{"id":1853,"date":"2016-01-25T01:03:26","date_gmt":"2016-01-25T01:03:26","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1853"},"modified":"2024-08-19T15:21:43","modified_gmt":"2024-08-19T15:21:43","slug":"galvanometro-como-amperimetro-e-como-voltimetro-ponte-de-wheatstone","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletrodinamica\/galvanometro-como-amperimetro-e-como-voltimetro-ponte-de-wheatstone\/","title":{"rendered":"Ponte de Wheatstone"},"content":{"rendered":"

Galvan\u00f4metro como Amper\u00edmetro e como Volt\u00edmetro \u2013 Ponte de Wheatstone<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Galvan\u00f4metro<\/b><\/span><\/span><\/span><\/p>\n

\u00a0O <\/b><\/span><\/span><\/span>galvan\u00f4metro \u00e9 um dispositivo que mede correntes de pequenas intensidades<\/b><\/span><\/span><\/span> e que \u00e9 composto, de uma maneira bem simples, por <\/b><\/span><\/span><\/span>muitos condutores retil\u00edneos sendo percorrido por uma corrente<\/b><\/span><\/span><\/span> <\/b>el\u00e9trica,<\/b><\/span><\/span><\/span> <\/b>mesmo princ\u00edpio utilizado na constru\u00e7\u00e3o de motores el\u00e9tricos.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

S\u00edmbolo de um galvan\u00f4metro<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Galvan\u00f4metro adaptado para amper\u00edmetro<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Q<\/b><\/span><\/span><\/span>uando voc\u00ea quer que o <\/b><\/span><\/span><\/span>galvan\u00f4metro me\u00e7a correntes maiores que as de seu fundo de escala (funcionando como amper\u00edmetro)<\/b><\/span><\/span><\/span> voc\u00ea <\/b><\/span><\/span><\/span>deve associar, em paralelo a ele, um resistor (R<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>) denominado shunt (em ingl\u00eas, desvio).
\n<\/b><\/span><\/span><\/span>O <\/b><\/span><\/span><\/span>conjunto todo<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>galvan\u00f4metro com resist\u00eancia R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0e a resist\u00eancia shunt paralela <\/b><\/span><\/span><\/span>a ele <\/b><\/span><\/span><\/span>constitui o amper\u00edmetro, que se transforma num galvan\u00f4metro de escala ampliada.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

i \"\"<\/b><\/span><\/span><\/span> <\/b>corrente total de fundo de escala que voc\u00ea quer medir<\/b><\/span><\/span><\/span><\/p>\n

i<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> corrente de fundo de escala do galvan\u00f4metro<\/b><\/span><\/span><\/span><\/p>\n

i<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0\"\" corrente que \u00e9 desviada para a <\/b><\/span><\/span><\/span>resist\u00eancia shunt (R<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>\u00a0 \u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> resist\u00eancia interna do galvan\u00f4metro<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Analise com aten\u00e7\u00e3o<\/b><\/span><\/span><\/span> esse <\/b><\/span><\/span><\/span>exemplo <\/b><\/span><\/span><\/span>num\u00e9rico:<\/b><\/span><\/span><\/span><\/p>\n

Voc\u00ea possui um <\/b><\/span><\/span><\/span>galvan\u00f4metro de resist\u00eancia interna R<\/b><\/span><\/span><\/span>G <\/b><\/span><\/span><\/sub><\/span>= 100 \u2126<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>corrente de fundo de escala<\/b><\/span><\/span><\/span> i<\/b><\/span><\/span><\/span>G <\/b><\/span><\/span><\/sub><\/span>= 10 mA.<\/b><\/span><\/span><\/span><\/p>\n

Para <\/b><\/span><\/span><\/span>voc\u00ea medir correntes de at\u00e9 i = 1 A<\/b><\/span><\/span><\/span> (quando a <\/b><\/span><\/span><\/span>corrente de fundo de escala do galvan\u00f4metro<\/b><\/span><\/span><\/span> estiver <\/b><\/span><\/span><\/span>marcando 10 mA<\/b><\/span><\/span><\/span>, na realidade <\/b><\/span><\/span><\/span>dever\u00e1 estar marcando 1 A<\/b><\/span><\/span><\/span>), voc\u00ea deve <\/b><\/span><\/span><\/span>transform\u00e1-lo num amper\u00edmetro, colocando em paralelo uma resist\u00eancia de (100\/99) \u2126.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Assim, a <\/b><\/span><\/span><\/span>corrente que faz o ponteiro do galvan\u00f4metro ir at\u00e9 o fundo de escala \u00e9 i = 1A<\/b><\/span><\/span><\/span> quando no <\/b><\/span><\/span><\/span>galvan\u00f4metro est\u00e1 passando<\/b><\/span><\/span><\/span> <\/b>0,01 A<\/b><\/span><\/span><\/span> e a parte que <\/b><\/span><\/span><\/span>desvia para o shunt \u00e9 i<\/b><\/span><\/span><\/span>S <\/b><\/span><\/span><\/sub><\/span>= 0,99 A.<\/b><\/span><\/span><\/span><\/b><\/p>\n

Assim, se o <\/b><\/span><\/span><\/span>galvan\u00f4metro estivesse marcando 5mA<\/b><\/span><\/span><\/span> (metade da escala), <\/b><\/span><\/span><\/span>na realidade a corrente<\/b><\/span><\/span><\/span> <\/b>medida seria de 0,5 A (metade de 1 A).<\/b><\/span><\/span><\/span><\/b><\/p>\n

Observe que o <\/b><\/span><\/span><\/span>fator de multiplica\u00e7\u00e3o \u00e9 n = (1 + R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>)=<\/b><\/span><\/span><\/span>1 + 100\/(100\/99<\/b><\/span><\/span><\/span>) =100<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>n = 100<\/b><\/span><\/span><\/span> (quando <\/b><\/span><\/span><\/span>deveria marcar 0,01 A estar\u00e1 marcando 100×0,01 = 1 A<\/b><\/span><\/span><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

Galvan\u00f4metro adaptado para volt\u00edmetro<\/b><\/span><\/span><\/span><\/p>\n

Quando voc\u00ea quer que o <\/b><\/span><\/span><\/span>galvan\u00f4metro me\u00e7a tens\u00f5es<\/b><\/span><\/span><\/span> (voltagens ou ddps) <\/b><\/span><\/span><\/span>maiores que as de seu<\/b><\/span><\/span><\/span> <\/b>fundo de escala voc\u00ea deve associar, em s\u00e9rie a ele, um resist\u00eancia (R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>) denominada resist\u00eancia multiplicadora.<\/b><\/span><\/span><\/span><\/p>\n

O conjunto todo, <\/b><\/span><\/span><\/span>galvan\u00f4metro com resist\u00eancia R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0e a resist\u00eancia multiplicadora em s\u00e9rie com ele constitui o <\/b><\/span><\/span><\/span>volt\u00edmetro<\/b><\/span><\/span><\/span>, que se transforma num galvan\u00f4metro de escala ampliada.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe que a <\/b><\/span><\/span><\/span>corrente i \u00e9 a mesma tanto no galvan\u00f4metro como na resist\u00eancia multiplicadora R<\/b><\/span><\/span><\/span>M\u00a0<\/b><\/span><\/span><\/sub><\/span>e que a <\/b><\/span><\/span><\/span>tens\u00e3o total (U) que \u00e9 a tens\u00e3o de fundo de escala indicada pelo volt\u00edmetro \u00e9 a soma da tens\u00e3o de fundo de escala no galvan\u00f4metro (U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>) com a tens\u00e3o na resist\u00eancia multiplicadora (U<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

U = U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0+ U<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>U<\/b><\/span><\/span><\/span>M <\/b><\/span><\/span><\/sub><\/span>= R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>.i<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>U<\/b><\/span><\/span><\/span>G <\/b><\/span><\/span><\/sub><\/span>= R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>.i<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>i = U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0\"\"<\/b><\/span><\/span><\/sub><\/span>\u00a0 U = U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0+ R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>.U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>U = U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>( 1 +<\/b><\/span><\/span><\/span> <\/b>R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>U = m.U<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0\"\"\u00a0 a <\/b><\/span><\/span><\/span>express\u00e3o\u00a0<\/b><\/span><\/span><\/span>m = (1 + R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span> \u00e9 chamada <\/b><\/span><\/span><\/span>fator de multiplica\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

Analise com aten\u00e7\u00e3o<\/b><\/span><\/span><\/span> esse <\/b><\/span><\/span><\/span>exemplo <\/b><\/span><\/span><\/span>num\u00e9rico:<\/b><\/span><\/span><\/span><\/p>\n

Voc\u00ea possui <\/b><\/span><\/span><\/span>um galvan\u00f4metro de resist\u00eancia interna R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>=100\u2126<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>corrente de fundo de escala<\/b><\/span><\/span><\/span> <\/b>i<\/b><\/span><\/span><\/span>G <\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span> <\/b>10mA.<\/b><\/span><\/span><\/span><\/b><\/p>\n

Para voc\u00ea <\/b><\/span><\/span><\/span>medir tens\u00f5es de at\u00e9 3V<\/b><\/span><\/span><\/span> (quando a <\/b><\/span><\/span><\/span>corrente de fundo de escala do galvan\u00f4metro<\/b><\/span><\/span><\/span> estiver <\/b><\/span><\/span><\/span>marcando 10mA, na realidade estar\u00e1 marcando 3V<\/b><\/span><\/span><\/span>), voc\u00ea deve<\/b><\/span><\/span><\/span>associar em s\u00e9rie uma resist\u00eancia multiplicadora de 200\u2126 de modo que ele se transforme num volt\u00edmetro que indique entre 0 e 3V\u00a0 —\u00a0 provando\u00a0 \"\" U=R<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>.i + R<\/b><\/span><\/span><\/span>M.<\/b><\/span><\/span><\/sub><\/span>i=100.0,01 + 200.0,01\u00a0 \"\"\u00a0 U=3V.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Ponte de Wheatstone<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

T<\/b><\/span><\/span><\/span>rata-se de uma <\/b><\/span><\/span><\/span>associa\u00e7\u00e3o de tr\u00eas resistores fixos e um vari\u00e1vel (reostato),<\/b><\/span><\/span><\/span> como representado <\/b><\/span><\/span><\/span>na figura.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Serve, dentre <\/b><\/span><\/span><\/span>outras coisas<\/b><\/span><\/span><\/span>, para <\/b><\/span><\/span><\/span>determinar a resist\u00eancia de um resistor.<\/b><\/span><\/span><\/span> <\/b>Conhecendo,<\/b><\/span><\/span><\/span> por exemplo, <\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>, R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0e R<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sub><\/span>, pode-se determinar R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>,<\/b><\/span><\/span><\/span> da seguinte maneira:<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Liga-se entre B e D um amper\u00edmetro muito sens\u00edvel (galvan\u00f4metro).<\/b><\/span><\/span><\/span><\/p>\n

\"\" Varia-se o reostato (resist\u00eancia vari\u00e1vel) R<\/b><\/span><\/span><\/span>X<\/b><\/span><\/span><\/sub><\/span>\u00a0at\u00e9 que a intensidade i<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0de corrente no amper\u00edmetro <\/b><\/span><\/span><\/span>se <\/b><\/span><\/span><\/span>torne nula (i<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>= 0).<\/b><\/span><\/span><\/span><\/b><\/p>\n

Nessa situa\u00e7\u00e3o, diz-se que<\/b><\/span><\/span><\/span>\u00a0a <\/b><\/span><\/span><\/span>ponte est\u00e1 em equil\u00edbrio<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span> Sendo\u00a0<\/b><\/span><\/span><\/span>nula a corrente no amper\u00edmetro, n\u00e3o existe diferen\u00e7a de potencial entre os pontos B e D.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Ponte de fio<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span>Se a <\/b><\/span><\/span><\/span>ponte est\u00e1 em equil\u00edbrio,<\/b><\/span><\/span><\/span> ou seja, se <\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.R<\/b><\/span><\/span><\/span>X <\/b><\/span><\/span><\/sub><\/span>= R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.R<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>,<\/b><\/span><\/span><\/span> voc\u00ea pode <\/b><\/span><\/span><\/span>tocar os pontos B e D<\/b><\/span><\/span><\/span> com as <\/b><\/span><\/span><\/span>m\u00e3os e n\u00e3o leva choque<\/b><\/span><\/span><\/span> e tamb\u00e9m <\/b><\/span><\/span><\/span>qualquer aparelho el\u00e9trico colocado entre B e D n\u00e3o funcionar\u00e1, pois V<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>D<\/b><\/span><\/span><\/sub><\/span> e nesse trecho n\u00e3o passa corrente el\u00e9trica.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Confira os exerc\u00edcios sugeridos!<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Galvan\u00f4metro como Amper\u00edmetro e como Volt\u00edmetro \u2013 Ponte de Wheatstone \u00a0 Galvan\u00f4metro \u00a0O galvan\u00f4metro \u00e9 um dispositivo que mede correntes de pequenas intensidades e que \u00e9 composto, de uma maneira bem simples, por muitos condutores retil\u00edneos sendo percorrido por uma corrente el\u00e9trica, mesmo princ\u00edpio utilizado na constru\u00e7\u00e3o de motores el\u00e9tricos. S\u00edmbolo de um galvan\u00f4metro Galvan\u00f4metro adaptado para amper\u00edmetro \u00a0Quando voc\u00ea<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1676,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-1853","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1853","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=1853"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1853\/revisions"}],"predecessor-version":[{"id":10532,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1853\/revisions\/10532"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1676"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}