{"id":7574,"date":"2020-11-16T16:44:57","date_gmt":"2020-11-16T19:44:57","guid":{"rendered":"https:\/\/www.antonioguilherme.web.br.com\/blog\/?page_id=7574"},"modified":"2023-07-05T10:06:07","modified_gmt":"2023-07-05T13:06:07","slug":"fusiveis","status":"publish","type":"page","link":"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/fusiveis\/","title":{"rendered":"Fus\u00edveis"},"content":{"rendered":"<p style=\"text-align: right;\"><span style=\"font-size: 14pt;\"><strong><em><span style=\"font-family: verdana, geneva, sans-serif;\">&#8220;Lei de Byrne: Em qualquer circuito el\u00e9trico, os equipamentos e a fia\u00e7\u00e3o queimar\u00e3o primeiro do que os fus\u00edveis.&#8221;<\/span><\/em><\/strong><\/span><\/p>\n<p style=\"text-align: right;\"><span style=\"font-size: 14pt; font-family: verdana, geneva, sans-serif;\">Robert Byrne<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Fus\u00edveis se encontram em equipamentos el\u00e9tricos, instala\u00e7\u00f5es industriais, instala\u00e7\u00f5es residenciais, e em sistemas de distribui\u00e7\u00e3o para prote\u00e7\u00e3o contra curtos-circuitos e sobrecorrentes el\u00e9tricas. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, s\u00e3o os dispositivos el\u00e9tricos mais conhecidos e populares pelo p\u00fablico em geral.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">O aumento anormal da corrente el\u00e9trica em equipamentos eletroeletr\u00f4nicos pode provocar o derretimento do condutor e inc\u00eandios catastr\u00f3ficos. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, descargas atmosf\u00e9ricas produzem elevadas correntes induzidas em linhas de transmiss\u00e3o, linhas telef\u00f4nicas e instala\u00e7\u00f5es el\u00e9tricas.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Esses dispositivos, simples e baratos, possuem funcionamento complexo que envolve aspectos el\u00e9tricos, mec\u00e2nicos e t\u00e9rmicos.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Os fus\u00edveis consistem basicamente em pequenos peda\u00e7os de material condutor de eletricidade dimensionados para suportar at\u00e9 determinada corrente e fundir sempre que esse valor for ultrapassado. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Eles s\u00e3o projetados para interromper rapidamente correntes elevadas, minimizando a energia dissipada e, consequentemente, os riscos de inc\u00eandio e outros danos.\u00a0 <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Essas caracter\u00edsticas resultaram em dispositivos pequenos e baratos. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, a sua destrui\u00e7\u00e3o ao funcionar requer a manuten\u00e7\u00e3o de estoque para que o sistema volte a funcionar rapidamente. Esse inconveniente resultou no desenvolvimento de disjuntores, que s\u00e3o mais caros e volumosos.<\/span><\/p>\n<h2 id='hist\u00f3ria-dos-fus\u00edveis'  id=\"boomdevs_1\"><span style=\"font-family: verdana, geneva, sans-serif;\">Hist\u00f3ria dos Fus\u00edveis<\/span><\/h2>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Conforme visto nas experi\u00eancias <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/experiencias\/experiencia-2\/\">Temperatura e a Resist\u00eancia El\u00e9trica<\/a>, <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/experiencias\/experiencia-4\/\">Efeitos Termomec\u00e2nicos da Corrente<\/a>, e <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/experiencias\/experiencia-5\/\">Fus\u00edveis<\/a>, a corrente el\u00e9trica nos condutores met\u00e1licos produz aquecimento e a resistividade desses materiais aumenta com a temperatura. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Em 1883, <a href=\"https:\/\/en.wikipedia.org\/wiki\/William_Henry_Preece\" target=\"_blank\" rel=\"noopener\">William Henry Preece<\/a> publicou o primeiro trabalho que relaciona a corrente de fus\u00e3o de um condutor met\u00e1lico com seu di\u00e2metro. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Preece, ex-aluno de Faraday, se tornou engenheiro-chefe dos correios Brit\u00e2nicos e a rede de tel\u00e9grafos com fio se mostrou muito sens\u00edvel \u00e0s descargas atmosf\u00e9ricas.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\"> Portanto, ele se envolveu com o problema de proteger a rede de tel\u00e9grafos contra sobrecorrentes. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Diversos dispositivos de prote\u00e7\u00e3o surgiram, mas todos esbarravam na quest\u00e3o de qual a corrente m\u00e1xima suport\u00e1vel. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Estes dispositivos deveriam suportar as correntes normais dos tel\u00e9grafos, mas precisam fundir com as sobrecorrentes. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Nascia a ideia do fus\u00edvel. <span id='easy-footnote-1-7574' 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\/fusiveis\/#easy-footnote-bottom-1-7574\" title=\" palavra originada do radical latino fusus, que significa fundido\"><sup>1<\/sup><\/a><\/span><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Preece realizou diversas experi\u00eancias com fios de diversos materiais, di\u00e2metros e comprimentos. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, os condutores estavam livres no espa\u00e7o de tal forma que n\u00e3o houvesse impedimentos para a transfer\u00eancia de calor.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Primeiramente, ele constatou que, descontado o efeito de resfriamento dos terminais<span id='easy-footnote-2-7574' 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\/fusiveis\/#easy-footnote-bottom-2-7574\" title=\"A Figura 1 mostra que a temperatura nos terminais do circuito deve ser levada em considera\u00e7\u00e3o. \"><sup>2<\/sup><\/a><\/span>, a corrente de fus\u00e3o permanecia a mesma independentemente do comprimento dos fios.\u00a0<\/span><\/p>\n<figure id=\"attachment_44219\" aria-describedby=\"caption-attachment-44219\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-44219\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_lab.jpg\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_lab.jpg 1200w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_lab-300x225.jpg 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_lab-1024x768.jpg 1024w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_lab-768x576.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-44219\" class=\"wp-caption-text\">Figura 1. Imagem t\u00e9rmica do fus\u00edvel de fio<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A independ\u00eancia do comprimento contraria o senso comum, mas se mostrou teoricamente correta. <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">Por\u00e9m, a corrente de fus\u00e3o dependia do di\u00e2metro e do material.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Al\u00e9m disso, Preece observou que o ponto de ocorr\u00eancia da fus\u00e3o variava, e atribuiu este comportamento a irregularidades nos fios.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Inicialmente, ele utilizou fios de Platina, Cobre, Prata e Ferro de diversos di\u00e2metros, mas todos com o mesmo comprimento. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Analisando os dados medidos, Preece constatou que a Equa\u00e7\u00e3o 1 fornecia a corrente de fus\u00e3o do fio, e a constante <strong>a<\/strong> dependia do material.<\/span><\/p>\n<figure id=\"attachment_22970\" aria-describedby=\"caption-attachment-22970\" style=\"width: 173px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece.png\"><img decoding=\"async\" class=\"wp-image-22970 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece.png\" alt=\"\" width=\"173\" height=\"56\" \/><\/a><figcaption id=\"caption-attachment-22970\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 1. F\u00f3rmula de Preece<\/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>I<\/em> \u00e9 a corrente [A];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">a \u00e9 a constante de Preece [A\/mm<sup>3\/2<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">d \u00e9 o di\u00e2metro do fio [mm].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 id='an\u00e1lise-te\u00f3rica'  id=\"boomdevs_2\"><span style=\"font-family: verdana, geneva, sans-serif;\">An\u00e1lise Te\u00f3rica<\/span><\/h3>\n<p>&nbsp;<\/p>\n<div class=\"mceTemp\"><span style=\"font-family: verdana, geneva, sans-serif;\">Para que a temperatura no fio se estabilize, a energia el\u00e9trica dissipada pelo condutor (P) deve se igualar \u00e0 energia t\u00e9rmica transferida do fio para o meio exterior (q), conforme a Equa\u00e7\u00e3o 2 e a Figura 1.<\/span><\/div>\n<figure id=\"attachment_44226\" aria-describedby=\"caption-attachment-44226\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-44226\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_1.png\" alt=\"\" width=\"600\" height=\"480\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_1.png 900w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_1-300x240.png 300w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2023\/05\/fusivel_1-768x614.png 768w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-44226\" class=\"wp-caption-text\">Figura 1. Modelo do fio<\/figcaption><\/figure>\n<figure id=\"attachment_22985\" aria-describedby=\"caption-attachment-22985\" style=\"width: 249px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_1.png\"><img decoding=\"async\" class=\"wp-image-22985 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_1.png\" alt=\"\" width=\"249\" height=\"51\" \/><\/a><figcaption id=\"caption-attachment-22985\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 2. Balan\u00e7o de pot\u00eancia no fio.<\/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;\">P \u00e9 a pot\u00eancia el\u00e9trica dissipada no fio [W];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">R \u00e9 a resist\u00eancia el\u00e9trica do fio [\u03a9};<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">I \u00e9 a corrente el\u00e9trica no fio [A];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">q \u00e9 o calor dissipado pelo fio para o meio ambiente [W];<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 3 mostra que o calor transferido do fio para o ar (q) depende do di\u00e2metro do fio (d), do comprimento do fio (L), e da densidade de energia dissipada (h).<\/span><\/p>\n<figure id=\"attachment_22986\" aria-describedby=\"caption-attachment-22986\" style=\"width: 249px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_2.png\"><img decoding=\"async\" class=\"wp-image-22986 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_2.png\" alt=\"\" width=\"249\" height=\"49\" \/><\/a><figcaption id=\"caption-attachment-22986\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 3.\u00a0 Calor dissipado pelo fio<\/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;\">q \u00e9 a pot\u00eancia dissipada pelo fio [W];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">h \u00e9 fluxo de calor dissipado por \u00e1rea do fio [W\/m<sup>2<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">d \u00e9 o di\u00e2metro do fio [m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">L \u00e9 o comprimento do fio [m].<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Como a descoberta de Peerce ocorreu 7 anos antes dos resultados de Drude, <\/span><span style=\"font-family: verdana, geneva, sans-serif;\">ele n\u00e3o relacionou sua constante com a resistividade, apesar de identificar sua rela\u00e7\u00e3o com as dimens\u00f5es e tipos de materiais. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Considerando a resistividade el\u00e9trica do fio, a Equa\u00e7\u00e3o 4 fornece o valor da resist\u00eancia em fun\u00e7\u00e3o das dimens\u00f5es do fio.<\/span><\/p>\n<figure id=\"attachment_22988\" aria-describedby=\"caption-attachment-22988\" style=\"width: 373px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_3.png\"><img decoding=\"async\" class=\"wp-image-22988 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_3.png\" alt=\"\" width=\"373\" height=\"92\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_3.png 373w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_3-300x74.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/a><figcaption id=\"caption-attachment-22988\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 4. Resist\u00eancia el\u00e9trica<\/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 do fio[\u03a9];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1 \u00e9 a resistividade el\u00e9trica do fio [\u03a9.m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">L \u00e9 o comprimento do fio[m];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">A \u00e9 a \u00e1rea da se\u00e7\u00e3o reta do fio[m<sup>2<\/sup>].<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">d \u00e9 o di\u00e2metro do fio [m]<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Substituindo as Equa\u00e7\u00f5es 3 e 4 na Equa\u00e7\u00e3o 2, obt\u00e9m-se que:<\/span><\/p>\n<figure id=\"attachment_22989\" aria-describedby=\"caption-attachment-22989\" style=\"width: 663px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_4.png\"><img decoding=\"async\" class=\"wp-image-22989 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_4.png\" alt=\"\" width=\"663\" height=\"242\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_4.png 663w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_4-300x110.png 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><\/a><figcaption id=\"caption-attachment-22989\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 5.<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que a Equa\u00e7\u00e3o 5 permite determinar a constante de Peerce da seguinte maneira:<\/span><\/p>\n<figure id=\"attachment_22993\" aria-describedby=\"caption-attachment-22993\" style=\"width: 216px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_5.png\"><img decoding=\"async\" class=\"wp-image-22993 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_5.png\" alt=\"\" width=\"216\" height=\"123\" \/><\/a><figcaption id=\"caption-attachment-22993\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 6. Constante de Peerce<\/figcaption><\/figure>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Equa\u00e7\u00e3o 6 mostra que a constante de Peerce depende da resistividade el\u00e9trica do material e do fluxo de calor dissipado pela \u00e1rea superficial do fio.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A resistividade el\u00e9trica j\u00e1 foi devidamente analisada no cap\u00edtulo de <a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-eletricas\/resistividade-eletrica\/\">Condutividade e Resistividade I<\/a>, mas a densidade de calor dissipado requer algumas considera\u00e7\u00f5es.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Supondo que a transfer\u00eancia de calor do fio para o meio ambiente ocorra apenas por Radia\u00e7\u00e3o T\u00e9rmica, pode-se aplicar a Lei de Stefan-Boltzmann. <span id='easy-footnote-3-7574' 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\/fusiveis\/#easy-footnote-bottom-3-7574\" title=\" Equa\u00e7\u00e3o 3 do cap\u00edtulo &lt;a href=&quot;https:\/\/www.antonioguilherme.web.br.com\/blog\/materiais-eletricos-e-magneticos\/propriedades-termicas\/radiacao-termica\/&quot;&gt;Radia\u00e7\u00e3o &lt;\/a&gt;T\u00e9rmica. \"><sup>3<\/sup><\/a><\/span><\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A partir da Lei de Stefan-Boltzmann, a Equa\u00e7\u00e3o 7 fornece o fluxo de calor no fio.<\/span><\/p>\n<figure id=\"attachment_22999\" aria-describedby=\"caption-attachment-22999\" style=\"width: 177px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_6.png\"><img decoding=\"async\" class=\"size-full wp-image-22999\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_6.png\" alt=\"\" width=\"177\" height=\"49\" \/><\/a><figcaption id=\"caption-attachment-22999\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 7. Fluxo de calor no fio devido \u00e0 radia\u00e7\u00e3o t\u00e9rmica<\/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;\">h \u00e9 fluxo de calor dissipado por \u00e1rea do fio [W\/m<sup>2<\/sup> ];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c3 \u00e9 a constante de <a href=\"http:\/\/en.wikipedia.org\/wiki\/Stefan%E2%80%93Boltzmann_constant\" target=\"_blank\" rel=\"noopener noreferrer\">Stefan-Boltzmann<\/a> [5,670 373 e<sup>-8<\/sup> W\/(m<sup>2 <\/sup>K<sup>4<\/sup>)];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">T \u00e9 a temperatura de equil\u00edbrio do fio [K]<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Substituindo a Equa\u00e7\u00e3o 7 na Equa\u00e7\u00e3o 6, obtemos a seguinte express\u00e3o:<\/span><\/p>\n<figure id=\"attachment_23000\" aria-describedby=\"caption-attachment-23000\" style=\"width: 544px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_7.png\"><img decoding=\"async\" class=\"wp-image-23000 size-full\" src=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_7.png\" alt=\"\" width=\"544\" height=\"123\" srcset=\"https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_7.png 544w, https:\/\/www.antonioguilherme.web.br.com\/blog\/wp-content\/uploads\/2020\/11\/preece_7-300x68.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/a><figcaption id=\"caption-attachment-23000\" class=\"wp-caption-text\">Equa\u00e7\u00e3o 8. Constante de Preece<\/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;\">a \u00e9 a constante de Peerce [A.m <sup>-3\/2<\/sup>];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">T \u00e9 a temperatura no fio [K];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c3 \u00e9 a constante de <a href=\"http:\/\/en.wikipedia.org\/wiki\/Stefan%E2%80%93Boltzmann_constant\" target=\"_blank\" rel=\"noopener noreferrer\">Stefan-Boltzmann<\/a> [ 5,670 373 e<sup>-8<\/sup> W\/(m<sup>2 <\/sup>K<sup>4<\/sup>)];<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">\u03c1 \u00e9 a resistividade el\u00e9trica do fio [\u03a9.m];<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Observa-se que a constante de Preece varia com o quadrado da temperatura do fio e, conforme visto anteriormente, a resistividade el\u00e9trica dos materiais tamb\u00e9m depende da temperatura.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Contudo, as temperaturas not\u00e1veis; temperatura de fus\u00e3o, temperatura de ebuli\u00e7\u00e3o e ponto de Drapper, apresentam valores bem definidos. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">Por isso, Preece determinou seu coeficiente para a temperatura de fus\u00e3o dos materiais porque os fios sempre rompem nessa temperatura.<\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A Tabela abaixo apresenta o coeficiente de Preece de diversos metais utilizados como condutores na engenharia el\u00e9trica. <\/span><\/p>\n<p><span style=\"font-family: verdana, geneva, sans-serif;\">A liga de Estanho e Chumbo, muito utilizada para <a href=\"https:\/\/en.wikipedia.org\/wiki\/Solder\" target=\"_blank\" rel=\"noopener\">soldar<\/a> componentes eletr\u00f4nicos e funcionar como fus\u00edvel, apresenta dados pouco precisos porque as propriedades das ligas dependem do percentual de sua composi\u00e7\u00e3o de cada elemento que as constitui.<\/span><\/p>\n<h2 class=\"wpdt-c\" id=\"wdt-table-title-49\">Coeficiente de Preece<\/h2>\n<div class=\"wpdt-c wdt-skin-aqua\">\n    \n    <input type=\"hidden\" id=\"wdtNonceFrontendServerSide_49\" name=\"wdtNonceFrontendServerSide_49\" value=\"20e91a4470\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/blog\/wp-json\/wp\/v2\/pages\/7574\" \/><input type=\"hidden\" id=\"wdtFrontendelementorNonce_49\" name=\"wdtFrontendelementorNonce_49\" value=\"debc3c7241\" \/>    <input type=\"hidden\" id=\"table_1_desc\"\n           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   <table id=\"table_1\"\n           class=\"   display nowrap wdt-no-display data-t data-t wpDataTable wpDataTableID-49 \"\n           style=\"\"\n           data-described-by='table_1_desc'\n           data-wpdatatable_id=\"49\">\n        \n        <!-- Table header -->\n        \n<thead>\n<tr>\n                    <th\n                        class=\" wdtheader sort numdata integer \"\n        style=\"\">        wdt_ID<\/th>        <th\n        data-class=\"expand\"                class=\" wdtheader \"\n        style=\"\">        Material<\/th>        <th\n                        class=\" wdtheader numdata float \"\n        style=\"\">        Coeficiente de Preece(A\/cm^3\/2)<\/th>        <th\n                        class=\" wdtheader sort numdata float \"\n        style=\"\">        Temperatura de Fus\u00e3o (C)<\/th>        <th\n                        class=\" wdtheader sort numdata float \"\n        style=\"\">        Condutividade El\u00e9trica (MS\/m)<\/th>    <\/tr>\n<\/thead>\n        <!-- \/Table header -->\n\n        <!-- Table body -->\n        \n<tbody>\n<!-- Table body -->\n<div data-id=\"49\"\n     class=\"wdt-timeline-item wdt-timeline-table_1\"\n     style=\"\">\n    <div class=\"wdt-table-loader\">\n        <div class=\"wdt-table-loader-row wdt-table-loader-header\">\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n            <div class=\"wdt-table-loader-header-cell wdt-animated-background\"><\/div>\n        <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n                    <div class=\"wdt-table-loader-row\">\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n                <div class=\"wdt-table-loader-cell wdt-animated-background\"><\/div>\n            <\/div>\n            <\/div>\n<\/div><!-- \/Table body -->\n                    <tr id=\"table_49_row_0\"\n            data-row-index=\"0\">\n                            <td style=\"\">1<\/td>\n                            <td style=\"\">Cobre<\/td>\n                            <td style=\"\">2,531<\/td>\n                            <td style=\"\">1.084,62<\/td>\n                            <td style=\"\">59,0<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_1\"\n            data-row-index=\"1\">\n                            <td style=\"\">2<\/td>\n                            <td style=\"\">Alum\u00ednio<\/td>\n                            <td style=\"\">1,874<\/td>\n                            <td style=\"\">660,32<\/td>\n                            <td style=\"\">38,0<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_2\"\n            data-row-index=\"2\">\n                            <td style=\"\">3<\/td>\n                            <td style=\"\">Platina<\/td>\n                            <td style=\"\">1,278<\/td>\n                            <td style=\"\">1.768,30<\/td>\n                            <td style=\"\">9,4<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_3\"\n            data-row-index=\"3\">\n                            <td style=\"\">4<\/td>\n                            <td style=\"\">Prata<\/td>\n                            <td style=\"\">1,292<\/td>\n                            <td style=\"\">961,78<\/td>\n                            <td style=\"\">62,0<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_4\"\n            data-row-index=\"4\">\n                            <td style=\"\">5<\/td>\n                            <td style=\"\">Ferro<\/td>\n                            <td style=\"\">0,778<\/td>\n                            <td style=\"\">1.538,00<\/td>\n                            <td style=\"\">10,0<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_5\"\n            data-row-index=\"5\">\n                            <td style=\"\">6<\/td>\n                            <td style=\"\">Estanho<\/td>\n                            <td style=\"\">0,406<\/td>\n                            <td style=\"\">231,93<\/td>\n                            <td style=\"\">9,1<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_6\"\n            data-row-index=\"6\">\n                            <td style=\"\">7<\/td>\n                            <td style=\"\">Estanho\/Chumbo (solda)<\/td>\n                            <td style=\"\">0,326<\/td>\n                            <td style=\"\">183,00<\/td>\n                            <td style=\"\">5,0<\/td>\n                    <\/tr>\n                            <tr id=\"table_49_row_7\"\n            data-row-index=\"7\">\n                            <td style=\"\">8<\/td>\n                            <td style=\"\">Chumbo<\/td>\n                            <td style=\"\">0,341<\/td>\n                            <td style=\"\">327,46<\/td>\n                            <td style=\"\">4,8<\/td>\n                    <\/tr>\n            <\/tbody>        <!-- \/Table body -->\n\n        <!-- Table footer -->\n        \n        <!-- \/Table footer -->\n    <\/table>\n\n<\/div><style>\ntable.wpDataTable td.numdata { text-align: right !important; }\n<\/style>\n<style>\n                    \n                                                                                    .wpdt-c .wpDataTablesWrapper table.wpDataTable thead tr:nth-child(2) th {\n        overflow: visible;\n    }\n\n            \/* table font color *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-family: Verdana, Geneva, sans-serif !important;\n    }\n\n            \/* table font size *\/\n    .wpdt-c.wpDataTablesWrapper table.wpdtSimpleTable,\n    .wpdt-c .wpDataTablesWrapper table.wpDataTable {\n        font-size: 24px !important;\n    }\n\n            \n                <\/style>\n<style>\n<\/style>\n<style>\n                            \n                                        \n                    \n<\/style>\n\n<p><span style=\"font-size: 12pt; font-family: arial, helvetica, sans-serif;\">Fontes: <a href=\"http:\/\/www.nessengr.com\/techdata\/fuse\/fuse.html\" target=\"_blank\" rel=\"noopener\">Ness Engineering Inc<\/a> , <a href=\"http:\/\/www.farnell.com\/datasheets\/315929.pdf\" target=\"_blank\" rel=\"noopener\">Propiedades da Solda<\/a> e <a href=\"https:\/\/ptable.com\/#Propriedades\" target=\"_blank\" rel=\"noopener\">Tabela Peri\u00f3dica<\/a><\/span><\/p>\n<h2 id='refer\u00eancias'  id=\"boomdevs_3\">Refer\u00eancias<\/h2>\n<ol>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">CHEN, K. C.; WARNE, K. L.; LIN, Y. T.; et al. Conductor fusing and gapping for bond wires, <strong>Progress In Electromagnetics Research M<\/strong>, vol.31,199-214,2013.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">JOHNS, A.T., WARNE, D.F., Electric Fuses, <strong>IET<\/strong>, 2008.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">PREECE, W. H., On the heating effects of electric currents, <strong>Proc. R. Soc. Lond, 36, p. 464-471, publicado em 1 jan. 1883<\/strong>.<\/span><\/li>\n<li><span style=\"font-family: verdana, geneva, sans-serif;\">PREECE, W. H., On the heating effects of electric currents II, <strong>Proc. R. Soc. Lond, 43, p. 280-295, publicado em 1 janeiro 1887<\/strong>.<\/span><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\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; 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