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class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Witryna"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Spis treści" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header 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">Spis treści</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">przypnij</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ukryj</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">Początek</div> </a> </li> <li id="toc-Związek_napięcia_z_natężeniem_pola_elektrycznego" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Związek_napięcia_z_natężeniem_pola_elektrycznego"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Związek napięcia z natężeniem pola elektrycznego</span> </div> </a> <ul id="toc-Związek_napięcia_z_natężeniem_pola_elektrycznego-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Napięcie_elektryczne_otwartego_źródła_prądu" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Napięcie_elektryczne_otwartego_źródła_prądu"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Napięcie elektryczne otwartego źródła prądu</span> </div> </a> <ul id="toc-Napięcie_elektryczne_otwartego_źródła_prądu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jednostka_napięcia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Jednostka_napięcia"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Jednostka napięcia</span> </div> </a> <ul id="toc-Jednostka_napięcia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pomiar_napięcia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pomiar_napięcia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Pomiar napięcia</span> </div> </a> <ul id="toc-Pomiar_napięcia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Napięcie_w_obwodach_prądu_zmiennego" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Napięcie_w_obwodach_prądu_zmiennego"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Napięcie w obwodach prądu zmiennego</span> </div> </a> <ul id="toc-Napięcie_w_obwodach_prądu_zmiennego-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zobacz_też" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zobacz_też"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Zobacz też</span> </div> </a> <ul id="toc-Zobacz_też-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Przypisy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Przypisy"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Przypisy</span> </div> </a> <ul id="toc-Przypisy-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="Spis treści" 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="Przełącz stan spisu treści" > <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">Przełącz stan spisu treści</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">Napięcie elektryczne</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="Przejdź do artykułu w innym języku. Treść dostępna w 99 językach" > <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-99" 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">99 języków</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_spanning" title="Elektriese spanning – afrikaans" lang="af" hreflang="af" data-title="Elektriese spanning" 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/%D8%AC%D9%87%D8%AF_%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A6%D9%8A" title="جهد كهربائي – arabski" lang="ar" hreflang="ar" data-title="جهد كهربائي" data-language-autonym="العربية" data-language-local-name="arabski" 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/G%C9%99rginlik_(elektrik)" title="Gərginlik (elektrik) – azerbejdżański" lang="az" hreflang="az" data-title="Gərginlik (elektrik)" data-language-autonym="Azərbaycanca" data-language-local-name="azerbejdżański" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%88%D9%88%D9%84%D8%AA%D8%A7%DA%98" title="وولتاژ – South Azerbaijani" lang="azb" hreflang="azb" data-title="وولتاژ" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%AD%E0%A6%AC" title="বিভব – bengalski" lang="bn" hreflang="bn" data-title="বিভব" data-language-autonym="বাংলা" data-language-local-name="bengalski" class="interlanguage-link-target"><span>বাংলা</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-ap" title="Tiān-ap – minnański" lang="nan" hreflang="nan" data-title="Tiān-ap" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnański" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B0%D0%BD%D0%BD%D0%B5" title="Электрычнае напружанне – białoruski" lang="be" hreflang="be" data-title="Электрычнае напружанне" data-language-autonym="Беларуская" data-language-local-name="białoruski" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BF%D1%80%D1%83%D0%B3%D0%B0" title="Напруга – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Напруга" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE_%D0%BD%D0%B0%D0%BF%D1%80%D0%B5%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Електрическо напрежение – bułgarski" lang="bg" hreflang="bg" data-title="Електрическо напрежение" data-language-autonym="Български" data-language-local-name="bułgarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Elektrische_Spaunnung" title="Elektrische Spaunnung – bawarski" lang="bar" hreflang="bar" data-title="Elektrische Spaunnung" data-language-autonym="Boarisch" data-language-local-name="bawarski" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Elektri%C4%8Dni_napon" title="Električni napon – bośniacki" lang="bs" hreflang="bs" data-title="Električni napon" data-language-autonym="Bosanski" data-language-local-name="bośniacki" 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/Difer%C3%A8ncia_de_potencial" title="Diferència de potencial – kataloński" lang="ca" hreflang="ca" data-title="Diferència de potencial" data-language-autonym="Català" data-language-local-name="kataloński" 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%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE_%D1%85%D0%B8%D0%B2%D1%80%D0%B5%D0%BB%C4%95%D1%85" title="Электро хиврелĕх – czuwaski" lang="cv" hreflang="cv" data-title="Электро хиврелĕх" data-language-autonym="Чӑвашла" data-language-local-name="czuwaski" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Boltahe" title="Boltahe – cebuański" lang="ceb" hreflang="ceb" data-title="Boltahe" data-language-autonym="Cebuano" data-language-local-name="cebuański" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Elektrick%C3%A9_nap%C4%9Bt%C3%AD" title="Elektrické napětí – czeski" lang="cs" hreflang="cs" data-title="Elektrické napětí" data-language-autonym="Čeština" data-language-local-name="czeski" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Foltedd" title="Foltedd – walijski" lang="cy" hreflang="cy" data-title="Foltedd" data-language-autonym="Cymraeg" data-language-local-name="walijski" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Elektrisk_sp%C3%A6nding" title="Elektrisk spænding – duński" lang="da" hreflang="da" data-title="Elektrisk spænding" data-language-autonym="Dansk" data-language-local-name="duński" 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_Spannung" title="Elektrische Spannung – niemiecki" lang="de" hreflang="de" data-title="Elektrische Spannung" data-language-autonym="Deutsch" data-language-local-name="niemiecki" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Pinge_(elekter)" title="Pinge (elekter) – estoński" lang="et" hreflang="et" data-title="Pinge (elekter)" data-language-autonym="Eesti" data-language-local-name="estoński" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CF%86%CE%BF%CF%81%CE%AC_%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%BF%CF%8D" title="Διαφορά δυναμικού – grecki" lang="el" hreflang="el" data-title="Διαφορά δυναμικού" data-language-autonym="Ελληνικά" data-language-local-name="grecki" 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/Voltage" title="Voltage – angielski" lang="en" hreflang="en" data-title="Voltage" data-language-autonym="English" data-language-local-name="angielski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Tensi%C3%B3n_(electricidad)" title="Tensión (electricidad) – hiszpański" lang="es" hreflang="es" data-title="Tensión (electricidad)" data-language-autonym="Español" data-language-local-name="hiszpański" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Elektra_tensio" title="Elektra tensio – esperanto" lang="eo" hreflang="eo" data-title="Elektra tensio" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Tensi%C3%B3n" title="Tensión – estremadurski" lang="ext" hreflang="ext" data-title="Tensión" data-language-autonym="Estremeñu" data-language-local-name="estremadurski" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Tentsio_(elektrizitatea)" title="Tentsio (elektrizitatea) – baskijski" lang="eu" hreflang="eu" data-title="Tentsio (elektrizitatea)" data-language-autonym="Euskara" data-language-local-name="baskijski" 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/%D9%88%D9%84%D8%AA%D8%A7%DA%98" title="ولتاژ – perski" lang="fa" hreflang="fa" data-title="ولتاژ" data-language-autonym="فارسی" data-language-local-name="perski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Tension_%C3%A9lectrique" title="Tension électrique – francuski" lang="fr" hreflang="fr" data-title="Tension électrique" data-language-autonym="Français" data-language-local-name="francuski" 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/Difr%C3%ADocht_poit%C3%A9insil" title="Difríocht poitéinsil – irlandzki" lang="ga" hreflang="ga" data-title="Difríocht poitéinsil" data-language-autonym="Gaeilge" data-language-local-name="irlandzki" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Tensi%C3%B3n_el%C3%A9ctrica" title="Tensión eléctrica – galicyjski" lang="gl" hreflang="gl" data-title="Tensión eléctrica" data-language-autonym="Galego" data-language-local-name="galicyjski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%84%EC%95%95" title="전압 – koreański" lang="ko" hreflang="ko" data-title="전압" data-language-autonym="한국어" data-language-local-name="koreański" class="interlanguage-link-target"><span>한국어</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%AC%D5%A1%D6%80%D5%B8%D6%82%D5%B4" title="Էլեկտրական լարում – ormiański" lang="hy" hreflang="hy" data-title="Էլեկտրական լարում" data-language-autonym="Հայերեն" data-language-local-name="ormiański" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A4%B0" title="विभवांतर – hindi" lang="hi" hreflang="hi" data-title="विभवांतर" 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/Napon" title="Napon – chorwacki" lang="hr" hreflang="hr" data-title="Napon" data-language-autonym="Hrvatski" data-language-local-name="chorwacki" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tegangan_listrik" title="Tegangan listrik – indonezyjski" lang="id" hreflang="id" data-title="Tegangan listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezyjski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Voltage" title="Voltage – interlingua" lang="ia" hreflang="ia" data-title="Voltage" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ubuvuve" title="Ubuvuve – zulu" lang="zu" hreflang="zu" data-title="Ubuvuve" data-language-autonym="IsiZulu" data-language-local-name="zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Rafspenna" title="Rafspenna – islandzki" lang="is" hreflang="is" data-title="Rafspenna" data-language-autonym="Íslenska" data-language-local-name="islandzki" 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/Tensione_elettrica" title="Tensione elettrica – włoski" lang="it" hreflang="it" data-title="Tensione elettrica" data-language-autonym="Italiano" data-language-local-name="włoski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%AA%D7%97_%D7%97%D7%A9%D7%9E%D7%9C%D7%99" title="מתח חשמלי – hebrajski" lang="he" hreflang="he" data-title="מתח חשמלי" data-language-autonym="עברית" data-language-local-name="hebrajski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Tegangan" title="Tegangan – jawajski" lang="jv" hreflang="jv" data-title="Tegangan" data-language-autonym="Jawa" data-language-local-name="jawajski" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9A%E1%83%94%E1%83%A5%E1%83%A2%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%AB%E1%83%90%E1%83%91%E1%83%95%E1%83%90" title="ელექტრული ძაბვა – gruziński" lang="ka" hreflang="ka" data-title="ელექტრული ძაბვა" data-language-autonym="ქართული" data-language-local-name="gruziński" 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/%D0%9A%D0%B5%D1%80%D0%BD%D0%B5%D1%83" title="Кернеу – kazachski" lang="kk" hreflang="kk" data-title="Кернеу" data-language-autonym="Қазақша" data-language-local-name="kazachski" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Volteji" title="Volteji – suahili" lang="sw" hreflang="sw" data-title="Volteji" data-language-autonym="Kiswahili" data-language-local-name="suahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D1%87%D1%8B%D2%A3%D0%B0%D0%BB%D1%83%D1%83%D1%81%D1%83" title="Электр чыңалуусу – kirgiski" lang="ky" hreflang="ky" data-title="Электр чыңалуусу" data-language-autonym="Кыргызча" data-language-local-name="kirgiski" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Tensio_electrica" title="Tensio electrica – łaciński" lang="la" hreflang="la" data-title="Tensio electrica" data-language-autonym="Latina" data-language-local-name="łaciński" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Spriegums" title="Spriegums – łotewski" lang="lv" hreflang="lv" data-title="Spriegums" data-language-autonym="Latviešu" data-language-local-name="łotewski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Elektrin%C4%97_%C4%AFtampa" title="Elektrinė įtampa – litewski" lang="lt" hreflang="lt" data-title="Elektrinė įtampa" data-language-autonym="Lietuvių" data-language-local-name="litewski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Tension_eletriga" title="Tension eletriga – lombardzki" lang="lmo" hreflang="lmo" data-title="Tension eletriga" data-language-autonym="Lombard" data-language-local-name="lombardzki" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Elektromos_fesz%C3%BClts%C3%A9g" title="Elektromos feszültség – węgierski" lang="hu" hreflang="hu" data-title="Elektromos feszültség" data-language-autonym="Magyar" data-language-local-name="węgierski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BF%D0%BE%D0%BD" title="Напон – macedoński" lang="mk" hreflang="mk" data-title="Напон" data-language-autonym="Македонски" data-language-local-name="macedoński" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Herinaratra" title="Herinaratra – malgaski" lang="mg" hreflang="mg" data-title="Herinaratra" data-language-autonym="Malagasy" data-language-local-name="malgaski" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B5%8B%E0%B5%BE%E0%B4%9F%E0%B5%8D%E0%B4%9F%E0%B4%A4" title="വോൾട്ടത – malajalam" lang="ml" hreflang="ml" data-title="വോൾട്ടത" data-language-autonym="മലയാളം" data-language-local-name="malajalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A4%B0" title="विभवांतर – marathi" lang="mr" hreflang="mr" data-title="विभवांतर" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Voltan" title="Voltan – malajski" lang="ms" hreflang="ms" data-title="Voltan" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D2%AF%D1%87%D0%B4%D1%8D%D0%BB" title="Хүчдэл – mongolski" lang="mn" hreflang="mn" data-title="Хүчдэл" data-language-autonym="Монгол" data-language-local-name="mongolski" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%97%E1%80%AD%E1%80%AF%E1%80%B7%E1%80%A1%E1%80%AC%E1%80%B8" title="ဗို့အား – birmański" lang="my" hreflang="my" data-title="ဗို့အား" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmański" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Elektrische_spanning" title="Elektrische spanning – niderlandzki" lang="nl" hreflang="nl" data-title="Elektrische spanning" data-language-autonym="Nederlands" data-language-local-name="niderlandzki" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9B%BB%E5%9C%A7" title="電圧 – japoński" lang="ja" hreflang="ja" data-title="電圧" data-language-autonym="日本語" data-language-local-name="japoński" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Elektrisk_sp%C3%A4%C3%A4nang" title="Elektrisk späänang – północnofryzyjski" lang="frr" hreflang="frr" data-title="Elektrisk späänang" data-language-autonym="Nordfriisk" data-language-local-name="północnofryzyjski" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no badge-Q17437798 badge-goodarticle mw-list-item" title="dobry artykuł"><a href="https://no.wikipedia.org/wiki/Elektrisk_spenning" title="Elektrisk spenning – norweski (bokmål)" lang="nb" hreflang="nb" data-title="Elektrisk spenning" data-language-autonym="Norsk bokmål" data-language-local-name="norweski (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Elektrisk_spenning" title="Elektrisk spenning – norweski (nynorsk)" lang="nn" hreflang="nn" data-title="Elektrisk spenning" data-language-autonym="Norsk nynorsk" data-language-local-name="norweski (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Tension_electrica" title="Tension electrica – oksytański" lang="oc" hreflang="oc" data-title="Tension electrica" data-language-autonym="Occitan" data-language-local-name="oksytański" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Elektr_kuchlanish" title="Elektr kuchlanish – uzbecki" lang="uz" hreflang="uz" data-title="Elektr kuchlanish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%8B%E0%A8%B2%E0%A8%9F%E0%A9%87%E0%A8%9C" title="ਵੋਲਟੇਜ – pendżabski" lang="pa" hreflang="pa" data-title="ਵੋਲਟੇਜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pendżabski" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%D9%88%D9%84%D9%B9%DB%8C%D8%AC" title="وولٹیج – Western Punjabi" lang="pnb" hreflang="pnb" data-title="وولٹیج" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%88%D9%84%D9%BC%DB%90%D8%AC" title="ولټېج – paszto" lang="ps" hreflang="ps" data-title="ولټېج" data-language-autonym="پښتو" data-language-local-name="paszto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Tens%C3%A3o_el%C3%A9trica" title="Tensão elétrica – portugalski" lang="pt" hreflang="pt" data-title="Tensão elétrica" data-language-autonym="Português" data-language-local-name="portugalski" 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/Tensiune_electric%C4%83" title="Tensiune electrică – rumuński" lang="ro" hreflang="ro" data-title="Tensiune electrică" data-language-autonym="Română" data-language-local-name="rumuński" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pinchikilla_mast%27ay" title="Pinchikilla mast'ay – keczua" lang="qu" hreflang="qu" data-title="Pinchikilla mast'ay" data-language-autonym="Runa Simi" data-language-local-name="keczua" class="interlanguage-link-target"><span>Runa Simi</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%BE%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%8F%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Электрическое напряжение – rosyjski" lang="ru" hreflang="ru" data-title="Электрическое напряжение" data-language-autonym="Русский" data-language-local-name="rosyjski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Voltage" title="Voltage – scots" lang="sco" hreflang="sco" data-title="Voltage" data-language-autonym="Scots" data-language-local-name="scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Tensioni_elektrik" title="Tensioni elektrik – albański" lang="sq" hreflang="sq" data-title="Tensioni elektrik" data-language-autonym="Shqip" data-language-local-name="albański" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%9D%E0%B6%BD%E0%B7%8A%E0%B6%A7%E0%B7%93%E0%B6%BA%E0%B6%AD%E0%B7%8F%E0%B7%80" title="වෝල්ටීයතාව – syngaleski" lang="si" hreflang="si" data-title="වෝල්ටීයතාව" data-language-autonym="සිංහල" data-language-local-name="syngaleski" 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/Voltage" title="Voltage – Simple English" lang="en-simple" hreflang="en-simple" data-title="Voltage" 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/Elektrick%C3%A9_nap%C3%A4tie" title="Elektrické napätie – słowacki" lang="sk" hreflang="sk" data-title="Elektrické napätie" data-language-autonym="Slovenčina" data-language-local-name="słowacki" 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/Elektri%C4%8Dna_napetost" title="Električna napetost – słoweński" lang="sl" hreflang="sl" data-title="Električna napetost" data-language-autonym="Slovenščina" data-language-local-name="słoweński" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%A4%DB%86%DA%B5%D8%AA%DB%8C%DB%95" title="ڤۆڵتیە – sorani" lang="ckb" hreflang="ckb" data-title="ڤۆڵتیە" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</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%B8_%D0%BD%D0%B0%D0%BF%D0%BE%D0%BD" title="Електрични напон – serbski" lang="sr" hreflang="sr" data-title="Електрични напон" data-language-autonym="Српски / srpski" data-language-local-name="serbski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Elektri%C4%8Dni_napon" title="Električni napon – serbsko-chorwacki" lang="sh" hreflang="sh" data-title="Električni napon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbsko-chorwacki" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Voltase" title="Voltase – sundajski" lang="su" hreflang="su" data-title="Voltase" data-language-autonym="Sunda" data-language-local-name="sundajski" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/J%C3%A4nnite" title="Jännite – fiński" lang="fi" hreflang="fi" data-title="Jännite" data-language-autonym="Suomi" data-language-local-name="fiński" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Elektrisk_sp%C3%A4nning" title="Elektrisk spänning – szwedzki" lang="sv" hreflang="sv" data-title="Elektrisk spänning" data-language-autonym="Svenska" data-language-local-name="szwedzki" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Boltahe" title="Boltahe – tagalski" lang="tl" hreflang="tl" data-title="Boltahe" data-language-autonym="Tagalog" data-language-local-name="tagalski" class="interlanguage-link-target"><span>Tagalog</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%AE%B4%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="மின்னழுத்தம் – tamilski" lang="ta" hreflang="ta" data-title="மின்னழுத்தம்" data-language-autonym="தமிழ்" data-language-local-name="tamilski" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D0%BA%D3%A9%D1%87%D3%99%D0%BD%D0%B5%D1%88%D0%B5" title="Электр көчәнеше – tatarski" lang="tt" hreflang="tt" data-title="Электр көчәнеше" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarski" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%8B%E0%B0%B2%E0%B1%8D%E0%B0%9F%E0%B1%87%E0%B0%9C%E0%B1%8D" title="వోల్టేజ్ – telugu" lang="te" hreflang="te" data-title="వోల్టేజ్" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%A3%E0%B8%87%E0%B8%94%E0%B8%B1%E0%B8%99%E0%B9%84%E0%B8%9F%E0%B8%9F%E0%B9%89%E0%B8%B2" title="แรงดันไฟฟ้า – tajski" lang="th" hreflang="th" data-title="แรงดันไฟฟ้า" data-language-autonym="ไทย" data-language-local-name="tajski" 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/Gerilim_(elektrik)" title="Gerilim (elektrik) – turecki" lang="tr" hreflang="tr" data-title="Gerilim (elektrik)" data-language-autonym="Türkçe" data-language-local-name="turecki" 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%B0_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B3%D0%B0" title="Електрична напруга – ukraiński" lang="uk" hreflang="uk" data-title="Електрична напруга" data-language-autonym="Українська" data-language-local-name="ukraiński" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a 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class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Wygląd"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header 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">Wygląd</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">przypnij</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ukryj</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">Z Wikipedii, wolnej encyklopedii</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="pl" dir="ltr"><p><b>Napięcie elektryczne</b> – różnica <a href="/wiki/Potencja%C5%82_elektryczny" title="Potencjał elektryczny">potencjałów elektrycznych</a> między dwoma punktami <a href="/wiki/Obw%C3%B3d_elektryczny" title="Obwód elektryczny">obwodu elektrycznego</a> lub <a href="/wiki/Pole_elektryczne" title="Pole elektryczne">pola elektrycznego</a>. Symbolem napięcia jest <i>U</i>. Napięcie elektryczne jest to stosunek <a href="/wiki/Praca_(fizyka)" title="Praca (fizyka)">pracy</a> wykonanej przeciwko polu, podczas przenoszenia <a href="/wiki/%C5%81adunek_elektryczny" title="Ładunek elektryczny">ładunku elektrycznego</a> między punktami, dla których określa się napięcie, do wartości tego ładunku. Wyraża to wzór: </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 U_{AB}=\varphi _{B}-\varphi _{A}={\frac {W_{A\longrightarrow B}}{q}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mo stretchy="false">⟶</mo> <mi>B</mi> </mrow> </msub> <mi>q</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{AB}=\varphi _{B}-\varphi _{A}={\frac {W_{A\longrightarrow B}}{q}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/490b28d8e8c91267406750ad492c3da4222e4769" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.401ex; height:5.843ex;" alt="{\displaystyle U_{AB}=\varphi _{B}-\varphi _{A}={\frac {W_{A\longrightarrow B}}{q}},}"></span></dd></dl> <p>przy czym zakłada się, że przenoszony ładunek jest na tyle mały, iż nie wpływa znacząco na zewnętrzne pole elektryczne<sup id="cite_ref-bolkowski_1-0" class="reference"><a href="#cite_note-bolkowski-1">[1]</a></sup>. </p><p>W przypadku źródła napięcia (prądu) elektrycznego napięcie jest jego najważniejszym parametrem i określa zdolność źródła energii elektrycznej do wykonania <a href="/wiki/Praca_(fizyka)" title="Praca (fizyka)">pracy</a>. Napięcie mierzone na zaciskach źródła napięcia jest mniejsze od <a href="/wiki/Si%C5%82a_elektromotoryczna" title="Siła elektromotoryczna">siły elektromotorycznej</a> źródła. Różnica ta spowodowana jest spadkiem napięcia na <a href="/wiki/Op%C3%B3r_wewn%C4%99trzny_ogniwa" title="Opór wewnętrzny ogniwa">oporze wewnętrznym</a> źródła. </p><p>Zależność pomiędzy spadkami napięć i siłami elektromotorycznymi w obwodach elektrycznych opisuje <a href="/wiki/Drugie_prawo_Kirchhoffa" class="mw-redirect" title="Drugie prawo Kirchhoffa">II prawo Kirchhoffa</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Związek_napięcia_z_natężeniem_pola_elektrycznego"><span id="Zwi.C4.85zek_napi.C4.99cia_z_nat.C4.99.C5.BCeniem_pola_elektrycznego"></span>Związek napięcia z natężeniem pola elektrycznego</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=1" title="Edytuj sekcję: Związek napięcia z natężeniem pola elektrycznego" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=1" title="Edytuj kod źródłowy sekcji: Związek napięcia z natężeniem pola elektrycznego"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Napięcie elektryczne można określić, znając <a href="/wiki/Nat%C4%99%C5%BCenie_pola_elektrycznego" title="Natężenie pola elektrycznego">natężenie pola elektrycznego</a>: </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 U_{AB}={\frac {W_{A\longrightarrow B}}{q}}=\int \limits _{A}^{B}{\vec {E}}\cdot \;d{\vec {l}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mo stretchy="false">⟶</mo> <mi>B</mi> </mrow> </msub> <mi>q</mi> </mfrac> </mrow> <mo>=</mo> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>E</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mspace width="thickmathspace" /> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>l</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{AB}={\frac {W_{A\longrightarrow B}}{q}}=\int \limits _{A}^{B}{\vec {E}}\cdot \;d{\vec {l}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6a8c39a7b2c5cab11e17d7c71667ec20b93035b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:28.873ex; height:9.176ex;" alt="{\displaystyle U_{AB}={\frac {W_{A\longrightarrow B}}{q}}=\int \limits _{A}^{B}{\vec {E}}\cdot \;d{\vec {l}}.}"></span></dd></dl> <p><a href="/wiki/Ca%C5%82ka" title="Całka">Całkowanie</a> odbywa się pomiędzy punktami A i B<sup id="cite_ref-bolkowski_1-1" class="reference"><a href="#cite_note-bolkowski-1">[1]</a></sup>, przy czym wartość całki nie zależy od wyboru drogi. Wynika stąd, że napięcie między dwoma punktami może być dodatnie, ujemne, a w szczególnych przypadkach – równe zero. </p> <div class="mw-heading mw-heading2"><h2 id="Napięcie_elektryczne_otwartego_źródła_prądu"><span id="Napi.C4.99cie_elektryczne_otwartego_.C5.BAr.C3.B3d.C5.82a_pr.C4.85du"></span>Napięcie elektryczne otwartego źródła prądu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=2" title="Edytuj sekcję: Napięcie elektryczne otwartego źródła prądu" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=2" title="Edytuj kod źródłowy sekcji: Napięcie elektryczne otwartego źródła prądu"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Napięcie elektryczne otwartego <a href="/wiki/%C5%B9r%C3%B3d%C5%82o_pr%C4%85du" title="Źródło prądu">źródła prądu</a> (bez poboru prądu) równe jest <a href="/wiki/Si%C5%82a_elektromotoryczna" title="Siła elektromotoryczna">sile elektromotorycznej</a> (SEM) tego źródła, co wynika z zależności: </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 U=\varepsilon -IR_{w},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>ε</mi> <mo>−</mo> <mi>I</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=\varepsilon -IR_{w},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9272f5542a2b27b7d02270e6e18eb1b977526703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.797ex; height:2.509ex;" alt="{\displaystyle U=\varepsilon -IR_{w},}"></span></dd></dl> <p>gdzie: </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 U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> – napięcie na zaciskach źródła,</dd> <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 \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"></span> – siła elektromotoryczna,</dd> <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_{w}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{w}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b49397922c9acec28b07e68bb26a9a351e5e3d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.173ex; height:2.509ex;" alt="{\displaystyle R_{w}}"></span> – opór wewnętrzny źródła,</dd> <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}"> <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> – natężenie prądu pobieranego ze źródła.</dd></dl> <p>Dla otwartego źródła: <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=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdc39ced67a35eb3fc06568fc2b6bae4f6a661f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.08ex; height:2.509ex;" alt="{\displaystyle I=0,}"></span> zatem </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 U=\varepsilon .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mi>ε</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=\varepsilon .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee7fe59d5330f998a9212635de108a9c65550468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.611ex; height:2.176ex;" alt="{\displaystyle U=\varepsilon .}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Jednostka_napięcia"><span id="Jednostka_napi.C4.99cia"></span>Jednostka napięcia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=3" title="Edytuj sekcję: Jednostka napięcia" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=3" title="Edytuj kod źródłowy sekcji: Jednostka napięcia"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jednostką napięcia jest <a href="/wiki/Wolt" title="Wolt">wolt</a> (V). Między dwoma punktami pola elektrycznego jest napięcie 1 <a href="/wiki/Wolt" title="Wolt">V</a>, jeżeli do przeniesienia między tymi punktami ładunku 1 <a href="/wiki/Kulomb" title="Kulomb">C</a> potrzebna jest praca 1 <a href="/wiki/D%C5%BCul" title="Dżul">J</a> </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 {1V={\frac {1J}{1C}}} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mi mathvariant="normal">V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mi mathvariant="normal">J</mi> </mrow> <mrow> <mn>1</mn> <mi mathvariant="normal">C</mi> </mrow> </mfrac> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {1V={\frac {1J}{1C}}} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05315f30ee13a43520d7b8b79151a54bcd17924f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.328ex; height:5.343ex;" alt="{\displaystyle \mathrm {1V={\frac {1J}{1C}}} ,}"></span></dd></dl> <p>a wymiar wolta </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 {V={\frac {kg\cdot m^{2}}{s^{3}\cdot A}}} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> <mo>⋅</mo> <msup> <mi mathvariant="normal">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⋅</mo> <mi mathvariant="normal">A</mi> </mrow> </mfrac> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {V={\frac {kg\cdot m^{2}}{s^{3}\cdot A}}} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f53828081dbd4ad9b5494b219d60128bc015697e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.384ex; height:6.009ex;" alt="{\displaystyle \mathrm {V={\frac {kg\cdot m^{2}}{s^{3}\cdot A}}} .}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Pomiar_napięcia"><span id="Pomiar_napi.C4.99cia"></span>Pomiar napięcia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=4" title="Edytuj sekcję: Pomiar napięcia" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=4" title="Edytuj kod źródłowy sekcji: Pomiar napięcia"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Przyrządy służące do pomiaru napięcia elektrycznego to <a href="/wiki/Woltomierz" title="Woltomierz">woltomierze</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Napięcie_w_obwodach_prądu_zmiennego"><span id="Napi.C4.99cie_w_obwodach_pr.C4.85du_zmiennego"></span>Napięcie w obwodach prądu zmiennego</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=5" title="Edytuj sekcję: Napięcie w obwodach prądu zmiennego" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=5" title="Edytuj kod źródłowy sekcji: Napięcie w obwodach prądu zmiennego"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>W obwodach prądu zmiennego napięcie może być opisane przy pomocy kilku pojęć, są to: wartość chwilowa, skuteczna, średnia i maksymalna. </p><p>Wartość <b>skuteczną</b> <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 U_{sk}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sk}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7d67608fb14004503edf9637d751717d3829403" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.447ex; height:2.509ex;" alt="{\displaystyle U_{sk}}"></span> napięcia elektrycznego okresowego o okresie <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 T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> określa się wzorem<sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</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 U_{sk}={\sqrt {{\frac {1}{T}}\int \limits _{0}^{T}u^{2}(t)\ dt}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </munderover> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>d</mi> <mi>t</mi> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sk}={\sqrt {{\frac {1}{T}}\int \limits _{0}^{T}u^{2}(t)\ dt}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f413e0d2917f6e2d1d037dda0b3609c5161996eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:22.823ex; height:9.843ex;" alt="{\displaystyle U_{sk}={\sqrt {{\frac {1}{T}}\int \limits _{0}^{T}u^{2}(t)\ dt}}.}"></span></dd></dl> <p>Wartością <b>średnią</b> <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 U_{sr}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sr}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30e21fa215a351916ae0f592766833f1b4db944" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.332ex; height:2.509ex;" alt="{\displaystyle U_{sr}}"></span> napięcia określa się napięcie o wartości: </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 U_{sr}={\frac {1}{T}}\int \limits _{0}^{T}u(t)\ dt.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </munderover> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>d</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sr}={\frac {1}{T}}\int \limits _{0}^{T}u(t)\ dt.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/338497774bdda9d62bb48e645b12fd0e37d41527" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:19.2ex; height:9.176ex;" alt="{\displaystyle U_{sr}={\frac {1}{T}}\int \limits _{0}^{T}u(t)\ dt.}"></span></dd></dl> <p>Dla <a href="/wiki/Pr%C4%85d_przemienny" title="Prąd przemienny">napięcia przemiennego</a> sinusoidalnego, którego przebieg można opisać wzorem<sup id="cite_ref-bolkowski2_4-0" class="reference"><a href="#cite_note-bolkowski2-4">[4]</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 u(t)=U_{max}\sin(\omega \cdot t+\varphi ),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(t)=U_{max}\sin(\omega \cdot t+\varphi ),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a5c5d631ccb63909594acab5905ee505f19b61f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.173ex; height:2.843ex;" alt="{\displaystyle u(t)=U_{max}\sin(\omega \cdot t+\varphi ),}"></span></dd></dl> <p><a href="/wiki/Warto%C5%9B%C4%87_skuteczna" title="Wartość skuteczna">wartość skuteczna</a> napięcia wynosi<sup id="cite_ref-bolkowski2_4-1" class="reference"><a href="#cite_note-bolkowski2-4">[4]</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 U_{sk}={\frac {1}{\sqrt {2}}}\ U_{max}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mtext> </mtext> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sk}={\frac {1}{\sqrt {2}}}\ U_{max}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3eb7a065b7007c88feb3ae4ded9c80757c8aee0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:16.133ex; height:6.176ex;" alt="{\displaystyle U_{sk}={\frac {1}{\sqrt {2}}}\ U_{max}}"></span></dd></dl> <p>wartość średnia jest równa 0, a średnia z wartości bezwzględnej<sup id="cite_ref-bolkowski2_4-2" class="reference"><a href="#cite_note-bolkowski2-4">[4]</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 U_{sr}={\frac {2}{\pi }}\ U_{max}\approx 0{,}637U_{max},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>π</mi> </mfrac> </mrow> <mtext> </mtext> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>≈</mo> <mn>0,637</mn> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sr}={\frac {2}{\pi }}\ U_{max}\approx 0{,}637U_{max},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a2ff3fa230b6ed042fdd8b3f6d37f1955a7c8d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.366ex; height:5.176ex;" alt="{\displaystyle U_{sr}={\frac {2}{\pi }}\ U_{max}\approx 0{,}637U_{max},}"></span></dd></dl> <p>gdzie: </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 U(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/666c639df532e88616357c4991cabce9a57b5611" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.431ex; height:2.843ex;" alt="{\displaystyle U(t)}"></span> – napięcie chwilowe w funkcji czasu <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 t,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea3ad87830a1055c7b85c04cf940cfd3b847ae6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.486ex; height:2.343ex;" alt="{\displaystyle t,}"></span></dd> <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 U_{max}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{max}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d755450de4a2a118d210708681c2eb199dd3788" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.072ex; height:2.509ex;" alt="{\displaystyle U_{max}}"></span> – napięcie maksymalne, równe jego <a href="/wiki/Amplituda" title="Amplituda">amplitudzie</a>,</dd> <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 U_{sk}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sk}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7d67608fb14004503edf9637d751717d3829403" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.447ex; height:2.509ex;" alt="{\displaystyle U_{sk}}"></span> – <a href="/wiki/Napi%C4%99cie_skuteczne" title="Napięcie skuteczne">napięcie skuteczne</a>,</dd> <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 U_{sr}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{sr}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30e21fa215a351916ae0f592766833f1b4db944" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.332ex; height:2.509ex;" alt="{\displaystyle U_{sr}}"></span> – napięcie średnie,</dd> <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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> – <a href="/wiki/Pulsacja" title="Pulsacja">pulsacja</a>,</dd> <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> – faza początkowa.</dd></dl> <p>W <a href="/wiki/Sie%C4%87_niskiego_napi%C4%99cia" title="Sieć niskiego napięcia">sieciach niskiego napięcia</a> w Polsce napięcie skuteczne <i>fazowe</i> (mierzone między przewodem fazowym, czyli będącym pod napięciem a ziemią) wynosi 230 <a href="/wiki/Wolt" title="Wolt">V</a>, zaś <i>międzyfazowe</i> (mierzone między przewodami dwóch faz) 400 V, co odpowiada amplitudom: <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 U_{max}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{max}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d755450de4a2a118d210708681c2eb199dd3788" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.072ex; height:2.509ex;" alt="{\displaystyle U_{max}}"></span> ≈ 325 V i 563 V. Pomiędzy napięciem fazowym <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 U_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7be3c3c86d5d87a48bec069e8477dd5a4823fcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.724ex; height:2.843ex;" alt="{\displaystyle U_{f}}"></span> a międzyfazowym <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 U_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fdf01ea5c43d1e338d8b847556322c42a8c65a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.647ex; height:2.843ex;" alt="{\displaystyle U_{p}}"></span> układu 3-fazowego, symetrycznego, gwiazdowego zachodzi następująca zależność<sup id="cite_ref-5" class="reference"><a href="#cite_note-5">[5]</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 U_{p}={\sqrt {3}}\,U_{f},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mspace width="thinmathspace" /> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{p}={\sqrt {3}}\,U_{f},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9b0ef5bfb774463956827140b90c9924d85869e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.601ex; height:3.176ex;" alt="{\displaystyle U_{p}={\sqrt {3}}\,U_{f},}"></span></dd></dl> <p>gdzie: </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 U_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fdf01ea5c43d1e338d8b847556322c42a8c65a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.647ex; height:2.843ex;" alt="{\displaystyle U_{p}}"></span> – <a href="/wiki/Napi%C4%99cie_mi%C4%99dzyfazowe" title="Napięcie międzyfazowe">napięcie międzyfazowe</a> (nazywane też przewodowym lub liniowym od ang. <i>line-to-line voltage</i>),</dd> <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 U_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7be3c3c86d5d87a48bec069e8477dd5a4823fcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.724ex; height:2.843ex;" alt="{\displaystyle U_{f}}"></span> – <a href="/wiki/Napi%C4%99cie_fazowe" title="Napięcie fazowe">napięcie fazowe</a>.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Zobacz_też"><span id="Zobacz_te.C5.BC"></span>Zobacz też</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=6" title="Edytuj sekcję: Zobacz też" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=6" title="Edytuj kod źródłowy sekcji: Zobacz też"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elektryczno%C5%9B%C4%87" title="Elektryczność">elektryczność</a></li> <li><a href="/wiki/Nat%C4%99%C5%BCenie_pr%C4%85du_elektrycznego" title="Natężenie prądu elektrycznego">natężenie prądu</a></li> <li><a href="/wiki/Rezystancja" title="Rezystancja">opór elektryczny</a></li> <li><a href="/wiki/Drugie_prawo_Kirchhoffa" class="mw-redirect" title="Drugie prawo Kirchhoffa">II prawo Kirchhoffa</a></li> <li><a href="/wiki/Prawo_Ohma" title="Prawo Ohma">prawo Ohma</a></li> <li><a href="/wiki/Sie%C4%87_wysokiego_napi%C4%99cia" title="Sieć wysokiego napięcia">sieć wysokiego napięcia</a></li> <li><a href="/wiki/Spadek_napi%C4%99cia" title="Spadek napięcia">spadek napięcia</a></li> <li><a href="/wiki/Woltomierz" title="Woltomierz">woltomierz</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Przypisy">Przypisy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&veaction=edit&section=7" title="Edytuj sekcję: Przypisy" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Napi%C4%99cie_elektryczne&action=edit&section=7" title="Edytuj kod źródłowy sekcji: Przypisy"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="do-not-make-smaller refsection"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-bolkowski-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-bolkowski_1-0">a</a></sup> <sup><a href="#cite_ref-bolkowski_1-1">b</a></sup></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Stanis%C5%82aw_Bolkowski" title="Stanisław Bolkowski">Bolkowski Stanisław</a>: <i>Elektrotechnika teoretyczna. Tom 1: Teoria obwodów elektrycznych</i>. Warszawa: Wydawnictwa Naukowo-Techniczne, 1986, s. 23. <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/8320407338" title="Specjalna:Książki/8320407338">ISBN <span class="isbn">83-204-0733-8</span></a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elektrotechnika+teoretyczna.+Tom+1%3A+Teoria+obwod%C3%B3w+elektrycznych&rft.au=Bolkowski+Stanis%C5%82aw&rft.pub=Wydawnictwa+Naukowo-Techniczne&rft.place=Warszawa&rft.pages=23&rft.isbn=83-204-0733-8"></span></cite></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Tadeusz_Janowski" title="Tadeusz Janowski">Tadeusz Janowski</a>: <i>Laboratorium podstaw elektrotechniki. Tom I</i>. Tadeusz Janowski (red.). Lublin: Wydawnictwa Uczelniane Politechniki Lubelskiej, 1994, s. 7–8.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Laboratorium+podstaw+elektrotechniki.+Tom+I&rft.aulast=Janowski&rft.aufirst=Tadeusz&rft.pub=Wydawnictwa+Uczelniane+Politechniki+Lubelskiej&rft.place=Lublin&rft.pages=7%E2%80%938"></span></cite></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Stanis%C5%82aw_Bolkowski" title="Stanisław Bolkowski">Bolkowski Stanisław</a>: <i>Elektrotechnika teoretyczna. Tom 1: Teoria obwodów elektrycznych</i>. Warszawa: Wydawnictwa Naukowo-Techniczne, 1986, s. 49. <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/8320407338" title="Specjalna:Książki/8320407338">ISBN <span class="isbn">83-204-0733-8</span></a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elektrotechnika+teoretyczna.+Tom+1%3A+Teoria+obwod%C3%B3w+elektrycznych&rft.au=Bolkowski+Stanis%C5%82aw&rft.pub=Wydawnictwa+Naukowo-Techniczne&rft.place=Warszawa&rft.pages=49&rft.isbn=83-204-0733-8"></span></cite></span> </li> <li id="cite_note-bolkowski2-4"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-bolkowski2_4-0">a</a></sup> <sup><a href="#cite_ref-bolkowski2_4-1">b</a></sup> <sup><a href="#cite_ref-bolkowski2_4-2">c</a></sup></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Stanis%C5%82aw_Bolkowski" title="Stanisław Bolkowski">Bolkowski Stanisław</a>: <i>Elektrotechnika Teoretyczna Tom 1: Teoria obwodów elektrycznych</i>. Warszawa: Wydawnictwa Naukowo-Techniczne, 1986, s. 51–52. <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/8320407338" title="Specjalna:Książki/8320407338">ISBN <span class="isbn">83-204-0733-8</span></a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elektrotechnika+Teoretyczna+Tom+1%3A+Teoria+obwod%C3%B3w+elektrycznych&rft.au=Bolkowski+Stanis%C5%82aw&rft.pub=Wydawnictwa+Naukowo-Techniczne&rft.place=Warszawa&rft.pages=51%E2%80%9352&rft.isbn=83-204-0733-8"></span></cite></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Stanis%C5%82aw_Bolkowski" title="Stanisław Bolkowski">Bolkowski Stanisław</a>: <i>Elektrotechnika teoretyczna. Tom 1: Teoria obwodów elektrycznych</i>. Warszawa: Wydawnictwa Naukowo-Techniczne, 1986, s. 207. <a href="/wiki/Specjalna:Ksi%C4%85%C5%BCki/8320407338" title="Specjalna:Książki/8320407338">ISBN <span class="isbn">83-204-0733-8</span></a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elektrotechnika+teoretyczna.+Tom+1%3A+Teoria+obwod%C3%B3w+elektrycznych&rft.au=Bolkowski+Stanis%C5%82aw&rft.pub=Wydawnictwa+Naukowo-Techniczne&rft.place=Warszawa&rft.pages=207&rft.isbn=83-204-0733-8"></span></cite></span> </li> </ol></div></div> <style data-mw-deduplicate="TemplateStyles:r74016753">.mw-parser-output #normdaten>div+div{margin-top:0.5em}.mw-parser-output #normdaten>div>div{background:var(--background-color-neutral,#eaecf0);padding:.2em .5em}.mw-parser-output #normdaten ul{margin:0;padding:0}.mw-parser-output #normdaten ul li:first-child{padding-left:.5em;border-left:1px solid var(--border-color-base,#a2a9b1)}</style> <div id="normdaten" class="catlinks"><div class="normdaten-typ-s"><div><a href="/wiki/Kontrola_autorytatywna" title="Kontrola autorytatywna">Kontrola autorytatywna</a> (<span class="description"><a href="/wiki/Skalar_(fizyka)" title="Skalar (fizyka)">wielkość skalarna</a></span>):</div><ul><li><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4056001-6">4056001-6</a></span></li><li><a href="/wiki/Centralna_Biblioteka_Narodowa_we_Florencji" title="Centralna Biblioteka Narodowa we Florencji">BNCF</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://thes.bncf.firenze.sbn.it/termine.php?id=17230">17230</a></span></li><li><a href="/wiki/Biblioteka_Narodowa_Republiki_Czeskiej" title="Biblioteka Narodowa Republiki Czeskiej">NKC</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://aut.nkp.cz/ph119852">ph119852</a></span></li><li><a href="/wiki/Biblioteka_Narodowa_(Warszawa)" title="Biblioteka Narodowa (Warszawa)">PLWABN</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810664358405606">9810664358405606</a></span></li></ul></div><div class="normdaten-andere"><div><a href="/wiki/Encyklopedia_internetowa" title="Encyklopedia internetowa">Encyklopedie internetowe</a>:</div> <ul><li><a href="/wiki/Wielka_Encyklopedia_Rosyjska" title="Wielka Encyklopedia Rosyjska">БРЭ</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://old.bigenc.ru/text/2248704">2248704</a></span></li> <li><a href="/wiki/Store_norske_leksikon" title="Store norske leksikon">SNL</a>: <span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=4342&url_prefix=https://snl.no/&id=elektrisk_spenning">elektrisk_spenning</a></span></li> <li><a href="https://www.wikidata.org/wiki/Property:P1296" class="extiw" title="d:Property:P1296">Catalana</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://www.enciclopedia.cat/ec-gec-0213152.xml">0213152</a></span>, <span class="uid"><a rel="nofollow" class="external text" href="https://www.enciclopedia.cat/ec-gec-0151178.xml">0151178</a></span></li> <li><a href="/wiki/Den_Store_Danske_Encyklop%C3%A6di" title="Den Store Danske Encyklopædi">DSDE</a>: <span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8313&url_prefix=https://lex.dk/&id=elektrisk_sp%C3%A6nding">elektrisk_spænding</a></span></li></ul> </div></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Źródło: „<a dir="ltr" href="https://pl.wikipedia.org/w/index.php?title=Napięcie_elektryczne&oldid=72877390">https://pl.wikipedia.org/w/index.php?title=Napięcie_elektryczne&oldid=72877390</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Specjalna:Kategorie" title="Specjalna:Kategorie">Kategorie</a>: <ul><li><a href="/wiki/Kategoria:Napi%C4%99cie_elektryczne" title="Kategoria:Napięcie elektryczne">Napięcie elektryczne</a></li><li><a href="/wiki/Kategoria:Elektryczno%C5%9B%C4%87" title="Kategoria:Elektryczność">Elektryczność</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Tę stronę ostatnio edytowano 15 lut 2024, 17:22.</li> <li id="footer-info-copyright">Tekst udostępniany na licencji <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pl">Creative Commons: uznanie autorstwa, na tych samych warunkach</a>, z możliwością obowiązywania dodatkowych ograniczeń. 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