{"id":145123,"date":"2024-03-21T14:05:50","date_gmt":"2024-03-21T14:05:50","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/formula-do-capacitor-cilindrico-uso-calculo\/"},"modified":"2024-03-22T05:54:55","modified_gmt":"2024-03-22T05:54:55","slug":"formula-do-capacitor-cilindrico-uso-calculo","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/","title":{"rendered":"F\u00f3rmula do Capacitor Cil\u00edndrico | Uso &#038; C\u00e1lculo"},"content":{"rendered":"<p class=\"sidekick\">Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.<\/p>\n<h2>Introdu\u00e7\u00e3o ao Capacitor Cil\u00edndrico<\/h2>\n<p>Capacitores s\u00e3o componentes vitais em circuitos el\u00e9tricos, armazenando e liberando energia el\u00e9trica. Eles v\u00eam em diferentes formas e tamanhos, cada um projetado para aplica\u00e7\u00f5es espec\u00edficas. O capacitor cil\u00edndrico, especificamente, \u00e9 uma forma interessante que consiste em dois condutores cil\u00edndricos conc\u00eantricos, usualmente separados por um material diel\u00e9trico. Este design oferece uma capacidade de armazenamento de carga eficiente e \u00e9 frequentemente utilizado em situa\u00e7\u00f5es onde o espa\u00e7o ou o campo el\u00e9trico m\u00e1ximo s\u00e3o fatores cr\u00edticos.<\/p>\n<h2>Usos do Capacitor Cil\u00edndrico<\/h2>\n<p>Capacitores cil\u00edndricos s\u00e3o comuns onde campos el\u00e9tricos uniformes s\u00e3o necess\u00e1rios, como em filtros de linha, aplica\u00e7\u00f5es de r\u00e1diofrequ\u00eancia e em equipamentos de medi\u00e7\u00e3o. A sua constru\u00e7\u00e3o f\u00edsica tamb\u00e9m lhes confere uma vantagem em termos de resist\u00eancia mec\u00e2nica e robustez, tornando-os adequados para ambientes adversos.<\/p>\n<h2>F\u00f3rmula do Capacitor Cil\u00edndrico<\/h2>\n<p>A capacidade de um capacitor \u00e9 medida em farads (F) e indica a quantidade de carga el\u00e9trica que o capacitor pode armazenar por unidade de tens\u00e3o aplicada. A f\u00f3rmula para calcular a capacit\u00e2ncia (C) de um capacitor cil\u00edndrico \u00e9 derivada considerando as propriedades geom\u00e9tricas dos cilindros e as propriedades do material diel\u00e9trico usado para separ\u00e1-los.<\/p>\n<p>A express\u00e3o matem\u00e1tica para a capacit\u00e2ncia de um capacitor cil\u00edndrico \u00e9:<\/p>\n<p>\\[ C = \\frac{2\\pi\\epsilon}{\\ln\\left(\\frac{b}{a}\\right)} \\]<\/p>\n<p>Onde:<\/p>\n<ul>\n<li>\\(\\epsilon\\) \u00e9 a permissividade do material diel\u00e9trico entre os cilindros;<\/li>\n<li>\\(a\\) \u00e9 o raio do cilindro interno;<\/li>\n<li>\\(b\\) \u00e9 o raio do cilindro externo;<\/li>\n<li>\\(\\pi\\) \u00e9 a constante Pi, aproximadamente 3.14159;<\/li>\n<li>\\(ln\\) \u00e9 o logaritmo natural.<\/li>\n<\/ul>\n<p>\u00c9 importante observar que a permissividade \\(\\epsilon\\) \u00e9 geralmente o produto da permissividade do v\u00e1cuo \\(\\epsilon_0\\) e a permissividade relativa do diel\u00e9trico \\(\\epsilon_r\\), tal que \\(\\epsilon = \\epsilon_0 \\epsilon_r\\).<\/p>\n<h2>C\u00e1lculo da Capacit\u00e2ncia<\/h2>\n<p>Vamos calcular a capacit\u00e2ncia de um capacitor cil\u00edndrico com um raio interno de 1 cm (0,01 m), um raio externo de 2 cm (0,02 m) e um diel\u00e9trico com uma permissividade relativa de 4. A permissividade do v\u00e1cuo (\\(\\epsilon_0\\)) \u00e9 uma constante aproximadamente igual a \\(8.854 \\times 10^{-12} F\/m\\).<\/p>\n<p>Primeiro, calculamos a permissividade do diel\u00e9trico:<\/p>\n<p>\\[ \\epsilon = \\epsilon_0 \\epsilon_r \\]<br \/>\n\\[ \\epsilon = (8.854 \\times 10^{-12}) \\times 4 \\]<br \/>\n\\[ \\epsilon = 3.5416 \\times 10^{-11} F\/m \\]<\/p>\n<p>Agora, aplicamos os valores na f\u00f3rmula da capacit\u00e2ncia:<\/p>\n<p>\\[ C = \\frac{2\\pi(3.5416 \\times 10^{-11})}{\\ln\\left(\\frac{0.02}{0.01}\\right)} \\]<br \/>\n\\[ C = \\frac{2 \\times 3.14159 \\times 3.5416 \\times 10^{-11}}{\\ln(2)} \\]<br \/>\n\\[ C \u2248 \\frac{2.22073 \\times 10^{-10}}{0.693147} \\]<br \/>\n\\[ C \u2248 3.203 \\times 10^{-10} F \\]<br \/>\n\\[ C \u2248 320.3 pF \\] <!-- pF \u00e9 picofarads, que \u00e9 igual a 10^-12 farads --><\/p>\n<p>O resultado \u00e9 que a capacit\u00e2ncia do nosso capacitor cil\u00edndrico \u00e9 aproximadamente 320.3 picofarads.<\/p>\n<h2>Conclus\u00e3o<\/h2>\n<p>Compreender o c\u00e1lculo da capacit\u00e2ncia de um capacitor cil\u00edndrico \u00e9 fundamental para projetar circuitos eficientes e para aplica\u00e7\u00f5es pr\u00e1ticas da engenharia eletr\u00f4nica. Embora o processo envolva algumas etapas matem\u00e1ticas, a f\u00f3rmula \u00e9 direta e um poderoso exemplo de como a f\u00edsica e a geometria se unem para nos ajudar a entender e a projetar componentes el\u00e9tricos no mundo real.<\/p>\n<p>Esperamos que esta explica\u00e7\u00e3o tenha tornado o conceito de capacitor cil\u00edndrico e seu c\u00e1lculo mais acess\u00edvel a todos, incentivando uma maior explora\u00e7\u00e3o no fascinante campo da eletricidade e do magnetismo.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_generate-full-width-content":"","footnotes":""},"categories":[84],"tags":[85],"class_list":["post-145123","post","type-post","status-publish","format-standard","hentry","category-ecuaciones","tag-ecuaciones","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>F\u00f3rmula do Capacitor Cil\u00edndrico | Uso &amp; C\u00e1lculo<\/title>\n<meta name=\"description\" content=\"Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"F\u00f3rmula do Capacitor Cil\u00edndrico | Uso &amp; C\u00e1lculo\" \/>\n<meta property=\"og:description\" content=\"Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/\" \/>\n<meta property=\"og:site_name\" content=\"Electricity - Magnetism\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-21T14:05:50+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-22T05:54:55+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Matan\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/#website\",\"url\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/\",\"name\":\"Electricity - Magnetism\",\"description\":\"All about electricity and magnetism.\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/#webpage\",\"url\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/\",\"name\":\"F\\u00f3rmula do Capacitor Cil\\u00edndrico | Uso & C\\u00e1lculo\",\"isPartOf\":{\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/#website\"},\"datePublished\":\"2024-03-21T14:05:50+00:00\",\"dateModified\":\"2024-03-22T05:54:55+00:00\",\"author\":{\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/#\/schema\/person\/68f28ba0ad08ef355b436c5222a40b29\"},\"description\":\"Descubra como os capacitores cil\\u00edndricos armazenam energia, suas aplica\\u00e7\\u00f5es pr\\u00e1ticas e aprenda a calcular sua capacit\\u00e2ncia com f\\u00f3rmulas simples.\",\"breadcrumb\":{\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/electricity-magnetism-page\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"F\\u00f3rmula do Capacitor Cil\\u00edndrico | Uso &#038; C\\u00e1lculo\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/#\/schema\/person\/68f28ba0ad08ef355b436c5222a40b29\",\"name\":\"Matan\",\"url\":\"https:\/\/www.electricity-magnetism.org\/pt-br\/author\/matan\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"F\u00f3rmula do Capacitor Cil\u00edndrico | Uso & C\u00e1lculo","description":"Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/","og_locale":"pt_BR","og_type":"article","og_title":"F\u00f3rmula do Capacitor Cil\u00edndrico | Uso & C\u00e1lculo","og_description":"Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.","og_url":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/","og_site_name":"Electricity - Magnetism","article_published_time":"2024-03-21T14:05:50+00:00","article_modified_time":"2024-03-22T05:54:55+00:00","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Matan","Est. tempo de leitura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/#website","url":"https:\/\/www.electricity-magnetism.org\/pt-br\/","name":"Electricity - Magnetism","description":"All about electricity and magnetism.","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.electricity-magnetism.org\/pt-br\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"WebPage","@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/#webpage","url":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/","name":"F\u00f3rmula do Capacitor Cil\u00edndrico | Uso & C\u00e1lculo","isPartOf":{"@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/#website"},"datePublished":"2024-03-21T14:05:50+00:00","dateModified":"2024-03-22T05:54:55+00:00","author":{"@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/#\/schema\/person\/68f28ba0ad08ef355b436c5222a40b29"},"description":"Descubra como os capacitores cil\u00edndricos armazenam energia, suas aplica\u00e7\u00f5es pr\u00e1ticas e aprenda a calcular sua capacit\u00e2ncia com f\u00f3rmulas simples.","breadcrumb":{"@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/formula-do-capacitor-cilindrico-uso-calculo\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.electricity-magnetism.org\/pt-br\/electricity-magnetism-page\/"},{"@type":"ListItem","position":2,"name":"F\u00f3rmula do Capacitor Cil\u00edndrico | Uso &#038; C\u00e1lculo"}]},{"@type":"Person","@id":"https:\/\/www.electricity-magnetism.org\/pt-br\/#\/schema\/person\/68f28ba0ad08ef355b436c5222a40b29","name":"Matan","url":"https:\/\/www.electricity-magnetism.org\/pt-br\/author\/matan\/"}]}},"_links":{"self":[{"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/posts\/145123","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/comments?post=145123"}],"version-history":[{"count":0,"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/posts\/145123\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/media?parent=145123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/categories?post=145123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.electricity-magnetism.org\/pt-br\/wp-json\/wp\/v2\/tags?post=145123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}