Impedancia - Wikipedia

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aria-controls="toc-Formalismu_matemáticu-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar subsección Formalismu matemáticu</span> </button> <ul id="toc-Formalismu_matemáticu-sublist" class="vector-toc-list"> <li id="toc-Definición" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Definición"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Definición</span> </div> </a> <ul id="toc-Definición-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Representación_binómica" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Representación_binómica"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Representación binómica</span> </div> </a> <ul id="toc-Representación_binómica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Admitancia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Admitancia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Admitancia</span> </div> </a> <ul id="toc-Admitancia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Representación_gráfica" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Representación_gráfica"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Representación gráfica</span> </div> </a> <ul id="toc-Representación_gráfica-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Cálculu_de_circuitos_coles_impedancias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cálculu_de_circuitos_coles_impedancias"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Cálculu de circuitos coles impedancias</span> </div> </a> <button aria-controls="toc-Cálculu_de_circuitos_coles_impedancias-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar subsección Cálculu de circuitos coles impedancias</span> </button> <ul id="toc-Cálculu_de_circuitos_coles_impedancias-sublist" class="vector-toc-list"> <li id="toc-Xeneradores_de_tensión_o_de_corriente_desfasaes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xeneradores_de_tensión_o_de_corriente_desfasaes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Xeneradores de tensión o de corriente desfasaes</span> </div> </a> <ul id="toc-Xeneradores_de_tensión_o_de_corriente_desfasaes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lleis_de_Kirchhoff" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lleis_de_Kirchhoff"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Lleis de Kirchhoff</span> </div> </a> <ul id="toc-Lleis_de_Kirchhoff-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xeneralización_de_la_llei_d'Ohm" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xeneralización_de_la_llei_d'Ohm"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Xeneralización de la llei d'Ohm</span> </div> </a> <ul id="toc-Xeneralización_de_la_llei_d'Ohm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Impedancias_en_serie_o_en_paralelu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Impedancias_en_serie_o_en_paralelu"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Impedancias en serie o en paralelu</span> </div> </a> <ul id="toc-Impedancias_en_serie_o_en_paralelu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interpretación_de_los_resultaos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interpretación_de_los_resultaos"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Interpretación de los resultaos</span> </div> </a> <ul id="toc-Interpretación_de_los_resultaos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xeneralización" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xeneralización"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Xeneralización</span> </div> </a> <ul id="toc-Xeneralización-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Orixe_de_les_impedancias" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Orixe_de_les_impedancias"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Orixe de les impedancias</span> </div> </a> <ul id="toc-Orixe_de_les_impedancias-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exemplos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Exemplos"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Exemplos</span> </div> </a> <button aria-controls="toc-Exemplos-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Alternar subsección Exemplos</span> </button> <ul id="toc-Exemplos-sublist" class="vector-toc-list"> <li id="toc-Impedancia_n'elementos_básicos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Impedancia_n'elementos_básicos"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Impedancia n'elementos básicos</span> </div> </a> <ul id="toc-Impedancia_n'elementos_básicos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Un_xenerador_únicu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Un_xenerador_únicu"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Un xenerador únicu</span> </div> </a> <ul id="toc-Un_xenerador_únicu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dos_xeneradores_desfasaos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dos_xeneradores_desfasaos"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Dos xeneradores desfasaos</span> </div> </a> <ul id="toc-Dos_xeneradores_desfasaos-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ver_tamién" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_tamién"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ver tamién</span> </div> </a> <ul id="toc-Ver_tamién-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografía" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografía"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Bibliografía</span> </div> </a> <ul id="toc-Bibliografía-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Conteníu" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Tabla de conteníos" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Cambiar a la tabla de contenidos" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Cambiar a la tabla de contenidos</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Impedancia</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir a un artículo en otro idioma. Disponible en 60 idiomas" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-60" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">60 llingües</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Elektriese_impedansie" title="Elektriese impedansie – afrikaans" lang="af" hreflang="af" data-title="Elektriese impedansie" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D9%88%D9%82%D8%A9" title="معاوقة – árabe" lang="ar" hreflang="ar" data-title="معاوقة" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0mpedans" title="İmpedans – azerbaixanu" lang="az" hreflang="az" data-title="İmpedans" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaixanu" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Импеданс – búlgaru" lang="bg" hreflang="bg" data-title="Импеданс" data-language-autonym="Български" data-language-local-name="búlgaru" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%BE%E0%A6%AE%E0%A6%97%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%95_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%A4%E0%A6%BF%E0%A6%B0%E0%A7%8B%E0%A6%A7_(%E0%A6%AC%E0%A7%88%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%A4%E0%A6%A8%E0%A7%80)" title="সামগ্রিক প্রতিরোধ (বৈদ্যুতিক বর্তনী) – bengalín" lang="bn" hreflang="bn" data-title="সামগ্রিক প্রতিরোধ (বৈদ্যুতিক বর্তনী)" data-language-autonym="বাংলা" data-language-local-name="bengalín" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Elektri%C4%8Dna_impedansa" title="Električna impedansa – bosniu" lang="bs" hreflang="bs" data-title="Električna impedansa" data-language-autonym="Bosanski" data-language-local-name="bosniu" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Imped%C3%A0ncia" title="Impedància – catalán" lang="ca" hreflang="ca" data-title="Impedància" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Impedance" title="Impedance – checu" lang="cs" hreflang="cs" data-title="Impedance" data-language-autonym="Čeština" data-language-local-name="checu" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Impedans" title="Impedans – danés" lang="da" hreflang="da" data-title="Impedans" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elektrische_Impedanz" title="Elektrische Impedanz – alemán" lang="de" hreflang="de" data-title="Elektrische Impedanz" data-language-autonym="Deutsch" data-language-local-name="alemán" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%B9%CE%BA%CE%AE_%CE%B5%CE%BC%CF%80%CE%AD%CE%B4%CE%B7%CF%83%CE%B7" title="Ηλεκτρική εμπέδηση – griegu" lang="el" hreflang="el" data-title="Ηλεκτρική εμπέδηση" data-language-autonym="Ελληνικά" data-language-local-name="griegu" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Electrical_impedance" title="Electrical impedance – inglés" lang="en" hreflang="en" data-title="Electrical impedance" data-language-autonym="English" data-language-local-name="inglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Elektra_impedanco" title="Elektra impedanco – esperanto" lang="eo" hreflang="eo" data-title="Elektra impedanco" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Impedancia" title="Impedancia – español" lang="es" hreflang="es" data-title="Impedancia" data-language-autonym="Español" data-language-local-name="español" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/N%C3%A4ivtakistus" title="Näivtakistus – estoniu" lang="et" hreflang="et" data-title="Näivtakistus" data-language-autonym="Eesti" data-language-local-name="estoniu" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Inpedantzia_elektriko" title="Inpedantzia elektriko – vascu" lang="eu" hreflang="eu" data-title="Inpedantzia elektriko" data-language-autonym="Euskara" data-language-local-name="vascu" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%85%D9%BE%D8%AF%D8%A7%D9%86%D8%B3_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="امپدانس الکتریکی – persa" lang="fa" hreflang="fa" data-title="امپدانس الکتریکی" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Impedanssi" title="Impedanssi – finlandés" lang="fi" hreflang="fi" data-title="Impedanssi" data-language-autonym="Suomi" data-language-local-name="finlandés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Imp%C3%A9dance_(%C3%A9lectricit%C3%A9)" title="Impédance (électricité) – francés" lang="fr" hreflang="fr" data-title="Impédance (électricité)" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Coisceas" title="Coisceas – irlandés" lang="ga" hreflang="ga" data-title="Coisceas" data-language-autonym="Gaeilge" data-language-local-name="irlandés" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%9B%D7%91%D7%94_%D7%97%D7%A9%D7%9E%D7%9C%D7%99%D7%AA" title="עכבה חשמלית – hebréu" lang="he" hreflang="he" data-title="עכבה חשמלית" data-language-autonym="עברית" data-language-local-name="hebréu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%AC%E0%A4%BE%E0%A4%A7%E0%A4%BE" title="प्रतिबाधा – hindi" lang="hi" hreflang="hi" data-title="प्रतिबाधा" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Elektri%C4%8Dna_impedancija" title="Električna impedancija – croata" lang="hr" hreflang="hr" data-title="Električna impedancija" data-language-autonym="Hrvatski" data-language-local-name="croata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Impedancia" title="Impedancia – húngaru" lang="hu" hreflang="hu" data-title="Impedancia" data-language-autonym="Magyar" data-language-local-name="húngaru" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%AC%D5%A5%D5%AF%D5%BF%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%AB%D5%B4%D5%BA%D5%A5%D5%A4%D5%A1%D5%B6%D5%BD" title="Էլեկտրական իմպեդանս – armeniu" lang="hy" hreflang="hy" data-title="Էլեկտրական իմպեդանս" data-language-autonym="Հայերեն" data-language-local-name="armeniu" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Impedansi_listrik" title="Impedansi listrik – indonesiu" lang="id" hreflang="id" data-title="Impedansi listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiu" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Samvi%C3%B0n%C3%A1m" title="Samviðnám – islandés" lang="is" hreflang="is" data-title="Samviðnám" data-language-autonym="Íslenska" data-language-local-name="islandés" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Impedenza" title="Impedenza – italianu" lang="it" hreflang="it" data-title="Impedenza" data-language-autonym="Italiano" data-language-local-name="italianu" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A4%E3%83%B3%E3%83%94%E3%83%BC%E3%83%80%E3%83%B3%E3%82%B9" title="インピーダンス – xaponés" lang="ja" hreflang="ja" data-title="インピーダンス" data-language-autonym="日本語" data-language-local-name="xaponés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Импеданс – kazaquistanín" lang="kk" hreflang="kk" data-title="Импеданс" data-language-autonym="Қазақша" data-language-local-name="kazaquistanín" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%98%A8%EC%A0%80%ED%95%AD" title="온저항 – coreanu" lang="ko" hreflang="ko" data-title="온저항" data-language-autonym="한국어" data-language-local-name="coreanu" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Impedansas" title="Impedansas – lituanu" lang="lt" hreflang="lt" data-title="Impedansas" data-language-autonym="Lietuvių" data-language-local-name="lituanu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D0%B8%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81%D0%B0" title="Електрична импеданса – macedoniu" lang="mk" hreflang="mk" data-title="Електрична импеданса" data-language-autonym="Македонски" data-language-local-name="macedoniu" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nap mw-list-item"><a href="https://nap.wikipedia.org/wiki/Impedenza" title="Impedenza – napolitanu" lang="nap" hreflang="nap" data-title="Impedenza" data-language-autonym="Napulitano" data-language-local-name="napolitanu" class="interlanguage-link-target"><span>Napulitano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Impedantie" title="Impedantie – neerlandés" lang="nl" hreflang="nl" data-title="Impedantie" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Elektrisk_impedans" title="Elektrisk impedans – noruegu Nynorsk" lang="nn" hreflang="nn" data-title="Elektrisk impedans" data-language-autonym="Norsk nynorsk" data-language-local-name="noruegu Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Impedans" title="Impedans – noruegu Bokmål" lang="nb" hreflang="nb" data-title="Impedans" data-language-autonym="Norsk bokmål" data-language-local-name="noruegu Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Impedancja" title="Impedancja – polacu" lang="pl" hreflang="pl" data-title="Impedancja" data-language-autonym="Polski" data-language-local-name="polacu" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Imped%C3%A2ncia_el%C3%A9trica" title="Impedância elétrica – portugués" lang="pt" hreflang="pt" data-title="Impedância elétrica" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Impedan%C8%9B%C4%83_electric%C4%83" title="Impedanță electrică – rumanu" lang="ro" hreflang="ro" data-title="Impedanță electrică" data-language-autonym="Română" data-language-local-name="rumanu" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B8%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Электрический импеданс – rusu" lang="ru" hreflang="ru" data-title="Электрический импеданс" data-language-autonym="Русский" data-language-local-name="rusu" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Elektri%C4%8Dna_impedansa" title="Električna impedansa – serbo-croata" lang="sh" hreflang="sh" data-title="Električna impedansa" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croata" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%94%E0%B6%AD%E0%B7%8A_%E0%B7%83%E0%B6%B8%E0%B7%8A%E0%B6%B6%E0%B7%8F%E0%B6%B0%E0%B6%B1%E0%B6%BA" title="විද්‍යුත් සම්බාධනය – cingalés" lang="si" hreflang="si" data-title="විද්‍යුත් සම්බාධනය" data-language-autonym="සිංහල" data-language-local-name="cingalés" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Electrical_impedance" title="Electrical impedance – Simple English" lang="en-simple" hreflang="en-simple" data-title="Electrical impedance" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Impedancia" title="Impedancia – eslovacu" lang="sk" hreflang="sk" data-title="Impedancia" data-language-autonym="Slovenčina" data-language-local-name="eslovacu" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Impedanca" title="Impedanca – eslovenu" lang="sl" hreflang="sl" data-title="Impedanca" data-language-autonym="Slovenščina" data-language-local-name="eslovenu" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Impedanca_elektrike" title="Impedanca elektrike – albanu" lang="sq" hreflang="sq" data-title="Impedanca elektrike" data-language-autonym="Shqip" data-language-local-name="albanu" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D0%B8%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81%D0%B0" title="Електрична импеданса – serbiu" lang="sr" hreflang="sr" data-title="Електрична импеданса" data-language-autonym="Српски / srpski" data-language-local-name="serbiu" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Impedans" title="Impedans – suecu" lang="sv" hreflang="sv" data-title="Impedans" data-language-autonym="Svenska" data-language-local-name="suecu" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%A9%E0%AF%86%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="மின்னெதிர்ப்பு – tamil" lang="ta" hreflang="ta" data-title="மின்னெதிர்ப்பு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B4%E0%B8%A1%E0%B8%9E%E0%B8%B5%E0%B9%81%E0%B8%94%E0%B8%99%E0%B8%8B%E0%B9%8C" title="อิมพีแดนซ์ – tailandés" lang="th" hreflang="th" data-title="อิมพีแดนซ์" data-language-autonym="ไทย" data-language-local-name="tailandés" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96z_empedans" title="Öz empedans – turcu" lang="tr" hreflang="tr" data-title="Öz empedans" data-language-autonym="Türkçe" data-language-local-name="turcu" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D1%96%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Електричний імпеданс – ucraín" lang="uk" hreflang="uk" data-title="Електричний імпеданс" data-language-autonym="Українська" data-language-local-name="ucraín" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%D9%82%DB%8C_%D9%85%D8%B3%D8%AF%D9%88%D8%AF%DB%8C%D8%AA" title="برقی مسدودیت – urdu" lang="ur" hreflang="ur" data-title="برقی مسدودیت" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tr%E1%BB%9F_kh%C3%A1ng" title="Trở kháng – vietnamín" lang="vi" hreflang="vi" data-title="Trở kháng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamín" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%98%BB%E6%8A%97" title="阻抗 – chinu wu" lang="wuu" hreflang="wuu" data-title="阻抗" data-language-autonym="吴语" data-language-local-name="chinu wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%99%D7%9E%D7%A4%D7%A2%D7%93%D7%90%D7%A0%D7%A5" title="אימפעדאנץ – yiddish" lang="yi" hreflang="yi" data-title="אימפעדאנץ" data-language-autonym="ייִדיש" data-language-local-name="yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%98%BB%E6%8A%97" title="阻抗 – chinu" lang="zh" hreflang="zh" data-title="阻抗" data-language-autonym="中文" data-language-local-name="chinu" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ti%C4%81n-kh%C3%AC_ch%C3%B3%CD%98-kh%C3%B2ng" title="Tiān-khì chó͘-khòng – chinu min nan" lang="nan" hreflang="nan" data-title="Tiān-khì chó͘-khòng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="chinu min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9B%BB%E9%98%BB%E6%8A%97" title="電阻抗 – cantonés" lang="yue" hreflang="yue" data-title="電阻抗" data-language-autonym="粵語" data-language-local-name="cantonés" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q179043#sitelinks-wikipedia" title="Editar los 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//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Robot_icon.svg/32px-Robot_icon.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div></div> </div> <div id="siteSub" class="noprint">De Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ast" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Impedancia_linea_bifiliar.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Impedancia_linea_bifiliar.jpg/220px-Impedancia_linea_bifiliar.jpg" decoding="async" width="220" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Impedancia_linea_bifiliar.jpg/330px-Impedancia_linea_bifiliar.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Impedancia_linea_bifiliar.jpg/440px-Impedancia_linea_bifiliar.jpg 2x" data-file-width="458" data-file-height="243" /></a><figcaption>Impedancia linea bifiliar</figcaption></figure> <p>La <b>impedancia</b> (Z) ye una midida d'oposición que presenta un circuitu a una corriente cuando s'aplica una <a href="/w/index.php?title=Tensi%C3%B3n_(eletricid%C3%A1)&action=edit&redlink=1" class="new" title="Tensión (eletricidá) (la páxina nun esiste)">tensión</a>. La impedancia estiende'l conceutu de <a href="/wiki/Resistencia_ll%C3%A9trica" title="Resistencia llétrica">resistencia</a> a los circuitos de <a href="/wiki/Corriente_alterna" class="mw-redirect" title="Corriente alterna">corriente alterna</a> (CA), y tien tanto magnitú como <a href="/w/index.php?title=Fase_(onda)&action=edit&redlink=1" class="new" title="Fase (onda) (la páxina nun esiste)">fase</a>, a diferencia de la resistencia, que namái tien magnitú. Cuando un circuitu ye alimentáu con <a href="/wiki/Corriente_continua" title="Corriente continua">corriente continua</a> (CC), la so impedancia ye igual a la resistencia, lo que puede ser interpretáu como la impedancia con ángulu de fase cero. </p><p>Por definición, la impedancia ye la rellación (cociente) ente'l <a href="/w/index.php?title=Fasor&action=edit&redlink=1" class="new" title="Fasor (la páxina nun esiste)">fasor</a> tensión y el fasor <a href="/wiki/Intensid%C3%A1_de_corriente_ll%C3%A9trica" title="Intensidá de corriente llétrica">intensidá de corriente</a>: </p> <style data-mw-deduplicate="TemplateStyles:r4219090">.mw-parser-output .ecuacion{padding:5px 10px;background-color:var(--background-color-base);color:var(--color-base);margin-left:30px;margin-bottom:0.8em;margin-top:0.5em;min-width:50%}.mw-parser-output .ecuacion .referencia{float:right;width:10%;text-align:end}.mw-parser-output .ecuacion cite{font-style:normal}</style><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z={\frac {V}{I}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>I</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z={\frac {V}{I}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29a62a3aada390892a13a0b520216d8d4ba35804" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.402ex; height:5.176ex;" alt="{\displaystyle Z={\frac {V}{I}}}" /></span> </p> </blockquote> <p>Onde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}" /></span> ye la impedancia, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> ye'l fasor tensión y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}" /></span> correspuende al fasor intensidá. </p><p>El conceutu de impedancia tien especial importancia si la corriente varia nel tiempu, y nesi casu les magnitúes describir con númberos complexos o funciones del analís harmónicu. El so módulu (dacuando inadecuadamente llamáu impedancia) establez la rellación ente los valores máximos o los valores eficaces de la tensión y de la corriente. La parte real de la impedancia ye la <a href="/wiki/Resistencia_ll%C3%A9trica" title="Resistencia llétrica">resistencia</a> y la so parte imaxinaria ye la <a href="/wiki/Reactancia" title="Reactancia">reactancia</a>. </p><p>El conceutu de impedancia dexa xeneralizar la <a href="/wiki/Llei_d%27Ohm" title="Llei d'Ohm">llei d'Ohm</a> nel estudiu de circuitos en corriente alterna (CA), dando llugar a la llamada <b>llei d'Ohm de corriente alterna</b> qu'indica: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219090" /><blockquote class="ecuacion" style="text-align:left"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I={\frac {V}{Z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>Z</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\frac {V}{Z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2febec2017057d38f7f19ec42e62b359dc7a3406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.894ex; height:5.176ex;" alt="{\displaystyle I={\frac {V}{Z}}}" /></span> </p> </blockquote> <p>El términu foi acuñáu por <a href="/w/index.php?title=Oliver_Heaviside&action=edit&redlink=1" class="new" title="Oliver Heaviside (la páxina nun esiste)">Oliver Heaviside</a> en 1886. Polo xeneral, la solución pa les corrientes y les tensiones d'un circuitu formáu por <a href="/wiki/Resistencia_ll%C3%A9trica" title="Resistencia llétrica">resistencies</a>, <a href="/wiki/Condensador_ll%C3%A9tricu" title="Condensador llétricu">condensadores</a> y <a href="/wiki/Inductancia" title="Inductancia">inductancies</a> y ensin nengún componente de comportamientu non llinial, son soluciones d'<a href="/w/index.php?title=Ecuaciones_diferenciales&action=edit&redlink=1" class="new" title="Ecuaciones diferenciales (la páxina nun esiste)">ecuaciones diferenciales</a>. Pero, cuando tolos xeneradores de tensión y de corriente tienen la mesma frecuencia constante y les sos amplitúes son constantes, les soluciones en <a href="/w/index.php?title=Est%C3%A1u_estacionariu&action=edit&redlink=1" class="new" title="Estáu estacionariu (la páxina nun esiste)">estáu estacionariu</a> (cuando tolos fenómenos transitorios sumieron) son sinusoidales y toles tensiones y corrientes tienen la mesma frecuencia que los xeneradores y amplitú constante. La fase, sicasí, va vese afeutada pela parte imaxinaria (reactancia) de la impedancia. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formalismu_matemáticu"><span id="Formalismu_matem.C3.A1ticu"></span>Formalismu matemáticu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=1" title="Editar seición: Formalismu matemáticu" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=1" title="Editar el código fuente de la sección: Formalismu matemáticu"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Definición"><span id="Definici.C3.B3n"></span>Definición</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=2" title="Editar seición: Definición" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=2" title="Editar el código fuente de la sección: Definición"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sía un componente llétricu o <a href="/wiki/Componente_electr%C3%B3nicu" title="Componente electrónicu">electrónicu</a> o un circuitu alimentáu por una corriente sinusoidal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I_{\circ }\cos(\omega t)}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I_{\circ }\cos(\omega t)}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f201a44820c344b20184360afa8826aa6358a1b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:7.424ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {I_{\circ }\cos(\omega t)}\,\!}" /></span>. Si la tensión ente los sos estremos ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{\circ }\cos(\omega t+\varphi )}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{\circ }\cos(\omega t+\varphi )}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4aee26e12812f4409999cec74f33208590791ac3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:10.013ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {V_{\circ }\cos(\omega t+\varphi )}\,\!}" /></span>, la <b>impedancia</b> del circuitu o del componente defínese como un <a href="/wiki/N%C3%BAmberu_complexu" title="Númberu complexu">númberu complexu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {Z}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {Z}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcda739e164db39c886189997f069309f1c638c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.575ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {Z}\,\!}" /></span>; qu'espresáu en forma polar tien un módulu igual al cociente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{\circ } \over I_{\circ }}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{\circ } \over I_{\circ }}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0714a155a097600d4dd62f0caf7be56b77cf5df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.081ex; margin-right: -0.387ex; margin-bottom: -0.257ex; width:2.802ex; height:3.509ex;" alt="{\displaystyle \scriptstyle {V_{\circ } \over I_{\circ }}\,\!}" /></span> y un argumentu que ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\varphi }\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>φ</mi> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\varphi }\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ddc05bdfdfbce38c32c2ffff5cac6880820a645" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:1.462ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {\varphi }\,\!}" /></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}|Z|&={V_{\circ } \over I_{\circ }}\\\arg(Z)&=\varphi \end{aligned}}\,\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>arg</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>Z</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>φ</mi> </mtd> </mtr> </mtable> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}|Z|&={V_{\circ } \over I_{\circ }}\\\arg(Z)&=\varphi \end{aligned}}\,\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b0340ba253abf9e81f2617e158c13013da57a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.515ex; margin-right: -0.387ex; margin-bottom: -0.323ex; width:14.596ex; height:8.843ex;" alt="{\displaystyle {\begin{aligned}|Z|&={V_{\circ } \over I_{\circ }}\\\arg(Z)&=\varphi \end{aligned}}\,\,\!}" /></span></dd></dl> <p>esto ye </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=\textstyle {V_{\circ } \over I_{\circ }}y^{j\varphi }=\textstyle {V_{\circ } \over I_{\circ }}\left(\cos \varphi +j\sin \varphi \right)\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> </mfrac> </mrow> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>φ</mi> </mrow> </msup> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>+</mo> <mi>j</mi> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=\textstyle {V_{\circ } \over I_{\circ }}y^{j\varphi }=\textstyle {V_{\circ } \over I_{\circ }}\left(\cos \varphi +j\sin \varphi \right)\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f0eed2de7d61bfc1c53b489deba9fb073a51a3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.169ex; margin-right: -0.387ex; margin-bottom: -0.336ex; width:32.825ex; height:4.009ex;" alt="{\displaystyle Z=\textstyle {V_{\circ } \over I_{\circ }}y^{j\varphi }=\textstyle {V_{\circ } \over I_{\circ }}\left(\cos \varphi +j\sin \varphi \right)\,\!}" /></span>.</dd></dl> <p>Como s'indicó enantes, la impedancia tamién se define pol cociente ente los fasores de tensión y corriente, representando la oposición total (Resistencia, Reactancia inductiva, Reactancia capacitiva) sobre la corriente. </p><p>Como la tensión y les corrientes son sinusoidales, pueden utilizase los <a href="/wiki/Corriente_alterna#Les_matemátiques_y_la_CA_senoidal#Valores_significativos" class="mw-redirect" title="Corriente alterna">valores pico</a> (amplitúes), los <a href="/wiki/Corriente_alterna#Les_matemátiques_y_la_CA_senoidal#Valores_significativos" class="mw-redirect" title="Corriente alterna">valores eficaces</a>, los <a href="/wiki/Corriente_alterna#Les_matemátiques_y_la_CA_senoidal#Valores_significativos" class="mw-redirect" title="Corriente alterna">valores pico a picu</a> o los <a href="/wiki/Corriente_alterna#Les_matemátiques_y_la_CA_senoidal#Valores_significativos" class="mw-redirect" title="Corriente alterna">valores medios</a>. Pero hai que curiar de tratalos uniformemente y nun entemecer los tipos. La resultancia de los cálculos va ser del mesmu tipu que l'utilizáu pa los xeneradores de tensión o de corriente. </p> <div class="mw-heading mw-heading3"><h3 id="Representación_binómica"><span id="Representaci.C3.B3n_bin.C3.B3mica"></span>Representación binómica</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=3" title="Editar seición: Representación binómica" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=3" title="Editar el código fuente de la sección: Representación binómica"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La impedancia puede representase en forma binómica como la suma d'una parte real y una parte imaxinaria: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=R+jX\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=R+jX\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b751fdbec9f1c02853adaeb10aed58269351da80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.708ex; height:2.509ex;" alt="{\displaystyle Z=R+jX\,}" /></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c4f2f602253dc3fcad851c80c2f3aba7de58505" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.247ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {R}}" /></span> ye la parte <b>resistiva</b> o <b>real</b> de la impedancia y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10b76fe8786617c81ca2ad016a8a37d65aa77edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.4ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {X}}" /></span> ye la parte <b>reactiva</b> o <b>imaxinaria</b> de la impedancia. Básicamente hai dos clases o tipos de reactancias: </p> <ul><li>Reactancia inductiva o <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f14ed86135c464841bbc6fba36cfb3997df2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.276ex; height:2.509ex;" alt="{\displaystyle X_{L}}" /></span>: Debida a la esistencia d'<a href="/wiki/Inductor" title="Inductor">inductores</a>.</li> <li>Reactancia capacitiva o <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe98111b842bc759e8ca808cfc6a23d3b2b0317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.406ex; height:2.509ex;" alt="{\displaystyle X_{C}}" /></span>: Debida a la esistencia de <a href="/w/index.php?title=Capacitor&action=edit&redlink=1" class="new" title="Capacitor (la páxina nun esiste)">capacitores</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Admitancia">Admitancia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=4" title="Editar seición: Admitancia" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=4" title="Editar el código fuente de la sección: Admitancia"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r4219085">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Ver tamién: <a href="/w/index.php?title=Admitancia&action=edit&redlink=1" class="new" title="Admitancia (la páxina nun esiste)">Admitancia</a></div> <p>La <b>admitancia</b> ye la inversa de la impedancia: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=\textstyle {1 \over Z}=y_{c}+jy_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>Z</mi> </mfrac> </mrow> <mo>=</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>+</mo> <mi>j</mi> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=\textstyle {1 \over Z}=y_{c}+jy_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d36a739e3c6bf0ff090e582b5defbb5fb8b03f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.019ex; height:3.509ex;" alt="{\displaystyle Y=\textstyle {1 \over Z}=y_{c}+jy_{s}}" /></span></dd></dl> <p>La <a href="/w/index.php?title=Conductancia&action=edit&redlink=1" class="new" title="Conductancia (la páxina nun esiste)">conductancia</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {y_{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {y_{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e628a192982315483d9b585ab89c99d799e1907" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.548ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {y_{c}}}" /></span> ye la parte real de la admitancia y la <a href="/w/index.php?title=Susceptancia&action=edit&redlink=1" class="new" title="Susceptancia (la páxina nun esiste)">susceptancia</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {y_{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {y_{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a067aa15f58ccba622f7c16e757758b5996b322" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.596ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {y_{s}}}" /></span> la parte imaxinaria de la admitancia. </p><p>La unidá de la admitancia, la conductancia y la susceptancia ye'l <a href="/wiki/Siemens_(unid%C3%A1)" title="Siemens (unidá)">siemens</a> (símbolu <b>S</b>). Un siemens ye'l recíprocu d'un <a href="/wiki/Ohmiu" title="Ohmiu">ohmiu</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Representación_gráfica"><span id="Representaci.C3.B3n_gr.C3.A1fica"></span>Representación gráfica</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=5" title="Editar seición: Representación gráfica" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=5" title="Editar el código fuente de la sección: Representación gráfica"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Ficheru:Wykres_wektorowy_by_Zureks.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Wykres_wektorowy_by_Zureks.svg/200px-Wykres_wektorowy_by_Zureks.svg.png" decoding="async" width="200" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Wykres_wektorowy_by_Zureks.svg/300px-Wykres_wektorowy_by_Zureks.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Wykres_wektorowy_by_Zureks.svg/400px-Wykres_wektorowy_by_Zureks.svg.png 2x" data-file-width="220" data-file-height="250" /></a><figcaption>Exemplu de fasores.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4219085" /><div role="note" class="hatnote navigation-not-searchable">Ver tamién: <a href="/w/index.php?title=Corriente_Alterna&action=edit&redlink=1" class="new" title="Corriente Alterna (la páxina nun esiste)">Corriente Alterna</a> y <a href="/w/index.php?title=Fasor&action=edit&redlink=1" class="new" title="Fasor (la páxina nun esiste)">Fasor</a></div> <p>Pueden representase les tensiones de los xeneradores de tensión y les tensiones ente los estremos de los componentes como vectores xiratorios nun <a href="/w/index.php?title=Planu_complexu&action=edit&redlink=1" class="new" title="Planu complexu (la páxina nun esiste)">planu complexu</a>. La magnitú (llargor) de los vectores ye'l módulu de la tensión y l'ángulu que faen con n'exa real ye igual al ángulu de desfase con respectu al xenerador de referencia. Esti tipu de diagrama tamién se llama <b>diagrama de Fresnel</b>. </p><p>Con un pocu de costume y un mínimu de conocencies de xeometría, eses representaciones son muncho más esplícites que los valores o les fórmules. De xacíu, esos dibuxos nun son, na nuesa dómina, un métodu gráficu de cálculu de circuitos. Son una manera de "ver" como les tensiones sumir. Esos dibuxos pueden facilitar la escritura de les fórmules finales, utilizando les propiedaes xeométriques. Van Atopar exemplos de la representación gráfica nos exemplos de baxo. </p> <div class="mw-heading mw-heading2"><h2 id="Cálculu_de_circuitos_coles_impedancias"><span id="C.C3.A1lculu_de_circuitos_coles_impedancias"></span>Cálculu de circuitos coles impedancias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=6" title="Editar seición: Cálculu de circuitos coles impedancias" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=6" title="Editar el código fuente de la sección: Cálculu de circuitos coles impedancias"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El formalismu de les impedancias consiste nunes poques regles que dexen calcular circuitos que contienen elementos resistivos, inductivos o capacitivos de manera similar al cálculu de circuitos resistivos en corriente continua. Eses regles namái son válides nos casos siguientes: </p> <ul><li>En réxime permanente con <a href="/wiki/Corriente_alterna" class="mw-redirect" title="Corriente alterna">corriente alterna</a> sinusoidal. Esto ye, que tolos xeneradores de tensión y de corriente son sinusoidales y de la mesma frecuencia, y que tolos fenómenos transitorios (conexones y desconexones sópites, falles de aislación repentines, etc.) s'atenuaron y sumieron dafechu.</li> <li>Si tolos componentes son lliniales. Esto ye, componentes o circuitos nos cualos l'amplitú (o'l valor eficaz) de la corriente ye puramente proporcional a la tensión aplicao. Esclúyense los componentes non lliniales como los diodos, bobines con nucleos de fierro y otros. Por ello, si'l circuitu contién inductancias o tresformadores con nucleu <a href="/w/index.php?title=Ferromagn%C3%A9tico&action=edit&redlink=1" class="new" title="Ferromagnético (la páxina nun esiste)">ferromagnético</a> (que nun son lliniales), los resultaos de los cálculos namái van poder ser averaos y eso, a condición de respetar la zona de trabayu de les inductancias.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Xeneradores_de_tensión_o_de_corriente_desfasaes"><span id="Xeneradores_de_tensi.C3.B3n_o_de_corriente_desfasaes"></span>Xeneradores de tensión o de corriente desfasaes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=7" title="Editar seición: Xeneradores de tensión o de corriente desfasaes" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=7" title="Editar el código fuente de la sección: Xeneradores de tensión o de corriente desfasaes"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si nun circuitu atopen dellos xeneradores de tensión o de corriente, escuéyese unu d'ellos como xenerador de referencia de fase. Si la verdadera tensión del xenerador de referencia ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{\circ }\cos(\omega t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{\circ }\cos(\omega t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53890e317bad4c2e3cfe8b6edd03d2140401893c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.272ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {V_{\circ }\cos(\omega t)}}" /></span>, pal cálculu coles impedancias vamos escribir la so tensión como <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{\circ }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{\circ }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ddfaa7b3a68da243fd1948c435003c0b4bc904e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.174ex; margin-bottom: -0.33ex; width:1.79ex; height:1.843ex;" alt="{\displaystyle \scriptstyle {V_{\circ }}}" /></span>. Si la tensión d'otru xenerador tien una meyora de fase de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f38856baffad5c084211db7f6d7f0523bfe6ab00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.052ex; height:1.343ex;" alt="{\displaystyle \scriptstyle {\alpha }}" /></span> con respectu al xenerador de referencia y la so corriente ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I_{1}\cos(\omega t+\alpha )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I_{1}\cos(\omega t+\alpha )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c55331d08145c98bd1944bc00251929e508a21a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.368ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {I_{1}\cos(\omega t+\alpha )}}" /></span>, pal cálculu coles impedancias vamos escribir la so corriente como <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I_{1}y^{j\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>α</mi> </mrow> </msup> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I_{1}y^{j\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c5553a1d1ae3509bde214ee16cd9702ff228deb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.944ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {I_{1}y^{j\alpha }}}" /></span>. L'<a href="/wiki/N%C3%BAmberu_complexu#Representación_trigonométrica_(polar)_y_representación_xeométrica" title="Númberu complexu">argumentu</a> de les tensiones y corrientes calculaes va ser el desfase d'eses tensiones o corrientes con respectu al xenerador tomáu como referencia. </p> <div class="mw-heading mw-heading3"><h3 id="Lleis_de_Kirchhoff">Lleis de Kirchhoff</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=8" title="Editar seición: Lleis de Kirchhoff" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=8" title="Editar el código fuente de la sección: Lleis de Kirchhoff"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les <a href="/wiki/Lleis_de_Kirchhoff" title="Lleis de Kirchhoff">lleis de Kirchhoff</a> aplicar de la mesma manera: "la suma de les corrientes que lleguen a un nodo ye cero" y "la suma de toles tensiones alredor d'una malla ye cero". Esta vegada, tantu les corrientes como les tensiones, son, polo xeneral, complexes. </p> <div class="mw-heading mw-heading3"><h3 id="Xeneralización_de_la_llei_d'Ohm"><span id="Xeneralizaci.C3.B3n_de_la_llei_d.27Ohm"></span>Xeneralización de la llei d'Ohm</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=9" title="Editar seición: Xeneralización de la llei d'Ohm" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=9" title="Editar el código fuente de la sección: Xeneralización de la llei d'Ohm"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La tensión ente les estremidaes d'una impedancia ye igual al productu de la corriente pola impedancia: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{z}=ZI_{z}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mi>Z</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{z}=ZI_{z}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a1d7908e5059d429852c29f757cb70bc097a65a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.548ex; height:2.509ex;" alt="{\displaystyle V_{z}=ZI_{z}\,}" /></span></dd></dl> <p>Tanto la impedancia, como la corriente y la tensión son, polo xeneral, complexes. </p> <div class="mw-heading mw-heading3"><h3 id="Impedancias_en_serie_o_en_paralelu">Impedancias en serie o en paralelu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=10" title="Editar seición: Impedancias en serie o en paralelu" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=10" title="Editar el código fuente de la sección: Impedancias en serie o en paralelu"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les impedancias trátense como les resistencies cola llei d'Ohm. La impedancia de delles impedancias coneutaes en serie ye igual a la so suma: </p> <dl><dd>Serie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=Z_{1}+Z_{2}+\cdots +Z_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=Z_{1}+Z_{2}+\cdots +Z_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f38b51d0262e53f0b55df8d8bcfa27c81e2795cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.113ex; height:2.509ex;" alt="{\displaystyle Z=Z_{1}+Z_{2}+\cdots +Z_{n}}" /></span></dd></dl> <p>La impedancia de delles impedancias coneutaes en paralelu ye igual al recíprocu de la suma de los sos recíprocos: </p> <dl><dd>Paralelu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle {Z}=\textstyle {1 \over \scriptstyle {{1 \over Z_{1}}+{1 \over Z_{2}}+\cdots +{1 \over Z_{n}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> </mrow> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {Z}=\textstyle {1 \over \scriptstyle {{1 \over Z_{1}}+{1 \over Z_{2}}+\cdots +{1 \over Z_{n}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddddbca54fc8441ece14ea55c0613776cd895c7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:19.154ex; height:5.676ex;" alt="{\displaystyle \textstyle {Z}=\textstyle {1 \over \scriptstyle {{1 \over Z_{1}}+{1 \over Z_{2}}+\cdots +{1 \over Z_{n}}}}}" /></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Interpretación_de_los_resultaos"><span id="Interpretaci.C3.B3n_de_los_resultaos"></span>Interpretación de los resultaos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=11" title="Editar seición: Interpretación de los resultaos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=11" title="Editar el código fuente de la sección: Interpretación de los resultaos"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La resultancia de corriente ye, xeneralmente, un númberu complexu. Esi númberu complexu interpretar de manera siguiente: </p> <ul><li>El <a href="/wiki/N%C3%BAmberu_complexu#Representación_trigonométrica_(polar)_y_representación_xeométrica" title="Númberu complexu">módulu</a> indica'l valor de la tensión o de la corriente calculada. Si los valores utilizaos pa los xeneradores yeren los valores pico, la resultancia tamién va ser un valor pico. Si los valores yeren valores eficaces, la resultancia tamién va ser un valor eficaz.</li> <li>L'<a href="/wiki/N%C3%BAmberu_complexu#Representación_trigonométrica_(polar)_y_representación_xeométrica" title="Númberu complexu">argumentu</a> d'esi númberu complexu da'l desfase con respectu al xenerador utilizáu como referencia de fase. Si l'argumentu ye positivu la tensión o la corriente calculaes van tar en meyora de fase.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Xeneralización"><span id="Xeneralizaci.C3.B3n"></span>Xeneralización</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=12" title="Editar seición: Xeneralización" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=12" title="Editar el código fuente de la sección: Xeneralización"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cuando tolos xeneradores nun tienen la mesma frecuencia o si les señales nun son sinusoidales, el formalismu de les impedancias nun puede aplicase direutamente. Tiense que descomponer el cálculu en delles etapes en caúna de les cuales puede utilizase el formalismu de impedancias. </p><p>Nel casu de tenese elementos lliniales, puede utilizase el <a href="/w/index.php?title=Teorema_de_superposici%C3%B3n&action=edit&redlink=1" class="new" title="Teorema de superposición (la páxina nun esiste)">teorema de superposición</a>: faise un cálculu separáu pa caúna de les frecuencies (remplazando en cada unu de los cálculos tolos xeneradores de tensión de frecuencia distinta por un cortucircuitu y tolos xeneradores de corriente de frecuencia distinta por un circuitu abiertu). Caúna de les tensiones y corrientes totales del circuitu va ser la suma de caúna de les tensiones o corrientes llograes à caúna de les frecuencies. De xacíu, pa faer estes postreres sumes hai qu'escribir caúna de les tensiones na forma real, cola dependencia del tiempu y el desfase: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{i}\cos(\omega _{i}t+\varphi _{i})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{i}\cos(\omega _{i}t+\varphi _{i})}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c3790aa4f1e1d603a47ee600ea70bc51be20557" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.669ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {V_{i}\cos(\omega _{i}t+\varphi _{i})}}" /></span> pa les tensiones y les fórmules similares pa les corrientes. </p><p>Si les señales nun son sinusoidales, pero son periódiques y <a href="/w/index.php?title=Continuid%C3%A1_(matem%C3%A1tiques)&action=edit&redlink=1" class="new" title="Continuidá (matemátiques) (la páxina nun esiste)">continues</a>, pueden descomponese les señales en <a href="/wiki/Serie_de_Fourier" title="Serie de Fourier">serie de Fourier</a> y utilizar el <a href="/w/index.php?title=Teorema_de_superposici%C3%B3n&action=edit&redlink=1" class="new" title="Teorema de superposición (la páxina nun esiste)">teorema de superposición</a> pa dixebrar el cálculu nun cálculu pa caúna de les frecuencies. La resultancia final va ser la suma de los resultaos pa caúna de les frecuencies de la descomposición en serie. </p> <div class="mw-heading mw-heading2"><h2 id="Orixe_de_les_impedancias">Orixe de les impedancias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=13" title="Editar seición: Orixe de les impedancias" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=13" title="Editar el código fuente de la sección: Orixe de les impedancias"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vamos tratar d'ilustrar el sentíu físicu de la parte imaxinaria <b>j</b> (onde s'utiliza esta lletra en cuenta de <i>i</i> pa evitar tracamundios cola intensidá) de les impedancias calculando, ensin utilizar estes, la corriente que circula por un circuitu formáu por una <a href="/wiki/Resistor" class="mw-redirect" title="Resistor">resistencia</a>, un <a href="/wiki/Inductor" title="Inductor">inductor</a> y un <a href="/wiki/Condensador_ll%C3%A9tricu" title="Condensador llétricu">condensador</a> en serie. </p><p>El circuitu ta alimentáu con una tensión sinusoidal y esperemos abondo por que tolos fenómenos transitorios sumieren. Tenemos un réxime permanente. Como'l sistema ye llinial, la corriente del réxime permanente va ser tamién sinusoidal y va tener la mesma frecuencia que la de la fonte orixinal. Lo único que nun sabemos sobre la corriente ye la so amplitú y el desfase que puede tener con al respective de la tensión d'alimentación. Asina, si la tensión d'alimentación ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V=V_{\circ }\cos(\omega t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V=V_{\circ }\cos(\omega t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0740a8dd2e167f6ae4ffd327b78de749bebcbf71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.815ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {V=V_{\circ }\cos(\omega t)}}" /></span> la corriente va ser de la forma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I=I_{\circ }\cos(\omega t+\varphi )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I=I_{\circ }\cos(\omega t+\varphi )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2558a9808efba6a13867a2319f511129ec4ccef0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.498ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {I=I_{\circ }\cos(\omega t+\varphi )}}" /></span>, onde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\varphi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>φ</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\varphi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e91b58216bc9292e743f8f07287193f7ded3bdda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.075ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {\varphi }}" /></span> ye'l desfase que nun conocemos. La ecuación a resolver va ser: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\circ }\cos(\omega t)=V_{R}+V_{L}+V_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\circ }\cos(\omega t)=V_{R}+V_{L}+V_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da716d6583ec1f8b2c9bedd6d533a1ca69d9165f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.16ex; height:2.843ex;" alt="{\displaystyle V_{\circ }\cos(\omega t)=V_{R}+V_{L}+V_{C}}" /></span></dd></dl></dd></dl> <p>onde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73d81b2c807759d9e63c399ea44137de6cab6d8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.135ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {V_{R}}}" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1e2993fd090f21849d29d217e9354d3b993b169" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.031ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {V_{L}}}" /></span> y <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{C}}:}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>:</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{C}}:}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b7d0d9abe8977153897e72b2496c15a984f702d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.594ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {V_{C}}:}" /></span> son les tensiones ente les estremidaes de la resistencia, la inductancia y el condensador. </p><p>Aplicando la llei d'Ohm a la resistencia. resulta: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{R}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{R}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/392e73bff272722b871f21c59ada54834a527a45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.222ex; height:2.509ex;" alt="{\displaystyle V_{R}\,}" /></span> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RI_{\circ }\cos(\omega t+\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RI_{\circ }\cos(\omega t+\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c62c39b289b6d614e8b0a7395a194a899bb98aec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.795ex; height:2.843ex;" alt="{\displaystyle RI_{\circ }\cos(\omega t+\varphi )}" /></span></dd></dl></dd></dl> <p>La definición de inductancia diznos que: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{L}={d\Phi c \over dt}={dLI \over dt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi mathvariant="normal">Φ</mi> <mi>c</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>L</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{L}={d\Phi c \over dt}={dLI \over dt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7756591c09dcb56684eab5281718715410b2cba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.447ex; height:5.509ex;" alt="{\displaystyle V_{L}={d\Phi c \over dt}={dLI \over dt}}" /></span></dd></dl></dd></dl> <p>Si L ye constante, queda: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{L}=L\textstyle {di \over dt}=L\textstyle {d\left(I_{\circ }\cos(\omega t+\varphi )\right) \over dt}=-\omega LI_{\circ }\sin(\omega t+\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mi>L</mi> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>i</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>L</mi> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>ω</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{L}=L\textstyle {di \over dt}=L\textstyle {d\left(I_{\circ }\cos(\omega t+\varphi )\right) \over dt}=-\omega LI_{\circ }\sin(\omega t+\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdd26b30f9d80e23b97e0a263de158b63ea6a055" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:48.436ex; height:4.343ex;" alt="{\displaystyle V_{L}=L\textstyle {di \over dt}=L\textstyle {d\left(I_{\circ }\cos(\omega t+\varphi )\right) \over dt}=-\omega LI_{\circ }\sin(\omega t+\varphi )}" /></span>.</dd></dl></dd></dl> <p>La definición de condensador diznos que: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I={{dq} \over {dt}}={{d(CV_{C})} \over {dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>C</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={{dq} \over {dt}}={{d(CV_{C})} \over {dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3728fd1ed2c3947d1e07b3ba55ed529bae6a0d95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.954ex; height:5.843ex;" alt="{\displaystyle I={{dq} \over {dt}}={{d(CV_{C})} \over {dt}}}" /></span></dd></dl></dd></dl> <p>Si C ye constante: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=C\cdot {\frac {dV}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mi>C</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>V</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=C\cdot {\frac {dV}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b0bc5b30ca70bfe1f373c065653789b2f17adf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.555ex; height:5.509ex;" alt="{\displaystyle I=C\cdot {\frac {dV}{dt}}}" /></span></dd></dl></dd></dl> <p>Faciendo la derivada, puede comprobase que: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{C}=\textstyle {1 \over \omega C}I_{\circ }\sin(\omega t+\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{C}=\textstyle {1 \over \omega C}I_{\circ }\sin(\omega t+\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e79eee369c7e5813181ba1e27f9a99f7c2df195" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:22.818ex; height:3.676ex;" alt="{\displaystyle V_{C}=\textstyle {1 \over \omega C}I_{\circ }\sin(\omega t+\varphi )}" /></span>.</dd></dl></dd></dl> <p>Asina, la ecuación qu'hai que resolver ye: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\circ }\cos(\omega t)=RI_{\circ }\cos(\omega t+\varphi )-\omega LI_{\circ }\sin(\omega t+\varphi )+\textstyle {1 \over \omega C}I_{\circ }\sin(\omega t+\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>R</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ω</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\circ }\cos(\omega t)=RI_{\circ }\cos(\omega t+\varphi )-\omega LI_{\circ }\sin(\omega t+\varphi )+\textstyle {1 \over \omega C}I_{\circ }\sin(\omega t+\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62565d2e35fcbc0d1cca1f61e751042f477c8e76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:68.263ex; height:3.676ex;" alt="{\displaystyle V_{\circ }\cos(\omega t)=RI_{\circ }\cos(\omega t+\varphi )-\omega LI_{\circ }\sin(\omega t+\varphi )+\textstyle {1 \over \omega C}I_{\circ }\sin(\omega t+\varphi )}" /></span></dd></dl></dd></dl> <p>Tenemos qu'atopar los valores de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I_{\circ }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I_{\circ }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0051012d4b60b8c92e4cbcf05702247fa82138" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.174ex; margin-bottom: -0.33ex; width:1.555ex; height:1.843ex;" alt="{\displaystyle \scriptstyle {I_{\circ }}}" /></span> y de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\varphi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>φ</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\varphi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e91b58216bc9292e743f8f07287193f7ded3bdda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.075ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {\varphi }}" /></span> que faigan qu'esta ecuación seya satisfecha pa tolos valores de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc897418b42b258380848692cb1a41f7bf481687" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.594ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {t}}" /></span>. </p><p>P'atopalos, imaxinemos qu'alimentamos otru circuitu idénticu con otra fonte de tensión sinusoidal que la so única diferencia ye qu'empieza con un cuartu de periodu de retrasu. Esto ye, que la tensión va ser <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V=V_{\circ }\cos(\omega t-{\pi \over 2})=V_{\circ }\sin(\omega t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V=V_{\circ }\cos(\omega t-{\pi \over 2})=V_{\circ }\sin(\omega t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bf7d5dc7e8b370a13dfbc376fd67d6c018c6371" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:21.064ex; height:2.843ex;" alt="{\displaystyle \scriptstyle {V=V_{\circ }\cos(\omega t-{\pi \over 2})=V_{\circ }\sin(\omega t)}}" /></span>. De la mesma manera, la solución tamién va tener el mesmu retrasu y la corriente va ser: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I=I_{\circ }\cos(\omega t+\varphi -{\pi \over 2})=I_{\circ }\sin(\omega t+\varphi )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I=I_{\circ }\cos(\omega t+\varphi -{\pi \over 2})=I_{\circ }\sin(\omega t+\varphi )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a609d004b7242a58fd4dd6d90e89e05714a51d42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:24.866ex; height:2.843ex;" alt="{\displaystyle \scriptstyle {I=I_{\circ }\cos(\omega t+\varphi -{\pi \over 2})=I_{\circ }\sin(\omega t+\varphi )}}" /></span>. La ecuación d'esti segundu circuitu tardiegu va ser: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\circ }\sin(\omega t)=RI_{\circ }\sin(\omega t+\varphi )+\omega LI_{\circ }\cos(\omega t+\varphi )-\textstyle {1 \over \omega C}I_{\circ }\cos(\omega t+\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>R</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>ω</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\circ }\sin(\omega t)=RI_{\circ }\sin(\omega t+\varphi )+\omega LI_{\circ }\cos(\omega t+\varphi )-\textstyle {1 \over \omega C}I_{\circ }\cos(\omega t+\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0431093e8a88bf506b0e5652ebd0d30ffe841697" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:68.263ex; height:3.676ex;" alt="{\displaystyle V_{\circ }\sin(\omega t)=RI_{\circ }\sin(\omega t+\varphi )+\omega LI_{\circ }\cos(\omega t+\varphi )-\textstyle {1 \over \omega C}I_{\circ }\cos(\omega t+\varphi )}" /></span></dd></dl></dd></dl> <p>Hai signos que camudaron porque'l cosenu tardiegu tresformar en senu, pero'l senu tardiegu tresformar en <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle {\mathbf {-} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold">−</mo> </mrow> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\mathbf {-} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f0f04066c8d20bf401a9d41c2176e204aac4828" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.511ex; margin-bottom: -0.682ex; width:2.078ex; height:1.009ex;" alt="{\displaystyle \textstyle {\mathbf {-} }}" /></span>cosenu. Agora vamos sumar los dos ecuaciones dempués de multiplicar la segunda por <b>j</b>. La idea ye de poder tresformar les espresiones de la forma <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\cos x+j\sin x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>j</mi> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\cos x+j\sin x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1de88664cb256f007834bd76a94ec62e787f440" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.217ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {\cos x+j\sin x}}" /></span> en <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {y^{jx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>x</mi> </mrow> </msup> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {y^{jx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/058737a5d34e670784d6171288782584bef90e00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.298ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {y^{jx}}}" /></span>, utilizando les <a href="/wiki/F%C3%B3rmula_d%27Euler" title="Fórmula d'Euler">fórmules d'Euler</a>. La resultancia ye: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\circ }y^{j\omega t}=RI_{\circ }y^{j\left(\omega t+\varphi \right)}+j\omega LI_{\circ }y^{j\left(\omega t+\varphi \right)}+\textstyle {1 \over j\omega C}I_{\circ }y^{j\left(\omega t+\varphi \right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>ω</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mi>R</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> </mrow> </msup> <mo>+</mo> <mi>j</mi> <mi>ω</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> </mrow> </msup> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> </mrow> </msup> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\circ }y^{j\omega t}=RI_{\circ }y^{j\left(\omega t+\varphi \right)}+j\omega LI_{\circ }y^{j\left(\omega t+\varphi \right)}+\textstyle {1 \over j\omega C}I_{\circ }y^{j\left(\omega t+\varphi \right)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/706d0277912da83e1e8d39dc82541caff819b522" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:52.6ex; height:4.176ex;" alt="{\displaystyle V_{\circ }y^{j\omega t}=RI_{\circ }y^{j\left(\omega t+\varphi \right)}+j\omega LI_{\circ }y^{j\left(\omega t+\varphi \right)}+\textstyle {1 \over j\omega C}I_{\circ }y^{j\left(\omega t+\varphi \right)}}" /></span></dd></dl></dd></dl> <p>Como <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {y^{j\omega t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>ω</mi> <mi>t</mi> </mrow> </msup> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {y^{j\omega t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8024b04b0762ffdca54a29d873b05deca23ac89e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.847ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {y^{j\omega t}}}" /></span> ye distintu de cero, puede estremase tola ecuación por esi factor: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\circ }=RI_{\circ }y^{j\varphi }+j\omega LI_{\circ }y^{j\varphi }+\textstyle {1 \over j\omega C}I_{\circ }y^{j\varphi }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mo>=</mo> <mi>R</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>φ</mi> </mrow> </msup> <mo>+</mo> <mi>j</mi> <mi>ω</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>φ</mi> </mrow> </msup> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>φ</mi> </mrow> </msup> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\circ }=RI_{\circ }y^{j\varphi }+j\omega LI_{\circ }y^{j\varphi }+\textstyle {1 \over j\omega C}I_{\circ }y^{j\varphi }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/998030932c76c37c2426166cb5c07a71f2b4267b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:36.392ex; height:4.009ex;" alt="{\displaystyle V_{\circ }=RI_{\circ }y^{j\varphi }+j\omega LI_{\circ }y^{j\varphi }+\textstyle {1 \over j\omega C}I_{\circ }y^{j\varphi }}" /></span></dd></dl></dd></dl> <p>deduzse: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\circ }y^{j\varphi }=\textstyle {V_{\circ } \over R+j\omega L+\scriptstyle {1 \over j\omega C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>φ</mi> </mrow> </msup> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mrow> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>ω</mi> <mi>L</mi> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\circ }y^{j\varphi }=\textstyle {V_{\circ } \over R+j\omega L+\scriptstyle {1 \over j\omega C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eab5de9300690f1f72496889a64c1de204b7fca7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:19.011ex; height:5.676ex;" alt="{\displaystyle I_{\circ }y^{j\varphi }=\textstyle {V_{\circ } \over R+j\omega L+\scriptstyle {1 \over j\omega C}}}" /></span></dd></dl></dd></dl> <p>A la izquierda tenemos los dos cuesas que queríamos calcular: l'amplitú de la corriente y el so desfase. L'amplitú va ser igual al módulu del númberu complexu de la derecha y el desfase va ser igual al argumentu del númberu complexu de la derecha.<br /> Y el términu de la derecha ye la resultancia del cálculu habitual utilizando'l formalismu de impedancias nel cual trátense les impedancias de les resistencies, condensadores y inductancias de la mesma manera que les resistencies cola llei d'Ohm.<br /> Vale la pena repitir que cuando escribimos: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=\textstyle {V_{\circ } \over R+j\omega L+\scriptstyle {1 \over j\omega C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msub> <mrow> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>ω</mi> <mi>L</mi> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=\textstyle {V_{\circ } \over R+j\omega L+\scriptstyle {1 \over j\omega C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b00df05cbbf5447d8a131d9ae0662ca9d180a8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.96ex; height:5.676ex;" alt="{\displaystyle I=\textstyle {V_{\circ } \over R+j\omega L+\scriptstyle {1 \over j\omega C}}}" /></span></dd></dl></dd></dl> <p>almitimos que la persona que llee esa fórmula sabe interpretala y nun va creer que la corriente pueda ser complexa o imaxinaria. El mesmu camientu esiste cuando atopamos espresiones como "alimentamos con una tensión <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {Ve^{j\omega t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>ω</mi> <mi>t</mi> </mrow> </msup> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {Ve^{j\omega t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51db2d896f42a5b1af8db7be1053c63a0800497d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.056ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {Ve^{j\omega t}}}" /></span>" o "la corriente ye complexa". </p><p>Como les señales son sinusoidales, los factores ente los valores eficaces, máximos, picu a picu o medios son fixos. Asina que, nel formalismu de impedancias, si los valores d'entrada son picu, los resultaos tamién van venir en picu. Igual pa eficaz o otros. Pero nun hai qu'entemecelos. </p> <div class="mw-heading mw-heading2"><h2 id="Exemplos">Exemplos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=14" title="Editar seición: Exemplos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=14" title="Editar el código fuente de la sección: Exemplos"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Impedancia_n'elementos_básicos"><span id="Impedancia_n.27elementos_b.C3.A1sicos"></span>Impedancia n'elementos básicos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=15" title="Editar seición: Impedancia n'elementos básicos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=15" title="Editar el código fuente de la sección: Impedancia n'elementos básicos"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La impedancia d'una resistencia ideal, solo contién una componente real: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Z_{R}=R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>=</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z_{R}=R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1756bb3fbd00d316ad29dc1b68134e1b3cbfd86b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.51ex; height:2.509ex;" alt="{\displaystyle \ Z_{R}=R}" /></span></dd></dl> <p>Nesti casu, la tensión y la corriente son proporcionales y tán en fase. </p><p>La impedancia nun inductor ideal o nun condensador ideal tien una componente puramente imaxinaria: </p><p>La impedancia nun inductor amontar cola frecuencia; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Z_{L}=j\omega L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mi>j</mi> <mi>ω</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z_{L}=j\omega L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22a71af1c2e6442bc2d17fa963f8084aa88532a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.605ex; height:2.509ex;" alt="{\displaystyle \ Z_{L}=j\omega L}" /></span></dd></dl> <p>La impedancia d'un condensador escai cuando la frecuencia crez; </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Z_{C}={\frac {-j}{\omega C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>j</mi> </mrow> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z_{C}={\frac {-j}{\omega C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dde97d8d45d5c885a4dbe6fea293110344f56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.796ex; height:5.509ex;" alt="{\displaystyle \ Z_{C}={\frac {-j}{\omega C}}}" /></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Un_xenerador_únicu"><span id="Un_xenerador_.C3.BAnicu"></span>Un xenerador únicu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=16" title="Editar seición: Un xenerador únicu" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=16" title="Editar el código fuente de la sección: Un xenerador únicu"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Ficheru:Imped1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/ca/Imped1.png" decoding="async" width="226" height="189" class="mw-file-element" data-file-width="226" data-file-height="189" /></a><figcaption> Una inductancia y una resistencia en serie alimentaes por un xenerador sinusoidal.</figcaption></figure> <p>Na diagrama de la derecha tenemos un xenerador sinusoidal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V=10\cos(\omega t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>=</mo> <mn>10</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V=10\cos(\omega t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e92950dc0dcc79419438181c83b3dfafdc5d2c4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.669ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {V=10\cos(\omega t)}}" /></span> de 10 voltios d'amplitú y de una frecuencia de 10 kHz. En serie hai una inductancia de 10 mH y una resistencia de 1,2 k<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\Omega }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\Omega }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4fa7b0596270320646f4bf1025af826e19c8d98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.187ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {\Omega }}" /></span>. </p><p>Calculemos la corriente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bd08471df067de2713427339044655ea19c8ed5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.829ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {I}}" /></span> que circula nel circuitu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=\textstyle {{V \over Z_{L}+Z_{R}}={V \over j\omega L+R}={10 \over j2\pi 10^{4}0,01+1200}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mrow> <mi>j</mi> <mi>ω</mi> <mi>L</mi> <mo>+</mo> <mi>R</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>10</mn> <mrow> <mi>j</mi> <mn>2</mn> <mi>π</mi> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mn>0</mn> <mo>,</mo> <mn>01</mn> <mo>+</mo> <mn>1200</mn> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=\textstyle {{V \over Z_{L}+Z_{R}}={V \over j\omega L+R}={10 \over j2\pi 10^{4}0,01+1200}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1656f15400bc8b7172d00a9091ba8d89987330f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:36.5ex; height:4.509ex;" alt="{\displaystyle I=\textstyle {{V \over Z_{L}+Z_{R}}={V \over j\omega L+R}={10 \over j2\pi 10^{4}0,01+1200}}}" /></span> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle {={10 \over 1200+j628,3}}=0{,}00654-j0{,}003424\,\mathrm {A} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>10</mn> <mrow> <mn>1200</mn> <mo>+</mo> <mi>j</mi> <mn>628</mn> <mo>,</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </mrow> <mo>=</mo> <mn>0,006</mn> <mn>54</mn> <mo>−</mo> <mi>j</mi> <mn>0,003</mn> <mn>424</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {={10 \over 1200+j628,3}}=0{,}00654-j0{,}003424\,\mathrm {A} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa83660f32830794eef0b4d14ad8e595b11c8d90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:37.711ex; height:3.843ex;" alt="{\displaystyle \textstyle {={10 \over 1200+j628,3}}=0{,}00654-j0{,}003424\,\mathrm {A} }" /></span></dd></dl></dd></dl> <p>Ye necesaria l'aplicación del cálculu con númberos complexos si utiliza esta notación. </p><p>El módulu de la corriente ye: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=\left|\textstyle {10 \over 1200+j628,3}\right|=7,38\,\mathrm {mA} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow> <mo>|</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>10</mn> <mrow> <mn>1200</mn> <mo>+</mo> <mi>j</mi> <mn>628</mn> <mo>,</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </mstyle> <mo>|</mo> </mrow> <mo>=</mo> <mn>7</mn> <mo>,</mo> <mn>38</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=\left|\textstyle {10 \over 1200+j628,3}\right|=7,38\,\mathrm {mA} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0f75b9f4ab18de953aeb454fd6e5f03569319ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:27.075ex; height:4.176ex;" alt="{\displaystyle I=\left|\textstyle {10 \over 1200+j628,3}\right|=7,38\,\mathrm {mA} }" /></span></dd></dl> <p>Como'l valor de la tensión del xenerador que tomamos foi un valor pico (amplitú), el valor de la corriente llográu tamién ye un valor pico. La corriente eficaz ye: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {I_{\mathrm {ef} }={7,38 \over {\sqrt {2}}}}=5,22\,\mathrm {mA} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>7</mn> <mo>,</mo> <mn>38</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo>=</mo> <mn>5</mn> <mo>,</mo> <mn>22</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">A</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {I_{\mathrm {ef} }={7,38 \over {\sqrt {2}}}}=5,22\,\mathrm {mA} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/471051fa167105ce3aec36e2ab6e68d3cddc0cba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:13.655ex; height:4.009ex;" alt="{\displaystyle \scriptstyle {I_{\mathrm {ef} }={7,38 \over {\sqrt {2}}}}=5,22\,\mathrm {mA} }" /></span> </p><p>La fase de la corriente ye'l <a href="/wiki/N%C3%BAmberu_complexu#Representación_trigonométrica_(polar)_y_representación_xeométrica" title="Númberu complexu">argumentu</a> del númberu complexu </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {10 \over 1200+j628,3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>10</mn> <mrow> <mn>1200</mn> <mo>+</mo> <mi>j</mi> <mn>628</mn> <mo>,</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {10 \over 1200+j628,3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a75d15541688da376cdc30428c4a6f310a75955" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:8.134ex; height:3.509ex;" alt="{\displaystyle \scriptstyle {10 \over 1200+j628,3}}" /></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {arg} \left(\textstyle {10 \over 1200+j628,3}\right)=-0{,}4823\,\,\mathrm {rad} =-27{,}63^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">g</mi> </mrow> <mrow> <mo>(</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>10</mn> <mrow> <mn>1200</mn> <mo>+</mo> <mi>j</mi> <mn>628</mn> <mo>,</mo> <mn>3</mn> </mrow> </mfrac> </mrow> </mstyle> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>0,482</mn> <mn>3</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mo>=</mo> <mo>−</mo> <mn>27</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <msup> <mn>63</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {arg} \left(\textstyle {10 \over 1200+j628,3}\right)=-0{,}4823\,\,\mathrm {rad} =-27{,}63^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a7eeaddf553f5977a8f1760b6b8caf218222898" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:42.988ex; height:4.843ex;" alt="{\displaystyle \mathrm {arg} \left(\textstyle {10 \over 1200+j628,3}\right)=-0{,}4823\,\,\mathrm {rad} =-27{,}63^{\circ }}" /></span>.</dd></dl> <p>La corriente ta en retardo de fase con al respective de la fase del xenerador. Eso ye lóxicu, una y bones el circuitu ye inductivu. </p> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Ficheru:DiagFresnel1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/86/DiagFresnel1.png" decoding="async" width="193" height="178" class="mw-file-element" data-file-width="193" data-file-height="178" /></a><figcaption> Diagrama de Fresnel (o fasor) d'una inductancia y una resistencia en serie. El círculu gris solo sirve d'ayuda al dibuxu del ángulu rectu ente la tensión de la resistencia y la tensión de la inductancia.</figcaption></figure> <p>Solo la resistencia estena potencia: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{R}=\textstyle {1 \over 2}R\left|I\right|^{2}=\textstyle {1 \over 2}1200\cdot \left(7{,}38\,10^{-3}\right)^{2}=32{,}7\,\,\mathrm {mW} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>R</mi> <msup> <mrow> <mo>|</mo> <mi>I</mi> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mn>1200</mn> <mo>⋅</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>38</mn> <mspace width="thinmathspace"></mspace> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>32</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>7</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">W</mi> </mrow> </mstyle> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{R}=\textstyle {1 \over 2}R\left|I\right|^{2}=\textstyle {1 \over 2}1200\cdot \left(7{,}38\,10^{-3}\right)^{2}=32{,}7\,\,\mathrm {mW} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6a0216668f77ce5feb3604b0affae7b8102af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:48.792ex; height:3.843ex;" alt="{\displaystyle P_{R}=\textstyle {1 \over 2}R\left|I\right|^{2}=\textstyle {1 \over 2}1200\cdot \left(7{,}38\,10^{-3}\right)^{2}=32{,}7\,\,\mathrm {mW} }" /></span></dd></dl> <p>La fracción <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {1 \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {1 \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42898d802a709d864f54ea127b9b1ec2712147a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.503ex; height:3.176ex;" alt="{\displaystyle \scriptstyle {1 \over 2}}" /></span> apaez porque'l valor de la corriente ye'l valor pico. </p><p>La tensión ente los estremos de la resistencia ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{R}=I\,R=(0{,}00654-j0{,}003424)\,1200=7{,}84-j4{,}109\,\,V_{\mathrm {picu} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>=</mo> <mi>I</mi> <mspace width="thinmathspace"></mspace> <mi>R</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>0,006</mn> <mn>54</mn> <mo>−</mo> <mi>j</mi> <mn>0,003</mn> <mn>424</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mn>1200</mn> <mo>=</mo> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>84</mn> <mo>−</mo> <mi>j</mi> <mn>4,109</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{R}=I\,R=(0{,}00654-j0{,}003424)\,1200=7{,}84-j4{,}109\,\,V_{\mathrm {picu} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97693d1b94187910a7eff4bfd48f89adc4e6526b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.914ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {V_{R}=I\,R=(0{,}00654-j0{,}003424)\,1200=7{,}84-j4{,}109\,\,V_{\mathrm {picu} }}}" /></span> </p><p>La tensión eficaz que se lleería con un voltímetru sería'l módulu d'esta tensión estremo por <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b6ac02637a190523aa10dde1b52ae41964dfff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.191ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {\sqrt {2}}}" /></span>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {6{,}26\,V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>26</mn> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {6{,}26\,V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/025cd66c2fea9ffb0631d20275cfeb0629b6c6e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.522ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {6{,}26\,V_{\mathrm {ef} }}}" /></span> </p><p>La tensión ente les estremidaes de la inductancia ye<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{L}=j\omega L\,I\,=j628{,}3\,(0{,}00654-j0{,}003424)=2{,}15+j4{,}109\,V_{\mathrm {picu} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mi>j</mi> <mi>ω</mi> <mi>L</mi> <mspace width="thinmathspace"></mspace> <mi>I</mi> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mi>j</mi> <mn>628</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>3</mn> <mspace width="thinmathspace"></mspace> <mo stretchy="false">(</mo> <mn>0,006</mn> <mn>54</mn> <mo>−</mo> <mi>j</mi> <mn>0,003</mn> <mn>424</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>15</mn> <mo>+</mo> <mi>j</mi> <mn>4,109</mn> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{L}=j\omega L\,I\,=j628{,}3\,(0{,}00654-j0{,}003424)=2{,}15+j4{,}109\,V_{\mathrm {picu} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af6577d07455289875fdec9a99c69f89fe4c39e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.517ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {V_{L}=j\omega L\,I\,=j628{,}3\,(0{,}00654-j0{,}003424)=2{,}15+j4{,}109\,V_{\mathrm {picu} }}}" /></span> </p><p>La tensión eficaz lleida col voltímetru sería, igualmente: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {3,28\,V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mo>,</mo> <mn>28</mn> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {3,28\,V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa0e92d4dad7901ca7eef4b784da24d6120d4b5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.522ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {3,28\,V_{\mathrm {ef} }}}" /></span> </p><p>Constatamos que la suma de los dos tensiones "complexes" da (teniendo en cuenta los redondeos) la tensión del xenerador. Sicasí, la suma de los dos tensiones lleíes con un voltímetru ye más grande que la del xenerador (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {7,07V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> <mo>,</mo> <mn>07</mn> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {7,07V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62acb86f9a2c77e5df459b347e7d5aa845d33728" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.135ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {7,07V_{\mathrm {ef} }}}" /></span>). Esa resultancia ye típicu de les midíes feches con un voltímetru en circuitos nos cualos les tensiones nun tán en fase. Un voltímetru mídenos módulos en valor eficaz, que nun podemos sumar direutamente yá que tamos tratando con fasores coles sos distintes orientaciones. </p> <div class="mw-heading mw-heading3"><h3 id="Dos_xeneradores_desfasaos">Dos xeneradores desfasaos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=17" title="Editar seición: Dos xeneradores desfasaos" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=17" title="Editar el código fuente de la sección: Dos xeneradores desfasaos"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Ficheru:Imped2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5d/Imped2.png" decoding="async" width="226" height="148" class="mw-file-element" data-file-width="226" data-file-height="148" /></a><figcaption> Condensador y resistencia en serie ente dos xeneradores senoidales desfasaos.</figcaption></figure> <p>Nel circuitu de la derecha, un condensador de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {1\,\mu F}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mi>μ</mi> <mi>F</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {1\,\mu F}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/292559e5c45f5ad3601ec4ce4698fb5713517c95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.431ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {1\,\mu F}}" /></span> y una resistencia de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {3\,k\Omega }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mspace width="thinmathspace"></mspace> <mi>k</mi> <mi mathvariant="normal">Ω</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {3\,k\Omega }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f0a63fcdf541970c133a6ca720e48bc576ce7f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.252ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {3\,k\Omega }}" /></span> en serie, tán coneutaos ente dos xeneradores sinusoidales. Tomamos como xeneradores dos fases del suministru <a href="/wiki/Sistema_trif%C3%A1sicu" title="Sistema trifásicu">trifásicu</a>. El xenerador d'esquierda va ser el nuesu xenerador de referencia <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{1}=230{\sqrt {2}}\cos(314\,t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>230</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>314</mn> <mspace width="thinmathspace"></mspace> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{1}=230{\sqrt {2}}\cos(314\,t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7541454c5d233a5675c05822fae337bb9e53e437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.038ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {V_{1}=230{\sqrt {2}}\cos(314\,t)}}" /></span>. El xenerador de derecha ta en meyora de fase de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {2\pi /3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {2\pi /3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1aa54784d3fa7f848d16593b35a0fa04f71523d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.408ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {2\pi /3}}" /></span>. Esto ye, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{2}=230{\sqrt {2}}\cos(314\,t+{2\pi \over 3})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>230</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>314</mn> <mspace width="thinmathspace"></mspace> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{2}=230{\sqrt {2}}\cos(314\,t+{2\pi \over 3})}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26c6c923fd1fce08d143657dd306881b0773ba9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.585ex; height:3.176ex;" alt="{\displaystyle \scriptstyle {V_{2}=230{\sqrt {2}}\cos(314\,t+{2\pi \over 3})}}" /></span>. Col formalismu de impedancias, el xenerador d'esquierda va ser <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{1}=230\,V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>230</mn> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{1}=230\,V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e317577f3e547e6fef5170c6ba9e044f37da0c2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.133ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {V_{1}=230\,V_{\mathrm {ef} }}}" /></span> y el de derecha <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{2}=230\,y^{j{2\pi \over 3}}\,V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>230</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mrow> </msup> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{2}=230\,y^{j{2\pi \over 3}}\,V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d89ff53e847546b518985f1b8c4a83c8886fa89d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.323ex; height:3.843ex;" alt="{\displaystyle \scriptstyle {V_{2}=230\,y^{j{2\pi \over 3}}\,V_{\mathrm {ef} }}}" /></span>. Empecemos calculando la diferencia de tensión ente los dos xeneradores: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{12}=230\,\left(1-y^{j{2\pi \over 3}}\right)=230\,\left(1-\cos \left(\textstyle {2\pi \over 3}\right)-j\sin \left(\textstyle {2\pi \over 3}\right)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mo>=</mo> <mn>230</mn> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>230</mn> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> <mo>)</mo> </mrow> <mo>−</mo> <mi>j</mi> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{12}=230\,\left(1-y^{j{2\pi \over 3}}\right)=230\,\left(1-\cos \left(\textstyle {2\pi \over 3}\right)-j\sin \left(\textstyle {2\pi \over 3}\right)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0a2fe2c8a8a855c0a4ddb1ba5a1de907295110b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:57.395ex; height:6.176ex;" alt="{\displaystyle V_{12}=230\,\left(1-y^{j{2\pi \over 3}}\right)=230\,\left(1-\cos \left(\textstyle {2\pi \over 3}\right)-j\sin \left(\textstyle {2\pi \over 3}\right)\right)}" /></span> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =230\,(1{,}5-j0{,}866)=345-j199{,}19\,V_{\mathrm {ef} }=398{,}37y^{-j0{,}5774}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>230</mn> <mspace width="thinmathspace"></mspace> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>5</mn> <mo>−</mo> <mi>j</mi> <mn>0,866</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>345</mn> <mo>−</mo> <mi>j</mi> <mn>199</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>19</mn> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>398</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>37</mn> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>0,577</mn> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =230\,(1{,}5-j0{,}866)=345-j199{,}19\,V_{\mathrm {ef} }=398{,}37y^{-j0{,}5774}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2efdcd45a01cffe7fc5303e635a45ce7c677f477" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:57.837ex; height:3.176ex;" alt="{\displaystyle =230\,(1{,}5-j0{,}866)=345-j199{,}19\,V_{\mathrm {ef} }=398{,}37y^{-j0{,}5774}}" /></span></dd></dl></dd></dl> <p>El módulu d'esta tensión ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {398{,}37V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mn>398</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>37</mn> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {398{,}37V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94a27f2816296ec31b9e09917ea4f74a0b3137b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.779ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {398{,}37V_{\mathrm {ef} }}}" /></span> y ta retardada de 0,5774 radianes (30°) con al respective de la tensión de referencia. </p> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Ficheru:DiagFresnel2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/8f/DiagFresnel2.png" decoding="async" width="216" height="214" class="mw-file-element" data-file-width="216" data-file-height="214" /></a><figcaption>Diagrama de Fresnel correspondiente al segundu exemplu. El primer círculu sirve de guía a les tensiones de los dos xeneradores. El segundu pal ángulu rectu ente la tensión del condensador y la de la resistencia.</figcaption></figure> <p>La corriente que circula ye: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=\textstyle {{V_{12} \over R+\scriptstyle {1 \over j\omega C}}={398{,}37\,y^{-j0{,}5236} \over {3000-j3185}}={398{,}37\,y^{-j0{,}5236} \over 4375{,}41\,y^{-j0{,}8153}}=0{,}0910\,y^{j0{,}2917}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mrow> <mi>R</mi> <mo>+</mo> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>398</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>37</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>0,523</mn> <mn>6</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3000</mn> <mo>−</mo> <mi>j</mi> <mn>3185</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>398</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>37</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>0,523</mn> <mn>6</mn> </mrow> </msup> </mrow> <mrow> <mn>4375</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>41</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>0,815</mn> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0,091</mn> <mn>0</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>0,291</mn> <mn>7</mn> </mrow> </msup> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=\textstyle {{V_{12} \over R+\scriptstyle {1 \over j\omega C}}={398{,}37\,y^{-j0{,}5236} \over {3000-j3185}}={398{,}37\,y^{-j0{,}5236} \over 4375{,}41\,y^{-j0{,}8153}}=0{,}0910\,y^{j0{,}2917}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4669d8a8b9b677e13564ecff6c190a9d76a7a2b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:58.606ex; height:6.343ex;" alt="{\displaystyle I=\textstyle {{V_{12} \over R+\scriptstyle {1 \over j\omega C}}={398{,}37\,y^{-j0{,}5236} \over {3000-j3185}}={398{,}37\,y^{-j0{,}5236} \over 4375{,}41\,y^{-j0{,}8153}}=0{,}0910\,y^{j0{,}2917}}}" /></span></dd></dl> <p>Como los valores de tensión utilizaos pa los xeneradores yeren valores eficaces, la corriente calculada tamién vien como valor eficaz: 91 mA en meyora de fase 16,71° con al respective de la tensión de referencia. </p><p>La tensión ente los estremos de la resistencia ye <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{R}=R\,I=3000\cdot 0{,}0910\,y^{j0{,}2917}=273\,y^{j0{,}2917}V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> <mo>=</mo> <mi>R</mi> <mspace width="thinmathspace"></mspace> <mi>I</mi> <mo>=</mo> <mn>3000</mn> <mo>⋅</mo> <mn>0,091</mn> <mn>0</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>0,291</mn> <mn>7</mn> </mrow> </msup> <mo>=</mo> <mn>273</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>0,291</mn> <mn>7</mn> </mrow> </msup> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{R}=R\,I=3000\cdot 0{,}0910\,y^{j0{,}2917}=273\,y^{j0{,}2917}V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b03b9e69bc08f3d00d7138b4526a60104e6ab05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.684ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {V_{R}=R\,I=3000\cdot 0{,}0910\,y^{j0{,}2917}=273\,y^{j0{,}2917}V_{\mathrm {ef} }}}" /></span> </p><p>La tensión ente los estremos del condensador ye:<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {V_{C}=Z_{C}\,I=-j3185\cdot 0{,}0910\,y^{j0{,}2917}=3185\,y^{-j{\pi \over 2}}0{,}0910\,y^{j0{,}2917}=289{,}83\,y^{-j1{,}2791}V_{\mathrm {ef} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mi>I</mi> <mo>=</mo> <mo>−</mo> <mi>j</mi> <mn>3185</mn> <mo>⋅</mo> <mn>0,091</mn> <mn>0</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>0,291</mn> <mn>7</mn> </mrow> </msup> <mo>=</mo> <mn>3185</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> <mn>0,091</mn> <mn>0</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>0,291</mn> <mn>7</mn> </mrow> </msup> <mo>=</mo> <mn>289</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>83</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>1,279</mn> <mn>1</mn> </mrow> </msup> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {V_{C}=Z_{C}\,I=-j3185\cdot 0{,}0910\,y^{j0{,}2917}=3185\,y^{-j{\pi \over 2}}0{,}0910\,y^{j0{,}2917}=289{,}83\,y^{-j1{,}2791}V_{\mathrm {ef} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b47c7870b33234a82378cd32336ad8cd1ed6f10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:58.159ex; height:3.509ex;" alt="{\displaystyle \scriptstyle {V_{C}=Z_{C}\,I=-j3185\cdot 0{,}0910\,y^{j0{,}2917}=3185\,y^{-j{\pi \over 2}}0{,}0910\,y^{j0{,}2917}=289{,}83\,y^{-j1{,}2791}V_{\mathrm {ef} }}}" /></span>. </p><p>La tensión ente les estremidaes del condensador ta en retardo de 73,3° con al respective de la tensión de referencia. Como nel exemplu precedente, la suma de los módulos de les tensiones (les que se midiríen con un voltímetru) de la resistencia y del condensador (563 V) ye más grande que la tensión total aplicada (398 V). La tensión nel puntu A del circuitu va ser: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{A}=V_{1}-V_{C}=230-289{,}83\,y^{-j1{,}2791}=230-(83,35-j277{,}6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>230</mn> <mo>−</mo> <mn>289</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>83</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>j</mi> <mn>1,279</mn> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>230</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mn>83</mn> <mo>,</mo> <mn>35</mn> <mo>−</mo> <mi>j</mi> <mn>277</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{A}=V_{1}-V_{C}=230-289{,}83\,y^{-j1{,}2791}=230-(83,35-j277{,}6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25ad2b93392f2635530952e24ac8cb71b1993a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:64.208ex; height:3.176ex;" alt="{\displaystyle V_{A}=V_{1}-V_{C}=230-289{,}83\,y^{-j1{,}2791}=230-(83,35-j277{,}6)}" /></span> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =146.65+j277{,}6=314\,y^{j1{,}085}\,V_{\mathrm {ef} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>146.65</mn> <mo>+</mo> <mi>j</mi> <mn>277</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>6</mn> <mo>=</mo> <mn>314</mn> <mspace width="thinmathspace"></mspace> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mn>1,085</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =146.65+j277{,}6=314\,y^{j1{,}085}\,V_{\mathrm {ef} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2313f3d3e100602859bd6ebf04777e5e5bd7eb4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:34.112ex; height:3.009ex;" alt="{\displaystyle =146.65+j277{,}6=314\,y^{j1{,}085}\,V_{\mathrm {ef} }}" /></span></dd></dl></dd></dl> <p>La tensión del puntu A ye más grande que la de cada xenerador. </p> <div class="mw-heading mw-heading2"><h2 id="Ver_tamién"><span id="Ver_tami.C3.A9n"></span>Ver tamién</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=18" title="Editar seición: Ver tamién" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=18" title="Editar el código fuente de la sección: Ver tamién"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Conductancia&action=edit&redlink=1" class="new" title="Conductancia (la páxina nun esiste)">Conductancia</a></li> <li><a href="/wiki/Conductor_ll%C3%A9tricu" title="Conductor llétricu">Conductor llétricu</a></li> <li><a href="/wiki/Conductivid%C3%A1_ll%C3%A9trica" title="Conductividá llétrica">Conductividá llétrica</a></li> <li><a href="/wiki/Resistencia_ll%C3%A9trica" title="Resistencia llétrica">Resistencia llétrica</a></li> <li><a href="/w/index.php?title=Resonancia_ll%C3%A9trica&action=edit&redlink=1" class="new" title="Resonancia llétrica (la páxina nun esiste)">Resonancia llétrica</a></li> <li><a href="/wiki/Superconductivid%C3%A1" title="Superconductividá">Superconductividá</a></li> <li><a href="/w/index.php?title=Impedancia_mec%C3%A1nica_en_cimentaciones_fondes&action=edit&redlink=1" class="new" title="Impedancia mecánica en cimentaciones fondes (la páxina nun esiste)">Impedancia mecánica en cimentaciones fondes</a></li> <li><a href="/wiki/N%C3%BAmberu_complexu" title="Númberu complexu">Númberu complexu</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Bibliografía"><span id="Bibliograf.C3.ADa"></span>Bibliografía</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedancia&veaction=edit&section=19" title="Editar seición: Bibliografía" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedancia&action=edit&section=19" title="Editar el código fuente de la sección: Bibliografía"><span>editar la fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite style="font-style:normal"> (1987) «Volume 5»,  GRUPU EDITORIAL OCÉANU: <i>Gran Enciclopedia de la Ciencia y la Téunica</i>. Barcelona:Ediciones Océano-Ésitu S.A.. <a href="/wiki/Especial:FuentesDeLibros/8470694529" class="internal mw-magiclink-isbn">ISBN 84-7069-452-9</a>.</cite></li></ul> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r2260362">.mw-parser-output .mw-authority-control .navbox hr:last-child{display:none}.mw-parser-output .mw-authority-control .navbox+.mw-mf-linked-projects{display:none}.mw-parser-output .mw-authority-control .mw-mf-linked-projects{display:flex;padding:0.5em;border:1px solid #c8ccd1;background-color:#eaecf0;color:#222222}.mw-parser-output .mw-authority-control .mw-mf-linked-projects ul li{margin-bottom:0}</style><div class="mw-authority-control navigation-not-searchable"><div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r4075543">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style></div><div role="navigation" class="navbox" aria-labelledby="Control_d&#039;autoridaes1824" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Control_d&#039;autoridaes1824" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Ayuda:Control_d%27autoridaes" title="Ayuda:Control d'autoridaes">Control d'autoridaes</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b>Proyeutos Wikimedia</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datos:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q179043" class="extiw" title="wikidata:Q179043">Q179043</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, 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style="white-space:nowrap;"><a href="/wiki/National_Diet_Library" class="mw-redirect" title="National Diet Library">NDL</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00564146">00564146</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Art_%26_Architecture_Thesaurus" title="Art & Architecture Thesaurus">AAT</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://vocab.getty.edu/page/aat/300390517">300390517</a></span></li> <li><b>Diccionarios y enciclopedies</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Enciclopedia_Brit%C3%A1nica" class="mw-redirect" title="Enciclopedia Británica">Britannica</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/electrical-impedance">url</a></span></li> <li><b>Identificadores médicos</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Medical_Subject_Headings" title="Medical Subject Headings">MeSH</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://meshb.nlm.nih.gov/record/ui?ui=D017097">D017097</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datos:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q179043" class="extiw" title="wikidata:Q179043">Q179043</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Electrical_impedance">Electrical impedance</a></span></span></li></ul> </div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div 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Impedancia - Wikipedia