{"id":2401,"date":"2015-03-06T15:18:05","date_gmt":"2015-03-06T18:18:05","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=2401"},"modified":"2023-12-12T15:49:47","modified_gmt":"2023-12-12T18:49:47","slug":"resistividade-eletrica","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/","title":{"rendered":"Condutividade El\u00e9trica CC"},"content":{"rendered":"<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\"><em>&#8220;<strong>Descobertas decorrem de acidentes que encontram mentes preparadas.&#8221;<\/strong><\/em><\/span><\/p>\n<p style=\"text-align: right;\"><span style=\"font-family: verdana, geneva, sans-serif; font-size: 14pt;\"><em>Albert Szent-Gyorgyi<\/em><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os materiais el\u00e9tricos dominam o mundo devido \u00e0 sua capacidade de conduzir eletricidade, denominada de condutividade el\u00e9trica. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os cabos el\u00e9tricos conectam as usinas de gera\u00e7\u00e3o de energia a todos os consumidores no planeta, e os telefones fixos n\u00e3o funcionariam sem os cabos telef\u00f4nicos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Resist\u00eancias el\u00e9tricas transformam eletricidade em calor. O chuveiro el\u00e9trico, o ferro de passar roupas, o secador de cabelos, o forno el\u00e9trico, e o fog\u00e3o el\u00e9trico fazem parte do conjunto de equipamentos onde a resist\u00eancia el\u00e9trica representa o elemento primordial para seu funcionamento. Al\u00e9m disso, resist\u00eancias el\u00e9tricas atuam como coadjuvantes no funcionamento dos equipamentos eletr\u00f4nicos e telecomunica\u00e7\u00f5es, tais como televis\u00e3o, computador, e telefone celular.<\/span><\/p>\n<h2 id='resistividade-e-condutividade-el\u00e9tricas'  id=\"boomdevs_1\"><span style=\"font-family: verdana, geneva, sans-serif;\">Resistividade e Condutividade El\u00e9tricas<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por se tratar de uma <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/\">grandeza extensiva<\/a>, a ci\u00eancia dos materiais n\u00e3o utiliza a resist\u00eancia el\u00e9trica porque seu valor depende das dimens\u00f5es do material. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Contudo, a Equa\u00e7\u00e3o 1 transforma a resist\u00eancia el\u00e9trica numa grandeza intensiva relativa ao volume, denominada de resistividade el\u00e9trica volum\u00e9trica.<\/span><\/p>\n<figure id=\"attachment_44181\" aria-describedby=\"caption-attachment-44181\" style=\"width: 250px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-44181\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/rhoe.png\" alt=\"\" width=\"250\" height=\"266\" \/><figcaption id=\"caption-attachment-44181\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. Resistividade e condutividade el\u00e9trica volum\u00e9tricas<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">R \u00e9 a resist\u00eancia el\u00e9trica [\u03a9].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a \u00e1rea da <strong>se\u00e7\u00e3o reta do condutor perpendicular ao fluxo da corrente el\u00e9trica<\/strong> [m<sup>2<\/sup>].<span id='easy-footnote-1-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-1-2401' title=' prestem aten\u00e7\u00e3o nesse detalhe'><sup>1<\/sup><\/a><\/span><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">L \u00e9 o comprimento do condutor na dire\u00e7\u00e3o da corrente el\u00e9trica[m].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c3<sub>ev<\/sub> \u00e9 a condutividade el\u00e9trica volum\u00e9trica do material [S\/m].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>ev<\/sub> \u00e9 a resistividade el\u00e9trica volum\u00e9trica do material [\u03a9.m].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Outra forma de definir a resistividade el\u00e9trica consiste na utiliza\u00e7\u00e3o da massa do material de acordo com a Equa\u00e7\u00e3o 2. Observa-se que a <strong>resistividade m\u00e1ssica equivale \u00e0 resistividade volum\u00e9trica multiplicada pela massa espec\u00edfica<\/strong> do material.<\/span><\/p>\n<figure id=\"attachment_44182\" aria-describedby=\"caption-attachment-44182\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-44182\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/resistividade_massa1-1.png\" alt=\"\" width=\"500\" height=\"539\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/resistividade_massa1-1.png 608w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/resistividade_massa1-1-278x300.png 278w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-44182\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Resistividade el\u00e9trica m\u00e1ssica<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">R \u00e9 a resist\u00eancia el\u00e9trica [\u03a9].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>em<\/sub> \u00e9 a resistividade el\u00e9trica m\u00e1ssica [\u03a9.kg\/m<sup>2<\/sup>].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a \u00e1rea da se\u00e7\u00e3o reta do condutor perpendicular ao fluxo da corrente el\u00e9trica [m<sup>2<\/sup>].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">L \u00e9 o comprimento do condutor na dire\u00e7\u00e3o da corrente el\u00e9trica[m].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>m<\/sub> \u00e9 a massa espec\u00edfica[kg\/m3].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>ev<\/sub> \u00e9 a resistividade el\u00e9trica volum\u00e9trica do material [\u03a9.m].<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, a massa espec\u00edfica relaciona as duas propriedades el\u00e9tricas.<\/span><\/p>\n<h2 id='modelo-de-drude'  id=\"boomdevs_2\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo de Drude<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Em 1827, <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Georg_Simon_Ohm\" target=\"_blank\" rel=\"noopener\">Georg Ohm<\/a> formulou sua famosa Lei, baseado em resultados emp\u00edricos, que relaciona tens\u00e3o e corrente num condutor. De acordo com sua teoria, essa rela\u00e7\u00e3o se mant\u00e9m constante e foi denominada de <strong>Resist\u00eancia El\u00e9trica<\/strong>. Contudo, ela depende do material e varia em fun\u00e7\u00e3o de energias externas.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A descoberta do El\u00e9tron revolucionou a f\u00edsica em 1897, e\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Paul_Drude\" target=\"_blank\" rel=\"noopener\">Paul Drude<\/a> publicou, em 1900<span id='easy-footnote-2-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-2-2401\" title=\" ano importante na f\u00edsica e eletricidade\"><sup>2<\/sup><\/a><\/span>, sua <a href=\"https:\/\/en.wikipedia.org\/wiki\/Drude_model\" target=\"_blank\" rel=\"noopener\">teoria<\/a> sobre a condu\u00e7\u00e3o el\u00e9trica reunindo as novas descobertas da F\u00edsica com o conhecimento emp\u00edrico de Ohm. Os \u00e1tomos de metais s\u00f3lidos se mant\u00eam unidos atrav\u00e9s da liga\u00e7\u00e3o met\u00e1lica, onde os el\u00e9trons de val\u00eancia permanecem livres para circular em todo o material. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, ele aplicou a mec\u00e2nica cl\u00e1ssica aos &#8220;el\u00e9trons livres&#8221;, para explicar os fen\u00f4menos de condu\u00e7\u00e3o el\u00e9trica e t\u00e9rmica, e a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Valence_(chemistry)#Historical_development\" target=\"_blank\" rel=\"noopener\">Val\u00eancia Qu\u00edmica<\/a>, proposta em 1884 para designar a capacidade de associa\u00e7\u00e3o qu\u00edmica entre elementos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Figura 1 ilustra o conceito utilizado por Drude. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O n\u00facleo do \u00e1tomo (azul) possui uma carga positiva proporcional ao n\u00famero at\u00f4mico do material (Za) e \u00e0 carga do El\u00e9tron (e). O n\u00facleo se encontra fixo na estrutura cristalina do material. Essa hip\u00f3tese, apesar de falsa, consiste numa primeira aproxima\u00e7\u00e3o que explica alguns fen\u00f4menos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os el\u00e9trons se encontram ao redor do n\u00facleo, que foram divididos em dois grupos, os <a href=\"https:\/\/en.wikipedia.org\/wiki\/Valence_electron\" target=\"_blank\" rel=\"noopener\">El\u00e9trons de Val\u00eancia<\/a> (Z em verde) e os demais (Z<sub>a<\/sub> em vermelho).\u00a0<\/span><\/p>\n<hr \/>\n<h4 id='revis\u00e3o'  id=\"boomdevs_3\">Revis\u00e3o<\/h4>\n<ol>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Como se determinam os el\u00e9trons de val\u00eancia dos elementos do <a href=\"https:\/\/youtu.be\/kcIYurM4s0M\" target=\"_blank\" rel=\"noopener\">grupo principal da tabela peri\u00f3dica<\/a>?<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Como se determinam os <a href=\"https:\/\/youtu.be\/0JNIYDtfXzw\" target=\"_blank\" rel=\"noopener\">El\u00e9trons de Val\u00eancia<\/a> dos <a href=\"https:\/\/youtu.be\/4uvF3zCtwz4\" target=\"_blank\" rel=\"noopener\">Elementos de Transi\u00e7\u00e3o<\/a> da tabela peri\u00f3dica?<\/span><\/li>\n<\/ol>\n<hr \/>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Drude considerou que os el\u00e9trons livres, poderiam se movimentar por todo o material como mol\u00e9culas de um g\u00e1s<span id='easy-footnote-3-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-3-2401\" title=\" a teoria dos gases representava a f\u00edsica mais moderna na ocasi\u00e3o\"><sup>3<\/sup><\/a><\/span>, colidindo eventualmente com as esferas fixas dos el\u00e9trons presos ao n\u00facleo.\u00a0<\/span><\/p>\n<figure id=\"attachment_10103\" aria-describedby=\"caption-attachment-10103\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Drude.png\"><img decoding=\"async\" class=\"wp-image-10103\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Drude.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Drude.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Drude-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Drude-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-10103\" class=\"wp-caption-text\">Figura 1. Modelo de Drude<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O primeiro passo da teoria de Drude consistiu em estimar a densidade desse &#8220;g\u00e1s&#8221; eletr\u00f4nico da seguinte maneira:<\/span><\/p>\n<figure id=\"attachment_10112\" aria-describedby=\"caption-attachment-10112\" style=\"width: 369px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/dens_eletrons.png\"><img decoding=\"async\" class=\"wp-image-10112 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/dens_eletrons.png\" alt=\"\" width=\"369\" height=\"89\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/dens_eletrons.png 369w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/dens_eletrons-300x72.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/a><figcaption id=\"caption-attachment-10112\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 3. Densidade de El\u00e9trons no material.<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n \u00e9 a densidade de El\u00e9trons Livres [elementos\/m<sup>3<\/sup>].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">N \u00e9 o n\u00famero total de El\u00e9trons Livres [elementos].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">V \u00e9 o volume total do material [m<sup>3<\/sup>].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">N<sub>a<\/sub> \u00e9 a <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/constantes-fisicas\/\">constante de Avogadro<\/a> [elementos\/mol];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Z \u00e9 n\u00famero de El\u00e9trons de Val\u00eancia [elementos].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>m<\/sub> \u00e9 a densidade do material [kg\/m<sup>3<\/sup>].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a massa at\u00f4mica do material [g\/mol].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este modelo utilizou as seguintes premissas:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Os el\u00e9trons livres n\u00e3o interagem com outros el\u00e9trons nem com os \u00edons nos intervalos entre colis\u00f5es;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A repuls\u00e3o el\u00e9trica entre os el\u00e9trons livres e os \u00edons altera abruptamente apenas a dire\u00e7\u00e3o do El\u00e9tron e, como numa colis\u00e3o el\u00e1stica <span id='easy-footnote-4-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-4-2401\" title=\" pode-se visualizar essa colis\u00e3o como a colis\u00e3o de uma bola de bilhar com uma bola de boliche\"><sup>4<\/sup><\/a><\/span> , a energia permanece constante;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O tempo m\u00e9dio entre colis\u00f5es, denominado de <strong>tempo de relaxa\u00e7\u00e3o<\/strong>, tempo entre colis\u00f5es, ou tempo m\u00e9dio livre constitui par\u00e2metro fundamental do modelo.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">O equil\u00edbrio t\u00e9rmico dos el\u00e9trons ocorre apenas atrav\u00e9s das colis\u00f5es.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h6 id='exerc\u00edcio-proposto'  id=\"boomdevs_4\">Exerc\u00edcio Proposto<\/h6>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Fa\u00e7a um gr\u00e1fico da densidade de el\u00e9trons livres de seis metais com elevada condutividade e seis com baixa.<\/span><\/p>\n<hr \/>\n<h3 id='modelo-para-corrente-cont\u00ednua'  id=\"boomdevs_5\"><span style=\"font-family: verdana, geneva, sans-serif;\">Modelo para Corrente Cont\u00ednua<\/span><\/h3>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Considerando todos os el\u00e9trons se movendo com velocidade v, a densidade de corrente possuir\u00e1 a mesma dire\u00e7\u00e3o, conforme mostra a Figura 2, e a Equa\u00e7\u00e3o 4 fornece a quantidade de cargas atravessando a \u00e1rea perpendicular \u00e0 velocidade das part\u00edculas -A.<\/span><\/p>\n<figure id=\"attachment_10156\" aria-describedby=\"caption-attachment-10156\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1.png\"><img decoding=\"async\" class=\"wp-image-10156\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1.png\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1.png 1920w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-300x225.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-1024x768.png 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-768x576.png 768w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-1536x1152.png 1536w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-2048x1536.png 2048w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-1200x900.png 1200w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/corrente_1-1980x1485.png 1980w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><figcaption id=\"caption-attachment-10156\" class=\"wp-caption-text\">Figura 2. El\u00e9trons Livres no Metal<\/figcaption><\/figure>\n<figure id=\"attachment_10165\" aria-describedby=\"caption-attachment-10165\" style=\"width: 348px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/eq_2_drude.png\"><img decoding=\"async\" class=\"wp-image-10165 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/eq_2_drude.png\" alt=\"\" width=\"348\" height=\"49\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/eq_2_drude.png 348w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/eq_2_drude-300x42.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/a><figcaption id=\"caption-attachment-10165\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4. Quantidade de cargas<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>Q<\/em> \u00e9 a quantidade de cargas atravessando a \u00e1rea A [C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19<\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>n<\/em> \u00e9 a densidade de El\u00e9trons Livres [elementos\/m<sup>3<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>A<\/em> \u00e9 a \u00e1rea perpendicular ao fluxo da corrente [m<sup>2<\/sup>]<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>v<\/em> \u00e9 a velocidade m\u00e9dia dos El\u00e9trons Livres ocasionada pelo campo el\u00e9trico [m\/s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>dt<\/em> \u00e9 o intervalo de tempo infinitesimal.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 5, obtida a partir da Equa\u00e7\u00e3o 4, fornece a densidade da corrente.<\/span><\/p>\n<figure id=\"attachment_10171\" aria-describedby=\"caption-attachment-10171\" style=\"width: 227px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/jnev.png\"><img decoding=\"async\" class=\"wp-image-10171 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/jnev.png\" alt=\"\" width=\"227\" height=\"47\" \/><\/a><figcaption id=\"caption-attachment-10171\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 5. Densidade de corrente<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>J<\/em> \u00e9 a densidade de corrente [A\/m<sup>2<\/sup>]<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19<\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>n<\/em> \u00e9 a densidade de El\u00e9trons Livres [elementos\/m<sup>3<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>v<\/em> \u00e9 a velocidade m\u00e9dia dos El\u00e9trons Livres ocasionada pelo campo el\u00e9trico [m\/s].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Contudo, os el\u00e9trons se movem em dire\u00e7\u00f5es aleat\u00f3rias e com velocidades proporcionais \u00e0 energia t\u00e9rmica e ao campo el\u00e9trico aplicado. Por isso, torna-se necess\u00e1rio considerar essas duas componentes separadamente.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Determina-se a componente da velocidade dos el\u00e9trons referente \u00e0 temperatura &#8211; v<sub>t<\/sub> &#8211; a partir da <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Teoria_cin%C3%A9tica_dos_gases\" target=\"_blank\" rel=\"noopener\">Teoria Cin\u00e9tica dos Gases<\/a> <\/span><span style=\"font-family: verdana, geneva, sans-serif;\"><span id='easy-footnote-5-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-5-2401\" title=\"Desenvolvida por Boltzmann e Maxwell\"><sup>5<\/sup><\/a><\/span> considerando a energia cin\u00e9tica dos el\u00e9trons igual \u00e0 energia cin\u00e9tica dos gases, de acordo com a Equa\u00e7\u00e3o 6.<\/span><\/p>\n<figure id=\"attachment_10175\" aria-describedby=\"caption-attachment-10175\" style=\"width: 467px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/vth.png\"><img decoding=\"async\" class=\"wp-image-10175 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/vth.png\" alt=\"\" width=\"467\" height=\"238\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/vth.png 467w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/vth-300x153.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/a><figcaption id=\"caption-attachment-10175\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 6. Energia cin\u00e9tica dos el\u00e9trons livres e a velocidade t\u00e9rmica<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>v<sub>t<\/sub><\/em> \u00e9 a velocidade t\u00e9rmica [m\/s]<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>k<\/em> \u00e9 a constante de Boltzmann [1,380 649\u00d710<sup>-23<\/sup> J\/K];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>T<\/em> \u00e9 a temperatura [K]<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa do El\u00e9tron [9,109 383 70\u00d710<sup>-31 <\/sup>kg];<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h6 id='reflex\u00e3o'  id=\"boomdevs_6\"><span style=\"font-family: verdana, geneva, sans-serif;\">Reflex\u00e3o<\/span><\/h6>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Estime a velocidade t\u00e9rmica do el\u00e9tron de acordo com a Equa\u00e7\u00e3o 6 e compare com a velocidade calculada a partir da Equa\u00e7\u00e3o 6 do Cap\u00edtulo de <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/estrutura-da-materia\/atomos\/fisica-quantica\/\">Mec\u00e2nica Qu\u00e2ntica<\/a>.\u00a0<\/span><\/p>\n<hr \/>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por outro lado, um campo el\u00e9trico aplicado ao El\u00e9tron produzir\u00e1 uma for\u00e7a dada por:<\/span><\/p>\n<figure id=\"attachment_10242\" aria-describedby=\"caption-attachment-10242\" style=\"width: 162px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Forca_eletro.png\"><img decoding=\"async\" class=\"wp-image-10242 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/Forca_eletro.png\" alt=\"\" width=\"162\" height=\"47\" \/><\/a><figcaption id=\"caption-attachment-10242\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 7. For\u00e7a produzida pelo campo el\u00e9trico no el\u00e9tron livre<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">De acordo com a F\u00edsica Cl\u00e1ssica, for\u00e7a constante provoca acelera\u00e7\u00e3o constante. Sem nenhuma outra for\u00e7a presente, esta acelera\u00e7\u00e3o levaria os El\u00e9trons a velocidades sempre crescentes. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como Ohm verificou que a corrente permanecia finita, existe outra for\u00e7a atuando para anular a acelera\u00e7\u00e3o m\u00e9dia nos el\u00e9trons livres. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Em fun\u00e7\u00e3o disso, Drude prop\u00f4s a exist\u00eancia de uma for\u00e7a de atrito decorrente da colis\u00e3o dos el\u00e9trons livres com os \u00edons do material.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A F\u00edsica Cl\u00e1ssica relaciona for\u00e7a com velocidade da seguinte maneira:<\/span><\/p>\n<figure id=\"attachment_10248\" aria-describedby=\"caption-attachment-10248\" style=\"width: 308px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/momento.png\"><img decoding=\"async\" class=\"wp-image-10248 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/momento.png\" alt=\"\" width=\"308\" height=\"49\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/momento.png 308w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/momento-300x48.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/a><figcaption id=\"caption-attachment-10248\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 8. Momento linear<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:\u00a0<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">p \u00e9 o momento linear;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">m \u00e9 a massa;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">v \u00e9 a velocidade;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">F \u00e9 a for\u00e7a;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u0394t \u00e9 um intervalo de tempo.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Para utilizar este conceito, Drude considerou a exist\u00eancia de colis\u00f5es el\u00e1sticas entre os el\u00e9trons livres e os \u00edons do material ocorrendo, na m\u00e9dia, a cada intervalo de tempo m\u00e9dio \u03c4. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Este intervalo de tempo se tornou conhecido como <strong>tempo de relaxa\u00e7\u00e3o<\/strong> porque representa o tempo m\u00e9dio gasto para os El\u00e9trons Livres perderem o momento adquirido pela a\u00e7\u00e3o do campo el\u00e9trico.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Mec\u00e2nica Cl\u00e1ssica associa for\u00e7a a varia\u00e7\u00f5es de momento da seguinte maneira:<\/span><\/p>\n<figure id=\"attachment_10252\" aria-describedby=\"caption-attachment-10252\" style=\"width: 211px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/momentoxforca.png\"><img decoding=\"async\" class=\"wp-image-10252 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/momentoxforca.png\" alt=\"\" width=\"211\" height=\"49\" \/><\/a><figcaption id=\"caption-attachment-10252\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 9. Varia\u00e7\u00e3o do momento linear<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u0394p \u00e9 a varia\u00e7\u00e3o do momento linear;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">F \u00e9 a for\u00e7a;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u0394t \u00e9 o intervalo de tempo.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Desta maneira, as colis\u00f5es dos el\u00e9trons resultariam numa for\u00e7a contr\u00e1ria \u00e0 for\u00e7a eletrost\u00e1tica &#8211; F<sub>r<\/sub>&#8211; de acordo com a Equa\u00e7\u00e3o 9.<\/span><\/p>\n<figure id=\"attachment_22597\" aria-describedby=\"caption-attachment-22597\" style=\"width: 211px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Fr.png\"><img decoding=\"async\" class=\"wp-image-22597 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/Fr.png\" alt=\"\" width=\"211\" height=\"78\" \/><\/a><figcaption id=\"caption-attachment-22597\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 10. For\u00e7a de &#8220;atrito&#8221;<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Igualando as equa\u00e7\u00f5es 7 e 10, obtem-se a velocidade de deriva, conforme mostrado na Equa\u00e7\u00e3o 11.<\/span><\/p>\n<figure id=\"attachment_22598\" aria-describedby=\"caption-attachment-22598\" style=\"width: 260px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/vd.png\"><img decoding=\"async\" class=\"size-full wp-image-22598\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/vd.png\" alt=\"\" width=\"260\" height=\"87\" \/><\/a><figcaption id=\"caption-attachment-22598\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 11. Velocidade de deriva<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>v<sub>d<\/sub><\/em> \u00e9 a velocidade de deriva[m\/s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19<\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>E<\/em> \u00e9 o campo el\u00e9trico [V\/m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>\u03c4<\/em> \u00e9 o tempo de relaxa\u00e7\u00e3o[s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa do El\u00e9tron [9,109 383 70\u00d710<sup>-31 <\/sup>kg];<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">De acordo com a Equa\u00e7\u00e3o 11, a <strong>Velocidade de Deriva<\/strong> depende do campo el\u00e9trico, uma grandeza extr\u00ednseca ao material. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, criou-se o conceito de <strong>Mobilidade dos El\u00e9trons &#8211; \u03bc<\/strong>, uma grandeza intr\u00ednseca para caracterizar a resist\u00eancia produzida pelas colis\u00f5es dos El\u00e9trons Livres nos materiais.<\/span><\/p>\n<figure id=\"attachment_10259\" aria-describedby=\"caption-attachment-10259\" style=\"width: 261px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/mobilidade_drude.png\"><img decoding=\"async\" class=\"wp-image-10259 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/mobilidade_drude.png\" alt=\"\" width=\"261\" height=\"78\" \/><\/a><figcaption id=\"caption-attachment-10259\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 12. Mobilidade dos El\u00e9trons<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03bc \u00e9 a mobilidade dos El\u00e9trons[m<sup>2<\/sup>\/(V.s)];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19 <\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>\u03c4<\/em> \u00e9 o tempo de relaxa\u00e7\u00e3o[s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa do El\u00e9tron [9,109 383 70\u00d710<sup>-31 <\/sup>kg];<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Obtem-se a Equa\u00e7\u00e3o 13 substituindo a Equa\u00e7\u00e3o 12 na Equa\u00e7\u00e3o 5. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Desta maneira, <strong>Drude forneceu uma explica\u00e7\u00e3o teorica para a Lei de Ohm.\u00a0<\/strong><\/span><\/p>\n<figure id=\"attachment_22600\" aria-describedby=\"caption-attachment-22600\" style=\"width: 285px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/drude_ohm.png\"><img decoding=\"async\" class=\"size-full wp-image-22600\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/10\/drude_ohm.png\" alt=\"\" width=\"285\" height=\"92\" \/><\/a><figcaption id=\"caption-attachment-22600\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 13. Lei de Ohm segundo Drude<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>n <\/em>\u00e9 a densidade de el\u00e9trons livres [elementos\/m<sup>3<\/sup>]<span id='easy-footnote-6-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-6-2401\" title=\" dada pela Equa\u00e7\u00e3o 5 \"><sup>6<\/sup><\/a><\/span>;<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19<\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>\u03c4<\/em> \u00e9 o tempo de relaxa\u00e7\u00e3o [s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa do El\u00e9tron [9,109 383 70\u00d710<sup>-31 <\/sup>kg];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>E<\/em> \u00e9 o campo el\u00e9trico [V\/m].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Finalmente, a equa\u00e7\u00e3o 14 fornece o valor da condutividade e da resistividade em fun\u00e7\u00e3o apenas das propriedades do material.<\/span><\/p>\n<figure id=\"attachment_10149\" aria-describedby=\"caption-attachment-10149\" style=\"width: 657px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_9-1.png\"><img decoding=\"async\" class=\"wp-image-10149 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_9-1.png\" alt=\"\" width=\"657\" height=\"101\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_9-1.png 657w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_9-1-300x46.png 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><\/a><figcaption id=\"caption-attachment-10149\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 14 Condutividade\/Resistividade<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c3 \u00e9 a condutividade do material [S\/m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">n \u00e9 a densidade de El\u00e9trons Livres [elementos\/cm<sup>3<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19<\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>\u03c4<\/em> \u00e9 o tempo de relaxa\u00e7\u00e3o [s].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa do El\u00e9tron [9,109 383 70\u00d710<sup>-31 <\/sup>kg];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1 \u00e9 a resistividade do material [\u03a9.m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">N<sub>a<\/sub> \u00e9 a constante de Avogadro [6,022 140 73 \u00d7 10<sup>23<\/sup> 1\/mol];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Z \u00e9 n\u00famero de El\u00e9trons de Val\u00eancia [elementos];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>m<\/sub> \u00e9 a densidade do material [g\/cm<sup>3<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a massa at\u00f4mica do material [g\/mol].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Todos os par\u00e2metros da equa\u00e7\u00e3o 14 se encontram determinados, exceto o tempo de relaxa\u00e7\u00e3o &#8211; \u03c4.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Contudo, pode-se estim\u00e1-lo a partir da medi\u00e7\u00e3o da condutividade ou resistividade uilizando a Equa\u00e7\u00e3o 15.<\/span><\/p>\n<figure id=\"attachment_10146\" aria-describedby=\"caption-attachment-10146\" style=\"width: 337px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_8.png\"><img decoding=\"async\" class=\"wp-image-10146 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_8.png\" alt=\"\" width=\"337\" height=\"99\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_8.png 337w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/05\/drude_8-300x88.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/a><figcaption id=\"caption-attachment-10146\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 15. Tempo de relaxa\u00e7\u00e3o<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Onde:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>\u03c4<\/em> \u00e9 o tempo de relaxa\u00e7\u00e3o[s];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>m<\/em> \u00e9 a massa do El\u00e9tron [9,109 383 70\u00d710<sup>-31 <\/sup>kg];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a massa at\u00f4mica do material [kg\/mol].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c3 \u00e9 a condutividade do material [S\/m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">N<sub>a<\/sub> \u00e9 a constante de Avogadro [6,022 140 73 \u00d7 10<sup>23<\/sup> 1\/mol];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">Z \u00e9 n\u00famero de El\u00e9trons de Val\u00eancia [elementos];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><em>e<\/em> \u00e9 a carga elementar [1,602 1766 3\u00d710<sup>-19<\/sup>C];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1<sub>m<\/sub> \u00e9 a densidade do material [ kg\/m<sup>3<\/sup>];<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<hr \/>\n<h6 id='exerc\u00edcio-proposto-1'  id=\"boomdevs_7\">Exerc\u00edcio Proposto<\/h6>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Calcule o tempo de relaxa\u00e7\u00e3o e este tempo dividido pela condutividade para o Cobre, Prata, Alum\u00ednio, Tungst\u00eanio, Ouro, Ferro e Chumbo.<\/span><\/p>\n<hr \/>\n<h2 id='conclus\u00f5es'  id=\"boomdevs_8\"><span style=\"font-family: verdana, geneva, sans-serif;\">Conclus\u00f5es<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O Modelo de Drude permitiu explicar a Lei de Ohm, a condutividade el\u00e9trica e t\u00e9rmica dos metais, a rela\u00e7\u00e3o entre condutividade el\u00e9trica e t\u00e9rmica, e as propriedades \u00f3ticas dos metais. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por outro lado, ela n\u00e3o consegue explicar a condutividade de isolantes e semicondutores, o Efeito Fotoel\u00e9trico, a Radia\u00e7\u00e3o do Corpo Negro, e o efeito Compton.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Portanto, a F\u00edsica precisou evoluir com novas teorias.<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<h2 id='refer\u00eancias'  id=\"boomdevs_9\"><span style=\"font-family: verdana, geneva, sans-serif;\">Refer\u00eancias<a id=\"Referencia\"><\/a><\/span><\/h2>\n<\/li>\n<\/ul>\n<ol style=\"list-style-type: decimal;\">\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">ASHCROFT, N.W., MERMIN, N.D., <strong>Solid State Physics<\/strong>, Harcourt, 1976.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">BEATY, H.W., FINK, D.G., <strong>Standard Handbook for Electrical Engineers<\/strong>, 15 edi\u00e7\u00e3o, McGraw-Hill, 2007.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">CHELIKOWSKY, J.R., COHEN, M.L., <strong>Semiconductors: A Pillar of Pure and Applied Physics<\/strong>, Journal of Applied Physics 117, 112812 (2015).<span id='easy-footnote-7-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-7-2401\" title=\" Artigo muito interessante sobre a resistividade no estudo de materiais\"><sup>7<\/sup><\/a><\/span><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">HAYNES, W.W., <strong>Handbook of Chemistry and Physics<\/strong>, 93 edi\u00e7\u00e3o, CRC, 2012.<span id='easy-footnote-8-2401' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/#easy-footnote-bottom-8-2401\" title=\"kindle\"><sup>8<\/sup><\/a><\/span><\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\"><span style=\"font-family: verdana, geneva, sans-serif;\">KASAP, S.; KOUGHIA C.; RUDA, H.E.; Electrical Conduction in Metals and Semiconductors<strong>.<\/strong> In: KASAP, S.; CAPPER, P.(Ed.); <strong>Springer Handbook of Electronic and Photonic Materials<\/strong>, <\/span><\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Springer, 2017.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">KITTEL, C., <strong>Introduction to Solid State Physics<\/strong>, 8 edi\u00e7\u00e3o, John Wiley &amp; Sons, 2005<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">NOTAROS, B.M., <strong>Eletromagnetismo<\/strong>, Pearson Education do Brasil, 2012.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">OHRING, M., <strong>Engineering Materials Science<\/strong>, Academic Press, 1995.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">QUINN, J.J., YI, K, <strong>Solid State Physics &#8211; Principles and Modern Applications<\/strong>, Springer-Verlag, 2009.<\/span><\/li>\n<\/ol>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; 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text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; border-start-start-radius: initial; inset: initial; box-shadow: initial; box-sizing: initial; break-after: initial; break-before: initial; break-inside: initial; buffered-rendering: initial; caption-side: initial; caret-color: initial; clear: initial; clip: initial; 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vector-effect: initial; vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; 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-webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; 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-webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; border-end-end-radius: initial; border-end-start-radius: initial; border-inline: initial; border-start-end-radius: initial; 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vertical-align: initial; visibility: initial; -webkit-app-region: initial; border-spacing: initial; -webkit-border-image: initial; -webkit-box-align: initial; -webkit-box-decoration-break: initial; -webkit-box-direction: initial; -webkit-box-flex: initial; -webkit-box-ordinal-group: initial; -webkit-box-orient: initial; -webkit-box-pack: initial; -webkit-box-reflect: initial; -webkit-highlight: initial; -webkit-hyphenate-character: initial; -webkit-line-break: initial; -webkit-line-clamp: initial; -webkit-mask-box-image: initial; -webkit-mask: initial; -webkit-mask-composite: initial; -webkit-perspective-origin-x: initial; -webkit-perspective-origin-y: initial; -webkit-print-color-adjust: initial; -webkit-rtl-ordering: initial; -webkit-ruby-position: initial; -webkit-tap-highlight-color: initial; -webkit-text-combine: initial; -webkit-text-decorations-in-effect: initial; -webkit-text-emphasis: initial; -webkit-text-emphasis-position: initial; -webkit-text-fill-color: initial; -webkit-text-security: initial; -webkit-text-stroke: initial; -webkit-transform-origin-x: initial; -webkit-transform-origin-y: initial; -webkit-transform-origin-z: initial; -webkit-user-drag: initial; -webkit-user-modify: initial; white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; 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white-space: initial; widows: initial; width: initial; will-change: initial; word-break: initial; word-spacing: initial; x: initial; y: initial; z-index: initial;\"><\/div>\n<div class=\"ms-editor-squiggler\" style=\"color: initial; font: initial; font-feature-settings: initial; font-kerning: initial; font-optical-sizing: initial; font-variation-settings: initial; forced-color-adjust: initial; text-orientation: initial; text-rendering: initial; -webkit-font-smoothing: initial; -webkit-locale: initial; -webkit-text-orientation: initial; -webkit-writing-mode: initial; writing-mode: initial; zoom: initial; place-content: initial; place-items: initial; place-self: initial; alignment-baseline: initial; animation: initial; appearance: initial; aspect-ratio: initial; backdrop-filter: initial; backface-visibility: initial; background: initial; background-blend-mode: initial; baseline-shift: initial; block-size: initial; border-block: initial; border: initial; border-radius: initial; border-collapse: initial; 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