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Средно квадратично – Уикипедия
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href="/wiki/%D0%9D%D0%B0%D1%87%D0%B0%D0%BB%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Уикипедия" src="/static/images/mobile/copyright/wikipedia-wordmark-bg.svg" style="width: 7.5em; height: 1.3125em;"> <img class="mw-logo-tagline" alt="Свободната енциклопедия" src="/static/images/mobile/copyright/wikipedia-tagline-bg.svg" width="120" height="12" style="width: 7.5em; height: 0.75em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A2%D1%8A%D1%80%D1%81%D0%B5%D0%BD%D0%B5" class="cdx-button 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<input type="hidden" name="title" value="Специални:Търсене"> </div> <button class="cdx-button cdx-search-input__end-button">Търсене</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Лични инструменти"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Облик"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Облик" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Облик</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_bg.wikipedia.org&uselang=bg" class=""><span>Направете дарение</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D1%8A%D0%B7%D0%B4%D0%B0%D0%B2%D0%B0%D0%BD%D0%B5_%D0%BD%D0%B0_%D1%81%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%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="Насърчаваме Ви да си създадете сметка и да влезете, въпреки че не е задължително." class=""><span>Създаване на сметка</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A0%D0%B5%D0%B3%D0%B8%D1%81%D1%82%D1%80%D0%B8%D1%80%D0%B0%D0%BD%D0%B5_%D0%B8%D0%BB%D0%B8_%D0%B2%D0%BB%D0%B8%D0%B7%D0%B0%D0%BD%D0%B5&returnto=%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="Препоръчваме Ви да влезете, въпреки, че не е задължително. [o]" accesskey="o" class=""><span>Влизане</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Допълнителни опции" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Лични инструменти" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Лични инструменти</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Потребителско меню" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_bg.wikipedia.org&uselang=bg"><span>Направете дарение</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D1%8A%D0%B7%D0%B4%D0%B0%D0%B2%D0%B0%D0%BD%D0%B5_%D0%BD%D0%B0_%D1%81%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%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="Насърчаваме Ви да си създадете сметка и да влезете, въпреки че не е задължително."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Създаване на сметка</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A0%D0%B5%D0%B3%D0%B8%D1%81%D1%82%D1%80%D0%B8%D1%80%D0%B0%D0%BD%D0%B5_%D0%B8%D0%BB%D0%B8_%D0%B2%D0%BB%D0%B8%D0%B7%D0%B0%D0%BD%D0%B5&returnto=%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="Препоръчваме Ви да влезете, въпреки, че не е задължително. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Влизане</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Страници за излезли от системата редактори <a href="/wiki/%D0%9F%D0%BE%D0%BC%D0%BE%D1%89:%D0%92%D1%8A%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" aria-label="Научете повече за редактирането"><span>научете повече</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%9C%D0%BE%D0%B8%D1%82%D0%B5_%D0%BF%D1%80%D0%B8%D0%BD%D0%BE%D1%81%D0%B8" title="Списък на промените, направени от този IP адрес [y]" accesskey="y"><span>Приноси</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%9C%D0%BE%D1%8F%D1%82%D0%B0_%D0%B1%D0%B5%D1%81%D0%B5%D0%B4%D0%B0" title="Дискусия относно редакциите от този адрес [n]" accesskey="n"><span>Беседа</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"><!-- CentralNotice --></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="Сайт"> <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="Съдържание" 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">Съдържание</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">преместване към страничната лента</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">скриване</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">Начало</div> </a> </li> <li id="toc-Определение" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Определение"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Определение</span> </div> </a> <ul id="toc-Определение-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Свойства" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Свойства"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Свойства</span> </div> </a> <ul id="toc-Свойства-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Употреба" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Употреба"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Употреба</span> </div> </a> <ul id="toc-Употреба-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-В_общи_вълнови_форми" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#В_общи_вълнови_форми"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>В общи вълнови форми</span> </div> </a> <ul id="toc-В_общи_вълнови_форми-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-В_електротехниката" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#В_електротехниката"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>В електротехниката</span> </div> </a> <button aria-controls="toc-В_електротехниката-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Превключване на подраздел В електротехниката</span> </button> <ul id="toc-В_електротехниката-sublist" class="vector-toc-list"> <li id="toc-Коефициент_на_полезно_действие_на_усилвателя" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Коефициент_на_полезно_действие_на_усилвателя"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Коефициент на полезно действие на усилвателя</span> </div> </a> <ul id="toc-Коефициент_на_полезно_действие_на_усилвателя-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Средноквадратична_непрекъснатост_на_пространствен_процес" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Средноквадратична_непрекъснатост_на_пространствен_процес"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Средноквадратична непрекъснатост на пространствен процес</span> </div> </a> <ul id="toc-Средноквадратична_непрекъснатост_на_пространствен_процес-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Средноквадратична_диференцируемост_на_едномерен_процес" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Средноквадратична_диференцируемост_на_едномерен_процес"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Средноквадратична диференцируемост на едномерен процес</span> </div> </a> <ul id="toc-Средноквадратична_диференцируемост_на_едномерен_процес-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Източници" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Източници"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Източници</span> </div> </a> <ul id="toc-Източници-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="Съдържание" 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="Скриване/показване на съдържанието" > <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">Скриване/показване на съдържанието</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">Средно квадратично</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="Към статията на друг език. Налична на 39 езика" > <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 езика</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 – арабски" lang="ar" hreflang="ar" data-title="جذر متوسط مربع" data-language-autonym="العربية" data-language-local-name="арабски" 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-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 – бенгалски" lang="bn" hreflang="bn" data-title="বর্গমূল গড় বর্গ" data-language-autonym="বাংলা" data-language-local-name="бенгалски" 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 – каталонски" lang="ca" hreflang="ca" data-title="Mitjana quadràtica" data-language-autonym="Català" data-language-local-name="каталонски" 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 – чешки" lang="cs" hreflang="cs" data-title="Kvadratický průměr" data-language-autonym="Čeština" data-language-local-name="чешки" 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 – датски" lang="da" hreflang="da" data-title="Effektiv værdi" data-language-autonym="Dansk" data-language-local-name="датски" 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 – немски" lang="de" hreflang="de" data-title="Quadratisches Mittel" data-language-autonym="Deutsch" data-language-local-name="немски" 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 – английски" lang="en" hreflang="en" data-title="Root mean square" data-language-autonym="English" data-language-local-name="английски" 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 – есперанто" lang="eo" hreflang="eo" data-title="Kvadrata averaĝo" data-language-autonym="Esperanto" data-language-local-name="есперанто" 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 – испански" lang="es" hreflang="es" data-title="Media cuadrática" data-language-autonym="Español" data-language-local-name="испански" 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 – естонски" lang="et" hreflang="et" data-title="Ruutkeskmine" data-language-autonym="Eesti" data-language-local-name="естонски" 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 – баски" lang="eu" hreflang="eu" data-title="Batezbesteko koadratiko" data-language-autonym="Euskara" data-language-local-name="баски" 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 – персийски" lang="fa" hreflang="fa" data-title="جذر میانگین مربعات" data-language-autonym="فارسی" data-language-local-name="персийски" 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 – фински" lang="fi" hreflang="fi" data-title="Neliöllinen keskiarvo" data-language-autonym="Suomi" data-language-local-name="фински" 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 – френски" lang="fr" hreflang="fr" data-title="Moyenne quadratique" data-language-autonym="Français" data-language-local-name="френски" 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 – иврит" lang="he" hreflang="he" data-title="שורש ממוצע הריבועים" data-language-autonym="עברית" data-language-local-name="иврит" 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 – хинди" lang="hi" hreflang="hi" data-title="वर्ग माध्य मूल" data-language-autonym="हिन्दी" data-language-local-name="хинди" 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 – унгарски" lang="hu" hreflang="hu" data-title="Négyzetes közép" data-language-autonym="Magyar" data-language-local-name="унгарски" 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 – индонезийски" lang="id" hreflang="id" data-title="Rata-rata kuadrat" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезийски" 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 – японски" lang="ja" hreflang="ja" data-title="二乗平均平方根" data-language-autonym="日本語" data-language-local-name="японски" 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 – казахски" lang="kk" hreflang="kk" data-title="Квадраттық орташалар" data-language-autonym="Қазақша" data-language-local-name="казахски" 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 – корейски" lang="ko" hreflang="ko" data-title="제곱평균제곱근" data-language-autonym="한국어" data-language-local-name="корейски" 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 – нидерландски" lang="nl" hreflang="nl" data-title="Kwadratisch gemiddelde" data-language-autonym="Nederlands" data-language-local-name="нидерландски" 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 – норвежки (букмол)" lang="nb" hreflang="nb" data-title="Kvadratisk gjennomsnitt" data-language-autonym="Norsk bokmål" data-language-local-name="норвежки (букмол)" 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 – полски" lang="pl" hreflang="pl" data-title="Średnia kwadratowa" data-language-autonym="Polski" data-language-local-name="полски" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Valor_eficaz" title="Valor eficaz – португалски" lang="pt" hreflang="pt" data-title="Valor eficaz" data-language-autonym="Português" data-language-local-name="португалски" 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/Medie_p%C4%83tratic%C4%83" title="Medie pătratică – румънски" lang="ro" hreflang="ro" data-title="Medie pătratică" data-language-autonym="Română" data-language-local-name="румънски" 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 – руски" lang="ru" hreflang="ru" data-title="Среднее квадратическое" data-language-autonym="Русский" data-language-local-name="руски" 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 – словашки" lang="sk" hreflang="sk" data-title="Kvadratický priemer" data-language-autonym="Slovenčina" data-language-local-name="словашки" 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 – сръбски" lang="sr" hreflang="sr" data-title="Квадратна средина" data-language-autonym="Српски / srpski" data-language-local-name="сръбски" 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 – шведски" lang="sv" hreflang="sv" data-title="Kvadratiskt medelvärde" data-language-autonym="Svenska" data-language-local-name="шведски" 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 – тайски" lang="th" hreflang="th" data-title="ค่าเฉลี่ยกำลังสอง" data-language-autonym="ไทย" data-language-local-name="тайски" 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 – турски" lang="tr" hreflang="tr" data-title="Karekök ortalama" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%B5%D1%80%D0%B5%D0%B4%D0%BD%D1%94_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B5" title="Середнє квадратичне – украински" lang="uk" hreflang="uk" data-title="Середнє квадратичне" data-language-autonym="Українська" data-language-local-name="украински" 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/%DA%86%DA%A9%D9%88%D8%B1%DB%8C_%D8%A7%D9%88%D8%B3%D8%B7" title="چکوری اوسط – урду" lang="ur" hreflang="ur" data-title="چکوری اوسط" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%C3%A1_tr%E1%BB%8B_hi%E1%BB%87u_d%E1%BB%A5ng" title="Giá trị hiệu dụng – виетнамски" lang="vi" hreflang="vi" data-title="Giá trị hiệu dụng" data-language-autonym="Tiếng Việt" data-language-local-name="виетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B9%B3%E6%96%B9%E5%B9%B3%E5%9D%87%E6%95%B0" title="平方平均数 – китайски" lang="zh" hreflang="zh" data-title="平方平均数" data-language-autonym="中文" data-language-local-name="китайски" 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/Q223323#sitelinks-wikipedia" title="Редактиране на междуезиковите препратки" class="wbc-editpage">Редактиране</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="Именни пространства"> <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/%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="Преглед на основната страница [c]" accesskey="c"><span>Статия</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%91%D0%B5%D1%81%D0%B5%D0%B4%D0%B0:%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&action=edit&redlink=1" rel="discussion" class="new" title="Беседа за страницата (страницата не съществува) [t]" accesskey="t"><span>Беседа</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" class="vector-dropdown-checkbox " aria-label="Промяна на езиковия вариант" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">български</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Прегледи"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/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"><span>Преглед</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%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&veaction=edit" title="Редактиране на страницата [v]" accesskey="v"><span>Редактиране</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%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&action=edit" title="Редактиране на изходния код на страницата [e]" accesskey="e"><span>Редактиране на кода</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%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&action=history" title="Предишни версии на страницата [h]" accesskey="h"><span>История</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Инструменти" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Инструменти</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Инструменти</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">преместване към страничната лента</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">скриване</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Допълнителни опции" > <div class="vector-menu-heading"> Действия </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/%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"><span>Преглед</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%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&veaction=edit" title="Редактиране на страницата [v]" accesskey="v"><span>Редактиране</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%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&action=edit" title="Редактиране на изходния код на страницата [e]" accesskey="e"><span>Редактиране на кода</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%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&action=history"><span>История</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Основни </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%9A%D0%B0%D0%BA%D0%B2%D0%BE_%D1%81%D0%BE%D1%87%D0%B8_%D0%BD%D0%B0%D1%81%D0%B0%D0%BC/%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="Списък на всички страници, сочещи насам [j]" accesskey="j"><span>Какво сочи насам</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D0%B2%D1%8A%D1%80%D0%B7%D0%B0%D0%BD%D0%B8_%D0%BF%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8/%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" rel="nofollow" title="Последните промени на страници, сочени от тази страница [k]" accesskey="k"><span>Свързани промени</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/MediaWiki:Uploadtext" title="Качи файлове [u]" accesskey="u"><span>Качване на файл</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B8" title="Списък на всички специални страници [q]" accesskey="q"><span>Специални страници</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%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&oldid=12329611" title="Постоянна препратка към тази версия на страницата"><span>Постоянна препратка</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%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&action=info" title="Повече за тази страница"><span>Информация за страницата</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A6%D0%B8%D1%82%D0%B8%D1%80%D0%B0%D0%BD%D0%B5&page=%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&id=12329611&wpFormIdentifier=titleform" title="Информация за начините за цитиране на тази страница"><span>Цитиране на статията</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:UrlShortener&url=https%3A%2F%2Fbg.wikipedia.org%2Fwiki%2F%25D0%25A1%25D1%2580%25D0%25B5%25D0%25B4%25D0%25BD%25D0%25BE_%25D0%25BA%25D0%25B2%25D0%25B0%25D0%25B4%25D1%2580%25D0%25B0%25D1%2582%25D0%25B8%25D1%2587%25D0%25BD%25D0%25BE"><span>Кратък URL адрес</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:QrCode&url=https%3A%2F%2Fbg.wikipedia.org%2Fwiki%2F%25D0%25A1%25D1%2580%25D0%25B5%25D0%25B4%25D0%25BD%25D0%25BE_%25D0%25BA%25D0%25B2%25D0%25B0%25D0%25B4%25D1%2580%25D0%25B0%25D1%2582%25D0%25B8%25D1%2587%25D0%25BD%25D0%25BE"><span>Изтегляне на QR код</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Отпечатване/изнасяне </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:Book&bookcmd=book_creator&referer=%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"><span>Създаване на книга</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:DownloadAsPdf&page=%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&action=show-download-screen"><span>Изтегляне като PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%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&printable=yes" title="Версия за печат на страницата [p]" accesskey="p"><span>Версия за печат</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> В други проекти </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q223323" title="Препратка към свързания обект от хранилището за данни [g]" accesskey="g"><span>Обект в Уикиданни</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Облик"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Облик</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">преместване към страничната лента</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">скриване</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">от Уикипедия, свободната енциклопедия</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="bg" dir="ltr"><p>В <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика">математиката</a> <b>средно квадратична (СК, ск)</b> или <b>ефективна стойност</b> (на <a href="/wiki/%D0%90%D0%BD%D0%B3%D0%BB%D0%B8%D0%B9%D1%81%D0%BA%D0%B8_%D0%B5%D0%B7%D0%B8%D0%BA" title="Английски език">английски</a>: <span lang="en" dir="ltr" style="font-style:italic">Root mean square</span>, <b>RMS</b> или <b>rms</b>), е <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика">статистическа</a> мярка за големината на променлива величина, която е частен случай на <a href="/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%BD%D0%B0_%D1%81%D1%82%D0%BE%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Средностепенна стойност">средностепенната стойност</a> при степенен показател <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 d=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28d2048804ba61b4fc8761e42223f561e0a7ce6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.477ex; height:2.176ex;" alt="{\displaystyle d=2}"></span>. Понятието е особено полезно, когато величините са положителни и отрицателни, например при <a href="/wiki/%D0%A1%D0%B8%D0%BD%D1%83%D1%81_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" class="mw-redirect" title="Синус (математика)">синусоидално</a> разпределение на стойностите. Терминът се използва в различни области на науката. В частност, чрез него се определя основното понятие в <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%B2%D0%B5%D1%80%D0%BE%D1%8F%D1%82%D0%BD%D0%BE%D1%81%D1%82%D0%B8%D1%82%D0%B5" title="Теория на вероятностите">теорията на вероятностите</a> и математическата <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика">статистика</a> – <a href="/wiki/%D0%94%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D0%B8%D1%8F_(%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%B2%D0%B5%D1%80%D0%BE%D1%8F%D1%82%D0%BD%D0%BE%D1%81%D1%82%D0%B8%D1%82%D0%B5)" title="Дисперсия (теория на вероятностите)">дисперсията</a> (квадратният корен от която се нарича <a href="/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_%D0%BE%D1%82%D0%BA%D0%BB%D0%BE%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5" title="Средноквадратично отклонение">средноквадратично отклонение</a>). Тясно свързан с това понятие е <a href="/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BD%D0%B0_%D0%BD%D0%B0%D0%B9-%D0%BC%D0%B0%D0%BB%D0%BA%D0%B8%D1%82%D0%B5_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B8" title="Метод на най-малките квадрати">методът на най-малките квадрати</a>, който има общонаучно значение. В частност, терминът широко се използва в <a href="/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%82%D0%B5%D1%85%D0%BD%D0%B8%D0%BA%D0%B0" class="mw-redirect" title="Електротехника">електротехниката</a>; напр. при дефиниране на ефективната стойност на <a href="/wiki/%D0%A2%D0%BE%D0%BA" class="mw-redirect" title="Ток">ток</a>, <a href="/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE_%D0%BD%D0%B0%D0%BF%D1%80%D0%B5%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Електрическо напрежение">напрежение</a> и <a href="/wiki/%D0%9C%D0%BE%D1%89%D0%BD%D0%BE%D1%81%D1%82" title="Мощност">мощност</a>.<sup id="cite_ref-Речник_на_научните_термини_1-0" class="reference"><a href="#cite_note-Речник_на_научните_термини-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-БЭС_2-0" class="reference"><a href="#cite_note-БЭС-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Определение"><span id=".D0.9E.D0.BF.D1.80.D0.B5.D0.B4.D0.B5.D0.BB.D0.B5.D0.BD.D0.B8.D0.B5"></span>Определение</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=1" title="Редактиране на раздел: Определение" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=1" title="Edit section's source code: Определение"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Средноквадратична стойност на набор от величини (или непрекъсната <a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Функция">функция</a>) е <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B5%D0%BD_%D0%BA%D0%BE%D1%80%D0%B5%D0%BD" title="Квадратен корен">квадратен корен</a> от <a href="/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%BE_%D0%B0%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%BE" class="mw-redirect" title="Средно аритметично">средно аритметичното</a> на квадратите на оригиналните стойности (или квадрата на функцията, която определя непрекъснатата форма). </p><p>В случай на набор от <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> стойности <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_{1},x_{2},\dots ,x_{n}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…<!-- … --></mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0416a78ac28f73940431b62ab4f8fd9ee84bbfde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.853ex; height:2.843ex;" alt="{\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}}"></span>, средноквадратичната стойност се определя чрез израза: </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 {ck} }={\sqrt {{{x_{1}}^{2}+{x_{2}}^{2}+\cdots +{x_{n}}^{2}} \over n}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">k</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>⋯<!-- ⋯ --></mo> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>n</mi> </mfrac> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\mathrm {ck} }={\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/60cddc582ba198fb39badcca68c5de19ee9d8a5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:31.788ex; height:6.176ex;" alt="{\displaystyle x_{\mathrm {ck} }={\sqrt {{{x_{1}}^{2}+{x_{2}}^{2}+\cdots +{x_{n}}^{2}} \over n}}.}"></span></dd></dl> <p>Може да бъде записана също и във вида: </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 {\overline {x}}={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}{x_{i}}^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <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> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {x}}={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}{x_{i}}^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99e7e85f9ec8a46a017028d3ba6f19e198d90ea9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:17.057ex; height:7.509ex;" alt="{\displaystyle {\overline {x}}={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}{x_{i}}^{2}}}.}"></span></dd></dl> <p>Претеглено средноквадратично се изчислява по формулата: </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 {\overline {x}}={\sqrt {{\frac {1}{\sum _{i=1}^{n}a_{i}}}\sum _{i=1}^{n}a_{i}{x_{i}}^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯<!-- ¯ --></mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <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> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </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> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {x}}={\sqrt {{\frac {1}{\sum _{i=1}^{n}a_{i}}}\sum _{i=1}^{n}a_{i}{x_{i}}^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f4ca68036f3f275005747ce25714b544beaeafc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:25.463ex; height:7.509ex;" alt="{\displaystyle {\overline {x}}={\sqrt {{\frac {1}{\sum _{i=1}^{n}a_{i}}}\sum _{i=1}^{n}a_{i}{x_{i}}^{2}}}.}"></span></dd></dl> <p>Съответната формула за непрекъсната функция (или форма) <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 f(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.927ex; height:2.843ex;" alt="{\displaystyle f(t)}"></span>, определена в интервала <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_{1}\leq t\leq T_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≤<!-- ≤ --></mo> <mi>t</mi> <mo>≤<!-- ≤ --></mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{1}\leq t\leq T_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2dd4b90746157322251391e1a894a0438e405ca7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.86ex; height:2.509ex;" alt="{\displaystyle T_{1}\leq t\leq T_{2}}"></span>, е: </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 f_{\mathrm {ck} }={\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"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">k</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 f_{\mathrm {ck} }={\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/2f5c783e3145f0c2b1d7057f955c50f3a5d92376" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:31.132ex; height:7.676ex;" alt="{\displaystyle f_{\mathrm {ck} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}},}"></span></dd></dl> <p>а средноквадратичната стойност за функция в целия обхват на време е: </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 f_{\mathrm {CK} }=\lim _{T\rightarrow \infty }{\sqrt {{1 \over {2T}}{\int _{-T}^{T}{[f(t)]}^{2}\,dt}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</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 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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\mathrm {CK} }=\lim _{T\rightarrow \infty }{\sqrt {{1 \over {2T}}{\int _{-T}^{T}{[f(t)]}^{2}\,dt}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdffab8c1d9d29e019402c8c439565b364dfd4da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.436ex; height:7.509ex;" alt="{\displaystyle f_{\mathrm {CK} }=\lim _{T\rightarrow \infty }{\sqrt {{1 \over {2T}}{\int _{-T}^{T}{[f(t)]}^{2}\,dt}}}.}"></span></dd></dl> <p>Когато функцията е периодична, средноквадратичната стойност за произволен обхват от време е равна на средноквадратичната стойност само за един пълен период на функцията. <sup id="cite_ref-Речник_на_научните_термини_1-1" class="reference"><a href="#cite_note-Речник_на_научните_термини-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Средноквадратичната стойност на непрекъсната функция или сигнал може да бъде приближена чрез изчисляване на средноквадратичната стойност на серии от дискретни стойности на функцията, взети през еднакъв интервал от време. </p><p>Във <a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%B5%D0%BD_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Функционален анализ">функционалния анализ</a> и теорията на измерването <b>средната квадратична конвергенция</b> се определя като <a href="/wiki/%D0%A1%D1%85%D0%BE%D0%B4%D0%B8%D0%BC%D0%BE%D1%81%D1%82" title="Сходимост">конвергенция</a> на <a href="/wiki/%D0%A0%D0%B5%D0%B4%D0%B8%D1%86%D0%B0" title="Редица">редица</a> в смисъла на <a href="/w/index.php?title=%D0%9D%D0%BE%D1%80%D0%BC%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" class="new" title="Норма (математика) (страницата не съществува)">нормата</a> за двумерно пространство <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 L^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba162c66ca85776c83557af5088cc6f8584d1912" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.637ex; height:2.676ex;" alt="{\displaystyle L^{2}}"></span>. </p><p>За означаване на СК се използват още символите <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 CK(x_{i})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>K</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CK(x_{i})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dda27e575994d3d1cff07ead282b35efe2a3eb57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.771ex; height:2.843ex;" alt="{\displaystyle CK(x_{i})}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q(x_{i})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q(x_{i})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14af98f28a0bdc720e50aae92b977b8d34be2374" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.777ex; height:2.843ex;" alt="{\displaystyle Q(x_{i})}"></span> и <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 {\sqrt {\langle x_{i}^{2}\rangle }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {\langle x_{i}^{2}\rangle }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/495493cbcf4c6dd9191bfb7278bced908bf3a54a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.517ex; height:4.843ex;" alt="{\displaystyle {\sqrt {\langle x_{i}^{2}\rangle }}}"></span> (нотация, често използвана във физиката, където ⟨ ⟩ означава средно аритметично). </p> <div class="mw-heading mw-heading2"><h2 id="Свойства"><span id=".D0.A1.D0.B2.D0.BE.D0.B9.D1.81.D1.82.D0.B2.D0.B0"></span>Свойства</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=2" title="Редактиране на раздел: Свойства" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=2" title="Edit section's source code: Свойства"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Средноквадратичното на набор от неотрицателни числа лежи между минималното и максималното число на набора.</li> <li>Средноквадратичната стойност е частен случай на <a href="/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%BD%D0%B0_%D1%81%D1%82%D0%BE%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Средностепенна стойност">средностепенната</a> и следователно се подчинява на неравенството на средните стойности. По-специално, за всякакви числа средноквадратичното не е по-малко от <a href="/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D0%B0%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%BE" class="mw-redirect" title="Средноаритметично">средноаритметичното</a>:</li></ul> <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 {x_{1}+x_{2}+\ldots +x_{n}}{n}}\leqslant {\sqrt {\frac {x_{1}^{2}+x_{2}^{2}+\ldots +x_{n}^{2}}{n}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>…<!-- … --></mo> <mo>+</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>⩽<!-- ⩽ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <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> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x_{1}+x_{2}+\ldots +x_{n}}{n}}\leqslant {\sqrt {\frac {x_{1}^{2}+x_{2}^{2}+\ldots +x_{n}^{2}}{n}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ca9170b5105c1f2ddfac5545c98628793421e65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:44.862ex; height:7.676ex;" alt="{\displaystyle {\frac {x_{1}+x_{2}+\ldots +x_{n}}{n}}\leqslant {\sqrt {\frac {x_{1}^{2}+x_{2}^{2}+\ldots +x_{n}^{2}}{n}}}.}"></span></dd></dl> <p>Например: <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 \langle 1,2,3,4\rangle ={\frac {1+2+3+4}{4}}=2,5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle 1,2,3,4\rangle ={\frac {1+2+3+4}{4}}=2,5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8ac62dc2e7f78b774d5178d7562c80533d6caf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:33.124ex; height:5.176ex;" alt="{\displaystyle \langle 1,2,3,4\rangle ={\frac {1+2+3+4}{4}}=2,5}"></span> e по-малко от </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CK(1,2,3,4)={\sqrt {\frac {1^{2}+2^{2}+3^{2}+4^{2}}{4}}}={\sqrt {\frac {30}{4}}}=2,7386.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>K</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>30</mn> <mn>4</mn> </mfrac> </msqrt> </mrow> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>7386.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CK(1,2,3,4)={\sqrt {\frac {1^{2}+2^{2}+3^{2}+4^{2}}{4}}}={\sqrt {\frac {30}{4}}}=2,7386.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2144b4bcd8b2f754cf5c8bef9b444e14fe4c3d99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:56.214ex; height:7.676ex;" alt="{\displaystyle CK(1,2,3,4)={\sqrt {\frac {1^{2}+2^{2}+3^{2}+4^{2}}{4}}}={\sqrt {\frac {30}{4}}}=2,7386.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Употреба"><span id=".D0.A3.D0.BF.D0.BE.D1.82.D1.80.D0.B5.D0.B1.D0.B0"></span>Употреба</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=3" title="Редактиране на раздел: Употреба" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=3" title="Edit section's source code: Употреба"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/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_%D0%BE%D1%82%D0%BA%D0%BB%D0%BE%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5" title="Средноквадратично отклонение">Стандартното отклонение</a> в съвкупността е средноквадратичната стойност на разликите от средната стойност. </p><p>Средноквадратичната стойност трябва да се използва, когато се търси осредняване на количество, което влияе на квадрата в дадено явление. Такъв е случаят например със скоростта на частиците в среда. Всяка частица <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bab39399bf5424f25d957cdc57c84a0622626d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.059ex; height:2.009ex;" alt="{\displaystyle p_{i}}"></span> се движи със скорост <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dffe5726650f6daac54829972a94f38eb8ec127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.927ex; height:2.009ex;" alt="{\displaystyle v_{i}}"></span> и произвежда <a href="/wiki/%D0%9A%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D0%B5%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D1%8F" title="Кинетична енергия">кинетична енергия</a>, равна на 1⁄2<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 mv_{i}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mv_{i}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3147c435bc031350f78ea8972c62496cf107746" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.222ex; height:3.176ex;" alt="{\displaystyle mv_{i}^{2}}"></span>. Средата отделя кинетична енергия </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}m\sum _{i=1}^{n}v_{i}^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <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>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}m\sum _{i=1}^{n}v_{i}^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6093d7240c0b47c75b9e8fa5bc07c3c7299ea15e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:10.997ex; height:6.843ex;" alt="{\displaystyle {\frac {1}{2}}m\sum _{i=1}^{n}v_{i}^{2}.}"></span></dd></dl> <p>Можем да опитаме да оценим скоростта <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span>, която, приложена към същия брой частици, ще даде същата кинетична енергия. Тази скорост е средната квадратична стойност на всички скорости. <sup id="cite_ref-Moyennes_(II)_3-0" class="reference"><a href="#cite_note-Moyennes_(II)-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Във физиката СК скорост се определя като корен квадратен от средната квадратна скорост на молекулите в газ. Средната квадратична скорост на идеален газ се изчислява с помощта на следното уравнение: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {v_{\mathrm {CK} }}={\sqrt {3RT \over {M}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>3</mn> <mi>R</mi> <mi>T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>M</mi> </mrow> </mfrac> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {v_{\mathrm {CK} }}={\sqrt {3RT \over {M}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d869481f293068f23d72a5933bd2aef453c8e004" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.293ex; height:6.176ex;" alt="{\displaystyle {v_{\mathrm {CK} }}={\sqrt {3RT \over {M}}},}"></span></dd></dl> <p>където <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> представлява идеалната газова <a href="/wiki/%D0%9A%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0" title="Константа">константа</a> (в този случай 8,314 J/(mol*K)), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> е температурата на газа в <a href="/wiki/%D0%9A%D0%B5%D0%BB%D0%B2%D0%B8%D0%BD" title="Келвин">келвини</a>, а <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 M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> е моларната маса на газа в <a href="/wiki/%D0%9A%D0%B8%D0%BB%D0%BE%D0%B3%D1%80%D0%B0%D0%BC" title="Килограм">килограми</a>. </p> <div class="mw-heading mw-heading2"><h2 id="В_общи_вълнови_форми"><span id=".D0.92_.D0.BE.D0.B1.D1.89.D0.B8_.D0.B2.D1.8A.D0.BB.D0.BD.D0.BE.D0.B2.D0.B8_.D1.84.D0.BE.D1.80.D0.BC.D0.B8"></span>В общи вълнови форми</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=4" title="Редактиране на раздел: В общи вълнови форми" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=4" title="Edit section's source code: В общи вълнови форми"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ако формата на вълната е периодична, връзките между амплитудите (пик или от пик до пик) и СК са фиксирани и известни, както са за всяка непрекъсната периодична вълна. </p><p>За нулева средна синусоида връзката между СК и амплитудата от пик до пик <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{PP}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{PP}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa49ddf5ca7cdeb9d2a1756aae4f308e64cec9d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.056ex; height:2.509ex;" alt="{\displaystyle V_{PP}}"></span> е </p> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Sine_wave_voltages.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Sine_wave_voltages.svg/270px-Sine_wave_voltages.svg.png" decoding="async" width="270" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Sine_wave_voltages.svg/405px-Sine_wave_voltages.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Sine_wave_voltages.svg/540px-Sine_wave_voltages.svg.png 2x" data-file-width="530" data-file-height="332" /></a><figcaption>СК стойности и амплитуди пик <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{PK}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{PK}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4682478961bdb28282adce8fde07bec62083e031" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.283ex; height:2.509ex;" alt="{\displaystyle V_{PK}}"></span> и от пик до пик <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{PP}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{PP}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa49ddf5ca7cdeb9d2a1756aae4f308e64cec9d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.056ex; height:2.509ex;" alt="{\displaystyle V_{PP}}"></span> на синусоидална вълна във времето <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, изразено чрез <a href="/wiki/%D0%A4%D0%B0%D0%B7%D0%B0" title="Фаза">фазата</a> в градуси.</figcaption></figure> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{PP}=2{\sqrt {2}}\times {\text{CK}}\approx 2,828\times {\text{CK}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>CK</mtext> </mrow> <mo>≈<!-- ≈ --></mo> <mn>2</mn> <mo>,</mo> <mn>828</mn> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>CK</mtext> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{PP}=2{\sqrt {2}}\times {\text{CK}}\approx 2,828\times {\text{CK}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7f4a0225e8b5c04d5cb806b19ffaf2ec6b1dcfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.497ex; height:3.009ex;" alt="{\displaystyle V_{PP}=2{\sqrt {2}}\times {\text{CK}}\approx 2,828\times {\text{CK}},}"></span></dd></dl> <p>а между СК <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{RMS}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>M</mi> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{RMS}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/827e9f02db4e4ea61705c5723be73c913a12e0d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.622ex; height:2.509ex;" alt="{\displaystyle V_{RMS}}"></span> и амплитудата пик <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{PK}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{PK}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4682478961bdb28282adce8fde07bec62083e031" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.283ex; height:2.509ex;" alt="{\displaystyle V_{PK}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CK={\frac {V_{PK}}{\sqrt {2}}}=0,707\times V_{PK}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>K</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>707</mn> <mo>×<!-- × --></mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CK={\frac {V_{PK}}{\sqrt {2}}}=0,707\times V_{PK}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/684c5cb54f0f8538d25ddd210d96791584800977" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:28.601ex; height:6.176ex;" alt="{\displaystyle CK={\frac {V_{PK}}{\sqrt {2}}}=0,707\times V_{PK}.}"></span></dd></dl> <p>За триъгълна или трионообразна вълна – съответно: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{PP}=2{\sqrt {3}}\times {\text{CK}}\approx 3,464\times {\text{CK}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>CK</mtext> </mrow> <mo>≈<!-- ≈ --></mo> <mn>3</mn> <mo>,</mo> <mn>464</mn> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>CK</mtext> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{PP}=2{\sqrt {3}}\times {\text{CK}}\approx 3,464\times {\text{CK}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fc46755eea8fb6353f380c8c5597083501b65ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.497ex; height:2.843ex;" alt="{\displaystyle V_{PP}=2{\sqrt {3}}\times {\text{CK}}\approx 3,464\times {\text{CK}},}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle CK={\frac {V_{PK}}{\sqrt {3}}}=0,577\times V_{PK}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>K</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> <msqrt> <mn>3</mn> </msqrt> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>577</mn> <mo>×<!-- × --></mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle CK={\frac {V_{PK}}{\sqrt {3}}}=0,577\times V_{PK}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f75f5b0fb2ef46a79be96e8d8dfe923e5b213d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:28.601ex; height:6.176ex;" alt="{\displaystyle CK={\frac {V_{PK}}{\sqrt {3}}}=0,577\times V_{PK}.}"></span></dd></dl> <p>За други форми на вълната, връзките са различни. В общия случай формата на вълната е произволна и може да не е периодична или непрекъсната. </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Waveforms.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Waveforms.svg/280px-Waveforms.svg.png" decoding="async" width="280" height="239" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Waveforms.svg/420px-Waveforms.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Waveforms.svg/560px-Waveforms.svg.png 2x" data-file-width="620" data-file-height="530" /></a><figcaption>Основни форми на вълни: синусоидална, квадратна (меандър), триъгълна и трионообразна.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Dutycycle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Dutycycle.svg/300px-Dutycycle.svg.png" decoding="async" width="300" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Dutycycle.svg/450px-Dutycycle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Dutycycle.svg/600px-Dutycycle.svg.png 2x" data-file-width="550" data-file-height="205" /></a><figcaption>Правоъгълна импулсна вълна с продължителност на импулса <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 \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ<!-- τ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span>, период <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> и коефициент на запълване <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 D={\frac {\tau }{T}}=1/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>τ<!-- τ --></mi> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D={\frac {\tau }{T}}=1/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8809ba7149d72cb193ba8539d20f494ff1206f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.081ex; height:4.676ex;" alt="{\displaystyle D={\frac {\tau }{T}}=1/3}"></span>.</figcaption></figure> <table class="wikitable" border="1"> <caption>СК на общи вълнови форми </caption> <tbody><tr> <th>Вълнови форми</th> <th>Формула</th> <th>СК </th></tr> <tr> <td><a href="/wiki/%D0%A1%D0%B8%D0%BD%D1%83%D1%81%D0%BE%D0%B8%D0%B4%D0%B0" class="mw-redirect" title="Синусоида">Синусоидална вълна</a></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<!-- 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/a960f23f52a92bfdb8bfb502d8af7cc40e258ff7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.049ex; 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/537230b274549a57d2ff6cc22b633007af3e010c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.934ex; height:6.343ex;" alt="{\displaystyle {\frac {A}{\sqrt {2}}}}"></span> </td></tr> <tr> <td><a href="/w/index.php?title=%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B0_%D0%B2%D1%8A%D0%BB%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Квадратна вълна (страницата не съществува)">Квадратна вълна</a> без пауза</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</mn> <mo>,</mo> <mn>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</mn> <mo>,</mo> <mn>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/0e02c91ead302bbb5746e87f5775f9310f320a8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.915ex; 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/c6aaf5ce10d6add44b973e28fb3d95f37abf3721" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.13ex; height:2.176ex;" alt="{\displaystyle A\,}"></span> </td></tr> <tr> <td>Квадратна вълна с пауза</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</mn> <mo>,</mo> <mn>25</mn> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mn>0</mn> <mo>,</mo> <mn>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</mn> <mo>,</mo> <mn>5</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> <mo>,</mo> <mn>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</mn> <mo>,</mo> <mn>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</mn> <mo>,</mo> <mn>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/7977ce994ab08968e7c6992d244a9332e0378c10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:35.857ex; 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/537230b274549a57d2ff6cc22b633007af3e010c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.934ex; height:6.343ex;" alt="{\displaystyle {\frac {A}{\sqrt {2}}}}"></span> </td></tr> <tr> <td><a href="/w/index.php?title=%D0%A2%D1%80%D0%B8%D0%BE%D0%BD%D0%BE%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BD%D0%B0_%D0%B2%D1%8A%D0%BB%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Трионообразна вълна (страницата не съществува)">Трионообразна вълна</a> </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=2A((ft)\%1)-A\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <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> <mo>−<!-- − --></mo> <mi>A</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=2A((ft)\%1)-A\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74822e1da58a60f5c590ca6ef2a6f6d5d2a51978" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.965ex; height:2.843ex;" alt="{\displaystyle y=2A((ft)\%1)-A\,}"></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/493b58bd59afb40d2fee15268dcc02d1c55c0ba9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.934ex; height:6.343ex;" alt="{\displaystyle A \over {\sqrt {3}}}"></span> </td></tr> <tr> <td colspan="3">Означения:<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> – времe<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> – чeстота<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=V_{PK}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=V_{PK}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/178039fb28c2e8b28acc20fdbb141e2212fe6d04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.124ex; height:2.509ex;" alt="{\displaystyle A=V_{PK}}"></span> – aмплитуда (пикова стойност)<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (...)\%1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo stretchy="false">)</mo> <mi mathvariant="normal">%<!-- % --></mi> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (...)\%1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a409a55aa36bbc6cf9a344cae57c364255e116fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.009ex; height:2.843ex;" alt="{\displaystyle (...)\%1}"></span> – <a href="/w/index.php?title=%D0%9E%D1%81%D1%82%D0%B0%D1%82%D1%8A%D0%BA_%D0%BE%D1%82_%D0%B5%D1%82%D0%B0%D0%B6%D0%BD%D0%BE_%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5&action=edit&redlink=1" class="new" title="Остатък от етажно деление (страницата не съществува)">остатък от етажното деление</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="В_електротехниката"><span id=".D0.92_.D0.B5.D0.BB.D0.B5.D0.BA.D1.82.D1.80.D0.BE.D1.82.D0.B5.D1.85.D0.BD.D0.B8.D0.BA.D0.B0.D1.82.D0.B0"></span>В електротехниката</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=5" title="Редактиране на раздел: В електротехниката" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=5" title="Edit section's source code: В електротехниката"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ефективните стойности на променливи ток <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06931e7bcffd32010f83c3d5dbef2d9bcbdcb670" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.451ex; height:2.843ex;" alt="{\displaystyle i(t)}"></span>, напрежение <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b375df3b65d282f8715835dc91ccb22f46993959" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle u(t)}"></span> и мощност <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b827c545ca1487214f0c498131228ef87718ece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:3.908ex; height:2.843ex;" alt="{\displaystyle p(t)}"></span> във времето <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> с период <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> са равни на съответните им постоянни стойности <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>, определящи същата енергия <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 E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> във верига със съпротивление <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=U\cdot I\cdot T=R\cdot I^{2}\cdot T=R\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>U</mi> <mo>⋅<!-- ⋅ --></mo> <mi>I</mi> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <mi>R</mi> <mo>⋅<!-- ⋅ --></mo> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <mi>R</mi> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=U\cdot I\cdot T=R\cdot I^{2}\cdot T=R\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11a5b674e191d89458e300ef8f78966ae1183c51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:49.207ex; height:6.509ex;" alt="{\displaystyle E=U\cdot I\cdot T=R\cdot I^{2}\cdot T=R\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t=}"></span> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ={\frac {U^{2}}{R}}\cdot T={\frac {1}{R}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t=P\cdot T=\int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>=</mo> <mi>P</mi> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <mi>p</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {U^{2}}{R}}\cdot T={\frac {1}{R}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t=P\cdot T=\int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf139f6b049ddf2af7ccfe1a6dc9c284b5c1404f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:59.145ex; height:6.509ex;" alt="{\displaystyle ={\frac {U^{2}}{R}}\cdot T={\frac {1}{R}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t=P\cdot T=\int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t.}"></span></dd></dl></dd></dl> <p><b>Ефективната стойност <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> на променлив ток</b> във времето с период <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> е равна на интензитета на постоянния ток, излъчващ същата енергия <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 E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> като <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06931e7bcffd32010f83c3d5dbef2d9bcbdcb670" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.451ex; height:2.843ex;" alt="{\displaystyle i(t)}"></span>, преминавайки през съпротивление <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> за период <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>: </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 E=R\cdot I^{2}\cdot T=R\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>R</mi> <mo>⋅<!-- ⋅ --></mo> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <mi>R</mi> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=R\cdot I^{2}\cdot T=R\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bacc027f9f73aec77c2c91d2b4b3b2e5f36e763" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:35.706ex; height:6.509ex;" alt="{\displaystyle E=R\cdot I^{2}\cdot T=R\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t}"></span></dd></dl> <p>Тогава ефективната стойност се изразява като квадратен корен от средно аритметичното на квадрата на тока за период <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f29e00e037acbecbe50897b33ce8b6d5ee688c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:26.007ex; height:7.676ex;" alt="{\displaystyle I={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}i^{2}(t)\cdot \mathrm {d} t}}}"></span></dd></dl> <p><b>Ефективната стойност <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span> на променливо напрежение</b> е стойността на постоянното напрежение, което излъчва същата енергия като променливото напрежение <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b375df3b65d282f8715835dc91ccb22f46993959" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle u(t)}"></span>, ако се приложи на изводите на същото съпротивление <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\frac {U^{2}}{R}}\cdot T={\frac {1}{R}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {U^{2}}{R}}\cdot T={\frac {1}{R}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fc8bca0e68d5d81db420522d19d077b396d6de6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:35.734ex; height:6.509ex;" alt="{\displaystyle E={\frac {U^{2}}{R}}\cdot T={\frac {1}{R}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t.}"></span></dd></dl> <p>От тук за ефективната стойност на напрежението се получава: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e02deef0a4cf21372cfc217ba831b87495696e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:27.145ex; height:7.676ex;" alt="{\displaystyle U={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}u^{2}(t)\cdot \mathrm {d} t}}}"></span></dd></dl> <p><b>Ефективната стойност <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> на променлива мощност</b> за период <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> е стойността на постоянната мощност, която съответства на същата енергия, излъчена от същото съпротивление <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=P\cdot T=\int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>P</mi> <mo>⋅<!-- ⋅ --></mo> <mi>T</mi> <mo>=</mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <mi>p</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=P\cdot T=\int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfbd3dbda74827e9116629014faba48045a61197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.254ex; height:6.509ex;" alt="{\displaystyle E=P\cdot T=\int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t.}"></span></dd></dl> <p>Математически се изразява чрез: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t}}=I^{2}\cdot R={\frac {U^{2}}{R}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>T</mi> </mrow> </msubsup> <mi>p</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </msqrt> </mrow> <mo>=</mo> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅<!-- ⋅ --></mo> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t}}=I^{2}\cdot R={\frac {U^{2}}{R}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99cf2539771427d4a42d6d9808a05c516fc7a0b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:42.182ex; height:7.676ex;" alt="{\displaystyle P={\sqrt {{\frac {1}{T}}\cdot \int _{t_{0}}^{t_{0}+T}p(t)\cdot \mathrm {d} t}}=I^{2}\cdot R={\frac {U^{2}}{R}}.}"></span></dd></dl> <p>Нарича се още <b>средна електрическа мощност</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {cp} }=P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {cp} }=P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bf78e7bb1d471bbcf7ce2300fb77c99d848c2af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.212ex; height:2.843ex;" alt="{\displaystyle P_{\mathrm {cp} }=P}"></span>. Ако токът и напрежението са променяща се функция във времето, във формулите за <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06931e7bcffd32010f83c3d5dbef2d9bcbdcb670" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.451ex; height:2.843ex;" alt="{\displaystyle i(t)}"></span> и <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b375df3b65d282f8715835dc91ccb22f46993959" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle u(t)}"></span> трябва да се замести видът на тази функция. Ако функцията е периодична (като променливотоковото захранване за масова употреба), средната мощност, разсейвана във времето, е средна стойност на мощността във всеки момент във формата на вълната или, еквивалентно, средният квадрат на тока или напрежението. Тогава, при постоянно съпротивление на консуматора <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=const}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=const}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b676ff578b80022ad07494d93f4f3a41acfee93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.322ex; height:2.176ex;" alt="{\displaystyle R=const}"></span> за средната мощност, изразена чрез тока се получава </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {cp} }=\langle i^{2}(t)R\rangle =R\langle i^{2}(t)\rangle =I_{CK}^{2}R,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>R</mi> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mo>=</mo> <mi>R</mi> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mo>=</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>K</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>R</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {cp} }=\langle i^{2}(t)R\rangle =R\langle i^{2}(t)\rangle =I_{CK}^{2}R,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e1dbf9568289aaca77c576774bd002667584eb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:35.198ex; height:3.343ex;" alt="{\displaystyle P_{\mathrm {cp} }=\langle i^{2}(t)R\rangle =R\langle i^{2}(t)\rangle =I_{CK}^{2}R,}"></span></dd></dl> <p>или изразена чрез напрежението </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {cp} }=\langle {\frac {u^{2}(t)}{R}}\rangle ={\frac {\langle u^{2}(t)\rangle }{R}}={\frac {U_{CK}^{2}}{R}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>R</mi> </mfrac> </mrow> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <msup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> </mrow> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>K</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>R</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {cp} }=\langle {\frac {u^{2}(t)}{R}}\rangle ={\frac {\langle u^{2}(t)\rangle }{R}}={\frac {U_{CK}^{2}}{R}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/553fb5e7ee6ea9deada1b08dd58b56b3344adad6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:34.033ex; height:6.176ex;" alt="{\displaystyle P_{\mathrm {cp} }=\langle {\frac {u^{2}(t)}{R}}\rangle ={\frac {\langle u^{2}(t)\rangle }{R}}={\frac {U_{CK}^{2}}{R}}.}"></span></dd></dl> <p>Чрез умножаване и коренуване на последните две уравнения средната мощност се изразява чрез ефективните стойности на напрежението и тока: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {cp} }=U_{CK}.I_{CK}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>K</mi> </mrow> </msub> <mo>.</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>K</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {cp} }=U_{CK}.I_{CK}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea33577f45a071cab9ef644ba95e431089cf7196" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.642ex; height:2.843ex;" alt="{\displaystyle P_{\mathrm {cp} }=U_{CK}.I_{CK}.}"></span></dd></dl> <p>Получените резултати се отнасят за случая, когато напрежението и токът са пропорционални (т.е. товарът <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> е чисто резистивен). Реактивните товари <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L},X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L},X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f9ca9a723c64c8df30eac055e700a3c92601a26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.715ex; height:2.509ex;" alt="{\displaystyle X_{L},X_{C}}"></span> не само разсейват енергия, но и я съхраняват, което води до загуби. </p><p>В обичайния случай, както е приблизително в мрежовото захранване, променливият ток е синусоидален: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i(t)=I_{\mathrm {m} }\sin(\omega t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i(t)=I_{\mathrm {m} }\sin(\omega t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36849a51caa6c36cfa14c9285a5f0c20465a3daa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.512ex; height:2.843ex;" alt="{\displaystyle i(t)=I_{\mathrm {m} }\sin(\omega t)}"></span>, където <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {m} }=V_{PK}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mi>K</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {m} }=V_{PK}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/263f1291f3fe4bd2f4c32103e8610e8f52e3cb98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.005ex; height:2.509ex;" alt="{\displaystyle I_{\mathrm {m} }=V_{PK}}"></span> e пиковата амплитуда на тока, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> е времето и <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\frac {2\pi }{T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π<!-- π --></mi> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ={\frac {2\pi }{T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/689caf6d9f39dbc57a3d4ee99c82c98e31193e72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.875ex; height:5.176ex;" alt="{\displaystyle \omega ={\frac {2\pi }{T}}}"></span> е ъгловата честота. Тогава: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {CK} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{(I_{\mathrm {m} }\sin(\omega t)}\,})^{2}dt}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</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> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mspace width="thinmathspace" /> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>t</mi> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {CK} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{(I_{\mathrm {m} }\sin(\omega t)}\,})^{2}dt}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0a4f85f2a4502705939d118821b92e4ee66ad30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:38.432ex; height:7.676ex;" alt="{\displaystyle I_{\mathrm {CK} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{(I_{\mathrm {m} }\sin(\omega t)}\,})^{2}dt}},}"></span></dd></dl> <p>Тъй като <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {m} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {m} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3732f76949ea7465224eb921257b57483abb129" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.624ex; height:2.509ex;" alt="{\displaystyle I_{\mathrm {m} }}"></span> е положителна константа, след тригонометрично преобразуване и интегриране се получава: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {CK} }=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{\sin ^{2}(\omega t)}\,dt}}}=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{1-\cos(2\omega t) \over 2}\,dt}}}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <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> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <mi>cos</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ω<!-- ω --></mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mrow> </msqrt> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {CK} }=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{\sin ^{2}(\omega t)}\,dt}}}=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{1-\cos(2\omega t) \over 2}\,dt}}}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95d0ee61b8077314128448928fdaffc5f30bc500" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:75.114ex; height:7.676ex;" alt="{\displaystyle I_{\mathrm {CK} }=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{\sin ^{2}(\omega t)}\,dt}}}=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{1-\cos(2\omega t) \over 2}\,dt}}}=}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}\left[{{t \over 2}-{\sin(2\omega t) \over 4\omega }}\right]_{T_{1}}^{T_{2}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <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> <msubsup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <mn>2</mn> </mfrac> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ω<!-- ω --></mi> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>4</mn> <mi>ω<!-- ω --></mi> </mrow> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <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> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}\left[{{t \over 2}-{\sin(2\omega t) \over 4\omega }}\right]_{T_{1}}^{T_{2}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9025353364116d8730cb7e1786adc74e6b286069" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.945ex; height:7.843ex;" alt="{\displaystyle =I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}\left[{{t \over 2}-{\sin(2\omega t) \over 4\omega }}\right]_{T_{1}}^{T_{2}}}},}"></span></dd></dl> <p>но тъй като интервалът <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_{2}-T_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{2}-T_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46319046abb75f3c2abe9791270199c7e08775f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.664ex; height:2.509ex;" alt="{\displaystyle T_{2}-T_{1}}"></span> е цял брой пълни цикли (по дефиниция на СК), <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 \sin(2\omega T_{2})-\sin(2\omega T_{1})=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ω<!-- ω --></mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−<!-- − --></mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ω<!-- ω --></mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(2\omega T_{2})-\sin(2\omega T_{1})=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/780a2c510a7bf83016e2e5f3b1198e590e196336" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.471ex; height:2.843ex;" alt="{\displaystyle \sin(2\omega T_{2})-\sin(2\omega T_{1})=0}"></span> и остава: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {CK} }=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}\left[{t \over 2}\right]_{T_{1}}^{T_{2}}}}=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{{T_{2}-T_{1}} \over 2}}}={I_{\mathrm {m} } \over {\sqrt {2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <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> <msubsup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <mn>2</mn> </mfrac> </mrow> <mo>]</mo> </mrow> <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> </msqrt> </mrow> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <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"> <mfrac> <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> <mn>2</mn> </mfrac> </mrow> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {CK} }=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}\left[{t \over 2}\right]_{T_{1}}^{T_{2}}}}=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{{T_{2}-T_{1}} \over 2}}}={I_{\mathrm {m} } \over {\sqrt {2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5d22e0a918e211e757ec01f19358c263deb80b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:59.471ex; height:8.009ex;" alt="{\displaystyle I_{\mathrm {CK} }=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}\left[{t \over 2}\right]_{T_{1}}^{T_{2}}}}=I_{\mathrm {m} }{\sqrt {{1 \over {T_{2}-T_{1}}}{{T_{2}-T_{1}} \over 2}}}={I_{\mathrm {m} } \over {\sqrt {2}}}.}"></span></dd></dl> <p>Подобен анализ води до аналогичното уравнение за синусоидално напрежение: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {CK} }={U_{\mathrm {m} } \over {\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {CK} }={U_{\mathrm {m} } \over {\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1225fbf9eb17f2da5d60cd86bb29ee575828ce4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:11.408ex; height:6.176ex;" alt="{\displaystyle U_{\mathrm {CK} }={U_{\mathrm {m} } \over {\sqrt {2}}}}"></span></dd></dl> <p>с пикова амплитуда <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {m} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {m} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3446ac289cd8412336fc8caa7f0c7091e7ec3785" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.189ex; height:2.509ex;" alt="{\displaystyle U_{\mathrm {m} }}"></span>. Струва си да се повтори, че тези две . </p><p>Получените решения за синусоидална вълна са полезни при изчисления на мощността. Ефективната (СК) стойност <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {CK} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {CK} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9d6527157b968a79d0f212d15b3a9907f5ec007" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.285ex; height:2.509ex;" alt="{\displaystyle U_{\mathrm {CK} }}"></span> на променливото напрежение е 230 V в Европа и 120 V в САЩ. Амплитудните пикови стойности могат да бъдат изчислени от СК стойности по горната формула, което означава <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {m} }=U_{\mathrm {CK} }\cdot {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {m} }=U_{\mathrm {CK} }\cdot {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db6b0de65722a71fccf138939cb910a449fdcf56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.349ex; height:3.009ex;" alt="{\displaystyle U_{\mathrm {m} }=U_{\mathrm {CK} }\cdot {\sqrt {2}}}"></span>, като се приеме, че източникът е чиста синусоида. Така за Европа пиковата стойност на мрежовото напрежение е <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {PK} }=325,27}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">K</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>325</mn> <mo>,</mo> <mn>27</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {PK} }=325,27}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a99a67da0bef81493e53b40a94d63c4fe9fbaed2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.162ex; height:2.509ex;" alt="{\displaystyle U_{\mathrm {PK} }=325,27}"></span> волта, а напрежението от пик до пик е два пъти повече – <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {PP} }=650,54}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>650</mn> <mo>,</mo> <mn>54</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {PP} }=650,54}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6aaa66c7be3a986878408e3788a3368096f61b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.003ex; height:2.509ex;" alt="{\displaystyle U_{\mathrm {PP} }=650,54}"></span> волта. В САЩ пиковата амплитуда е около 170 волта, а от пик до пик е около 340 волта. </p><p>Аналогично може да се изчисли и пиковата мощност. Тя няма особено физическо значение и се използва най-често в <a href="/w/index.php?title=%D0%97%D0%B2%D1%83%D0%BA%D0%BE%D0%B2%D0%B0_%D1%82%D0%B5%D1%85%D0%BD%D0%B8%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Звукова техника (страницата не съществува)">звуковата техника</a>. </p> <table class="wikitable centre"> <caption>Ефективни стойности за прости променливи сигнали </caption> <tbody><tr> <th>Сигнал </th> <th>Форма на вълната </th> <th width="20%"><i>I</i> </th> <th width="20%"><i>U</i> </th> <th width="20%"><i>P</i> </th></tr> <tr> <td>Синусоидален </td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Simple_sine_wave.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Simple_sine_wave.svg/100px-Simple_sine_wave.svg.png" decoding="async" width="100" height="75" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Simple_sine_wave.svg/150px-Simple_sine_wave.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Simple_sine_wave.svg/200px-Simple_sine_wave.svg.png 2x" data-file-width="512" data-file-height="384" /></a></span> </td> <td align="center"><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 {I_{\mathrm {max} }}{\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {I_{\mathrm {max} }}{\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d583e89e5f7ee9fa8ac242ab5463d517e917290" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:5.15ex; height:6.176ex;" alt="{\displaystyle {\frac {I_{\mathrm {max} }}{\sqrt {2}}}}"></span> </td> <td align="center"><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 {U_{\mathrm {max} }}{\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {U_{\mathrm {max} }}{\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/784ed17d5944e8ea6860180d24c94bcc1543cdd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:5.715ex; height:6.176ex;" alt="{\displaystyle {\frac {U_{\mathrm {max} }}{\sqrt {2}}}}"></span> </td> <td align="center"><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 {P_{\mathrm {max} }}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {P_{\mathrm {max} }}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/217eef30cde1afd8c86cbbc608eee883e43c9926" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.619ex; height:5.176ex;" alt="{\displaystyle {\frac {P_{\mathrm {max} }}{2}}}"></span> </td></tr> <tr> <td>Триъгълен </td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Triangle_wave.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Triangle_wave.svg/100px-Triangle_wave.svg.png" decoding="async" width="100" height="75" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Triangle_wave.svg/150px-Triangle_wave.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Triangle_wave.svg/200px-Triangle_wave.svg.png 2x" data-file-width="1000" data-file-height="750" /></a></span> </td> <td align="center"><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 {I_{\mathrm {max} }}{\sqrt {3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <msqrt> <mn>3</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {I_{\mathrm {max} }}{\sqrt {3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a776039e77dcb6390f155472e08d87416ab84062" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:5.15ex; height:6.176ex;" alt="{\displaystyle {\frac {I_{\mathrm {max} }}{\sqrt {3}}}}"></span> </td> <td align="center"><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 {U_{\mathrm {max} }}{\sqrt {3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <msqrt> <mn>3</mn> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {U_{\mathrm {max} }}{\sqrt {3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/555fbade33bb11b746c40aa6fb4c5d29eb8b7628" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:5.715ex; height:6.176ex;" alt="{\displaystyle {\frac {U_{\mathrm {max} }}{\sqrt {3}}}}"></span> </td> <td align="center"><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 {P_{\mathrm {max} }}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {P_{\mathrm {max} }}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4b174feba19b44908acf27510b9c50b464baf42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.619ex; height:5.176ex;" alt="{\displaystyle {\frac {P_{\mathrm {max} }}{3}}}"></span> </td></tr> <tr> <td>Квадратен симетричен <br />(без пауза) </td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Square_wave.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Square_wave.svg/100px-Square_wave.svg.png" decoding="async" width="100" height="75" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Square_wave.svg/150px-Square_wave.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Square_wave.svg/200px-Square_wave.svg.png 2x" data-file-width="1000" data-file-height="750" /></a></span> </td> <td align="center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {max} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {max} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2e3ae131f4cb6a62441f4beedeef61c6b76f932" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.314ex; height:2.509ex;" alt="{\displaystyle I_{\mathrm {max} }}"></span> </td> <td align="center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\mathrm {max} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\mathrm {max} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50ff47e02c4fe94af8d4be1c2e2a400992582f12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.879ex; height:2.509ex;" alt="{\displaystyle U_{\mathrm {max} }}"></span> </td> <td align="center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {max} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {max} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbe333f446faeb268b5e8f7227412e30c16785d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.783ex; height:2.509ex;" alt="{\displaystyle P_{\mathrm {max} }}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Коефициент_на_полезно_действие_на_усилвателя"><span id=".D0.9A.D0.BE.D0.B5.D1.84.D0.B8.D1.86.D0.B8.D0.B5.D0.BD.D1.82_.D0.BD.D0.B0_.D0.BF.D0.BE.D0.BB.D0.B5.D0.B7.D0.BD.D0.BE_.D0.B4.D0.B5.D0.B9.D1.81.D1.82.D0.B2.D0.B8.D0.B5_.D0.BD.D0.B0_.D1.83.D1.81.D0.B8.D0.BB.D0.B2.D0.B0.D1.82.D0.B5.D0.BB.D1.8F"></span>Коефициент на полезно действие на усилвателя</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=6" title="Редактиране на раздел: Коефициент на полезно действие на усилвателя" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=6" title="Edit section's source code: Коефициент на полезно действие на усилвателя"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Коефициент на полезно действие на електронния усилвател е съотношението на средната изходна мощност към средната входна мощност <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q={\frac {P_{u}}{P_{B}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q={\frac {P_{u}}{P_{B}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/844ecef29c5ad3c4ab8703d66b143079121d6945" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:7.976ex; height:5.509ex;" alt="{\displaystyle q={\frac {P_{u}}{P_{B}}}}"></span>. Ако изходът е резистивен, средната изходна мощност може да се намери по описания начин чрез СК стойности на изходния ток и напрежение на сигналите. Въпреки това, средната стойност на тока трябва да се използва за изчисляване на входната мощност. Тоест, мощността, доставена от усилвателя чрез постоянното напрежение <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcc9fcb0ce866995b80e65e290d442ddf072441f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.069ex; height:2.509ex;" alt="{\displaystyle U_{C}}"></span> е </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {B} }(t)=I_{y}U_{C}+I_{\mathrm {u} }(t)U_{C}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {B} }(t)=I_{y}U_{C}+I_{\mathrm {u} }(t)U_{C}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b19b1765a052e2c6fa7262884b6c65649b2a238" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.891ex; height:3.009ex;" alt="{\displaystyle P_{\mathrm {B} }(t)=I_{y}U_{C}+I_{\mathrm {u} }(t)U_{C}\,}"></span></dd></dl> <p>където <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f3eedd0871fd35e1fd8992c53812cd60d1b07c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.072ex; height:2.843ex;" alt="{\displaystyle I_{y}}"></span> е работният ток на усилвателя. Ясно е, че тъй като <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcc9fcb0ce866995b80e65e290d442ddf072441f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.069ex; height:2.509ex;" alt="{\displaystyle U_{C}}"></span> е константа, средното време на <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\mathrm {B} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {B} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcea02a827c14aa42e232cee88724d6c801d9566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.888ex; height:2.509ex;" alt="{\displaystyle P_{\mathrm {B} }}"></span> зависи от <i>средната времева</i> стойност на <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\mathrm {u} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {u} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505b227a98a82af26274c5d0fb917800638cb84f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.169ex; height:2.509ex;" alt="{\displaystyle I_{\mathrm {u} }}"></span>, а не от неговата СК стойност. Това е </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 \langle P_{\mathrm {B} }(t)\rangle =I_{y}U_{C}+\langle I_{\mathrm {u} }(t)\rangle U_{C}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>+</mo> <mo fence="false" stretchy="false">⟨<!-- ⟨ --></mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle P_{\mathrm {B} }(t)\rangle =I_{y}U_{C}+\langle I_{\mathrm {u} }(t)\rangle U_{C}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58f8c5627607811bc706ed05b2dbf4c46fb1772b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.157ex; height:3.009ex;" alt="{\displaystyle \langle P_{\mathrm {B} }(t)\rangle =I_{y}U_{C}+\langle I_{\mathrm {u} }(t)\rangle U_{C}.\,}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Средноквадратична_непрекъснатост_на_пространствен_процес"><span id=".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.B0_.D0.BD.D0.B5.D0.BF.D1.80.D0.B5.D0.BA.D1.8A.D1.81.D0.BD.D0.B0.D1.82.D0.BE.D1.81.D1.82_.D0.BD.D0.B0_.D0.BF.D1.80.D0.BE.D1.81.D1.82.D1.80.D0.B0.D0.BD.D1.81.D1.82.D0.B2.D0.B5.D0.BD_.D0.BF.D1.80.D0.BE.D1.86.D0.B5.D1.81"></span>Средноквадратична непрекъснатост на пространствен процес</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=7" title="Редактиране на раздел: Средноквадратична непрекъснатост на пространствен процес" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=7" title="Edit section's source code: Средноквадратична непрекъснатост на пространствен процес"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Определение</b> — <a href="/w/index.php?title=%D0%9F%D1%80%D0%BE%D1%86%D0%B5%D1%81_%D0%BE%D1%82_%D0%B2%D1%82%D0%BE%D1%80%D0%B8_%D1%80%D0%B5%D0%B4&action=edit&redlink=1" class="new" title="Процес от втори ред (страницата не съществува)">Процес от втори ред</a> <i>X</i> върху пространствено множество <i>S</i> ⊂ ℝ<i><sup>d</sup></i> е непрекъснат средноквадратично, ако за всяка <a href="/wiki/%D0%A1%D1%85%D0%BE%D0%B4%D0%B8%D0%BC%D0%BE%D1%81%D1%82" title="Сходимост">конвергентна</a> последователност <i>s<sub>n</sub> → s</i> от <i>S</i>, <b>E</b>[<i>X</i>(<i>s<sub>n</sub></i>) − <i>X</i>(s)]<sup>2</sup> → 0. </p><p><b>Характеризиране</b> — Центриран <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 L^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba162c66ca85776c83557af5088cc6f8584d1912" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.637ex; height:2.676ex;" alt="{\displaystyle L^{2}}"></span> процес е непрекъснат средноквадратично навсякъде, ако неговата <a href="/w/index.php?title=%D0%9A%D0%BE%D0%B2%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D1%8F&action=edit&redlink=1" class="new" title="Ковариация (страницата не съществува)">ковариация</a> е непрекъсната по диагонала на неговото пространствено множество. </p><p>Непрекъснатостта по диагонала означава, че ковариацията <i>C</i>(<i>s, s</i>) е непрекъсната за всички <i>s</i> в пространственото множество. </p><p><b>Теорема</b> — Ако присъщ <a href="/w/index.php?title=%D0%93%D0%B0%D1%83%D1%81%D0%BE%D0%B2%D1%81%D0%BA%D0%B8_%D0%BF%D1%80%D0%BE%D1%86%D0%B5%D1%81&action=edit&redlink=1" class="new" title="Гаусовски процес (страницата не съществува)">Гаусовски процес</a> с <a href="/w/index.php?title=%D0%92%D0%B0%D1%80%D0%B8%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D0%B0&action=edit&redlink=1" class="new" title="Вариограма (страницата не съществува)">вариограма</a> <i>γ</i> проверява <i>γ</i>(<i>h</i>) ≤ |log∥<i>h</i>∥|<sup>−(1+ε)</sup> в близост до началото, тогава той почти сигурно е <a href="/wiki/%D0%9D%D0%B5%D0%BF%D1%80%D0%B5%D0%BA%D1%8A%D1%81%D0%BD%D0%B0%D1%82%D0%BE%D1%81%D1%82" title="Непрекъснатост">непрекъснат</a>. </p><p>Такъв е случаят с всички стандартни модели на вариограми, с изключение на модела с ефект на самородно късче. </p><p><b>Теорема</b> — Един присъщ процес е средноквадратично непрекъснат, ако неговата вариограма е непрекъсната в началото. </p><p><a href="/w/index.php?title=%D0%A1%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D1%80%D0%B5%D0%BD_%D0%BF%D1%80%D0%BE%D1%86%D0%B5%D1%81&action=edit&redlink=1" class="new" title="Стационарен процес (страницата не съществува)">Стационарен процес</a> от втори ред е средноквадратично непрекъснат, ако неговата ковариация е непрекъсната в началото.<sup id="cite_ref-Стохастични_процеси_4-0" class="reference"><a href="#cite_note-Стохастични_процеси-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Moyennes_(II)_3-1" class="reference"><a href="#cite_note-Moyennes_(II)-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Средноквадратична_диференцируемост_на_едномерен_процес"><span id=".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.B0_.D0.B4.D0.B8.D1.84.D0.B5.D1.80.D0.B5.D0.BD.D1.86.D0.B8.D1.80.D1.83.D0.B5.D0.BC.D0.BE.D1.81.D1.82_.D0.BD.D0.B0_.D0.B5.D0.B4.D0.BD.D0.BE.D0.BC.D0.B5.D1.80.D0.B5.D0.BD_.D0.BF.D1.80.D0.BE.D1.86.D0.B5.D1.81"></span>Средноквадратична диференцируемост на едномерен процес</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=8" title="Редактиране на раздел: Средноквадратична диференцируемост на едномерен процес" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=8" title="Edit section's source code: Средноквадратична диференцируемост на едномерен процес"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="boilerplate plainlinks stub"><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/23px-Wiki_letter_w.svg.png" decoding="async" width="23" height="23" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/35px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/46px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span> <sup><i>Този раздел е празен или е <a href="/wiki/%D0%A3%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%9C%D1%8A%D0%BD%D0%B8%D1%87%D0%B5" title="Уикипедия:Мъниче">мъниче</a>. Можете да помогнете на Уикипедия, като го <a class="external text" href="https://bg.wikipedia.org/w/index.php?title=%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&action=edit">разширите</a>.</i></sup></div> <div class="mw-heading mw-heading2"><h2 id="Източници"><span id=".D0.98.D0.B7.D1.82.D0.BE.D1.87.D0.BD.D0.B8.D1.86.D0.B8"></span>Източници</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=9" title="Редактиране на раздел: Източници" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=9" title="Edit section's source code: Източници"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Речник_на_научните_термини-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Речник_на_научните_термини_1-0"><sup><i><b>а</b></i></sup></a> <a href="#cite_ref-Речник_на_научните_термини_1-1"><sup><i><b>б</b></i></sup></a></span> <span class="reference-text">Речник на научните термини – Е. Б. Уваров, А. Айзакс. Издателство „Петър Берон“, 1992.</span> </li> <li id="cite_note-БЭС-2"><span class="mw-cite-backlink"><a href="#cite_ref-БЭС_2-0">↑</a></span> <span class="reference-text"><cite id="CITEREFКвадратичное_среднее2000" class="book" style="font-style:normal">Квадратичное среднее. Большой Энциклопедический словарь.  2000.<span class="cite-lang"> <small style="color: var(--color-subtle, #54595d);">(на руски)</small></span></cite></span> </li> <li id="cite_note-Moyennes_(II)-3"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Moyennes_(II)_3-0"><sup><i><b>а</b></i></sup></a> <a href="#cite_ref-Moyennes_(II)_3-1"><sup><i><b>б</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://images.math.cnrs.fr/Moyennes-II-la-moyenne-quadratique.html?lang=fr">Moyennes (II) : la moyenne quadratique </a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221208172507/http://images.math.cnrs.fr/Moyennes-II-la-moyenne-quadratique.html?lang=fr">Архив на оригинала от</a> 2022-12-08 в <a href="/wiki/Wayback_Machine" class="mw-redirect" title="Wayback Machine">Wayback Machine</a>. – Ecrit par Kloeckner, BenoîtLe, 15 août 2009.</span> </li> <li id="cite_note-Стохастични_процеси-4"><span class="mw-cite-backlink"><a href="#cite_ref-Стохастични_процеси_4-0">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100123200347/http://www.fmi.uni-sofia.bg/fmi/statist/library/proc/proc.htm">Въведение в стохастичните процеси</a> – Г. Бошнаков, Стилян Стоев, Д. Въндев, 1999–2008.</span> </li> </ol></div> <table cellspacing="2" style="clear:both; background:white; border:1px dotted rgb(153, 153, 153); padding:.3em; margin-top:.8em; margin-bottom:.5em; font-size:85%;"> <tbody><tr> <td width="90px"><span typeof="mw:File"><a href="/wiki/%D0%9A%D1%80%D0%B8%D0%B5%D0%B9%D1%82%D0%B8%D0%B2_%D0%9A%D0%BE%D0%BC%D1%8A%D0%BD%D1%81" title="Криейтив Комънс"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/CC_BY-SA_icon.svg/60px-CC_BY-SA_icon.svg.png" decoding="async" width="60" height="21" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/CC_BY-SA_icon.svg/90px-CC_BY-SA_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/CC_BY-SA_icon.svg/120px-CC_BY-SA_icon.svg.png 2x" data-file-width="88" data-file-height="31" /></a></span> <span typeof="mw:File"><a href="/wiki/%D0%9B%D0%B8%D1%86%D0%B5%D0%BD%D0%B7_%D0%B7%D0%B0_%D1%81%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0_%D0%B4%D0%BE%D0%BA%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%86%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%93%D0%9D%D0%A3" title="Лиценз за свободна документация на ГНУ"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Heckert_GNU_white.svg/20px-Heckert_GNU_white.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Heckert_GNU_white.svg/30px-Heckert_GNU_white.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Heckert_GNU_white.svg/40px-Heckert_GNU_white.svg.png 2x" data-file-width="535" data-file-height="523" /></a></span> </td> <td style="font-style:italic">Тази страница частично или изцяло представлява превод на страницата <a href="https://en.wikipedia.org/wiki/Special:PermaLink/347203459" class="extiw" title="en:Special:PermaLink/347203459">Root mean square</a> и страницата <a href="https://fr.wikipedia.org/wiki/Special:PermaLink/144555277" class="extiw" title="fr:Special:PermaLink/144555277">Valeur efficace</a> в Уикипедия на английски и френски език. Оригиналните текстове, както и този превод, са защитени от <a href="/wiki/%D0%9A%D1%80%D0%B8%D0%B5%D0%B9%D1%82%D0%B8%D0%B2_%D0%9A%D0%BE%D0%BC%D1%8A%D0%BD%D1%81" title="Криейтив Комънс">Лиценза „Криейтив Комънс – Признание – Споделяне на споделеното“</a>, а за творби, създадени преди юни 2009 година – от <a href="/wiki/%D0%9B%D0%B8%D1%86%D0%B5%D0%BD%D0%B7_%D0%B7%D0%B0_%D1%81%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0_%D0%B4%D0%BE%D0%BA%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%86%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%93%D0%9D%D0%A3" title="Лиценз за свободна документация на ГНУ">Лиценза за свободна документация на ГНУ</a>. Прегледайте историята на редакциите на оригиналните страници <a href="https://en.wikipedia.org/wiki/Special:PageHistory/Root_mean_square" class="extiw" title="en:Special:PageHistory/Root mean square">тук</a> и <a href="https://fr.wikipedia.org/wiki/Special:PageHistory/Valeur_efficace" class="extiw" title="fr:Special:PageHistory/Valeur efficace">тук</a>, за да видите списъка на техните съавтори. ​ <p><b>ВАЖНО:</b> Този шаблон се отнася единствено до <a href="/wiki/%D0%A3:%D0%90%D0%9F" class="mw-redirect" title="У:АП">авторските права</a> върху съдържанието на статията. Добавянето му не отменя изискването да се посочват <a href="/wiki/%D0%A3:%D0%A6%D0%98" class="mw-redirect" title="У:ЦИ">конкретни източници на твърденията</a>, които да бъдат <a href="/wiki/%D0%A3:%D0%91%D0%98" class="mw-redirect" title="У:БИ">благонадеждни</a>. </p> </td></tr></tbody></table> <table cellspacing="2" style="clear:both; background:var(--background-color-base, #fff); color:inherit; border:1px dotted var(--border-color-base, #a2a9b1); padding:.3em; margin-top:.8em; margin-bottom:.5em; font-size:85%;"> <tbody><tr> <td width="90px"><span typeof="mw:File"><a href="/wiki/%D0%9A%D1%80%D0%B8%D0%B5%D0%B9%D1%82%D0%B8%D0%B2_%D0%9A%D0%BE%D0%BC%D1%8A%D0%BD%D1%81" title="Криейтив Комънс"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/CC_BY-SA_icon.svg/60px-CC_BY-SA_icon.svg.png" decoding="async" width="60" height="21" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/CC_BY-SA_icon.svg/90px-CC_BY-SA_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/CC_BY-SA_icon.svg/120px-CC_BY-SA_icon.svg.png 2x" data-file-width="88" data-file-height="31" /></a></span> <span typeof="mw:File"><a href="/wiki/%D0%9B%D0%B8%D1%86%D0%B5%D0%BD%D0%B7_%D0%B7%D0%B0_%D1%81%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0_%D0%B4%D0%BE%D0%BA%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%86%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%93%D0%9D%D0%A3" title="Лиценз за свободна документация на ГНУ"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Heckert_GNU_white.svg/20px-Heckert_GNU_white.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Heckert_GNU_white.svg/30px-Heckert_GNU_white.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Heckert_GNU_white.svg/40px-Heckert_GNU_white.svg.png 2x" data-file-width="535" data-file-height="523" /></a></span> </td> <td style="font-style:italic">Тази страница частично или изцяло представлява <a href="/wiki/%D0%A3%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%9F%D1%80%D0%B5%D0%B2%D0%BE%D0%B4" title="Уикипедия:Превод">превод</a> на страницата <a href="https://ru.wikipedia.org/wiki/Special:Permalink/106217420" class="extiw" title="ru:Special:Permalink/106217420">„Среднее квадратическое“</a> в Уикипедия на руски. Оригиналният текст, както и този превод, са защитени от <a href="/wiki/%D0%9A%D1%80%D0%B8%D0%B5%D0%B9%D1%82%D0%B8%D0%B2_%D0%9A%D0%BE%D0%BC%D1%8A%D0%BD%D1%81" title="Криейтив Комънс">Лиценза „Криейтив Комънс – Признание – Споделяне на споделеното“</a>, а за съдържание, създадено преди юни 2009 година – от <a href="/wiki/%D0%9B%D0%B8%D1%86%D0%B5%D0%BD%D0%B7_%D0%B7%D0%B0_%D1%81%D0%B2%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0_%D0%B4%D0%BE%D0%BA%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%86%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%93%D0%9D%D0%A3" title="Лиценз за свободна документация на ГНУ">Лиценза за свободна документация на ГНУ</a>. Прегледайте <a href="https://ru.wikipedia.org/wiki/Special:PageHistory/%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" class="extiw" title="ru:Special:PageHistory/Среднее квадратическое">историята на редакциите</a> на оригиналната страница, както и на <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:PageHistory/%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="Специални:PageHistory/Средно квадратично">преводната страница</a>, за да видите списъка на съавторите. ​ <p><b>ВАЖНО:</b> Този шаблон се отнася единствено до <a href="/wiki/%D0%A3:%D0%90%D0%9F" class="mw-redirect" title="У:АП">авторските права</a> върху съдържанието на статията. Добавянето му не отменя изискването да се посочват <a href="/wiki/%D0%A3:%D0%A6%D0%98" class="mw-redirect" title="У:ЦИ">конкретни източници на твърденията</a>, които да бъдат <a href="/wiki/%D0%A3:%D0%91%D0%98" class="mw-redirect" title="У:БИ">благонадеждни</a>.​ </p> </td></tr></tbody></table> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐66695f89d8‐vt4pp Cached time: 20241119183023 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.180 seconds Real time usage: 0.380 seconds Preprocessor visited node count: 1434/1000000 Post‐expand include size: 8570/2097152 bytes Template argument size: 1109/2097152 bytes Highest expansion depth: 14/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 8104/5000000 bytes Lua time usage: 0.016/10.000 seconds Lua memory usage: 1028574/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 87.406 1 -total 30.39% 26.567 1 Шаблон:Lang 29.56% 25.839 1 Шаблон:Cite_book 26.95% 23.553 1 Шаблон:Cite 13.22% 11.551 1 Шаблон:Webarchive 11.97% 10.459 1 Шаблон:Източник_БДС_17377 9.67% 8.450 1 Шаблон:Превод_от_2 7.65% 6.688 1 Шаблон:If_empty 3.97% 3.469 3 Шаблон:Заглавие 3.78% 3.306 1 Шаблон:Превод_от --> <!-- Saved in parser cache with key bgwiki:pcache:291822:|#|:idhash:canonical and timestamp 20241119183023 and revision id 12329611. 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