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vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Indice</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">nascondi</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inizio</div> </a> </li> <li id="toc-Circuiti_in_serie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Circuiti_in_serie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Circuiti in serie</span> </div> </a> <button aria-controls="toc-Circuiti_in_serie-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>Attiva/disattiva la sottosezione Circuiti in serie</span> </button> <ul id="toc-Circuiti_in_serie-sublist" class="vector-toc-list"> <li id="toc-Resistori_in_serie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resistori_in_serie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Resistori in serie</span> </div> </a> <ul id="toc-Resistori_in_serie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Condensatori_in_serie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Condensatori_in_serie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Condensatori in serie</span> </div> </a> <ul id="toc-Condensatori_in_serie-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Circuiti_in_parallelo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Circuiti_in_parallelo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Circuiti in parallelo</span> </div> </a> <button aria-controls="toc-Circuiti_in_parallelo-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>Attiva/disattiva la sottosezione Circuiti in parallelo</span> </button> <ul id="toc-Circuiti_in_parallelo-sublist" class="vector-toc-list"> <li id="toc-Resistori_in_parallelo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resistori_in_parallelo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Resistori in parallelo</span> </div> </a> <ul id="toc-Resistori_in_parallelo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Condensatori_in_parallelo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Condensatori_in_parallelo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Condensatori in parallelo</span> </div> </a> <ul id="toc-Condensatori_in_parallelo-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-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="Indice" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Circuiti in serie e in parallelo</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="Vai a una voce in un'altra lingua. Disponibile in 30 lingue" > <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-30" 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">30 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D8%B1%D8%A9_%D8%A7%D9%84%D8%AA%D9%88%D8%A7%D9%84%D9%8A_%D8%A3%D9%88_%D8%A7%D9%84%D8%AA%D9%88%D8%A7%D8%B2%D9%8A" title="دارة التوالي أو التوازي - arabo" lang="ar" hreflang="ar" data-title="دارة التوالي أو التوازي" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D0%BD%D0%B8_%D0%B8_%D1%83%D1%81%D0%BF%D0%BE%D1%80%D0%B5%D0%B4%D0%BD%D0%B8_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8_%D0%B2%D0%B5%D1%80%D0%B8%D0%B3%D0%B8" title="Последователни и успоредни електрически вериги - bulgaro" lang="bg" hreflang="bg" data-title="Последователни и успоредни електрически вериги" data-language-autonym="Български" data-language-local-name="bulgaro" 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%AE%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%B0%E0%A6%BE%E0%A6%B2_%E0%A6%93_%E0%A6%B6%E0%A7%8D%E0%A6%B0%E0%A7%87%E0%A6%A3%E0%A6%BF_%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%A4%E0%A6%A8%E0%A7%80" title="সমান্তরাল ও শ্রেণি বর্তনী - bengalese" lang="bn" hreflang="bn" data-title="সমান্তরাল ও শ্রেণি বর্তনী" data-language-autonym="বাংলা" data-language-local-name="bengalese" 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/Serijska_i_paralelna_mre%C5%BEa" title="Serijska i paralelna mreža - bosniaco" lang="bs" hreflang="bs" data-title="Serijska i paralelna mreža" data-language-autonym="Bosanski" data-language-local-name="bosniaco" 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/Circuits_en_s%C3%A8rie_i_circuits_en_paral%C2%B7lel" title="Circuits en sèrie i circuits en paral·lel - catalano" lang="ca" hreflang="ca" data-title="Circuits en sèrie i circuits en paral·lel" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A3%D0%BC%D0%BB%C4%83%D0%BD-%D1%85%D1%8B%C3%A7%D0%BB%C4%83%D0%BD_%D1%82%D0%B0%D1%82%D0%B0_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%BB%D0%B5%D0%BB%D0%BB%C4%95_%C3%A7%D1%8B%D1%85%C4%83%D0%BD%D1%82%D0%B0%D1%80%D0%B0%D1%81%D1%81%D0%B8" title="Умлăн-хыçлăн тата параллеллĕ çыхăнтарасси - ciuvascio" lang="cv" hreflang="cv" data-title="Умлăн-хыçлăн тата параллеллĕ çыхăнтарасси" data-language-autonym="Чӑвашла" data-language-local-name="ciuvascio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Series_and_parallel_circuits" title="Series and parallel circuits - inglese" lang="en" hreflang="en" data-title="Series and parallel circuits" data-language-autonym="English" data-language-local-name="inglese" 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/Seria_kaj_paralela_cirkvitoj" title="Seria kaj paralela cirkvitoj - esperanto" lang="eo" hreflang="eo" data-title="Seria kaj paralela cirkvitoj" 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/Circuitos_en_serie_y_en_paralelo" title="Circuitos en serie y en paralelo - spagnolo" lang="es" hreflang="es" data-title="Circuitos en serie y en paralelo" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D8%A7%D8%B1%D9%87%D8%A7%DB%8C_%D8%B3%D8%B1%DB%8C_%D9%88_%D9%85%D9%88%D8%A7%D8%B2%DB%8C" title="مدارهای سری و موازی - persiano" lang="fa" hreflang="fa" data-title="مدارهای سری و موازی" data-language-autonym="فارسی" data-language-local-name="persiano" 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/Sarjaan-_ja_rinnankytkent%C3%A4" title="Sarjaan- ja rinnankytkentä - finlandese" lang="fi" hreflang="fi" data-title="Sarjaan- ja rinnankytkentä" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%99%D7%91%D7%95%D7%A8_%D7%91%D7%98%D7%95%D7%A8_%D7%95%D7%91%D7%9E%D7%A7%D7%91%D7%99%D7%9C" title="חיבור בטור ובמקביל - ebraico" lang="he" hreflang="he" data-title="חיבור בטור ובמקביל" data-language-autonym="עברית" data-language-local-name="ebraico" 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%B6%E0%A5%8D%E0%A4%B0%E0%A5%87%E0%A4%A3%E0%A5%80_%E0%A4%94%E0%A4%B0_%E0%A4%B8%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A4%B0_%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%AA%E0%A4%A5" title="श्रेणी और समानांतर परिपथ - hindi" lang="hi" hreflang="hi" data-title="श्रेणी और समानांतर परिपथ" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%BB%D5%B8%D6%80%D5%A4%D5%A1%D5%AF%D5%A1%D5%B6_%D6%87_%D5%A6%D5%B8%D6%82%D5%A3%D5%A1%D5%B0%D5%A5%D5%BC_%D5%B4%D5%AB%D5%A1%D6%81%D5%B8%D6%82%D5%B4%D5%B6%D5%A5%D6%80" title="Հաջորդական և զուգահեռ միացումներ - armeno" lang="hy" hreflang="hy" data-title="Հաջորդական և զուգահեռ միացումներ" data-language-autonym="Հայերեն" data-language-local-name="armeno" 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/Rangkaian_seri_dan_paralel" title="Rangkaian seri dan paralel - indonesiano" lang="id" hreflang="id" data-title="Rangkaian seri dan paralel" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%9B%B4%E5%88%97%E5%9B%9E%E8%B7%AF%E3%81%A8%E4%B8%A6%E5%88%97%E5%9B%9E%E8%B7%AF" title="直列回路と並列回路 - giapponese" lang="ja" hreflang="ja" data-title="直列回路と並列回路" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%98%E1%83%9B%E1%83%93%E1%83%94%E1%83%95%E1%83%A0%E1%83%9D%E1%83%91%E1%83%98%E1%83%97%E1%83%98_%E1%83%93%E1%83%90_%E1%83%9E%E1%83%90%E1%83%A0%E1%83%90%E1%83%9A%E1%83%94%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%AC%E1%83%A0%E1%83%94%E1%83%93%E1%83%94%E1%83%91%E1%83%98" title="მიმდევრობითი და პარალელური წრედები - georgiano" lang="ka" hreflang="ka" data-title="მიმდევრობითი და პარალელური წრედები" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D3%A8%D1%82%D0%BA%D1%96%D0%B7%D0%B3%D1%96%D1%88%D1%82%D0%B5%D1%80%D0%B4%D1%96_%D1%82%D1%96%D0%B7%D0%B1%D0%B5%D0%BA%D1%82%D0%B5%D0%B9_%D0%B6%D3%99%D0%BD%D0%B5_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%BB%D0%B5%D0%BB%D1%8C_%D0%B6%D0%B0%D0%BB%D2%93%D0%B0%D1%83" title="Өткізгіштерді тізбектей және параллель жалғау - kazako" lang="kk" hreflang="kk" data-title="Өткізгіштерді тізбектей және параллель жалғау" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Circuit_in_serie_e_in_parallel" title="Circuit in serie e in parallel - lombardo" lang="lmo" hreflang="lmo" data-title="Circuit in serie e in parallel" data-language-autonym="Lombard" data-language-local-name="lombardo" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Virknes_un_paral%C4%93lais_sl%C4%93gums" title="Virknes un paralēlais slēgums - lettone" lang="lv" hreflang="lv" data-title="Virknes un paralēlais slēgums" data-language-autonym="Latviešu" data-language-local-name="lettone" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D0%B8_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%BB%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%81%D0%BE%D0%B5%D0%B4%D0%B8%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5" title="Последовательное и параллельное соединение - russo" lang="ru" hreflang="ru" data-title="Последовательное и параллельное соединение" data-language-autonym="Русский" data-language-local-name="russo" 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/Redna_i_uporedna_kola" title="Redna i uporedna kola - serbo-croato" lang="sh" hreflang="sh" data-title="Redna i uporedna kola" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Series_and_parallel_circuits" title="Series and parallel circuits - Simple English" lang="en-simple" hreflang="en-simple" data-title="Series and parallel circuits" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Serijska_i_paralelna_kola" title="Serijska i paralelna kola - serbo" lang="sr" hreflang="sr" data-title="Serijska i paralelna kola" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a 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vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</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="it" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Series_and_parallel_circuits2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Series_and_parallel_circuits2.svg/350px-Series_and_parallel_circuits2.svg.png" decoding="async" width="350" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Series_and_parallel_circuits2.svg/525px-Series_and_parallel_circuits2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Series_and_parallel_circuits2.svg/700px-Series_and_parallel_circuits2.svg.png 2x" data-file-width="497" data-file-height="190" /></a><figcaption>Circuiti serie (sinistra) e parallelo (destra) con due <a href="/wiki/Resistore" title="Resistore">resistori</a> e misuratori di <a href="/wiki/Tensione_elettrica" title="Tensione elettrica">tensione</a> e <a href="/wiki/Corrente_elettrica" title="Corrente elettrica">corrente</a>.</figcaption></figure> <p>I <b>circuiti in serie e in parallelo</b> indicano <a href="/wiki/Componente_elettrico" title="Componente elettrico">componenti elettrici</a> in un <a href="/wiki/Circuito_elettrico" title="Circuito elettrico">circuito elettrico</a> (ad esempio <a href="/wiki/Resistore" title="Resistore">resistori</a>, <a href="/wiki/Condensatore_(elettrotecnica)" title="Condensatore (elettrotecnica)">condensatori</a>, <a href="/wiki/Induttore" title="Induttore">induttori</a> e <a href="/wiki/Generatore_di_tensione" title="Generatore di tensione">generatori di tensione</a>) che possono essere collegati fra loro in serie oppure in parallelo per mezzo di <a href="/wiki/Conduttore_elettrico" title="Conduttore elettrico">conduttori elettrici</a> (ad esempio fili <a href="/wiki/Metallo" title="Metallo">metallici</a>) che <a href="/wiki/Trasferimento_di_elettroni" title="Trasferimento di elettroni">trasportano</a> al loro interno gli <a href="/wiki/Elettrone" title="Elettrone">elettroni</a> per il funzionamento dei circuiti. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Circuiti_in_serie">Circuiti in serie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=1" title="Modifica la sezione Circuiti in serie" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=1" title="Edit section's source code: Circuiti in serie"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si parla di <b>collegamento in serie</b> quando due o più componenti sono collegati in modo da essere attraversati da una <a href="/wiki/Corrente_elettrica" title="Corrente elettrica">corrente elettrica</a> di uguale intensità; nel caso di componenti elettrici a due terminali (detti <a href="/wiki/Bipoli" class="mw-redirect" title="Bipoli">bipoli</a>) il collegamento in serie prevede che l'estremità di ciascuno di essi sia collegata solo con l'estremità di un altro, come se fossero persone che si prendono per mano a formare una catena. L'alimentazione viene fornita tramite i morsetti liberi del primo e dell'ultimo bipolo. </p> <div class="mw-heading mw-heading3"><h3 id="Resistori_in_serie">Resistori in serie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=2" title="Modifica la sezione Resistori in serie" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=2" title="Edit section's source code: Resistori in serie"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Conoscendo il valore della resistenza (in <a href="/wiki/Ohm" title="Ohm">ohm</a>) e l'intensità della corrente elettrica (in <a href="/wiki/Ampere" title="Ampere">ampere</a>) è possibile determinare la tensione elettrica (in <a href="/wiki/Volt" title="Volt">volt</a>) su una resistenza con la <a href="/wiki/Legge_di_Ohm" title="Legge di Ohm">legge di Ohm</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> (valida sia in corrente continua sia in corrente alternata). </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=RI}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mi>R</mi> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=RI}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fcad83d0a39502adfd06625bd34b1136c30b32e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.821ex; height:2.176ex;" alt="{\displaystyle V=RI}"></span></dd></dl> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Resistors_in_series.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Resistors_in_series.svg/390px-Resistors_in_series.svg.png" decoding="async" width="390" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Resistors_in_series.svg/585px-Resistors_in_series.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Resistors_in_series.svg/780px-Resistors_in_series.svg.png 2x" data-file-width="390" data-file-height="106" /></a></span> </p><p>Conoscendo la <a href="/wiki/Tensione_elettrica" title="Tensione elettrica">tensione elettrica</a> <i>V</i> ai capi del resistore e il valore della sua resistenza <i>R</i>, è possibile calcolare l'intensità della corrente elettrica <i>I</i> che circola utilizzando la formula inversa: </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=RI\implies I={\frac {V}{R}}\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mi>R</mi> <mi>I</mi> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>R</mi> </mfrac> </mrow> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=RI\implies I={\frac {V}{R}}\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9592fb05cbfd247f47f00d2d1d75e9b4950a327" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.746ex; height:5.343ex;" alt="{\displaystyle V=RI\implies I={\frac {V}{R}}\;}"></span></dd></dl> <p>Le resistenze in serie sono attraversate tutte dalla stessa corrente quindi si ha: </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 V_{\text{tot}}=V_{1}+V_{2}+\cdots +V_{n}=R_{1}I+R_{2}I+\cdots +R_{n}I=(R_{1}+R_{2}+\cdots +R_{n})I=R_{\text{equivalente}}I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>tot</mtext> </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"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>I</mi> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>I</mi> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mi>I</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>I</mi> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>equivalente</mtext> </mrow> </msub> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{tot}}=V_{1}+V_{2}+\cdots +V_{n}=R_{1}I+R_{2}I+\cdots +R_{n}I=(R_{1}+R_{2}+\cdots +R_{n})I=R_{\text{equivalente}}I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b42ce8600f0f48b3e6c1ba86d8a513d92a7cf85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:92.241ex; height:3.009ex;" alt="{\displaystyle V_{\text{tot}}=V_{1}+V_{2}+\cdots +V_{n}=R_{1}I+R_{2}I+\cdots +R_{n}I=(R_{1}+R_{2}+\cdots +R_{n})I=R_{\text{equivalente}}I}"></span> </p><p>La resistenza totale di <i>n</i> resistori in serie è data dalla somma delle resistenze di ciascun resistore:<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </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 {R_{\mathrm {equivalente} }}=R_{1}+R_{2}+\cdots +R_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {R_{\mathrm {equivalente} }}=R_{1}+R_{2}+\cdots +R_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd02f73cd2714dfeb4274f9740c5463eba7d36fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:33.1ex; height:2.843ex;" alt="{\displaystyle {R_{\mathrm {equivalente} }}=R_{1}+R_{2}+\cdots +R_{n}}"></span></dd></dl> <p>Il collegamento in serie di resistori a volte si adotta per necessità. Un tipico esempio è il circuito che genera l'alta tensione nei vecchi <a href="/wiki/Oscilloscopio" title="Oscilloscopio">oscilloscopi</a> a <a href="/wiki/Tubo_catodico" class="mw-redirect" title="Tubo catodico">tubo catodico</a>; Un resistore da 50 Megaohm avente ai suoi capi una tensione di 2000 volt, va incontro a conseguenze distruttive nel caso si verifichi un <a href="/wiki/Arco_voltaico" class="mw-redirect" title="Arco voltaico">arco voltaico</a>; per prevenire questo rischio, il costruttore realizza il resistore da 50 Megaohm collegando in serie 5 resistori da 10 Megaohm, conseguentemente ciascun resistore vede ai suoi capi una tensione di 400 volt, un valore di tutta sicurezza. </p> <div class="mw-heading mw-heading3"><h3 id="Condensatori_in_serie">Condensatori in serie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=3" title="Modifica la sezione Condensatori in serie" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=3" title="Edit section's source code: Condensatori in serie"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Capacitors_in_series.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Capacitors_in_series.svg/937px-Capacitors_in_series.svg.png" decoding="async" width="937" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Capacitors_in_series.svg/1406px-Capacitors_in_series.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Capacitors_in_series.svg/1874px-Capacitors_in_series.svg.png 2x" data-file-width="937" data-file-height="208" /></a></span> </p><p>La capacità totale di <i>n</i> condensatori in serie è data dalla seguente relazione: </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 {\frac {1}{C_{\mathrm {totale} }}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</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>C</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>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{C_{\mathrm {totale} }}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49a0da9199426244cb7dd9796cbf330b1b626926" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.005ex; height:5.676ex;" alt="{\displaystyle {\frac {1}{C_{\mathrm {totale} }}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}}"></span></dd></dl> <p>La tensione di funzionamento di una serie di condensatori è data dalla somma delle singole tensioni di funzionamento. </p><p>All'interno di ogni condensatore le cariche positive si raggruppano su una armatura in modo uguale alle cariche negative su quella opposta; poiché ogni armatura "positiva" di un condensatore è collegata a quella "negativa" del vicino, la quantità di carica positiva su un'armatura dovrà essere uguale alla carica negativa di quella collegata, il che fa sì che su tutti i condensatori sia presente la stessa quantità di carica <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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span>. </p><p>Di conseguenza la tensione elettrica ai capi di ciascun elemento è diversa: </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_{i}={\frac {Q}{C_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{i}={\frac {Q}{C_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7f5c0adc220119b0d0243058efe8f1cf7289ac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.551ex; height:5.843ex;" alt="{\displaystyle V_{i}={\frac {Q}{C_{i}}}}"></span></dd></dl> <p>Ne discende che il condensatore di capacità più piccola deve sopportare la tensione più grande. </p> <div class="mw-heading mw-heading2"><h2 id="Circuiti_in_parallelo">Circuiti in parallelo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=4" title="Modifica la sezione Circuiti in parallelo" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=4" title="Edit section's source code: Circuiti in parallelo"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si parla di <b>collegamento in parallelo</b> quando i componenti sono collegati ad una coppia di conduttori in modo che la <a href="/wiki/Tensione_elettrica" title="Tensione elettrica">tensione elettrica</a> sia applicata a tutti quanti allo stesso modo. Riprendendo l'esempio delle persone, queste sono disposte fra due corde distese e parallele, ed ogni persona stringe ciascuna corda con una mano in modo che ognuno tenga con la mano destra la stessa corda che tutti gli altri tengono con la mano destra, e lo stesso per la mano sinistra. Inoltre gli utilizzatori sono paralleli l'uno all'altro e svolgono funzione indipendente: se uno non funziona gli altri funzionano. </p> <div class="mw-heading mw-heading3"><h3 id="Resistori_in_parallelo">Resistori in parallelo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=5" title="Modifica la sezione Resistori in parallelo" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=5" title="Edit section's source code: Resistori in parallelo"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Resistors_in_parallel.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Resistors_in_parallel.svg/301px-Resistors_in_parallel.svg.png" decoding="async" width="301" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Resistors_in_parallel.svg/452px-Resistors_in_parallel.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/09/Resistors_in_parallel.svg/602px-Resistors_in_parallel.svg.png 2x" data-file-width="301" data-file-height="177" /></a></span> </p><p>La resistenza totale di n resistori in parallelo è data dalla relazione: </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 {R_{\mathrm {totale} }}={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>R</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>R</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>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {R_{\mathrm {totale} }}={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d68caa02ae1e89b41efbb10387ca85ca07bc1714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:30.164ex; height:7.009ex;" alt="{\displaystyle {R_{\mathrm {totale} }}={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}}}}"></span></dd></dl> <p>ovvero è il reciproco della somma dei reciproci delle resistenze dei singoli resistori </p><p>Poiché alle resistenze in parallelo viene applicata la stessa tensione, si ha: </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 I_{\text{tot}}=I_{1}+I_{2}+\cdots +I_{n}={\frac {V}{R_{1}}}+{\frac {V}{R_{2}}}+\cdots +{\frac {V}{R_{n}}}=V\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}\right)={\frac {V}{R_{\text{equivalente}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>tot</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <msub> <mi>R</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> <mi>V</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>V</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>R</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>R</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>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>equivalente</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\text{tot}}=I_{1}+I_{2}+\cdots +I_{n}={\frac {V}{R_{1}}}+{\frac {V}{R_{2}}}+\cdots +{\frac {V}{R_{n}}}=V\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}\right)={\frac {V}{R_{\text{equivalente}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66d8c32f27a2b3ea3ebcf0690041df91cc99e7b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:94.693ex; height:6.176ex;" alt="{\displaystyle I_{\text{tot}}=I_{1}+I_{2}+\cdots +I_{n}={\frac {V}{R_{1}}}+{\frac {V}{R_{2}}}+\cdots +{\frac {V}{R_{n}}}=V\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}\right)={\frac {V}{R_{\text{equivalente}}}}}"></span> </p><p>La formula sopra citata si semplifica nel caso di due soli resistori. In questo caso si avrà: </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 {R_{\mathrm {equivalente} }}={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}}}={\frac {1}{\frac {R_{1}+R_{2}}{R_{1}R_{2}}}}\implies R_{\mathrm {equivalente} }={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>R</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>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mfrac> <mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mfrac> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹</mo> <mspace width="thickmathspace" /> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">v</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {R_{\mathrm {equivalente} }}={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}}}={\frac {1}{\frac {R_{1}+R_{2}}{R_{1}R_{2}}}}\implies R_{\mathrm {equivalente} }={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62ec6eaeffc892c0ce1a826edafddcff6489904f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:61.886ex; height:7.509ex;" alt="{\displaystyle {R_{\mathrm {equivalente} }}={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}}}={\frac {1}{\frac {R_{1}+R_{2}}{R_{1}R_{2}}}}\implies R_{\mathrm {equivalente} }={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Condensatori_in_parallelo">Condensatori in parallelo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=6" title="Modifica la sezione Condensatori in parallelo" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=6" title="Edit section's source code: Condensatori in parallelo"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Capacitors_in_parallel.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Capacitors_in_parallel.svg/512px-Capacitors_in_parallel.svg.png" decoding="async" width="512" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Capacitors_in_parallel.svg/768px-Capacitors_in_parallel.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Capacitors_in_parallel.svg/1024px-Capacitors_in_parallel.svg.png 2x" data-file-width="512" data-file-height="241" /></a></span> </p><p>La capacità totale di n condensatori in parallelo è in questo caso la somma delle singole capacità:<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </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 C_{\mathrm {totale} }=C_{1}+C_{2}+\cdots +C_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {totale} }=C_{1}+C_{2}+\cdots +C_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09dade773624b754a2f49ee31d196c45c654756d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:28.66ex; height:2.509ex;" alt="{\displaystyle C_{\mathrm {totale} }=C_{1}+C_{2}+\cdots +C_{n}}"></span></dd></dl> <p>Un esempio di condensatori collegati in parallelo si può trovare negli <a href="/wiki/Alimentatore_elettrico" title="Alimentatore elettrico">alimentatori</a> per computer e negli apparecchi Hi-Fi; se necessita una capacità di 20.000 microfarad, è più conveniente impiegare 5 condensatori da 4000 microfarad piuttosto di uno solo da 20.000. Una soluzione analoga si può verificare con i resistori; se in un circuito occorre dissipare in calore 100 watt tramite un resistore da 50 ohm, a volte risulta più conveniente impiegare due resistori da 100 ohm - 50 watt, collegati in parallelo. </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=7" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=7" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFTurchetti">Turchetti</a>, p. 221</cite>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFTurchetti">Turchetti</a>, p. 223</cite>.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFTurchetti">Turchetti</a>, p. 227</cite>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=8" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=8" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFTurchetti" class="citation libro" style="font-style:normal"> Enrico Turchetti, Romana Fasi, <a rel="nofollow" class="external text" href="http://books.google.it/books?id=17cjPQAACAAJ"><span style="font-style:italic;">Elementi di Fisica</span></a>, 1ª ed., Zanichelli, 1998, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/88-08-09755-2" title="Speciale:RicercaISBN/88-08-09755-2">88-08-09755-2</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=9" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=9" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Circuito_elettrico" title="Circuito elettrico">Circuito elettrico</a></li> <li><a href="/wiki/Corrente_elettrica" title="Corrente elettrica">Corrente elettrica</a></li> <li><a href="/wiki/Legge_di_Ohm" title="Legge di Ohm">Legge di Ohm</a></li> <li><a href="/wiki/Parallelo_(simbolo)" title="Parallelo (simbolo)">Parallelo (simbolo)</a></li> <li><a href="/wiki/Antiserie" title="Antiserie">Antiserie</a></li> <li><a href="/wiki/Antiparallelo" title="Antiparallelo">Antiparallelo</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&veaction=edit&section=10" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Circuiti_in_serie_e_in_parallelo&action=edit&section=10" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><span class="plainlinks" title="commons:Category:Series and parallel circuits"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Series_and_parallel_circuits?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file su <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Series_and_parallel_circuits?uselang=it">circuiti in serie e in parallelo</a></span></b></li></ul> <div class="noprint" style="width:100%; 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