='https://es.wikipedia.org/wiki/Regla_de_la_mano_izquierda'><span>regla de la mano izquierda</span></a></strong><span>. Se trata de coger el hilo conductor con dicha mano, con el pulgar extendido y señalando el sentido de la corriente, o sea el flujo de electrones desde el polo negativo al positivo, en un solenoide los polos se localizan según la dirección de la corriente en las espiras. Al interior del solenoide las líneas de fuerza van de sur a norte y por el exterior de norte a sur.</span></p><h4 id='151-bobinas'><span>1.5.1 Bobinas</span></h4><p><span>Ya sabemos que es un componente electrónico que debido al fenómeno de la </span><strong><a href='https://es.wikipedia.org/wiki/Autoinducci%C3%B3n'><span>autoinducción</span></a></strong><span> almacena energía  en forma de campo magnético. </span></p></div></div>
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diff --git a/es.telecomlobby.com/radio_aficion/URE_1.md b/es.telecomlobby.com/radio_aficion/URE_1.md
index 0ec51419..b9d1af69 100644
--- a/es.telecomlobby.com/radio_aficion/URE_1.md
+++ b/es.telecomlobby.com/radio_aficion/URE_1.md
@@ -1,62 +1,58 @@
-# Teoría eléctrica y electromagnética y apuntes sobre la «La Maquina»
+# Teoría eléctrica y electromagnética
 
 ![Felipe VI URE](http://telecomlobby.com/Images/felipe_vi_ure_riccardo_giuntoli_radioham_notes.webp)
 
-Subiendo una montaña Genovesa, allí fue la primera vez que cargaba con una radio en 27Mhz y banda lateral en mi mochila, soñaba con conectarme con países lejanos y gente desconocida. Allí fue, cerca del 1992. Desde aquella fecha mucha vida ha pasado delante de mis ojos, felicidad, trabajos, amores y muertes. Ahora en el 2020, debajo de esta QSL donde se representa rey Felipe VI de España y su identificación en la radio afición empiezo a estudiar y apuntar mis notas en esta parte de mi pagina web. Pagina donde se subraya que estoy estudiando esta arte con el fin de salir del control neuronal vía radio que ha sido activado sobre mi organismo en Noviembre 2017. Estudio también para juntarme a ti, Saray. Mujer que amo.
+Subiendo una **[montaña Genovesa](https://it.wikipedia.org/wiki/Monte_Fasce)**, allí fue la primera vez que cargaba con una radio en 27Mhz AM, FM y banda lateral en mi mochila, soñaba con conectarme con países lejanos y gente desconocida. Allí fue, cerca del 1992. Desde aquella fecha mucha vida ha pasado delante de mis ojos, felicidad, trabajos, amores y muertes. Ahora en el 2022, con la conciencia de ser victima de trata de pesonas, debajo de esta QSL donde se representa rey Felipe VI de España y su identificación en la radio afición empiezo a estudiar y apuntar mis notas en este apartado de mi pagina web. Pagina donde se subraya que estoy estudiando esta arte con el fin de salir del control neuronal vía radio que ha sido activado de forma continua sobre mi organismo en Noviembre 2017, que seguramente me ve como individuo obyectivo, como victima de trata, desde finales de los noventa, y que se encuentra físicamente en la ciudad donde vivo, Barcelona.
 
 #### 1.1 Estructura de la materia
 
-Tanto los cuerpos sólidos como los líquidos y gases están compuestos de pequeñas partículas cuyas propiedades son idénticas al cuerpo al cual pertenecen. Se llaman **moléculas** [[1]](https://es.wikipedia.org/wiki/Mol%C3%A9cula) y presentan espacios entra ellos.río*
+Tanto los cuerpos sólidos como los líquidos y gases están compuestos de pequeñas partículas cuyas propiedades son idénticas al cuerpo al cual pertenecen. Se llaman **[moléculas](https://es.wikipedia.org/wiki/Mol%C3%A9cula)** y presentan espacios entra ellos.
 
 #### 1.1.1 Molécula
 
 Están en continuo movimiento y entre ellas existen fuerzas atractivas y repulsivas según el estado en que se encuentre la materia:
 
-- **Sólidos** [[2]](https://es.wikipedia.org/wiki/S%C3%B3lido), atractivas.
-- **Líquidos** [[3]](https://es.wikipedia.org/wiki/L%C3%ADquido), equilibradas.
-- **Gases** [[4]](https://es.wikipedia.org/wiki/Gas), repulsivas.
+- **[Sólidos](https://es.wikipedia.org/wiki/S%C3%B3lido)**, atractivas.
+- **[Líquidos](https://es.wikipedia.org/wiki/L%C3%ADquido)**, equilibradas.
+- **[Gases](https://es.wikipedia.org/wiki/Gas)**, repulsivas.
 
-Mediante **calor** [[5]](https://es.wikipedia.org/wiki/Calor) podemos pasar de estado sólido a líquido y de líquido a gaseoso. Mediante el **frío** [[6]](https://es.wikipedia.org/wiki/Fr%C3%ADo) el revés. 
+Mediante **[calor](https://es.wikipedia.org/wiki/Calor)** podemos pasar de estado sólido a líquido y de líquido a gaseoso. Mediante el **[frío](https://es.wikipedia.org/wiki/Fr%C3%ADo)** el revés. 
 
-> En la red de neuroestimuladores inalámbricos que ven individuos objetivo como clientes del complejo sistema de radio que la compone muchas veces se puede apreciar algo parecido a humo sobresalir de nuestro cuerpo. Es muy posible que los ingenieros que hayan programado este magnifico sistema de radio quieran representar un flujo de calor desde el interior del cuerpo humano hacía fuera. Por esto en red neuronal mensajería subliminal se habla de «maquina a vapor».
-
-Cada molécula está compuesta por distintos átomos según el **elemento químico** [[7]](https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico) que constituyan.
+Cada molécula está compuesta por distintos átomos según el **[elemento químico](https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico)** que constituyan.
 
 #### 1.1.2 Átomo
 
 ![Tabla elementos](https://telecomlobby.com/Images/tabla_elementos.webp)
 
-Una molécula la podemos descomponer en partículas muchos menores llamadas **átomos** [[8]](https://es.wikipedia.org/wiki/%C3%81tomo). Toda la materia que existe en la naturaleza está formada por cuerpos simples denominados elementos. El átomo es la parte más pequeña de estos cuerpos que conserva las características originales de un elemento cualquiera.
+Una molécula la podemos descomponer en partículas muchos menores llamadas **[átomos](https://es.wikipedia.org/wiki/%C3%81tomo)**. Toda la materia que existe en la naturaleza está formada por cuerpos simples denominados elementos. El átomo es la parte más pequeña de estos cuerpos que conserva las características originales de un elemento cualquiera.
 
-Para entender la **electricidad** [[9]](https://es.wikipedia.org/wiki/Electricidad) hay que estudiar átomo y componentes.
+Para entender la **[electricidad](https://es.wikipedia.org/wiki/Electricidad)** hay que estudiar átomo y componentes.
 
-Cada átomo consta de dos partes el núcleo y la corteza, el núcleo está cargado con carga eléctrica positiva y se compone básicamente de **protones** [[10]](https://es.wikipedia.org/wiki/Prot%C3%B3n), partículas con carga positiva, y **neutrones** [[11]](https://es.wikipedia.org/wiki/Neutr%C3%B3n), partículas con **masa** [[12]](https://es.wikipedia.org/wiki/Masa) pero sin **carga** [[13]](https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica). Alrededor del núcleo, existen una o más capas, cuyo conjunto se denomina corteza, donde describen órbitas a gran velocidad los **electrones** [[14]](https://es.wikipedia.org/wiki/Electr%C3%B3n), partículas de carga negativa fuertemente atraídos por la carga positiva de este y resulta extremadamente difícil cambiarlos de órbita; los de las órbitas exteriores pueden llegar a abandonar un átomo para pasar a otro, o bien quedar como electrones libres.
+Cada átomo consta de dos partes el núcleo y la corteza, el núcleo está cargado con carga eléctrica positiva y se compone básicamente de **[protones](https://es.wikipedia.org/wiki/Prot%C3%B3n)**  partículas con carga positiva, y **[neutrones](https://es.wikipedia.org/wiki/Neutr%C3%B3n)**, partículas con **[masa](https://es.wikipedia.org/wiki/Masa)** pero sin **[carga](https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica)**. Alrededor del núcleo, existen una o más capas, cuyo conjunto se denomina corteza, donde describen órbitas a gran velocidad los **[electrones](https://es.wikipedia.org/wiki/Electr%C3%B3n)**, partículas de carga negativa fuertemente atraídos por la carga positiva de este y resulta extremadamente difícil cambiarlos de órbita; los de las órbitas exteriores pueden llegar a abandonar un átomo para pasar a otro, o bien quedar como electrones libres.
 
 #### 1.1.3 Ionización o electrización. Carga eléctrica.
 
 ![Ionización](https://telecomlobby.com/Images/tabla_ionizacion.webp)
 
-Si no sometidos a la acción de ninguna fuerza externa el átomo es neutro del punto de vista eléctrico. Si perdiese electrones, quedaría cargado positivamente y se denominaría **ion** [[15]](https://es.wikipedia.org/wiki/Ion) positivo, al revés o sea con un exceso de electrones tiene carga negativa y tendremos un ion negativo.
+Si no sometidos a la acción de ninguna fuerza externa el átomo es neutro del punto de vista eléctrico. Si perdiese electrones, quedaría cargado positivamente y se denominaría **[ion](https://es.wikipedia.org/wiki/Ion)** positivo, al revés o sea con un exceso de electrones tiene carga negativa y tendremos un ion negativo.
 
 La carga eléctrica es un estado de desequilibrio entre el número de electrones y protones; los cuerpos con cargas de distinto signo se atraen entre sí mientras que los que poseen el mismo tipo de carga se repelen. 
 
 #### 1.1.4 Conductores, semiconductores y aislantes.
 
-Las capas más externas de la corteza del átomo si no están semillenas o sea a tener menos del 50% de su capacidad de electrones existe el peligro de abandono de estos en dichas capas; toman el nombre de electrones libres. Un cuerpo conductor de electricidad es una sustancia compuesta por átomos cuya capa más externa no llega a estar semillena de electrones asegurando así el paso de la **corriente** [[16]](https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica) que otra cosa no es que un flujo de electrones libres desde un cuerpo con carga negativa a otro con carga positiva.
+Las capas más externas de la corteza del átomo si no están semillenas o sea a tener menos del 50% de su capacidad de electrones existe el peligro de abandono de estos en dichas capas; toman el nombre de electrones libres. Un cuerpo conductor de electricidad es una sustancia compuesta por átomos cuya capa más externa no llega a estar semillena de electrones asegurando así el paso de la **[corriente](https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica)** que otra cosa no es que un flujo de electrones libres desde un cuerpo con carga negativa a otro con carga positiva.
 
 Los metales tienen una pequeña energía de ionización, tienden a tener un gran número de electrones libres y por ello son buenos conductores de la electricidad. Un aislador o aislante lo forma sustancias que presentan gran resistencia a que las cargas que las forman se desplacen y por tanto no conducen, en condiciones normales, la electricidad.
 
->  Los productos necesarios a cubrir nuestro cuerpo humano del ser receptores y clientes finales de la red de monitorio neuronal son sin duda ninguna aislantes.
-
-Un **semiconductor** [[17]](https://es.wikipedia.org/wiki/Semiconductor) es un elemento que cambia comportamiento dependiendo donde en que campo eléctrico se encuentre. 
+Un **[semiconductor](https://es.wikipedia.org/wiki/Semiconductor)** es un elemento que cambia comportamiento dependiendo donde en que campo eléctrico se encuentre. 
 
 #### 1.1.5 Conductividad.
 
 Propiedad que tienen los cuerpos o las sustancias de transmitir de un punto a otro de su masa el calor o la electricidad.
 
-La **Comisión Electrotécnica Internacional** [[18]](https://www.iec.ch/) definió como patrón de la conductividad eléctrica la de un hilo de cobre de 1 metro de longitud y un gramo de masa, que da una resistencia de 0,15388 Ω a 20 °C a lo cual asignó una **conductividad eléctrica** [[19]](https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica) de 100% IACS, a toda **aleación** [[20]](https://es.wikipedia.org/wiki/Aleaci%C3%B3n) de cobre con una conductividad mayor se le denomina de alta conductividad.
+La **[Comisión Electrotécnica Internacional](https://www.iec.ch/)** definió como patrón de la conductividad eléctrica la de un hilo de cobre de 1 metro de longitud y un gramo de masa, que da una resistencia de 0,15388 Ω a 20 °C a lo cual asignó una **[conductividad eléctrica](https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica)** de 100% IACS, a toda **[aleación](https://es.wikipedia.org/wiki/Aleaci%C3%B3n)** de cobre con una conductividad mayor se le denomina de alta conductividad.
 
-**Conductancia** [[21]](https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica) es la medida de la facilidad con que la electricidad fluye a través de un circuito o de un objeto. La unidad de medida de conductancia es el **Siemens** [[22]](https://es.wikipedia.org/wiki/Siemens_(unidad)) y de la conductividad el Siemens/m.
+**[Conductancia](https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica)** es la medida de la facilidad con que la electricidad fluye a través de un circuito o de un objeto. La unidad de medida de conductancia es el **[Siemens](https://es.wikipedia.org/wiki/Siemens_(unidad))** y de la conductividad el Siemens/m.
 
 Siendo lambda λ un coeficiente de conductividad propio de cada materia podemos expresar la conductancia como 
 
@@ -66,39 +62,39 @@ Conductancia = \frac{λxsuperficie(cm^2)}{longitud(cm)}\\
 \end{align*}
 $$
 
-La inversa de la conductividad es la **resistividad** [[23]](https://es.wikipedia.org/wiki/Resistividad) que expresa la **resistencia** [[24]](https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica) de un conductor de las medidas antes mencionadas, que es la inversa de la conductancia, la temperatura del conductor influye en la resistencia, si aumenta la resistencia también lo hará y viceversa; ocurre en los cuerpos conductores; en los semiconductores el fenómeno es inverso.
+La inversa de la conductividad es la **[resistividad](https://es.wikipedia.org/wiki/Resistividad)** que expresa la **[resistencia](https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica)** de un conductor de las medidas antes mencionadas, que es la inversa de la conductancia, la temperatura del conductor influye en la resistencia, si aumenta la resistencia también lo hará y viceversa; ocurre en los cuerpos conductores; en los semiconductores el fenómeno es inverso.
 
 #### 1.1.6 campo eléctrico: intensidad de campo. Unidad de campo: voltios/metro. Potencial. Apantallamiento de campos eléctricos.
 
-Una carga eléctrica es la cantidad de electricidad acumulada en un cuerpo y se mide en una unidad denominada **Culombio** [[25]](https://es.wikipedia.org/wiki/Culombio) que equivale a:
+Una carga eléctrica es la cantidad de electricidad acumulada en un cuerpo y se mide en una unidad denominada **[Culombio](https://es.wikipedia.org/wiki/Culombio)** que equivale a:
 $$
 \begin{align*}
 C = 6,24x10^{18} electrones\\
 \end{align*}
 $$
-En cualquier punto del espacio en donde exista una carga eléctrica se origina un **campo eléctrico** [[26]](https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico) que se manifiesta, experimentalmente, por la fuerza de origen eléctrico a que se halla sometida cualquier carga que se sitúe en el otro punto de su alrededor.
+En cualquier punto del espacio en donde exista una carga eléctrica se origina un **[campo eléctrico](https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico)** que se manifiesta, experimentalmente, por la fuerza de origen eléctrico a que se halla sometida cualquier carga que se sitúe en el otro punto de su alrededor.
 
-La **ley de Coulomb** [[27]](https://es.wikipedia.org/wiki/Ley_de_Coulomb) dice que el valor de la fuerza con que se atraen o se repelen dos cargas puntuales en reposo es directamente proporcional al producto de dichas cargas e inversamente proporcional al cuadrado de la distancia que las separa:
+La **[ley de Coulomb](https://es.wikipedia.org/wiki/Ley_de_Coulomb)** dice que el valor de la fuerza con que se atraen o se repelen dos cargas puntuales en reposo es directamente proporcional al producto de dichas cargas e inversamente proporcional al cuadrado de la distancia que las separa:
 $$
 \begin{align*}
 F = k\frac{q_1q_2}{d^2}\\
 \end{align*}
 $$
-estando la carga q1 situada en un punto P a una distancia d de otra carga puntual q2. La intensidad del **campo eléctrico** [[28]](https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico) en un punto se define como la fuerza ejercida sobre la unidad de carga eléctrica positiva colocada en el citado punto, y viene dada por la expresión:
+estando la carga q1 situada en un punto P a una distancia d de otra carga puntual q2. La intensidad del **[campo eléctrico](https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico)** en un punto se define como la fuerza ejercida sobre la unidad de carga eléctrica positiva colocada en el citado punto, y viene dada por la expresión:
 $$
 \begin{align*}
 E = \frac{F}{q_2}=k\frac{q_1}{q_2}\\
 \end{align*}
 $$
-La intensidad del campo eléctrico, en un punto dado, se mide en **voltios** [[29]](https://es.wikipedia.org/wiki/Voltio) partido por metro.
+La intensidad del campo eléctrico, en un punto dado, se mide en **[voltios](https://es.wikipedia.org/wiki/Voltio)** partido por metro.
 
-Si interponemos entre un campo eléctrico y un punto dado una pantalla de material conductor, el citado punto no recibe la influencia del campo eléctrico. Este efecto se conoce como **apantallamiento** [[30]](https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico) o blindaje. El **potencial eléctrico** [[31]](https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico) en un punto es el trabajo que debe realizar una fuerza eléctrica para mover una carga positiva q desde el infinito con potencial cero hasta ese punto, dividido por dicha carga. Es el trabajo que debe realizar una fuerza externa para traer una carga unitaria q desde el infinito hasta el punto considerado en contra de la fuerza eléctrica dividido por esa carga:
+Si interponemos entre un campo eléctrico y un punto dado una pantalla de material conductor, el citado punto no recibe la influencia del campo eléctrico. Este efecto se conoce como **[apantallamiento](https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico)** o blindaje. El **[potencial eléctrico](https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico)** en un punto es el trabajo que debe realizar una fuerza eléctrica para mover una carga positiva `q` desde el infinito con potencial cero hasta ese punto, dividido por dicha carga. Es el trabajo que debe realizar una fuerza externa para traer una carga unitaria q desde el infinito hasta el punto considerado en contra de la fuerza eléctrica dividido por esa carga:
 $$
 \begin{align*}
 V = \frac{F}{q}\\
 \end{align*}
 $$
-Se puede representar el potencial eléctrico mediante las denominadas **superficies equipotenciales** [[32]](https://es.wikipedia.org/wiki/Superficie_equipotencial), que son el lugar geométrico de los puntos del espacio en los que el potencial tiene un mismo valor o, dicho de otra manera, las superficies en las que todos sus puntos de un campo de fuerza que tienen el mismo potencial.
+Se puede representar el potencial eléctrico mediante las denominadas **[superficies equipotenciales](https://es.wikipedia.org/wiki/Superficie_equipotencial)**, que son el lugar geométrico de los puntos del espacio en los que el potencial tiene un mismo valor o, dicho de otra manera, las superficies en las que todos sus puntos de un campo de fuerza que tienen el mismo potencial.
 
 #### 1.2 Teoría eléctrica. 
 
@@ -108,29 +104,29 @@ Se puede representar el potencial eléctrico mediante las denominadas **superfic
 
 Se denomina corriente eléctrica al paso de electrones a lo largo de un conductor que une dos puntos con distinta carga eléctrica. 
 
-La **corriente continua** [[33]](https://es.wikipedia.org/wiki/Corriente_continua) es un flujo continuo de electrones a través de un conductor entre dos puntos de distinto potencial y sus valores son constantes, las cargas eléctricas circulan siempre en la misma dirección; es continua toda corriente que mantenga la misma **polaridad** [[34]](https://bit.ly/3nqudHw).
+La **[corriente continua](https://es.wikipedia.org/wiki/Corriente_continua)** es un flujo continuo de electrones a través de un conductor entre dos puntos de distinto potencial y sus valores son constantes, las cargas eléctricas circulan siempre en la misma dirección; es continua toda corriente que mantenga la misma **[polaridad](https://bit.ly/3nqudHw)**.
 
-La **corriente alterna** [[35]](https://es.wikipedia.org/wiki/Corriente_alterna) a la corriente eléctrica en la que la magnitud y dirección varían cíclicamente.
+La **[corriente alterna](https://es.wikipedia.org/wiki/Corriente_alterna)** a la corriente eléctrica en la que la magnitud y dirección varían cíclicamente.
 
-Para que circule la corriente eléctrica deben desplazarse los electrones, lo que precisa una fuerza que los empuje la llamada **fuerza electromotriz** [[36]](https://es.wikipedia.org/wiki/Fuerza_electromotriz) que es producida por una diferencia de potencial o **voltaje** [[37]](https://bit.ly/36B9Hgz).
+Para que circule la corriente eléctrica deben desplazarse los electrones, lo que precisa una fuerza que los empuje la llamada **[fuerza electromotriz](https://es.wikipedia.org/wiki/Fuerza_electromotriz)** que es producida por una diferencia de potencial o **[voltaje](https://bit.ly/36B9Hgz)**.
 
-La intensidad de una corriente eléctrica depende, para una misma diferencia de potencial, del diámetro del **conductor** [[38]](https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico), que opone siempre una **resistencia** [[39]](https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica).
+La intensidad de una corriente eléctrica depende, para una misma diferencia de potencial, del diámetro del **[conductor](https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico)**, que opone siempre una **[resistencia](https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica)**.
 
-Podemos hacer una comparación de términos entre **hidráulica** [[40]](https://es.wikipedia.org/wiki/Hidr%C3%A1ulica) y electricidad:
+Podemos hacer una comparación de términos entre **[hidráulica](https://es.wikipedia.org/wiki/Hidr%C3%A1ulica)** y electricidad:
 
 - Desnivel; diferencia de potencial.
-- **Fuerza hidráulica** [[41]](https://bit.ly/2IxeKX7); fuerza electromotriz.
+- **[Fuerza hidráulica](https://bit.ly/2IxeKX7)**; fuerza electromotriz.
 - Tubería; conductor.
 - Caudal de agua; intensidad de corriente
 - Partículas de agua; electrones. 
 
 Existen seis formas elementales de producción de corriente eléctrica. 
 
-Un **circuito eléctrico** [[42]](https://es.wikipedia.org/wiki/Circuito) es un conjunto de conductores por el que circula la corriente eléctrica y en el cual hay intercalados, generalmente, elementos productores y consumidores de la misma.
+Un **[circuito eléctrico](https://es.wikipedia.org/wiki/Circuito)** es un conjunto de conductores por el que circula la corriente eléctrica y en el cual hay intercalados, generalmente, elementos productores y consumidores de la misma.
 
 #### 1.2.2 Unidades eléctricas fundamentales: voltios, amperios y ohmios
 
-El voltaje es la presión eléctrica o diferencia del nivel de cargas que existe entre dos puntos como resultado de la presencia de una **fuerza electromotriz** [[43]](https://es.wikipedia.org/wiki/Fuerza_electromotriz) entra ellos. Para medirla se utiliza el **Voltio** [[44]](https://es.wikipedia.org/wiki/Voltio); 1 V es la fuerza electromotriz necesaria para producir una corriente de 1 **amperio** [[45]](https://es.wikipedia.org/wiki/Amperio) en un circuito cuya resistencia sea de 1 **ohmio** [[46]](https://es.wikipedia.org/wiki/Ohmio):
+El voltaje es la presión eléctrica o diferencia del nivel de cargas que existe entre dos puntos como resultado de la presencia de una **[fuerza electromotriz](https://es.wikipedia.org/wiki/Fuerza_electromotriz)** entra ellos. Para medirla se utiliza el **[Voltio](https://es.wikipedia.org/wiki/Voltio)**: 1 V es la fuerza electromotriz necesaria para producir una corriente de 1 **[amperio](https://es.wikipedia.org/wiki/Amperio)** en un circuito cuya resistencia sea de 1 **[ohmio](https://es.wikipedia.org/wiki/Ohmio)**:
 $$
 \begin{align*}
 Voltios = amperios x ohmios
@@ -147,11 +143,11 @@ Amperio = \frac{Culombio}{segundo}
 $$
 La resistencia es la dificultad o facilidad que encuentra la corriente eléctrica para circular a través de un material.
 
-La unidad de resistencia es el ohmio Ω. representa la resistencia de un conductor en el que, con una diferencia de potencial aplicada en sus extremos de 1 V circula una corriente de 1 A de intensidad.
+La unidad de resistencia es el ohmio Ω. representa la resistencia de un conductor en el que, con una diferencia de potencial aplicada en sus extremos de 1 V circula una corriente de 1 `A` de intensidad.
 
 #### 1.2.3 Ley de Ohm
 
-Al pasar una corriente I por una resistencia R se produce una caída de tensión o ddp que se expresa con la fórmula:
+Al pasar una corriente `I` por una resistencia `R` se produce una caída de tensión o ddp que se expresa con la fórmula:
 $$
 \begin{align*}
 E = IxR
@@ -161,7 +157,7 @@ Si aumenta la resistencia disminuye la intensidad y viceversa.
 
 #### 1.2.4 Aplicación de la Ley de Ohm. Resistencias. Agrupación de resistencias.
 
-Si tomamos dos conductores de la misma forma y tamaño pero de distintos materiales y les aplicamos una misma fem, las corrientes que circularán serán distintas, porque cada material, al tener una conductividad distinta, tiene una resistencia al paso de la corriente diferente.
+Si tomamos dos conductores de la misma forma y tamaño pero de distintos materiales y les aplicamos una misma `fem`, las corrientes que circularán serán distintas, porque cada material, al tener una conductividad distinta, tiene una resistencia al paso de la corriente diferente.
 
 Una resistencia es un elemento o componente de un circuito eléctrico formado por un encapsulado de material que una cierta cantidad de resistencia y con dos rabillos o puntos para su conexión a un circuito.
 
@@ -184,7 +180,7 @@ R = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}\\\\
 I = I_1+I_2+I_3
 \end{align*}
 $$
-Un **shunt** [[47]](https://bit.ly/3eZMHfb) es una resistencia acoplada en paralelo con cualquier elemento de un circuito para derivar corriente por ella. Una aplicación típica son los aparatos de medida que soportan poca intensidad de corriente, **galvanómetro** [[48]](https://es.wikipedia.org/wiki/Galvan%C3%B3metro) G, por lo que es preciso limitar ésta adoptando una resistencia en paralelo Rs. 
+Un **[shunt](https://bit.ly/3eZMHfb)** es una resistencia acoplada en paralelo con cualquier elemento de un circuito para derivar corriente por ella. Una aplicación típica son los aparatos de medida que soportan poca intensidad de corriente, **[galvanómetro](https://es.wikipedia.org/wiki/Galvan%C3%B3metro)** `G`, por lo que es preciso limitar ésta adoptando una resistencia en paralelo `Rs`. 
 
 #### 1.2.5 Código de colores de las resistencias.
 
@@ -196,7 +192,7 @@ El conjunto de dichos anillos nos da la lectura del número de ohmios de la resi
 
 #### 1.2.6 Disipación de potencia en las resistencias
 
-Una resistencia se intercala en un circuito para obstaculizar el paso de la corriente y transformar en calor el voltaje que no necesitamos ne un punto dado. Se conoce como **efecto Joule** [[49]](https://es.wikipedia.org/wiki/Efecto_Joule). Todo conducto por lo que circula una corriente experimenta un aumento de su temperatura. La ley de joule enuncia que la cantidad de calor desprendida en un conductor por el paso de una corriente constante es proporcional al cuadrado de la intensidad de la corriente, a la resistencia del conductor y al tiempo que dure el paso. se llama potencia de disipación, medidas en vatios, al producto del votake por la intensidad que ha de circular por la resistencia:
+Una resistencia se intercala en un circuito para obstaculizar el paso de la corriente y transformar en calor el voltaje que no necesitamos ne un punto dado. Se conoce como **[efecto Joule](https://es.wikipedia.org/wiki/Efecto_Joule)**. Todo conducto por lo que circula una corriente experimenta un aumento de su temperatura. La ley de joule enuncia que la cantidad de calor desprendida en un conductor por el paso de una corriente constante es proporcional al cuadrado de la intensidad de la corriente, a la resistencia del conductor y al tiempo que dure el paso. Se llama potencia de disipación, medidas en vatios, al producto del voltaje por la intensidad que ha de circular por la resistencia:
 $$
 \begin{align*}
 P = V xI
@@ -204,26 +200,32 @@ P = V xI
 $$
 Si la resistencia disipa una potencia mayor que aquélla para la que está preparada, se quema, cortándose el hilo del que está hecha o fundiéndose el material resistivo. Disipación máxima es la potencia calorífica que podemos suministrar a un resistencia sin que la temperatura se eleve peligrosamente.
 
-Los valores de disipación de potencia más frecuentes de las resistencias son los de 0,125W, 0,25W, 0,5W y 1 W.
+Los valores de disipación de potencia más frecuentes de las resistencias son los de `0,125W`, `0,25W`, `0,5W` y `1W`.
 
 #### 1.2.7 Coeficientes negativos y positivos de temperatura NTP y PTC
 
-Un **termistor** [[50]](https://es.wikipedia.org/wiki/Termistor) NTC es una resistencia cuyo valor se va reduciendo a medida que aumenta la temperatura. Análogamente a un NTC un termistor PTC es una resistencia cuyo valor va aumentando a medida que aumenta la temperatura.
+![Simbolo electronico generico CEI](https://upload.wikimedia.org/wikipedia/commons/1/10/Thermistor.svg)
+
+Un **[termistor](https://es.wikipedia.org/wiki/Termistor)** `NTC` es una resistencia cuyo valor se va reduciendo a medida que aumenta la temperatura. Análogamente a un `NTC` un termistor `PTC` es una resistencia cuyo valor va aumentando a medida que aumenta la temperatura.
 
 #### 1.2.8 Otros tipos de resistencias.
 
-Una resistencia ajustable permite fijar su valor dentro de un rango mediante una abrazadera móvil en contacto con el elemento resistivo. Un **reóstato** [[51]]() es una resistencia variable que se usa en los circuitos de gran consumo, empleándose para regular la corriente en máquinas y motores. Un **potenciómetro** [[52]](https://es.wikipedia.org/wiki/Potenci%C3%B3metro) es una resistencia variable que puede ser variada por el usuario para realizar cualquier función. Es lineal cuando su resistencia es proporcional al desplazamiento del cursor ya que se desliza por una pista uniforme. En el no lineal al ser la pista de diferente grosor, la respuesta, la resistencia, no corresponde al desplazamiento del cursor. Estos últimos suelen tener una respuesta que se aproxima a la función logaritmo.
+Una resistencia ajustable permite fijar su valor dentro de un rango mediante una abrazadera móvil en contacto con el elemento resistivo. Un **[reóstato](https://es.wikipedia.org/wiki/Reostato)** es una resistencia variable que se usa en los circuitos de gran consumo, empleándose para regular la corriente en máquinas y motores. 
+
+![Simbolo electronico europeo](https://upload.wikimedia.org/wikipedia/commons/1/1c/Potentiometer_symbol_Europe.svg)
+
+Un **[potenciómetro](https://es.wikipedia.org/wiki/Potenci%C3%B3metro)** es una resistencia variable que puede ser variada por el usuario para realizar cualquier función. Es lineal cuando su resistencia es proporcional al desplazamiento del cursor ya que se desliza por una pista uniforme. En el no lineal al ser la pista de diferente grosor, la respuesta, la resistencia, no corresponde al desplazamiento del cursor. Estos últimos suelen tener una respuesta que se aproxima a la función logaritmo.
 
 #### 1.2.9 Leyes de Kirchhoff
 
-Las leyes de **Kirchhoff** [[53]](https://es.wikipedia.org/wiki/Gustav_Kirchhoff) son útiles al análisis de múltiples tipos de circuitos:
+Las leyes de **[Kirchhoff](https://es.wikipedia.org/wiki/Gustav_Kirchhoff)** son útiles al análisis de múltiples tipos de circuitos:
 
 1. La suma de las intensidades de corriente que llegan a un nudo de un circuito es igual a la suma de las intensidades que salen de él. 
 2. En un circuito cerrado o malla la suma de todas las caídas de tensión es igual a la suma de todas las subidas de tensión, la suma algebraica de las tensiones en todo circuito cerrado es cero.
 
 #### 1.2.10 Potencia eléctrica. Unidad de potencia: el vatio.
 
-La corriente eléctrica puede desarrollar un trabajo, la relación que hay entre un trabajo y tiempo de la **potencia** [[54]](https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica) que es la expresión de la cantidad del trabajo producido en la unidad de tiempo. La unidad de potencia es el **vatio** [[55]](https://es.wikipedia.org/wiki/Vatio):
+La corriente eléctrica puede desarrollar un trabajo, la relación que hay entre un trabajo y tiempo de la **[potencia](https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica)** que es la expresión de la cantidad del trabajo producido en la unidad de tiempo. La unidad de potencia es el **[vatio](https://es.wikipedia.org/wiki/Vatio)**:
 $$
 \begin{align*}
 Potencia = tensiónxintensidad\\\\
@@ -232,7 +234,7 @@ P=ExI
 $$
 
 
-Donde P es expresada en vatios, la tensión en voltios, y la intensidad en amperios. Aplicando la ley de Ohm sabemos que la tensión es igual a la intensidad por la resistencia. O sea obtenemos:
+Donde `P` es expresada en vatios, la tensión en voltios, y la intensidad en amperios. Aplicando la ley de Ohm sabemos que la tensión es igual a la intensidad por la resistencia. O sea obtenemos:
 $$
 \begin{align*}
 P = I^{2}xR
@@ -244,9 +246,9 @@ $$
 P = 20^{2}x100=40000W=40kW
 \end{align*}
 $$
-Los múltiplos del vatio son el kilowatio y el **caballo de vapor** [[56]](https://es.wikipedia.org/wiki/Caballo_de_vapor) equivalente a 1kW o el horse power HP a 736 vatios. 
+Los múltiplos del vatio son el kilowatio y el **[caballo de vapor](https://es.wikipedia.org/wiki/Caballo_de_vapor)** equivalente a 1kW o el **[caballo de fuerza](https://es.wikipedia.org/wiki/Caballo_de_fuerza)** `HP` a 736W. 
 
-La energía eléctrica se expresa como la potencia consumida durante una unidad de tiempo, como unidad se emplea el kilovatio-hora kWh que equivale a la energía eléctrica consumida por un aparato al ser atravesado por una corriente de 1 amperio, a una tensión de 1000 V y durante una hora, puede corresponder a cualquier otra combinación de los tres valores cuyo producto total sea 1kW:
+La energía eléctrica se expresa como la potencia consumida durante una unidad de tiempo, como unidad se emplea el **[kilovatio hora](https://es.wikipedia.org/wiki/Kilovatio_hora)** `kWh` que equivale a la energía eléctrica consumida por un aparato al ser atravesado por una corriente de 1 amperio, a una tensión de 1000 V y durante una hora, puede corresponder a cualquier otra combinación de los tres valores cuyo producto total sea 1kW:
 $$
 \begin{align*}
 Consumo=intensidadxvoltajextiempo\\\\
@@ -258,24 +260,26 @@ $$
 
 ![Condensadores](https://telecomlobby.com/Images/condensadores.webp)
 
-Constan de dos placas conductoras separadas por un cuerpo no conductor llamado **dieléctrico** [[57]](https://es.wikipedia.org/wiki/Diel%C3%A9ctrico):
+Constan de dos placas conductoras separadas por un cuerpo no conductor llamado **[dieléctrico](https://es.wikipedia.org/wiki/Diel%C3%A9ctrico)**:
 
 - aire
 - aceite
-- vidrio (por esto el jefe de la banda de actores no estatales de Barcelona lo he encontrado viviendo en una nave industrial abandonada ya que el techo y las paredes están lleno de **fibra de vidrio** [[58]](https://es.wikipedia.org/wiki/Fibra_de_vidrio))
-- **mica** [[59]](https://es.wikipedia.org/wiki/Mica)
-- **polietileno** [[60]](https://es.wikipedia.org/wiki/Polietileno)
+- vidrio
+- **[mica](https://es.wikipedia.org/wiki/Mica)**
+- **[polietileno](https://es.wikipedia.org/wiki/Polietileno)**
 
-Las placas suelen ser láminas de **estaño** [[61]](https://es.wikipedia.org/wiki/Esta%C3%B1o) alternando con láminas del dieléctrico usado; los **condensadores** [[62]](https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico) tienen la capacidad de acumular una determinada carga eléctrica a un voltaje determinado, la acumula en carga y la restituye en descarga al resto del circuito. Al cerrarlo una placa queda asociada al polo positivo y otra al negativo de la pila o fuente que la alimente, la armadura conectada al polo positivo va cediendo electrones a éste, mientras que la otra armadura recoge electrones del polo negativo, se puede apreciar el flujo de corriente intercalando un **amperímetro** [[63]](https://es.wikipedia.org/wiki/Amper%C3%ADmetro). Se pueden recargar hasta que entre las placas de éstos se llega a alcanzar un voltaje igual al existente en los bornes de la batería o fuente que los alimente. Si se abre el interruptor desconectando la alimentación de las armaduras estas quedan cargadas el circuito queda abierto y se mantiene la diferencia de potencia entre las armaduras; aparece un campo eléctrico desde la placa positiva a la negativa en el que habrá más dispersión de líneas de fuerza cuanto más alejadas estén. El condensador se descarga  instantáneamente si se unen o cortocircuitan las placas del mismo pero si se añade una resistencia de un valor dado la descarga durará un tiempo determinado. 
+![](https://upload.wikimedia.org/wikipedia/commons/9/9e/Condensator_tekening.png)
 
-Tanto descarga como carga no son instantáneas y además tampoco tienen forma lineal sino **exponencial** [[64]](https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial), su capacidad eléctrica es:
+Las placas suelen ser láminas de **[estaño](https://es.wikipedia.org/wiki/Esta%C3%B1o)** alternando con láminas del dieléctrico usado; los **[condensadores](https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico)** tienen la capacidad de acumular una determinada carga eléctrica a un voltaje determinado, la acumula en carga y la restituye en descarga al resto del circuito. Al cerrarlo una placa queda asociada al polo positivo y otra al negativo de la pila o fuente que la alimente, la armadura conectada al polo positivo va cediendo electrones a éste, mientras que la otra armadura recoge electrones del polo negativo, se puede apreciar el flujo de corriente intercalando un **[amperímetro](https://es.wikipedia.org/wiki/Amper%C3%ADmetro)**. Se pueden recargar hasta que entre las placas de éstos se llega a alcanzar un voltaje igual al existente en los bornes de la batería o fuente que los alimente. Si se abre el interruptor desconectando la alimentación de las armaduras estas quedan cargadas el circuito queda abierto y se mantiene la diferencia de potencia entre las armaduras; aparece un campo eléctrico desde la placa positiva a la negativa en el que habrá más dispersión de líneas de fuerza cuanto más alejadas estén. El condensador se descarga  instantáneamente si se unen o cortocircuitan las placas del mismo pero si se añade una resistencia de un valor dado la descarga durará un tiempo determinado. 
+
+Tanto descarga como carga no son instantáneas y además tampoco tienen forma lineal sino **[exponencial](https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial)**, su capacidad eléctrica es:
 $$
 \begin{align*}
 Capacidad eléctrica=\frac{carga eléctrica}{voltaje}\\\\
 V=\frac{Q}{V}
 \end{align*}
 $$
-Un **faradio** [[65]](https://es.wikipedia.org/wiki/Faradio) es la capacidad de un condensador al que aplicada una fem de 1 voltio adquiere una carga de 1 culombio. El microfaradio μF equivale a 10-6 F y el nanofaradio nF a 10-9F, el picofaradio a 10-12F.
+Un **[faradio](https://es.wikipedia.org/wiki/Faradio)** es la capacidad de un condensador al que aplicada una fem de 1 voltio adquiere una carga de 1 culombio. El microfaradio μF equivale a 10-6 F y el nanofaradio nF a 10-9F, el picofaradio a 10-12F.
 
 La energía almacenada en condensador se expresa por la fórmula:
 $$
@@ -285,9 +289,9 @@ W = \mbox{1/2}CV^{2}
 $$
 O sea que depende de su capacidad y del voltaje aplicado.
 
-Se llama **constante dieléctrica** [[66]](https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica) a la relación que hay entre la capacidad de un condensador formado por un determinado dieléctrico y su capacidad de un condensador formado por un determinado dieléctrico y su capacidad en el vacío. Se denomina **rigidez dieléctrica** [[67]](https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica) o tensión de trabajo de un condensador a aquella que puede soportar sin que se perfore su dieléctrico. La tensión de prueba es aquella a la que el fabricante somete al condensador sin que se haya producido la perforación y es siempre mayor que la tensión de trabajo.
+Se llama **[constante dieléctrica](https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica)** a la relación que hay entre la capacidad de un condensador formado por un determinado dieléctrico y su capacidad de un condensador formado por un determinado dieléctrico y su capacidad en el vacío. Se denomina **[rigidez dieléctrica](https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica)** o tensión de trabajo de un condensador a aquella que puede soportar sin que se perfore su dieléctrico. La tensión de prueba es aquella a la que el fabricante somete al condensador sin que se haya producido la perforación y es siempre mayor que la tensión de trabajo.
 
-Los condensadores como otros componentes varían de valor con la temperatura, el parámetro se denomina **coeficiente de temperatura** [[68]](https://es.wikipedia.org/wiki/Coeficiente_de_temperatura) que puede ser positivo o negativo. Los cerámicos o de mica son muy estables en frente de la temperatura. 
+Los condensadores como otros componentes varían de valor con la temperatura, el parámetro se denomina **[coeficiente de temperatura](https://es.wikipedia.org/wiki/Coeficiente_de_temperatura)** que puede ser positivo o negativo. Los cerámicos o de mica son muy estables en frente de la temperatura. 
 
 #### 1.3.1 Relación entre capacidad, dimensiones y dieléctrico
 
@@ -300,11 +304,11 @@ La capacidad de un condensador depende de dos magnitudes:
 
 ![Tabla colores condesadores](https://telecomlobby.com/Images/tabla_colores_condensadores.webp)
 
-Los variables cambian su capacidad variando la superficie de sus placas. Se usan para sintonizar circuitos **oscilantes** [[69]](https://es.wikipedia.org/wiki/Oscilaci%C3%B3n). 
+Los **[variables](https://es.wikipedia.org/wiki/Condensador_variable)** cambian su capacidad variando la superficie de sus placas. Se usan para sintonizar circuitos **[oscilantes](https://es.wikipedia.org/wiki/Oscilaci%C3%B3n)**. 
 
 Los ajustables o trimmer utilizados para ajustar la capacidad.
 
-Los fijos que pueden ser **polarizados** [[70]](https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica) o no. Los non polarizados se clasifican según el tipo de dieléctrico que utilizan como hemos visto. Los **electrolíticos** [[71]](https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico) tienen dieléctrico líquido o en papel impregnado.
+Los fijos que pueden ser **[polarizados](https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica)** o no. Los non polarizados se clasifican según el tipo de dieléctrico que utilizan como hemos visto. Los **[electrolíticos](https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico)** tienen dieléctrico líquido o en papel impregnado.
 
 Al ser pequeños los condensadores se emplean, generalmente, códigos de bandas de colores para indicar su capacidad expresada en picofaradios. Las bandas indican su capacidad, su tolerancia y su tensión máxima. 
 
@@ -328,186 +332,45 @@ En paralelo la capacidad total es la suma de las capacidades de todos ellos.
 
 ![Iman](https://telecomlobby.com/Images/iman.webp)
 
-Un **imán** [[72]](https://es.wikipedia.org/wiki/Im%C3%A1n) crea a su alrededor un campo de atracción de sustancias tales como el hierro y que se denomina **campo magnético** [[73]](https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico) y es el espacio en que un imán ejerce su influencia.
+Un **[imán](https://es.wikipedia.org/wiki/Im%C3%A1n)** crea a su alrededor un campo de atracción de sustancias tales como el hierro y que se denomina **[campo magnético](https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico)** y es el espacio en que un imán ejerce su influencia.
 
 Se crea un campo magnético en los alrededores de un conductor recorrido por una corriente eléctrica, si no hay corriente no hay campo cosa que no ocurre con los imanes. 
 
 #### 1.4.1 magnetismo.
 
-Se llama **magnetismo** [[74]](https://es.wikipedia.org/wiki/Magnetismo) al conjunto de fenómenos originados por los campos magnéticos. Un imán puede ser **magnetita** [[75]](https://es.wikipedia.org/wiki/Magnetita), **acero** [[76]](https://es.wikipedia.org/wiki/Acero) o bien alguna aleación. Los extremos se llaman polos, norte y sur. Al centro la línea neutra. El magnetismo es formado por las líneas ovales de fuerza entra los dos polos.
+Se llama **[magnetismo](https://es.wikipedia.org/wiki/Magnetismo)** al conjunto de fenómenos originados por los campos magnéticos. Un imán puede ser **[magnetita](https://es.wikipedia.org/wiki/Magnetita)**, **[acero](https://es.wikipedia.org/wiki/Acero)** o bien alguna aleación. Los extremos se llaman polos, norte y sur. Al centro la línea neutra. El magnetismo es formado por las líneas ovales de fuerza entra los dos polos.
 
-Una aguja imantada que gire libremente siempre se orientará en la dirección norte-sur. La tierra produce un campo magnético y llamamos a los dos polos **norte geográfico** [[77]](https://es.wikipedia.org/wiki/Polo_norte) y **sur geográfico** [[78]](https://es.wikipedia.org/wiki/Polo_sur). Polos de mismo nombre se repelen y los de nombre contrario se atraen. 
+Una aguja imantada que gire libremente siempre se orientará en la dirección norte-sur. La tierra produce un campo magnético y llamamos a los dos polos **[norte geográfico](https://es.wikipedia.org/wiki/Polo_norte)** y **[sur geográfico](https://es.wikipedia.org/wiki/Polo_sur)**. Polos de mismo nombre se repelen y los de nombre contrario se atraen. 
 
 #### 1.4.2 Características de un campo magnético.
 
-El total de las líneas de fuerza se denomina **flujo magnético** [[79]](https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico). El numero de líneas que salen es igual al que entran de la superficie. La unidad de flujo magnético es el **Weber** [[80]](https://bit.ly/36XehpI). Un Wb es el flujo magnético que al atravesar un circuito de una sola espira produce en ella una fuerza electromotriz de un voltio si se anula dicho flujo en un segundo por decrecimiento uniforme.
+El total de las líneas de fuerza se denomina **[flujo magnético](https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico)**. El numero de líneas que salen es igual al que entran de la superficie. La unidad de flujo magnético es el **[Weber](https://bit.ly/36XehpI)**. Un `Wb` es el flujo magnético que al atravesar un circuito de una sola espira produce en ella una fuerza electromotriz de un voltio si se anula dicho flujo en un segundo por decrecimiento uniforme.
 
-### External links
+La **[densidad de flujo](https://es.wikipedia.org/wiki/Inducci%C3%B3n_magn%C3%A9tica)** es el **[Tesla](https://es.wikipedia.org/wiki/Tesla_(unidad))** `T` que es la inducción magnética uniforme que repartida sobre una superificie de un metro cuadrado, produce a través de esa superficie un flujo magnetico de un `Wb`.
 
-1. https://es.wikipedia.org/wiki/Mol%C3%A9cula
+La **[reluctancia](https://es.wikipedia.org/wiki/Reluctancia_magn%C3%A9tica)** es la propiedad de los cuerpos de oponerse a la creación de un flujo magnético. Menos el hierro y sus aleaciones los demás cuerpos tienen un reluctancia muy parecida a la del vacío, concepto análogo a la resistencia eléctrica. 
 
-2. https://es.wikipedia.org/wiki/S%C3%B3lido
+La **[permeabilidad](https://es.wikipedia.org/wiki/Permeabilidad_magn%C3%A9tica)** es el inverso de la reluctacia, mejor dicho es la mayor facilidad con que puede crearse un campo magnético en un cuerpo frente al esfuerzo necesario para crearlo en el aire.
 
-3. https://es.wikipedia.org/wiki/L%C3%ADquido
+#### 1.5 Electromagnetismo
 
-4. https://es.wikipedia.org/wiki/Gas
+![](https://live.staticflickr.com/2448/4074152433_abe5f9210e_n.jpg)
 
-5. https://es.wikipedia.org/wiki/Calor
+Conjunto de acciones y reacciones producidas por los campos eléctricos y magnéticos sobre la materia. Todo conductor por ser recorrido por una corriente eléctrica genera a su alrededor un campo magnético. Se demuestra colocando una aguja imantada móvil cerca del conductor. El campo creado por un conductor recto, un hilo, es débil, se puede reforzar enrollándolo en forma de bucle o espira. Cuanto más lo enrollemos, más reforzaremos el campo magnético creado, siendo máximo al formar múltiples bucles hasta conseguir:
 
-6. https://es.wikipedia.org/wiki/Fr%C3%ADo
+![](https://upload.wikimedia.org/wikipedia/commons/4/4b/Inductor.svg)
 
-7. https://es.wikipedia.org/wiki/Elemento_qu%C3%ADmico
+- Un inductor o **[bobina](https://es.wikipedia.org/wiki/Inductor)**.
+- Un **[solenoide](https://es.wikipedia.org/wiki/Solenoide)**.
 
-8. https://es.wikipedia.org/wiki/%C3%81tomo
+Si colocamos un conductor dentro de un campo magnético de flujo variable, el campo induce en el conductor una `fem`; si el campo fuera constante no haría falta nada más que mover el conductor. Se produce así un fenómeno denominado **[inducción electromagnética](https://es.wikipedia.org/wiki/Inducci%C3%B3n_electromagn%C3%A9tica)**, la corriente inducida será tanto mayor cuanto mayor sea la rapidez con que varíe el campo magnético o la corriente que lo genera. 
 
-9. https://es.wikipedia.org/wiki/Electricidad
+Para conocer la dirección del campo creado por el paso de la corriente pro un conductor basta con observar la **[regla de la mano izquierda](https://es.wikipedia.org/wiki/Regla_de_la_mano_izquierda)**. Se trata de coger el hilo conductor con dicha mano, con el pulgar extendido y señalando el sentido de la corriente, o sea el flujo de electrones desde el polo negativo al positivo, en un solenoide los polos se localizan según la dirección de la corriente en las espiras. Al interior del solenoide las líneas de fuerza van de sur a norte y por el exterior de norte a sur.
 
-10. https://es.wikipedia.org/wiki/Prot%C3%B3n
+#### 1.5.1 Bobinas
 
-11. https://es.wikipedia.org/wiki/Neutr%C3%B3n
+Ya sabemos que es un componente electrónico que debido al fenómeno de la **[autoinducción](https://es.wikipedia.org/wiki/Autoinducci%C3%B3n)** almacena energía  en forma de campo magnético. Típicamente constituida por un bobinado de hilo conductor aislado, normalmente cobre. Existen con núcleo de aire o con núcleo de un material forroso para augmentar su **[inductancia](https://es.wikipedia.org/wiki/Inductancia)**. Introduciendo un **[núcleo ferromagnético](https://es.wikipedia.org/wiki/Ferromagnetismo#:~:text=Los%20materiales%20ferromagn%C3%A9ticos%20son%20pr%C3%A1cticos,campo%20magn%C3%A9tico%20en%20el%20n%C3%BAcleo.)** el número de líneas de fuerza del campo de la bobina aumenta muy significativamente. 
 
-12. https://es.wikipedia.org/wiki/Masa
+#### 1.5.2 Inductancia. Unidad de inductancia: el henrio.
 
-13. https://es.wikipedia.org/wiki/Carga_el%C3%A9ctrica
-
-14. https://es.wikipedia.org/wiki/Electr%C3%B3n
-
-15. https://es.wikipedia.org/wiki/Ion
-
-16. https://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica
-
-17. https://es.wikipedia.org/wiki/Semiconductor
-
-18. https://www.iec.ch/
-
-19. https://es.wikipedia.org/wiki/Conductividad_el%C3%A9ctrica
-
-20. https://es.wikipedia.org/wiki/Aleaci%C3%B3n
-
-21. https://es.wikipedia.org/wiki/Conductancia_el%C3%A9ctrica
-
-22. https://es.wikipedia.org/wiki/Siemens_(unidad)
-
-23. https://es.wikipedia.org/wiki/Resistividad
-
-24. https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica
-
-25. https://es.wikipedia.org/wiki/Culombio
-
-26. https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico
-
-27. https://es.wikipedia.org/wiki/Ley_de_Coulomb
-
-28. https://es.wikipedia.org/wiki/Campo_el%C3%A9ctrico
-
-29. https://es.wikipedia.org/wiki/Voltio
-
-30. https://es.wikipedia.org/wiki/Apantallamiento_el%C3%A9ctrico
-
-31. https://es.wikipedia.org/wiki/Potencial_el%C3%A9ctrico
-
-32. https://es.wikipedia.org/wiki/Superficie_equipotencial
-
-33. https://es.wikipedia.org/wiki/Corriente_continua
-
-34. https://bit.ly/3nqudHw
-
-35. https://es.wikipedia.org/wiki/Corriente_alterna
-
-36. https://es.wikipedia.org/wiki/Fuerza_electromotriz
-
-37. https://bit.ly/36B9Hgz
-
-38. https://es.wikipedia.org/wiki/Conductor_el%C3%A9ctrico
-
-39. https://es.wikipedia.org/wiki/Resistencia_el%C3%A9ctrica
-
-40. https://es.wikipedia.org/wiki/Hidr%C3%A1ulica
-
-41. https://bit.ly/2IxeKX7
-
-42. https://es.wikipedia.org/wiki/Circuito
-
-43. https://es.wikipedia.org/wiki/Fuerza_electromotriz
-
-44. https://es.wikipedia.org/wiki/Voltio
-
-45. https://es.wikipedia.org/wiki/Amperio
-
-46. https://es.wikipedia.org/wiki/Ohmio
-
-47. https://bit.ly/3eZMHfb
-
-48. https://es.wikipedia.org/wiki/Galvan%C3%B3metro
-
-49. https://es.wikipedia.org/wiki/Efecto_Joule
-
-50. https://es.wikipedia.org/wiki/Termistor
-
-51. https://es.wikipedia.org/wiki/Reostato
-
-52. https://es.wikipedia.org/wiki/Potenci%C3%B3metro
-
-53. https://es.wikipedia.org/wiki/Gustav_Kirchhoff
-
-54. https://es.wikipedia.org/wiki/Potencia_el%C3%A9ctrica
-
-55. https://es.wikipedia.org/wiki/Vatio
-
-56. https://es.wikipedia.org/wiki/Caballo_de_vapor
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-57. https://es.wikipedia.org/wiki/Diel%C3%A9ctrico
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-58. https://es.wikipedia.org/wiki/Fibra_de_vidrio
-
-59. https://es.wikipedia.org/wiki/Mica
-
-60. https://es.wikipedia.org/wiki/Polietileno
-
-61. https://es.wikipedia.org/wiki/Esta%C3%B1o
-
-62. https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico
-
-63. https://es.wikipedia.org/wiki/Amper%C3%ADmetro
-
-64. https://es.wikipedia.org/wiki/Funci%C3%B3n_exponencial
-
-65. https://es.wikipedia.org/wiki/Faradio
-
-66. https://es.wikipedia.org/wiki/Constante_diel%C3%A9ctrica
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-67. https://es.wikipedia.org/wiki/Rigidez_diel%C3%A9ctrica
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-68. https://es.wikipedia.org/wiki/Coeficiente_de_temperatura
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-69. https://es.wikipedia.org/wiki/Oscilaci%C3%B3n
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-70. https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_el%C3%A9ctrica
-
-71. https://es.wikipedia.org/wiki/Condensador_electrol%C3%ADtico
-
-72. https://es.wikipedia.org/wiki/Im%C3%A1n
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-73. https://es.wikipedia.org/wiki/Campo_magn%C3%A9tico
-
-74. https://es.wikipedia.org/wiki/Magnetismo
-
-75. https://es.wikipedia.org/wiki/Magnetita
-
-76. https://es.wikipedia.org/wiki/Acero
-
-77. https://es.wikipedia.org/wiki/Polo_norte
-
-78. https://es.wikipedia.org/wiki/Polo_sur
-
-79. https://es.wikipedia.org/wiki/Flujo_magn%C3%A9tico
-
-80. https://bit.ly/36XehpI
-
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-    
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\ No newline at end of file
+La inductancia de una bobina se define como la propiedad que tiene de oponerse a los cambios de la corriente que pasa a través de ella. En corriente continua la intensidad de régimen se establece con un ligero retraso, tanto mayor cuanto mayor ser el coeficiente de autoinducción L debido a la extracorriente cierre.
\ No newline at end of file