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accesskey="n"><span>Vitalap</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div 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="Wiki"> <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="Tartalomjegyzék" 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">Tartalomjegyzék</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">áthelyezés az oldalsávba</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">elrejtés</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">Bevezető</div> </a> </li> <li id="toc-Értelmezése_és_mértékegységei" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Értelmezése_és_mértékegységei"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Értelmezése és mértékegységei</span> </div> </a> <ul id="toc-Értelmezése_és_mértékegységei-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-A_fajlagos_ellenállás_hőmérsékletfüggése" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#A_fajlagos_ellenállás_hőmérsékletfüggése"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>A fajlagos ellenállás hőmérsékletfüggése</span> </div> </a> <ul id="toc-A_fajlagos_ellenállás_hőmérsékletfüggése-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Néhány_anyag_fajlagos_ellenállása_és_20_°C-ra_vonatkozó_hőfoktényezője[1][2]" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Néhány_anyag_fajlagos_ellenállása_és_20_°C-ra_vonatkozó_hőfoktényezője[1][2]"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Néhány anyag fajlagos ellenállása és 20 °C-ra vonatkozó hőfoktényezője<sup><span>[</span>1<span>]</span></sup><sup><span>[</span>2<span>]</span></sup></span> </div> </a> <ul id="toc-Néhány_anyag_fajlagos_ellenállása_és_20_°C-ra_vonatkozó_hőfoktényezője[1][2]-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kapcsolódó_szócikkek" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kapcsolódó_szócikkek"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Kapcsolódó szócikkek</span> </div> </a> <ul id="toc-Kapcsolódó_szócikkek-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jegyzetek" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Jegyzetek"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Jegyzetek</span> </div> </a> <ul id="toc-Jegyzetek-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Források" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Források"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Források</span> </div> </a> <ul id="toc-Források-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-További_információk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#További_információk"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>További információk</span> </div> </a> <ul id="toc-További_információk-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="Tartalomjegyzék" 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="Tartalomjegyzék kinyitása/becsukása" > <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">Tartalomjegyzék kinyitása/becsukása</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">Fajlagos ellenállás</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="Ugrás egy más nyelvű szócikkre. Elérhető 55 nyelven" > <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-55" 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">55 nyelv</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Electrical_resistivity" title="Electrical resistivity – angol" lang="en" hreflang="en" data-title="Electrical resistivity" data-language-autonym="English" data-language-local-name="angol" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Elektriese_resistiwiteit" title="Elektriese resistiwiteit – afrikaans" lang="af" hreflang="af" data-title="Elektriese resistiwiteit" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%82%D8%A7%D9%88%D9%85%D9%8A%D8%A9" title="مقاومية – arab" lang="ar" hreflang="ar" data-title="مقاومية" data-language-autonym="العربية" data-language-local-name="arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Resistivid%C3%A1" title="Resistividá – asztúr" lang="ast" hreflang="ast" data-title="Resistividá" data-language-autonym="Asturianu" data-language-local-name="asztúr" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A3%D0%B4%D0%B7%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D0%B5_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D0%B5_%D1%81%D1%83%D0%BF%D1%80%D0%B0%D1%86%D1%96%D1%9E%D0%BB%D0%B5%D0%BD%D0%BD%D0%B5" title="Удзельнае электрычнае супраціўленне – belarusz" lang="be" hreflang="be" data-title="Удзельнае электрычнае супраціўленне" data-language-autonym="Беларуская" data-language-local-name="belarusz" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%84%D0%B8%D1%87%D0%BD%D0%BE_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE_%D1%81%D1%8A%D0%BF%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Специфично електрическо съпротивление – bolgár" lang="bg" hreflang="bg" data-title="Специфично електрическо съпротивление" data-language-autonym="Български" data-language-local-name="bolgár" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Resistivitat" title="Resistivitat – katalán" lang="ca" hreflang="ca" data-title="Resistivitat" data-language-autonym="Català" data-language-local-name="katalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rezistivita" title="Rezistivita – cseh" lang="cs" hreflang="cs" data-title="Rezistivita" data-language-autonym="Čeština" data-language-local-name="cseh" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D0%B0%D0%B9%D0%BB%D0%B0%D0%B2%D0%BB%D0%B0_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE_%D1%85%D0%B8%D1%80%C4%95%C3%A7%D1%82%C4%83%D1%80%D1%83" title="Пайлавла электро хирĕçтăру – csuvas" lang="cv" hreflang="cv" data-title="Пайлавла электро хирĕçтăру" data-language-autonym="Чӑвашла" data-language-local-name="csuvas" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Gwrthedd" title="Gwrthedd – walesi" lang="cy" hreflang="cy" data-title="Gwrthedd" data-language-autonym="Cymraeg" data-language-local-name="walesi" 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_resistivitet" title="Elektrisk resistivitet – dán" lang="da" hreflang="da" data-title="Elektrisk resistivitet" data-language-autonym="Dansk" data-language-local-name="dán" 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/Spezifischer_Widerstand" title="Spezifischer Widerstand – német" lang="de" hreflang="de" data-title="Spezifischer Widerstand" data-language-autonym="Deutsch" data-language-local-name="német" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%B9%CE%B4%CE%B9%CE%BA%CE%AE_%CE%B7%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%B9%CE%BA%CE%AE_%CE%B1%CE%BD%CF%84%CE%AF%CF%83%CF%84%CE%B1%CF%83%CE%B7" title="Ειδική ηλεκτρική αντίσταση – görög" lang="el" hreflang="el" data-title="Ειδική ηλεκτρική αντίσταση" data-language-autonym="Ελληνικά" data-language-local-name="görög" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Elektra_rezistivo" title="Elektra rezistivo – eszperantó" lang="eo" hreflang="eo" data-title="Elektra rezistivo" data-language-autonym="Esperanto" data-language-local-name="eszperantó" 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/Resistividad" title="Resistividad – spanyol" lang="es" hreflang="es" data-title="Resistividad" data-language-autonym="Español" data-language-local-name="spanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Eritakistus" title="Eritakistus – észt" lang="et" hreflang="et" data-title="Eritakistus" data-language-autonym="Eesti" data-language-local-name="észt" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erresistibitate_elektriko" title="Erresistibitate elektriko – baszk" lang="eu" hreflang="eu" data-title="Erresistibitate elektriko" data-language-autonym="Euskara" data-language-local-name="baszk" 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%85%D9%82%D8%A7%D9%88%D9%85%D8%AA%E2%80%8C%D9%88%DB%8C%DA%98%D9%87_%D9%88_%D8%B1%D8%B3%D8%A7%D9%86%D9%86%D8%AF%DA%AF%DB%8C_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="مقاومت‌ویژه و رسانندگی الکتریکی – perzsa" lang="fa" hreflang="fa" data-title="مقاومت‌ویژه و رسانندگی الکتریکی" data-language-autonym="فارسی" data-language-local-name="perzsa" 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/Resistiivisyys" title="Resistiivisyys – finn" lang="fi" hreflang="fi" data-title="Resistiivisyys" data-language-autonym="Suomi" data-language-local-name="finn" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9sistivit%C3%A9" title="Résistivité – francia" lang="fr" hreflang="fr" data-title="Résistivité" data-language-autonym="Français" data-language-local-name="francia" 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/Friotachas" title="Friotachas – ír" lang="ga" hreflang="ga" data-title="Friotachas" data-language-autonym="Gaeilge" data-language-local-name="ír" 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/Resistividade" title="Resistividade – gallego" lang="gl" hreflang="gl" data-title="Resistividade" data-language-autonym="Galego" data-language-local-name="gallego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he badge-Q70893996 mw-list-item" title=""><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A7%D7%93%D7%9D_%D7%94%D7%AA%D7%A0%D7%92%D7%93%D7%95%D7%AA_%D7%97%D7%A9%D7%9E%D7%9C%D7%99%D7%AA" title="מקדם התנגדות חשמלית – héber" lang="he" hreflang="he" data-title="מקדם התנגדות חשמלית" data-language-autonym="עברית" data-language-local-name="héber" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%B0%E0%A5%8B%E0%A4%A7%E0%A4%95%E0%A4%A4%E0%A4%BE" title="प्रतिरोधकता – hindi" lang="hi" hreflang="hi" data-title="प्रतिरोधकता" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id badge-Q70893996 mw-list-item" title=""><a href="https://id.wikipedia.org/wiki/Resistivitas_listrik" title="Resistivitas listrik – indonéz" lang="id" hreflang="id" data-title="Resistivitas listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéz" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Resistivit%C3%A0_elettrica" title="Resistività elettrica – olasz" lang="it" hreflang="it" data-title="Resistività elettrica" data-language-autonym="Italiano" data-language-local-name="olasz" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9B%BB%E6%B0%97%E6%8A%B5%E6%8A%97%E7%8E%87" title="電気抵抗率 – japán" lang="ja" hreflang="ja" data-title="電気抵抗率" data-language-autonym="日本語" data-language-local-name="japán" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B9%84%EC%A0%80%ED%95%AD" title="비저항 – koreai" lang="ko" hreflang="ko" data-title="비저항" data-language-autonym="한국어" data-language-local-name="koreai" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%AApatn%C4%93j%C4%81_pretest%C4%ABba" title="Īpatnējā pretestība – lett" lang="lv" hreflang="lv" data-title="Īpatnējā pretestība" data-language-autonym="Latviešu" data-language-local-name="lett" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D0%BE%D1%82%D0%BF%D0%BE%D1%80%D0%BD%D0%BE%D1%81%D1%82" title="Електрична отпорност – macedón" lang="mk" hreflang="mk" data-title="Електрична отпорност" data-language-autonym="Македонски" data-language-local-name="macedón" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Soortelijke_weerstand" title="Soortelijke weerstand – holland" lang="nl" hreflang="nl" data-title="Soortelijke weerstand" data-language-autonym="Nederlands" data-language-local-name="holland" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Resistivitet" title="Resistivitet – norvég (nynorsk)" lang="nn" hreflang="nn" data-title="Resistivitet" data-language-autonym="Norsk nynorsk" data-language-local-name="norvég (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Resistivitet" title="Resistivitet – norvég (bokmål)" lang="nb" hreflang="nb" data-title="Resistivitet" data-language-autonym="Norsk bokmål" data-language-local-name="norvég (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A8%BF%E0%A8%9C%E0%A8%B2%E0%A8%88_%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%A4%E0%A8%BF%E0%A8%B0%E0%A9%8B%E0%A8%A7%E0%A8%95%E0%A8%A4%E0%A8%BE" title="ਬਿਜਲਈ ਪ੍ਰਤਿਰੋਧਕਤਾ – pandzsábi" lang="pa" hreflang="pa" data-title="ਬਿਜਲਈ ਪ੍ਰਤਿਰੋਧਕਤਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandzsábi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rezystywno%C5%9B%C4%87" title="Rezystywność – lengyel" lang="pl" hreflang="pl" data-title="Rezystywność" data-language-autonym="Polski" data-language-local-name="lengyel" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Arzistivit%C3%A0" title="Arzistività – Piedmontese" lang="pms" hreflang="pms" data-title="Arzistività" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A8%D8%B1%D9%82%DB%8C_%D9%85%D8%B2%D8%A7%D8%AD%D9%85%D8%AA" title="برقی مزاحمت – Western Punjabi" lang="pnb" hreflang="pnb" data-title="برقی مزاحمت" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Resistividade" title="Resistividade – portugál" lang="pt" hreflang="pt" data-title="Resistividade" data-language-autonym="Português" data-language-local-name="portugál" 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/Rezistivitate_electric%C4%83" title="Rezistivitate electrică – román" lang="ro" hreflang="ro" data-title="Rezistivitate electrică" data-language-autonym="Română" data-language-local-name="román" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%B4%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D1%81%D0%BE%D0%BF%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Удельное электрическое сопротивление – orosz" lang="ru" hreflang="ru" data-title="Удельное электрическое сопротивление" data-language-autonym="Русский" data-language-local-name="orosz" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Electrical_resistivity" title="Electrical resistivity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Electrical resistivity" 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/Mern%C3%BD_elektrick%C3%BD_odpor" title="Merný elektrický odpor – szlovák" lang="sk" hreflang="sk" data-title="Merný elektrický odpor" data-language-autonym="Slovenčina" data-language-local-name="szlovák" 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/Specifi%C4%8Dna_upornost" title="Specifična upornost – szlovén" lang="sl" hreflang="sl" data-title="Specifična upornost" data-language-autonym="Slovenščina" data-language-local-name="szlovén" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Kuperekera_magetsi" title="Kuperekera magetsi – sona" lang="sn" hreflang="sn" data-title="Kuperekera magetsi" data-language-autonym="ChiShona" data-language-local-name="sona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sr badge-Q70893996 mw-list-item" title=""><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D0%BE%D1%82%D0%BF%D0%BE%D1%80%D0%BD%D0%BE%D1%81%D1%82" title="Електрична отпорност – szerb" lang="sr" hreflang="sr" data-title="Електрична отпорност" data-language-autonym="Српски / srpski" data-language-local-name="szerb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Elektrisk_resistivitet" title="Elektrisk resistivitet – svéd" lang="sv" hreflang="sv" data-title="Elektrisk resistivitet" data-language-autonym="Svenska" data-language-local-name="svéd" 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/Konduksiyong_elektrikal" title="Konduksiyong elektrikal – tagalog" lang="tl" hreflang="tl" data-title="Konduksiyong elektrikal" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96zdiren%C3%A7" title="Özdirenç – török" lang="tr" hreflang="tr" data-title="Özdirenç" data-language-autonym="Türkçe" data-language-local-name="török" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A7%D0%B0%D0%B3%D1%8B%D1%88%D1%82%D1%8B%D1%80%D0%BC%D0%B0_%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D0%BA%D0%B0%D1%80%D1%88%D1%8B%D0%BB%D1%8B%D0%B3%D1%8B" title="Чагыштырма электр каршылыгы – tatár" lang="tt" hreflang="tt" data-title="Чагыштырма электр каршылыгы" data-language-autonym="Татарча / tatarça" data-language-local-name="tatár" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B8%D1%82%D0%BE%D0%BC%D0%B8%D0%B9_%D0%BE%D0%BF%D1%96%D1%80" title="Питомий опір – ukrán" lang="uk" hreflang="uk" data-title="Питомий опір" data-language-autonym="Українська" data-language-local-name="ukrán" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%B2%D8%A7%D8%AD%D9%85%DB%8C%D8%AA" title="مزاحمیت – urdu" lang="ur" hreflang="ur" data-title="مزاحمیت" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi badge-Q70893996 mw-list-item" title=""><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_tr%E1%BB%9F_su%E1%BA%A5t" title="Điện trở suất – vietnámi" lang="vi" hreflang="vi" data-title="Điện trở suất" data-language-autonym="Tiếng Việt" data-language-local-name="vietnámi" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/D%C3%ABg%C3%ABrluwiin" title="Dëgërluwiin – volof" lang="wo" hreflang="wo" data-title="Dëgërluwiin" data-language-autonym="Wolof" data-language-local-name="volof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%94%B5%E9%98%BB%E7%8E%87" title="电阻率 – wu kínai" lang="wuu" hreflang="wuu" data-title="电阻率" data-language-autonym="吴语" data-language-local-name="wu kínai" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%94%B5%E9%98%BB%E7%8E%87" title="电阻率 – kínai" lang="zh" hreflang="zh" data-title="电阻率" data-language-autonym="中文" data-language-local-name="kínai" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q108193#sitelinks-wikipedia" title="Nyelvközi hivatkozások szerkesztése" class="wbc-editpage">Hivatkozások szerkesztése</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Névterek"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Fajlagos_ellen%C3%A1ll%C3%A1s" title="A lap megtekintése [c]" accesskey="c"><span>Szócikk</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Vita:Fajlagos_ellen%C3%A1ll%C3%A1s" rel="discussion" title="Az oldal tartalmának megvitatása [t]" accesskey="t"><span>Vitalap</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" 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data-event-name="pinnable-header.vector-page-tools.unpin">elrejtés</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="További lehetőségek" > <div class="vector-menu-heading"> Műveletek </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Fajlagos_ellen%C3%A1ll%C3%A1s"><span>Olvasás</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit" title="Az oldal forráskódjának szerkesztése [e]" accesskey="e"><span>Szerkesztés</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=history"><span>Laptörténet</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet 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title="Állandó hivatkozás ezen lap ezen változatához"><span>Hivatkozás erre a változatra</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=info" title="További információk erről a lapról"><span>Lapinformációk</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:Hivatkoz%C3%A1s&page=Fajlagos_ellen%C3%A1ll%C3%A1s&id=27526881&wpFormIdentifier=titleform" title="Információk a lap idézésével kapcsolatban"><span>Hogyan hivatkozz erre a lapra?</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:UrlShortener&url=https%3A%2F%2Fhu.wikipedia.org%2Fwiki%2FFajlagos_ellen%25C3%25A1ll%25C3%25A1s"><span>Rövidített URL készítése</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1lis:QrCode&url=https%3A%2F%2Fhu.wikipedia.org%2Fwiki%2FFajlagos_ellen%25C3%25A1ll%25C3%25A1s"><span>QR-kód 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Az ezüstnek a legkisebb a fajlagos ellenállása</figcaption></figure> <p>A <b>fajlagos ellenállás</b> a különféle anyagok elektromos áramot akadályozó tulajdonságát jellemzi. <i>A homogén, mindenütt azonos keresztmetszetű, állandó hőmérsékletű huzalnál az <a href="/wiki/Elektromos_ellen%C3%A1ll%C3%A1s" title="Elektromos ellenállás">ellenállás</a> és a keresztmetszet szorzatának, valamint a huzal hosszának a hányadosa a huzal anyagára jellemző állandó</i>. Ezt a hányadost az adott anyag <i>fajlagos ellenállásának</i> nevezzük. Jele <i>ρ</i>, képlettel: </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 \rho ={\frac {RA}{l}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>A</mi> </mrow> <mi>l</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {RA}{l}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93e82bd906e44ac7bb4f0b84b6d7c6f3c5997629" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.644ex; height:5.509ex;" alt="{\displaystyle \rho ={\frac {RA}{l}}}"></span>.</dd></dl> <p>A fajlagos ellenállás <a href="/wiki/SI-m%C3%A9rt%C3%A9kegys%C3%A9grendszer" title="SI-mértékegységrendszer">SI-mértékegysége</a>: ohm·méter (Ω·m). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Értelmezése_és_mértékegységei"><span id=".C3.89rtelmez.C3.A9se_.C3.A9s_m.C3.A9rt.C3.A9kegys.C3.A9gei"></span>Értelmezése és mértékegységei</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=1" title="Szakasz szerkesztése: Értelmezése és mértékegységei"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Azonos anyagú, de különböző méretű huzalokon végzett mérésekkel igazolható, hogy az állandó hőmérsékletű, homogén, mindenütt azonos keresztmetszetű, huzalnál az <i>R</i> ellenállás és az <i>A</i> keresztmetszet szorzatának, valamint a huzal <i>l</i> hosszának a hányadosa a huzal anyagára jellemző állandó. Az ezzel a hányadossal értelmezhető <a href="/wiki/Fizikai_mennyis%C3%A9g" title="Fizikai mennyiség">fizikai mennyiséget</a> az adott anyag <i>fajlagos ellenállásának</i> nevezzük. Jele <i>ρ</i>, képlettel: </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 \rho ={\frac {RA}{l}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>A</mi> </mrow> <mi>l</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {RA}{l}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93e82bd906e44ac7bb4f0b84b6d7c6f3c5997629" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.644ex; height:5.509ex;" alt="{\displaystyle \rho ={\frac {RA}{l}}}"></span>.</dd></dl> <p>A fajlagos ellenállás SI-mértékegysége ohm·méter (Ω·m), mert: </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 [\rho ]={\frac {[R]\cdot [A]}{[l]}}={\frac {\Omega \cdot \mathrm {m} ^{2}}{\mathrm {m} }}=\Omega \cdot \mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>ρ</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>R</mi> <mo stretchy="false">]</mo> <mo>⋅</mo> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">[</mo> <mi>l</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi mathvariant="normal">Ω</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [\rho ]={\frac {[R]\cdot [A]}{[l]}}={\frac {\Omega \cdot \mathrm {m} ^{2}}{\mathrm {m} }}=\Omega \cdot \mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/563ad045741eb51f95ed63bd8e7740121e44f173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:32.877ex; height:6.509ex;" alt="{\displaystyle [\rho ]={\frac {[R]\cdot [A]}{[l]}}={\frac {\Omega \cdot \mathrm {m} ^{2}}{\mathrm {m} }}=\Omega \cdot \mathrm {m} }"></span>.</dd></dl> <p>A gyakorlatban használják még az Ω·mm²/m egységet is. A két mértékegység közti kapcsolat: </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 1\ {\frac {\Omega \cdot \mathrm {mm} ^{2}}{\mathrm {m} }}=10^{-6}\ \Omega \cdot \mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mtext> </mtext> <mi mathvariant="normal">Ω</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\ {\frac {\Omega \cdot \mathrm {mm} ^{2}}{\mathrm {m} }}=10^{-6}\ \Omega \cdot \mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a410b075620b7e55a7c6552d9cddb9a3579406d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.492ex; height:5.676ex;" alt="{\displaystyle 1\ {\frac {\Omega \cdot \mathrm {mm} ^{2}}{\mathrm {m} }}=10^{-6}\ \Omega \cdot \mathrm {m} }"></span></dd></dl> <p>A fajlagos ellenállás kiszámítható atomi adatokból is: </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 \rho ={\frac {2m_{e}v_{\mathrm {term} }}{ne^{2}\lambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mi>n</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>λ</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {2m_{e}v_{\mathrm {term} }}{ne^{2}\lambda }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ad3466246c48a3479f9fe7ccf6d47cce32420e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.081ex; height:5.509ex;" alt="{\displaystyle \rho ={\frac {2m_{e}v_{\mathrm {term} }}{ne^{2}\lambda }}}"></span>,</dd></dl> <p>ahol <i>m</i><sub>e</sub> az <a href="/wiki/Elektron" title="Elektron">elektron</a> tömege, <i>e</i> a töltése, <i>n</i> a vezetési elektronok <a href="/wiki/Koncentr%C3%A1ci%C3%B3" title="Koncentráció">koncentrációja</a>, <i>v</i><sub>term</sub> az elektronok hőmozgásból származó <i>termikus sebessége</i>, a <i>λ</i> az elektronok <a href="/wiki/K%C3%B6zepes_szabad_%C3%BAthossz" title="Közepes szabad úthossz">közepes szabad úthossza</a> a vezetőben. </p> <div class="mw-heading mw-heading2"><h2 id="A_fajlagos_ellenállás_hőmérsékletfüggése"><span id="A_fajlagos_ellen.C3.A1ll.C3.A1s_h.C5.91m.C3.A9rs.C3.A9kletf.C3.BCgg.C3.A9se"></span>A fajlagos ellenállás hőmérsékletfüggése</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=2" title="Szakasz szerkesztése: A fajlagos ellenállás hőmérsékletfüggése"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A mérések szerint <i>az anyagok fajlagos ellenállása függ a hőmérséklettől</i>. Melegítés hatására a <a href="/wiki/F%C3%A9mek" title="Fémek">fémek</a> fajlagos ellenállása általában növekszik, a <a href="/wiki/Grafit" title="Grafit">grafit</a>, a <a href="/wiki/F%C3%A9lvezet%C5%91" title="Félvezető">félvezetők</a>, az <a href="/wiki/Elektrolit" title="Elektrolit">elektrolitok</a> fajlagos ellenállása pedig általában csökken. </p><p>A <i>fémes vezetők</i> fajlagos ellenállásának relatív megváltozása közönséges hőmérsékleteken, nem túl nagy tartományban (pl.0 °C – 100 °C között) megközelítőleg egyenesen arányos a hőmérséklet-változással, azaz az </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 {\rho -\rho _{0}}{\rho _{0}}}=\alpha _{0}(T-T_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\rho -\rho _{0}}{\rho _{0}}}=\alpha _{0}(T-T_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837ace1bcbe5c3b6514cb85920d3f8b81979f8a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.473ex; height:5.676ex;" alt="{\displaystyle {\frac {\rho -\rho _{0}}{\rho _{0}}}=\alpha _{0}(T-T_{0})}"></span></dd></dl> <p>képletben szereplő <i>α</i> állandó. A fenti képletben szereplő, és az </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 \alpha _{0}={\frac {\rho -\rho _{0}}{\rho _{0}(T-T_{0})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{0}={\frac {\rho -\rho _{0}}{\rho _{0}(T-T_{0})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95eecd33be3e00f78dff413d6bdcea51529831d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:17.43ex; height:6.009ex;" alt="{\displaystyle \alpha _{0}={\frac {\rho -\rho _{0}}{\rho _{0}(T-T_{0})}}}"></span></dd></dl> <p>összefüggéssel értelmezhető mennyiséget az adott anyag adott <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55b9e7d7b96196b5a6a26f4349caa3ac82fd67e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{0}}"></span> hőmérséklet környékén mért <i>ellenállás hőfoktényezőjének</i> (vagy <i>hőmérsékleti tényezőjének</i>, röviden <i>hőfoktényezőjének</i>) nevezzük. (A <i>T</i><sub>0</sub> kiindulási hőmérséklet többnyire 0 °C vagy 20 °C, az ehhez tartozó fajlagos ellenállást <i>ρ</i><sub>0</sub> jelöli. Az anyagok hőfoktényezőjének megadásakor meg kell adni, hogy az adatok milyen kiindulási hőmérsékletre vonatkoznak.) A hőfoktényező SI-mértékegysége: </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 \left[\alpha \right]={\frac {\left[\rho -\rho _{0}\right]}{\left[\rho _{0}\right]\cdot \left[T-T_{0}\right]}}={\frac {\Omega \cdot \mathrm {m} }{\Omega \cdot \mathrm {m} \cdot \mathrm {K} }}={\frac {1}{\mathrm {K} }}=\mathrm {K} ^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mi>α</mi> <mo>]</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>[</mo> <mrow> <mi>ρ</mi> <mo>−</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <mrow> <mrow> <mo>[</mo> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>]</mo> </mrow> <mo>⋅</mo> <mrow> <mo>[</mo> <mrow> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>]</mo> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">K</mi> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">K</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">K</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[\alpha \right]={\frac {\left[\rho -\rho _{0}\right]}{\left[\rho _{0}\right]\cdot \left[T-T_{0}\right]}}={\frac {\Omega \cdot \mathrm {m} }{\Omega \cdot \mathrm {m} \cdot \mathrm {K} }}={\frac {1}{\mathrm {K} }}=\mathrm {K} ^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/457451911ac8ab8eabca97b90cccb49486a500ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:45.824ex; height:6.509ex;" alt="{\displaystyle \left[\alpha \right]={\frac {\left[\rho -\rho _{0}\right]}{\left[\rho _{0}\right]\cdot \left[T-T_{0}\right]}}={\frac {\Omega \cdot \mathrm {m} }{\Omega \cdot \mathrm {m} \cdot \mathrm {K} }}={\frac {1}{\mathrm {K} }}=\mathrm {K} ^{-1}}"></span></dd></dl> <p>A hőmérsékletváltozást a gyakorlatban többnyire <a href="/wiki/Celsius-sk%C3%A1la" title="Celsius-skála">Celsius-fokban</a> mérjük, ezért a hőfoktényező másik mértékegysége: </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 \left[\alpha \right]={\frac {1}{\mathrm {^{\circ }C} }}=(\mathrm {^{\circ }C} )^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mi>α</mi> <mo>]</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi mathvariant="normal">C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mi mathvariant="normal">C</mi> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[\alpha \right]={\frac {1}{\mathrm {^{\circ }C} }}=(\mathrm {^{\circ }C} )^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73f76bba7d53527e180f830390a753b90b33b5d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.421ex; height:5.343ex;" alt="{\displaystyle \left[\alpha \right]={\frac {1}{\mathrm {^{\circ }C} }}=(\mathrm {^{\circ }C} )^{-1}}"></span></dd></dl> <p>Mivel a hőmérsékletváltozás mérőszáma a Celsius-skálán és a <a href="/wiki/Kelvin" title="Kelvin">Kelvin-skálán</a> mindig ugyanakkora, ezért a hőfoktényező fenti két mértékegysége is megegyezik. </p> <div class="mw-heading mw-heading2"><h2 id="Néhány_anyag_fajlagos_ellenállása_és_20_°C-ra_vonatkozó_hőfoktényezője[1][2]"><span id="N.C3.A9h.C3.A1ny_anyag_fajlagos_ellen.C3.A1ll.C3.A1sa_.C3.A9s_20_.C2.B0C-ra_vonatkoz.C3.B3_h.C5.91fokt.C3.A9nyez.C5.91je.5B1.5D.5B2.5D"></span>Néhány anyag fajlagos ellenállása és 20 °C-ra vonatkozó hőfoktényezője<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><sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=3" title="Szakasz szerkesztése: Néhány anyag fajlagos ellenállása és 20 °C-ra vonatkozó hőfoktényezője[1][2]"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:Insulator_railways.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Insulator_railways.jpg/220px-Insulator_railways.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Insulator_railways.jpg/330px-Insulator_railways.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Insulator_railways.jpg/440px-Insulator_railways.jpg 2x" data-file-width="3067" data-file-height="2044" /></a><figcaption>Vasúti felsővezeték szigetelője. A porcelánnak nagy a fajlagos ellenállása, ezért jó szigetelő</figcaption></figure> <table width="55%" class="wikitable sortable"> <tbody><tr> <th>Anyag </th> <th>Fajlagos ellenállás (10<sup>−6</sup> Ω·m) </th> <th>Hőfoktényező (10<sup>−3</sup> 1/°C) </th></tr> <tr> <td width="24%"><a href="/wiki/Ez%C3%BCst" title="Ezüst">Ezüst</a> </td> <td width="38%" align="center">0,016 </td> <td width="38%" align="center">4,1 </td></tr> <tr> <td><a href="/wiki/R%C3%A9z" title="Réz">Réz</a> </td> <td align="center">0,017 </td> <td align="center">4,0 </td></tr> <tr> <td><a href="/wiki/Arany_(k%C3%A9miai_elem)" title="Arany (kémiai elem)">Arany</a> </td> <td align="center">0,023 </td> <td align="center">4,0 </td></tr> <tr> <td><a href="/wiki/Alum%C3%ADnium" title="Alumínium">Alumínium</a> </td> <td align="center">0,028 </td> <td align="center">3,6 </td></tr> <tr> <td><a href="/wiki/Higany" title="Higany">Higany</a> </td> <td align="center">0,958 </td> <td align="center">0,92 </td></tr> <tr> <td><a href="/w/index.php?title=Konstant%C3%A1n&action=edit&redlink=1" class="new" title="Konstantán (a lap nem létezik)">Konstantán</a> </td> <td align="center">0,50 </td> <td align="center">0,03 </td></tr> <tr> <td><a href="/wiki/Volfr%C3%A1m" title="Volfrám">Wolfrám</a> </td> <td>0,055 </td> <td>4,1 </td></tr> <tr> <td><a href="/wiki/Magn%C3%A9zium" title="Magnézium">Magnézium</a> </td> <td>0,045 </td> <td>3,9 </td></tr> <tr> <td><a href="/wiki/Cink" title="Cink">Horgany</a> </td> <td>0,063 </td> <td>3,7 </td></tr> <tr> <td><a href="/wiki/S%C3%A1rgar%C3%A9z" title="Sárgaréz">Sárgaréz</a> </td> <td>0,07 .. 0,09 </td> <td>1,5 </td></tr> <tr> <td><a href="/wiki/Nikkel" title="Nikkel">Nikkel</a> </td> <td>0.08 .. 0,11 </td> <td>3,7 .. 6 </td></tr> <tr> <td><a href="/wiki/Vas" title="Vas">Vas</a> </td> <td>0,1 .. 0,15 </td> <td>4,5 .. 6 </td></tr> <tr> <td><a href="/wiki/%C3%93n" title="Ón">Ón</a> </td> <td>0,11 </td> <td>4,2 </td></tr> <tr> <td><a href="/wiki/Platina" title="Platina">Platina</a> </td> <td>0,11 - 0,14 </td> <td>2 .. 3 </td></tr> <tr> <td><a href="/wiki/%C3%93lom" title="Ólom">Ólom</a> </td> <td>0,21 </td> <td>4,2 </td></tr> <tr> <td>Újezüst </td> <td>0,3 </td> <td>0,25 </td></tr> <tr> <td>arany-króm </td> <td>0,33 </td> <td>0,001 </td></tr> <tr> <td><a href="/wiki/Nikkelin" title="Nikkelin">Nikkelin</a> </td> <td>0,43 </td> <td>0,23 </td></tr> <tr> <td><a href="/wiki/Manganin" title="Manganin">Manganin</a> </td> <td>0,43 </td> <td>0,01 </td></tr> <tr> <td>Novokonstant </td> <td>0,45 </td> <td>-0,01 .. -0,04 </td></tr> <tr> <td>Rheotan </td> <td>0,47 </td> <td>0,23 </td></tr> <tr> <td>Isabellin </td> <td>0,5 </td> <td>0,02 .. 0,04 </td></tr> <tr> <td>Konstantán </td> <td>0,5 </td> <td>-0,03 </td></tr> <tr> <td>Kruppin </td> <td>0,85 </td> <td>0,7 </td></tr> <tr> <td>Krómnikkel </td> <td>1,1 </td> <td>0,1 </td></tr> <tr> <td><a href="/wiki/Bizmut" title="Bizmut">Bizmut</a> </td> <td>1,2 </td> <td>4,2 </td></tr> <tr> <td>Megapyr </td> <td>1,4 </td> <td>0,025 </td></tr> <tr> <td>Kantál </td> <td>1,45 </td> <td>0,014 </td></tr> <tr> <td><a href="/wiki/%C3%9Cveg" title="Üveg">Üveg</a>* </td> <td align="center">10<sup>17</sup> </td> <td> </td></tr> <tr> <td><a href="/wiki/Porcel%C3%A1n" title="Porcelán">Porcelán</a>* </td> <td align="center">10<sup>18</sup> </td> <td> </td></tr> <tr> <td><a href="/wiki/Borosty%C3%A1n_(fossz%C3%ADlia)" title="Borostyán (fosszília)">Borostyán</a>* </td> <td align="center">10<sup>22</sup> </td> <td> </td></tr></tbody></table> <dl><dd>*<i>Csak nagyságrend</i></dd></dl> <p>Az anyagok fajlagos ellenállása elég alacsony hőmérsékleten a fentieknél bonyolultabban változik. A fajlagos ellenállás bizonyos fémeknél, illetve kerámiáknál az <a href="/wiki/Abszol%C3%BAt_nulla_fok" title="Abszolút nulla fok">abszolút nulla fok</a> (azaz 0 K) közelében gyakorlatilag nullává válik. Ezt a jelenséget <a href="/wiki/Szupravezet%C3%A9s" title="Szupravezetés">szupravezetésnek</a>, az ilyen anyagot <i>szupravezetőnek</i> nevezzük. </p> <div class="mw-heading mw-heading2"><h2 id="Kapcsolódó_szócikkek"><span id="Kapcsol.C3.B3d.C3.B3_sz.C3.B3cikkek"></span>Kapcsolódó szócikkek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=4" title="Szakasz szerkesztése: Kapcsolódó szócikkek"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elektromos_ellen%C3%A1ll%C3%A1s" title="Elektromos ellenállás">Elektromos ellenállás</a></li> <li><a href="/wiki/Szupravezet%C3%A9s" title="Szupravezetés">Szupravezetés</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Jegyzetek">Jegyzetek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=5" title="Szakasz szerkesztése: Jegyzetek"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="ref-1col"><div style="-moz-column-count:2; -webkit-column-count:2; column-count:2; -webkit-column-gap: 3em; -moz-column-gap: 3em; column-gap: 3em;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">*Budó Ágoston: <i>Kísérleti fizika II.</i>, Budapest, Tankönyvkiadó, 1971., 95. oldal</span> </li> <li id="cite_note-:0-2"><span class="mw-cite-backlink"><a href="#cite_ref-:0_2-0">↑</a></span> <span class="reference-text"><cite class="book citation" style="font-style:normal">Karl-Heinz Schubert (DM2AXE).szerk.: Magyari Béla (YR5MB, HA5-052): <i>Rádióamatőrök Műhelykönyve</i> ford.: Taróczi Jenő (HA5-132):. Műszaki Könyvkiadó Budapest. ETO: 621.689.62.007.72 (1968)</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=R%C3%A1di%C3%B3amat%C5%91r%C3%B6k+M%C5%B1helyk%C3%B6nyve&rft.au=Karl-Heinz+Schubert+%28DM2AXE%29&rft.date=1968&rft.pub=M%C5%B1szaki+K%C3%B6nyvkiad%C3%B3+Budapest"><span style="display: none;"> </span></span></span> </li> </ol></div></div><div class="ref-1col"><div style="-moz-column-count:2; -webkit-column-count:2; column-count:2; -webkit-column-gap: 3em; -moz-column-gap: 3em; column-gap: 3em;"></div></div> <div class="mw-heading mw-heading2"><h2 id="Források"><span id="Forr.C3.A1sok"></span>Források</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=6" title="Szakasz szerkesztése: Források"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Budó Ágoston: <i>Kísérleti fizika II.</i>, Budapest, Tankönyvkiadó, 1971</li> <li>Ifj. Zátonyi Sándor: <i>Fizika 10.</i>, Budapest, Nemzeti Tankönyvkiadó, 2009 <a href="/wiki/Speci%C3%A1lis:K%C3%B6nyvforr%C3%A1sok/9789631963205" title="Speciális:Könyvforrások/9789631963205">ISBN 978 963 19 6320 5</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="További_információk"><span id="Tov.C3.A1bbi_inform.C3.A1ci.C3.B3k"></span>További információk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fajlagos_ellen%C3%A1ll%C3%A1s&action=edit&section=7" title="Szakasz szerkesztése: További információk"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Fizikakönyv.hu – <a rel="nofollow" class="external text" href="http://www.fizikakonyv.hu/126.pdf">A vezeték ellenállása</a></li></ul> <p><br /> </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r26593303">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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