Valor eficaz – Wikipédia, a enciclopédia livre

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class="vector-toc-list"> </ul> </li> <li id="toc-Utilização" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Utilização"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Utilização</span> </div> </a> <ul id="toc-Utilização-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relação_entre_média_aritmética_e_desvio_padrão" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relação_entre_média_aritmética_e_desvio_padrão"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Relação entre média aritmética e desvio padrão</span> </div> </a> <ul id="toc-Relação_entre_média_aritmética_e_desvio_padrão-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-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="Conteúdo" 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="Alternar o índice" > <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">Alternar o índice</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">Valor eficaz</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir para um artigo noutra língua. Disponível em 39 línguas" > <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-39" 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">39 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D8%B0%D8%B1_%D9%85%D8%AA%D9%88%D8%B3%D8%B7_%D9%85%D8%B1%D8%A8%D8%B9" title="جذر متوسط مربع — árabe" lang="ar" hreflang="ar" data-title="جذر متوسط مربع" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B5_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе квадратычнае — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Сярэдняе квадратычнае" 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%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%BE_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE" title="Средно квадратично — búlgaro" lang="bg" hreflang="bg" data-title="Средно квадратично" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%97%E0%A6%AE%E0%A7%82%E0%A6%B2_%E0%A6%97%E0%A6%A1%E0%A6%BC_%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%97" title="বর্গমূল গড় বর্গ — bengalês" lang="bn" hreflang="bn" data-title="বর্গমূল গড় বর্গ" data-language-autonym="বাংলা" data-language-local-name="bengalês" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Mitjana_quadr%C3%A0tica" title="Mitjana quadràtica — catalão" lang="ca" hreflang="ca" data-title="Mitjana quadràtica" data-language-autonym="Català" data-language-local-name="catalão" 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/Kvadratick%C3%BD_pr%C5%AFm%C4%9Br" title="Kvadratický průměr — checo" lang="cs" hreflang="cs" data-title="Kvadratický průměr" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Effektiv_v%C3%A6rdi" title="Effektiv værdi — dinamarquês" lang="da" hreflang="da" data-title="Effektiv værdi" data-language-autonym="Dansk" data-language-local-name="dinamarquês" 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/Quadratisches_Mittel" title="Quadratisches Mittel — alemão" lang="de" hreflang="de" data-title="Quadratisches Mittel" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Root_mean_square" title="Root mean square — inglês" lang="en" hreflang="en" data-title="Root mean square" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kvadrata_avera%C4%9Do" title="Kvadrata averaĝo — esperanto" lang="eo" hreflang="eo" data-title="Kvadrata averaĝo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Media_cuadr%C3%A1tica" title="Media cuadrática — espanhol" lang="es" hreflang="es" data-title="Media cuadrática" data-language-autonym="Español" data-language-local-name="espanhol" 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/Ruutkeskmine" title="Ruutkeskmine — estónio" lang="et" hreflang="et" data-title="Ruutkeskmine" data-language-autonym="Eesti" data-language-local-name="estónio" 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/Batezbesteko_koadratiko" title="Batezbesteko koadratiko — basco" lang="eu" hreflang="eu" data-title="Batezbesteko koadratiko" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%B0%D8%B1_%D9%85%DB%8C%D8%A7%D9%86%DA%AF%DB%8C%D9%86_%D9%85%D8%B1%D8%A8%D8%B9%D8%A7%D8%AA" title="جذر میانگین مربعات — persa" lang="fa" hreflang="fa" data-title="جذر میانگین مربعات" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Neli%C3%B6llinen_keskiarvo" title="Neliöllinen keskiarvo — finlandês" lang="fi" hreflang="fi" data-title="Neliöllinen keskiarvo" data-language-autonym="Suomi" data-language-local-name="finlandês" 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/Moyenne_quadratique" title="Moyenne quadratique — francês" lang="fr" hreflang="fr" data-title="Moyenne quadratique" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%95%D7%A8%D7%A9_%D7%9E%D7%9E%D7%95%D7%A6%D7%A2_%D7%94%D7%A8%D7%99%D7%91%D7%95%D7%A2%D7%99%D7%9D" title="שורש ממוצע הריבועים — hebraico" lang="he" hreflang="he" data-title="שורש ממוצע הריבועים" data-language-autonym="עברית" data-language-local-name="hebraico" 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%B5%E0%A4%B0%E0%A5%8D%E0%A4%97_%E0%A4%AE%E0%A4%BE%E0%A4%A7%E0%A5%8D%E0%A4%AF_%E0%A4%AE%E0%A5%82%E0%A4%B2" title="वर्ग माध्य मूल — hindi" lang="hi" hreflang="hi" data-title="वर्ग माध्य मूल" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/N%C3%A9gyzetes_k%C3%B6z%C3%A9p" title="Négyzetes közép — húngaro" lang="hu" hreflang="hu" data-title="Négyzetes közép" data-language-autonym="Magyar" data-language-local-name="húngaro" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rata-rata_kuadrat" title="Rata-rata kuadrat — indonésio" lang="id" hreflang="id" data-title="Rata-rata kuadrat" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%8C%E4%B9%97%E5%B9%B3%E5%9D%87%E5%B9%B3%E6%96%B9%E6%A0%B9" title="二乗平均平方根 — japonês" lang="ja" hreflang="ja" data-title="二乗平均平方根" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D1%82%D1%8B%D2%9B_%D0%BE%D1%80%D1%82%D0%B0%D1%88%D0%B0%D0%BB%D0%B0%D1%80" title="Квадраттық орташалар — cazaque" lang="kk" hreflang="kk" data-title="Квадраттық орташалар" data-language-autonym="Қазақша" data-language-local-name="cazaque" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%9C%EA%B3%B1%ED%8F%89%EA%B7%A0%EC%A0%9C%EA%B3%B1%EA%B7%BC" title="제곱평균제곱근 — coreano" lang="ko" hreflang="ko" data-title="제곱평균제곱근" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Kwadratisch_gemiddelde" title="Kwadratisch gemiddelde — neerlandês" lang="nl" hreflang="nl" data-title="Kwadratisch gemiddelde" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kvadratisk_gjennomsnitt" title="Kvadratisk gjennomsnitt — norueguês bokmål" lang="nb" hreflang="nb" data-title="Kvadratisk gjennomsnitt" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%9Arednia_kwadratowa" title="Średnia kwadratowa — polaco" lang="pl" hreflang="pl" data-title="Średnia kwadratowa" data-language-autonym="Polski" data-language-local-name="polaco" 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/Media_quadr%C3%A0tica" title="Media quadràtica — Piedmontese" lang="pms" hreflang="pms" data-title="Media quadràtica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Medie_p%C4%83tratic%C4%83" title="Medie pătratică — romeno" lang="ro" hreflang="ro" data-title="Medie pătratică" data-language-autonym="Română" data-language-local-name="romeno" 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%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%B5%D0%B5_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5" title="Среднее квадратическое — russo" lang="ru" hreflang="ru" data-title="Среднее квадратическое" data-language-autonym="Русский" data-language-local-name="russo" 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/Root_mean_square" title="Root mean square — Simple English" lang="en-simple" hreflang="en-simple" data-title="Root mean square" 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/Kvadratick%C3%BD_priemer" title="Kvadratický priemer — eslovaco" lang="sk" hreflang="sk" data-title="Kvadratický priemer" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0" title="Квадратна средина — sérvio" lang="sr" hreflang="sr" data-title="Квадратна средина" data-language-autonym="Српски / srpski" data-language-local-name="sérvio" 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/Kvadratiskt_medelv%C3%A4rde" title="Kvadratiskt medelvärde — sueco" lang="sv" hreflang="sv" data-title="Kvadratiskt medelvärde" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B9%88%E0%B8%B2%E0%B9%80%E0%B8%89%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%81%E0%B8%B3%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%AD%E0%B8%87" title="ค่าเฉลี่ยกำลังสอง — tailandês" lang="th" hreflang="th" data-title="ค่าเฉลี่ยกำลังสอง" data-language-autonym="ไทย" data-language-local-name="tailandês" 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/Karek%C3%B6k_ortalama" title="Karekök ortalama — turco" lang="tr" hreflang="tr" data-title="Karekök ortalama" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a 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typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/20px-Disambig_grey.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/30px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/40px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></span></span> <b>Nota:</b> Este artigo é sobre um conceito <a href="/wiki/Estat%C3%ADstica" title="Estatística">estatístico</a>. Se procura outros conceitos com as mesmas iniciais, veja <a href="/wiki/RMS" class="mw-disambig" title="RMS">RMS</a>.</div> <p>Em <a href="/wiki/Matem%C3%A1tica" title="Matemática">matemática</a>, a <b>raiz do valor quadrático médio</b> ou <b>RMS</b> (do <a href="/wiki/L%C3%ADngua_inglesa" title="Língua inglesa">inglês</a> <i>root mean square</i>) ou <b>valor eficaz</b> é uma medida <a href="/wiki/Estat%C3%ADstica" title="Estatística">estatística</a> da <a href="/wiki/Magnitude" class="mw-disambig" title="Magnitude">magnitude</a> de uma quantidade variável. Pode-se calcular para uma série de valores discretos ou para uma <a href="/wiki/Fun%C3%A7%C3%A3o_matem%C3%A1tica" class="mw-redirect" title="Função matemática">função</a> variável contínua. O nome deriva do fato de que é a <a href="/wiki/Raiz_quadrada" title="Raiz quadrada">raiz quadrada</a> da <a href="/wiki/M%C3%A9dia_aritm%C3%A9tica" title="Média aritmética">média aritmética</a> dos <a href="/wiki/Exponencia%C3%A7%C3%A3o" title="Exponenciação">quadrados</a> dos valores. É um caso especial da <a href="/w/index.php?title=M%C3%A9dia_generalizada&action=edit&redlink=1" class="new" title="Média generalizada (página não existe)">potência média</a> com o expoente <i>p</i> = 2. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definição"><span id="Defini.C3.A7.C3.A3o"></span>Definição</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valor_eficaz&veaction=edit&section=1" title="Editar secção: Definição" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Valor_eficaz&action=edit&section=1" title="Editar código-fonte da secção: Definição"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O RMS para uma coleção de N valores {<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, ... , <i>x</i><sub>N</sub>} é dado pela fórmula <b>(1)</b>: </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)x_{\mathrm {rms} }={\sqrt {{1 \over N}\sum _{i=1}^{N}x_{i}^{2}}}={\sqrt {{x_{1}^{2}+x_{2}^{2}+\cdots +x_{N}^{2}} \over N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mi>N</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1)x_{\mathrm {rms} }={\sqrt {{1 \over N}\sum _{i=1}^{N}x_{i}^{2}}}={\sqrt {{x_{1}^{2}+x_{2}^{2}+\cdots +x_{N}^{2}} \over N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83c30b6b3e9663d933a0792aebef24528416b12f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:47.452ex; height:8.009ex;" alt="{\displaystyle (1)x_{\mathrm {rms} }={\sqrt {{1 \over N}\sum _{i=1}^{N}x_{i}^{2}}}={\sqrt {{x_{1}^{2}+x_{2}^{2}+\cdots +x_{N}^{2}} \over N}}}"></span></dd></dl> <p>Para uma função variável contínua <b>f(t)</b> definida sobre o intervalo T<sub>1</sub> ≤ <b>t</b> ≤ T<sub>2</sub> o RMS é dado pela expressão: </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 (2)x_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msubsup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2)x_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87df7929f81018fea1736b120e552f8794ad9a5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:35.357ex; height:7.676ex;" alt="{\displaystyle (2)x_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}}.}"></span></dd></dl> <p>O valor <i>rms</i> para uma função ao longo do tempo é: </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 (3)f_{\mathrm {rms} }=\lim _{T\rightarrow \infty }\left({\sqrt {{1 \over {2T}}{\int _{-T}^{T}{[f(t)]}^{2}\,dt}}}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>T</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msubsup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (3)f_{\mathrm {rms} }=\lim _{T\rightarrow \infty }\left({\sqrt {{1 \over {2T}}{\int _{-T}^{T}{[f(t)]}^{2}\,dt}}}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/460a7b2bd257870337c1e259b720aac3b16ee59a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:38.673ex; height:7.676ex;" alt="{\displaystyle (3)f_{\mathrm {rms} }=\lim _{T\rightarrow \infty }\left({\sqrt {{1 \over {2T}}{\int _{-T}^{T}{[f(t)]}^{2}\,dt}}}\right).}"></span></dd></dl> <p>O RMS ao longo do tempo para uma <a href="/wiki/Fun%C3%A7%C3%A3o_peri%C3%B3dica" title="Função periódica">função periódica</a> é igual ao RMS de um período da função. O valor RMS de uma função ou sinal contínuos pode ser avaliado, tomando o RMS de uma série de amostras, igualmente espaçadas no tempo. </p> <div class="mw-heading mw-heading2"><h2 id="Equações_para_calcular_os_valores_RMS_de_formas_de_onda_comuns"><span id="Equa.C3.A7.C3.B5es_para_calcular_os_valores_RMS_de_formas_de_onda_comuns"></span>Equações para calcular os valores RMS de formas de onda comuns</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valor_eficaz&veaction=edit&section=2" title="Editar secção: Equações para calcular os valores RMS de formas de onda comuns" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Valor_eficaz&action=edit&section=2" title="Editar código-fonte da secção: Equações para calcular os valores RMS de formas de onda comuns"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <td colspan="3">Grandezas e Unidades:<br />'<i><b>t:'</b></i> tempo em Segundos (s)<br />'<i><b>f:'</b></i> Frequencia em Hertz (Hz)<br />'<i><b>a:'</b></i> amplitude (valor de pico). Pode ser qualquer grandeza física, ex.: Corrente (Ampéres), Tensão (Volts), Força (Newtons), etc<br />'<i><b>%:'</b></i> é a operação "Resto da divisão"<br />Ex.:<br />10 / 3 = 3,333333...<br />10 % 3 = 0,3333333... </td></tr> <tr> <td>Forma de Onda</td> <td>Equação </td><td>RMS </td></tr> <tr><td>Senoide <sup>(pt-BR) </sup>/ Sinusoide <sup>(pt-PT)</sup> </td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=a\sin(2\pi ft)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=a\sin(2\pi ft)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/437bd8b56b5d1a0751999aeb8f16f83a902bf0df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.536ex; height:2.843ex;" alt="{\displaystyle y=a\sin(2\pi ft)\,}"></span> </td><td><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 {a}{\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dda608aff02ad5e622be07bf57b0390d88958b84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.934ex; height:5.676ex;" alt="{\displaystyle {\frac {a}{\sqrt {2}}}}"></span> </td></tr><tr> <td>Onda Quadrada </td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y={\begin{cases}a&((ft)\%1)<0.5\\-a&((ft)\%1)>0.5\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mo><</mo> <mn>0.5</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>a</mi> </mtd> <mtd> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mo>></mo> <mn>0.5</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y={\begin{cases}a&((ft)\%1)<0.5\\-a&((ft)\%1)>0.5\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34f690140d3c9af2a35cce9fb70163782a26999b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.014ex; height:6.176ex;" alt="{\displaystyle y={\begin{cases}a&((ft)\%1)<0.5\\-a&((ft)\%1)>0.5\end{cases}}}"></span> </td><td><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 a\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}"></span> </td></tr> <tr> <td>Senoide / Sinusoide e Modificada </td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y={\begin{cases}0&((ft)\%1)<0.25\\a&0.25<((ft)\%1)<0.5\\0&0.5<((ft)\%1)<0.75\\-a&((ft)\%1)>0.75\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mo><</mo> <mn>0.25</mn> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mn>0.25</mn> <mo><</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mo><</mo> <mn>0.5</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0.5</mn> <mo><</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mo><</mo> <mn>0.75</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>a</mi> </mtd> <mtd> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mo>></mo> <mn>0.75</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y={\begin{cases}0&((ft)\%1)<0.25\\a&0.25<((ft)\%1)<0.5\\0&0.5<((ft)\%1)<0.75\\-a&((ft)\%1)>0.75\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05e06cd64aa856479249b0cda99a22de9a85ec39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:34.57ex; height:11.509ex;" alt="{\displaystyle y={\begin{cases}0&((ft)\%1)<0.25\\a&0.25<((ft)\%1)<0.5\\0&0.5<((ft)\%1)<0.75\\-a&((ft)\%1)>0.75\end{cases}}}"></span> </td><td><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 {a}{\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dda608aff02ad5e622be07bf57b0390d88958b84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.934ex; height:5.676ex;" alt="{\displaystyle {\frac {a}{\sqrt {2}}}}"></span> </td></tr> <tr> <td>Onda "Dente-de-Serra" </td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=0.5-2a((ft)\%1)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mn>0.5</mn> <mo>−</mo> <mn>2</mn> <mi>a</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>f</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">%</mi> <mn>1</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=0.5-2a((ft)\%1)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad1775b480e4ed0bc6e45d742e8dfe81a587c107" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.681ex; height:2.843ex;" alt="{\displaystyle y=0.5-2a((ft)\%1)\,}"></span> </td><td><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 a \over {\sqrt {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle a \over {\sqrt {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6df5978459e4f28c850c4e386055219fcf0d3de0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.934ex; height:5.676ex;" alt="{\displaystyle a \over {\sqrt {3}}}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Utilização"><span id="Utiliza.C3.A7.C3.A3o"></span>Utilização</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valor_eficaz&veaction=edit&section=3" title="Editar secção: Utilização" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Valor_eficaz&action=edit&section=3" title="Editar código-fonte da secção: Utilização"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O valor eficaz de uma função é frequentemente usado na <a href="/wiki/F%C3%ADsica" title="Física">física</a> e na <a href="/wiki/Eletr%C3%B4nica" title="Eletrônica">eletrônica</a>. Por exemplo, nós podemos calcular a <a href="/wiki/Pot%C3%AAncia_(f%C3%ADsica)" class="mw-redirect" title="Potência (física)">Potência</a> <i>P</i> dissipada por um <a href="/wiki/Condutor_el%C3%A9trico" title="Condutor elétrico">condutor elétrico</a> de resistência <i>R</i>. Ela é fácil de se calcular quando uma corrente constante (I) percorre o condutor, que é simplesmente: </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 (4)\qquad \qquad P=I^{2}R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mspace width="2em" /> <mspace width="2em" /> <mi>P</mi> <mo>=</mo> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (4)\qquad \qquad P=I^{2}R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f40b34d22d91e7b8e33c2ba666fb931b76505dd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.141ex; height:3.176ex;" alt="{\displaystyle (4)\qquad \qquad P=I^{2}R}"></span></dd></dl> <p>ou, considerando uma <a href="/wiki/Tens%C3%A3o_el%C3%A9trica" title="Tensão elétrica">tensão eléctrica</a> V, é aplicada a uma resistência R, fica: </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 (5)\qquad \qquad P={V^{2} \over R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mspace width="2em" /> <mspace width="2em" /> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (5)\qquad \qquad P={V^{2} \over R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d535b858d66d8c310b7c9659cb90549250c2470c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.913ex; height:5.843ex;" alt="{\displaystyle (5)\qquad \qquad P={V^{2} \over R}}"></span></dd></dl> <p>Mas e se a corrente é uma função I(<i>t</i>) que varia seu valor no tempo? É neste momento que se utiliza o valor eficaz. Neste caso, pode-se substituir o valor da corrente constante <i>I</i> pelo valor eficaz da função I(<i>t</i>) na equação acima para se obter a potência dissipada média, assim: </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 (6)\qquad \qquad P=I_{\mathrm {rms} }^{2}R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>6</mn> <mo stretchy="false">)</mo> <mspace width="2em" /> <mspace width="2em" /> <mi>P</mi> <mo>=</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (6)\qquad \qquad P=I_{\mathrm {rms} }^{2}R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b22a9d6e4d520072c57d1d38288a944fbe71eee9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.787ex; height:3.009ex;" alt="{\displaystyle (6)\qquad \qquad P=I_{\mathrm {rms} }^{2}R}"></span></dd></dl> <p>Alternativamente, se a tensão é uma função V(<i>t</i>) que varia seu valor no tempo, a potência dissipada média é dada pela equação: </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 (7)\qquad \qquad P={V_{\mathrm {rms} }^{2} \over R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mspace width="2em" /> <mspace width="2em" /> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (7)\qquad \qquad P={V_{\mathrm {rms} }^{2} \over R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/703dd1a469ebf2e4dd8b9d54b7143584b09e3e42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.191ex; height:5.676ex;" alt="{\displaystyle (7)\qquad \qquad P={V_{\mathrm {rms} }^{2} \over R}}"></span></dd></dl> <p>No caso comum da <a href="/wiki/Corrente_alternada" title="Corrente alternada">corrente alternada</a>, quando I(<i>t</i>) é uma corrente <a href="/wiki/Sen%C3%B3ide" class="mw-redirect" title="Senóide">senoidal</a>, tal como se verifica na energia eléctrica distribuída na rede pública, o valor RMS é fácil de calcular a partir da equação (2) acima indicada. O resultado é: </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 (8)\qquad \qquad {I_{\mathrm {rms} }}={I_{p} \over {\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>8</mn> <mo stretchy="false">)</mo> <mspace width="2em" /> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (8)\qquad \qquad {I_{\mathrm {rms} }}={I_{p} \over {\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/766fa503f6dc85dc54bef81a75abb7574e79b441" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:23.212ex; height:6.509ex;" alt="{\displaystyle (8)\qquad \qquad {I_{\mathrm {rms} }}={I_{p} \over {\sqrt {2}}}}"></span></dd></dl> <p>ou, no caso da tensão: </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 (9)\qquad \qquad {V_{\mathrm {rms} }}={V_{p} \over {\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>9</mn> <mo stretchy="false">)</mo> <mspace width="2em" /> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (9)\qquad \qquad {V_{\mathrm {rms} }}={V_{p} \over {\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/592835cffe33dce92d53982d4411fd3deedddfe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:23.544ex; height:6.509ex;" alt="{\displaystyle (9)\qquad \qquad {V_{\mathrm {rms} }}={V_{p} \over {\sqrt {2}}}}"></span></dd></dl> <p>em que <i>I</i><sub><i>p</i></sub> e <i>V</i><sub><i>p</i></sub> são os valores de pico (amplitude). </p><p>O valor RMS pode ser calculado usando a equação (2) para qualquer forma de onda, por exemplo, um sinal de áudio ou de rádio. Assim, podemos calcular a potência média fornecida a uma carga específica. Por esta razão, as tensões indicadas em tomadas de energia e equipamentos eléctricos, (127V ou 220V) são os valores RMS e não os valores de pico (amplitudes). </p><p>No campo de áudio, potência média é frequentemente (e de forma errada) designada <a href="/w/index.php?title=Pot%C3%AAncia_de_%C3%81udio&action=edit&redlink=1" class="new" title="Potência de Áudio (página não existe)">potência RMS</a>. Isto deve-se provavelmente derivado de Tensão RMS ou corrente RMS. Além disso, como o valor RMS implica alguma forma de valor médio, expressões como "potência RMS de pico", frequentemente utilizadas em anúncios de amplificadores de áudio, não têm qualquer significado. </p> <div class="mw-heading mw-heading2"><h2 id="Relação_entre_média_aritmética_e_desvio_padrão"><span id="Rela.C3.A7.C3.A3o_entre_m.C3.A9dia_aritm.C3.A9tica_e_desvio_padr.C3.A3o"></span>Relação entre média aritmética e desvio padrão</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valor_eficaz&veaction=edit&section=4" title="Editar secção: Relação entre média aritmética e desvio padrão" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Valor_eficaz&action=edit&section=4" title="Editar código-fonte da secção: Relação entre média aritmética e desvio padrão"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se <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 {\bar {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/466e03e1c9533b4dab1b9949dad393883f385d80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.009ex;" alt="{\displaystyle {\bar {x}}}"></span> for a <a href="/wiki/M%C3%A9dia_aritm%C3%A9tica" title="Média aritmética">média aritmética</a> e <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 \sigma _{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebf4ab08fe163a6c495cad6f4d67653287c4044c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \sigma _{x}}"></span> o <a href="/wiki/Desvio_padr%C3%A3o" title="Desvio padrão">desvio padrão</a> de uma população, então: </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 x_{\mathrm {rms} }^{2}={\bar {x}}^{2}+\sigma _{x}^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\mathrm {rms} }^{2}={\bar {x}}^{2}+\sigma _{x}^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12c441f6c680ee8e6fb06af787ec16f90e294dfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.693ex; height:3.009ex;" alt="{\displaystyle x_{\mathrm {rms} }^{2}={\bar {x}}^{2}+\sigma _{x}^{2}.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Valor_eficaz&veaction=edit&section=5" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Valor_eficaz&action=edit&section=5" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Desvio_padr%C3%A3o" title="Desvio padrão">Desvio padrão</a></li> <li><a href="/wiki/Tabela_de_s%C3%ADmbolos_matem%C3%A1ticos" class="mw-redirect" title="Tabela de símbolos matemáticos">Tabela de símbolos matemáticos</a></li></ul> <table class="noprint" style="border-top:none; 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