{"id":11316,"date":"2024-11-08T13:04:21","date_gmt":"2024-11-08T13:04:21","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11316"},"modified":"2024-12-03T13:03:59","modified_gmt":"2024-12-03T13:03:59","slug":"ponte-de-wheatstone-en","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletrodinamica\/ponte-de-wheatstone-en\/","title":{"rendered":"Wheatstone Bridge EN"},"content":{"rendered":"

WHEATSTONE BRIDGE<\/span><\/h1>\n
\n

Galvanometer as Ammeter and as Voltmeter \u2013 Wheatstone Bridge<\/span><\/b><\/p>\n

 <\/p>\n

Galvanometer<\/span><\/b><\/p>\n

\u00a0The\u00a0<\/span><\/b>galvanometer is a device that measures low-intensity currents\u00a0<\/span><\/b>and is composed, in a very simple way, of\u00a0<\/span><\/b>many straight conductors running an\u00a0<\/span><\/b>electric current,\u00a0<\/b>the same principle used in the construction of electric motors.<\/b><\/span><\/b><\/b><\/b><\/b><\/p>\n

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Symbol of a galvanometer<\/span><\/b><\/p>\n

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Galvanometer adapted for ammeter<\/span><\/b><\/p>\n

\u00a0When\u00a0<\/span><\/b>you want the\u00a0<\/span><\/b>galvanometer to measure currents greater than its full scale (functioning as an ammeter)\u00a0<\/span><\/b>you\u00a0<\/span><\/b>must associate, in parallel to it, a resistor (R\u00a0<\/span><\/b>S<\/span><\/b><\/sub>\u00a0) called a shunt (in English, deviation).<\/span>
\n<\/b>The\u00a0<\/span><\/b>whole set\u00a0<\/span><\/b>,\u00a0<\/span><\/b>galvanometer with resistance R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0\u00a0and the shunt resistance parallel\u00a0<\/span><\/b>to it\u00a0<\/span><\/b>constitutes the ammeter, which becomes a large-scale galvanometer.<\/span><\/b><\/p>\n

\"\"<\/p>\n

i\u00a0<\/span>\"\"<\/b>full scale total current you want to measure<\/b><\/span><\/b><\/b><\/p>\n

i\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0full-scale current of the galvanometer<\/b><\/span>\u00a0\"\"<\/b><\/b><\/p>\n

i\u00a0<\/span><\/b>S<\/span><\/b><\/sub>\u00a0current that is shunted to the\u00a0<\/b>shunt resistance (R\u00a0<\/b>S<\/b><\/sub>\u00a0)<\/b><\/span>\u00a0\"\"<\/b><\/b><\/b><\/b>\u00a0 \u00a0\u00a0<\/b><\/p>\n

R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0internal resistance of galvanometer<\/b><\/span>\u00a0\"\"<\/b><\/b><\/p>\n

\"\"<\/p>\n

Carefully analyze\u00a0<\/span><\/b>this numerical\u00a0<\/span><\/b>example\u00a0<\/span><\/b>:<\/span><\/b><\/p>\n

You have a\u00a0<\/span><\/b>galvanometer with internal resistance R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0= 100 \u03a9\u00a0<\/span><\/b>and\u00a0<\/span><\/b>full-scale current\u00a0<\/span><\/b>i\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0= 10 mA.<\/span><\/b><\/p>\n

To\u00a0<\/span><\/b>measure currents up to i = 1 A\u00a0<\/span><\/b>(when the\u00a0<\/span><\/b>full-scale current of the galvanometer\u00a0<\/span><\/b>is\u00a0<\/span><\/b>marking 10 mA\u00a0<\/span><\/b>, it should actually\u00a0<\/span><\/b>be marking 1 A\u00a0<\/span><\/b>), you must\u00a0<\/span><\/b>transform it into an ammeter, placing a resistance of (100\/99) \u03a9 in parallel.<\/span><\/b><\/p>\n

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Thus, the\u00a0<\/span><\/b>current that makes the galvanometer pointer go to the full scale is i = 1A\u00a0<\/span><\/b>when\u00a0<\/span><\/b>0.01 A\u00a0<\/b><\/span>is passing through the galvanometer\u00a0<\/span><\/b>and the part that\u00a0<\/b>diverts to the shunt is i\u00a0<\/b>S<\/b><\/sub>\u00a0= 0.99 A.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Thus, if the\u00a0<\/span><\/b>galvanometer were marking 5 mA\u00a0<\/span><\/b>(half of the scale),\u00a0<\/span><\/b>in reality the measured current\u00a0<\/span><\/b>would be 0.5 A (half of 1 A).<\/b><\/span><\/b><\/b><\/b><\/p>\n

Note that the\u00a0<\/span><\/b>multiplication factor is n = (1 + R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0\/R\u00a0<\/span><\/b>S<\/span><\/b><\/sub>\u00a0)=\u00a0<\/span><\/b>1 + 100\/(100\/99\u00a0<\/span><\/b>) =100\u00a0<\/span><\/b>n = 100\u00a0<\/b>(when\u00a0<\/b>it should mark 0.01 A it will be marking 100\u00d70.01 = 1 A\u00a0<\/b>).<\/b><\/span>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/p>\n

Galvanometer adapted for voltmeter<\/span><\/b><\/p>\n

When you want the\u00a0<\/span><\/b>galvanometer to measure voltages\u00a0<\/span><\/b>(voltages or ddps)\u00a0<\/span><\/b>greater than its\u00a0<\/span><\/b>full scale, you must associate, in series with it, a resistance (R\u00a0<\/b>M<\/b><\/sub>\u00a0) called a multiplier resistance.<\/b><\/span><\/b><\/b><\/b><\/b><\/p>\n

The entire set,\u00a0<\/span><\/b>galvanometer with resistance R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0\u00a0and the multiplier resistance in series with it constitutes the\u00a0<\/span><\/b>voltmeter\u00a0<\/span><\/b>, which becomes a large-scale galvanometer.<\/span><\/b><\/p>\n

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Note that the\u00a0<\/span><\/b>current i is the same in both the galvanometer and the multiplier resistance R\u00a0<\/span><\/b>M\u00a0<\/span><\/b><\/sub>\u00a0and that the\u00a0<\/span><\/b>total voltage (U) which is the full-scale voltage indicated by the voltmeter is the sum of the full-scale voltage in the galvanometer (U\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0) and the voltage in the multiplier resistance (U\u00a0<\/span><\/b>M<\/span><\/b><\/sub>\u00a0).<\/span><\/b><\/p>\n

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U = U\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0\u00a0+ U\u00a0<\/span><\/b>M<\/span><\/b><\/sub>\u00a0U\u00a0<\/b>M<\/b><\/sub>\u00a0= R\u00a0<\/b>M<\/b><\/sub>\u00a0.i\u00a0<\/b>U\u00a0<\/b>G<\/b><\/sub>\u00a0= R\u00a0<\/b>G<\/b><\/sub>\u00a0.i\u00a0<\/b>i = U\u00a0<\/b>G<\/b><\/sub>\u00a0\/R\u00a0<\/b>G<\/b><\/sub>\u00a0\u00a0 U = U\u00a0<\/b>G<\/b><\/sub>\u00a0\u00a0+ R\u00a0<\/b>M<\/b><\/sub>\u00a0.U\u00a0<\/b>G<\/b><\/sub>\u00a0\/R\u00a0<\/b>G<\/b><\/sub>\u00a0U = U\u00a0<\/b>G<\/b><\/sub>\u00a0( 1 +\u00a0<\/b>R\u00a0<\/b>M<\/b><\/sub>\u00a0\/R\u00a0<\/b>G<\/b><\/sub>\u00a0)\u00a0<\/b>U = mU\u00a0<\/b>G<\/b><\/sub>\u00a0\u00a0 the\u00a0<\/b>expression\u00a0\u00a0<\/b>m = (1 + R\u00a0<\/b>M<\/b><\/sub>\u00a0\/R\u00a0<\/b>G<\/b><\/sub>\u00a0)\u00a0<\/b>is called\u00a0<\/b>the multiplication factor.<\/b><\/span>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/sub><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b>\u00a0<\/b><\/b><\/b><\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b>\u00a0<\/b><\/b><\/b>\u00a0<\/b>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Carefully analyze\u00a0<\/span><\/b>this numerical\u00a0<\/span><\/b>example\u00a0<\/span><\/b>:<\/span><\/b><\/p>\n

You have\u00a0<\/span><\/b>a galvanometer with internal resistance R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0= 100\u03a9\u00a0<\/span><\/b>and\u00a0<\/span><\/b>full-scale current\u00a0<\/span><\/b>i\u00a0<\/b>G<\/b><\/sub>\u00a0=\u00a0<\/b>10mA.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

To\u00a0<\/span><\/b>measure voltages up to 3V\u00a0<\/span><\/b>(when the\u00a0<\/span><\/b>full-scale current of the galvanometer\u00a0<\/span><\/b>is\u00a0<\/span><\/b>marking 10mA, it will actually be marking 3V\u00a0<\/span><\/b>), you must\u00a0<\/span><\/b>connect a 200\u03a9 multiplier resistance in series so that it becomes a voltmeter that indicates between 0 and 3V \u2014 proving\u00a0\u00a0<\/span>\"\"U=R\u00a0<\/span><\/b>G<\/span><\/b><\/sub>\u00a0.i + R\u00a0<\/span><\/b>M.i<\/span><\/b><\/sub>\u00a0=100.0.01 + 200.0.01\u00a0\u00a0<\/span>\"\"\u00a0 U=3V.<\/span><\/b><\/p>\n

 <\/p>\n

Wheatstone Bridge<\/span><\/b><\/p>\n

 <\/p>\n

It\u00a0<\/span><\/b>is a\u00a0<\/span><\/b>combination of three fixed resistors and one variable resistor (rheostat),\u00a0<\/span><\/b>as shown\u00a0<\/span><\/b>in the figure.<\/span><\/b><\/p>\n

\"\"<\/p>\n

It serves, among\u00a0<\/span><\/b>other things\u00a0<\/span><\/b>, to\u00a0<\/span><\/b>determine the resistance of a resistor.\u00a0<\/span><\/b>Knowing,\u00a0<\/b>for example,\u00a0<\/b>R\u00a0<\/b>1<\/b><\/sub>\u00a0, R\u00a0<\/b>2<\/b><\/sub>\u00a0\u00a0and R\u00a0<\/b>4<\/b><\/sub>\u00a0, one can determine R\u00a0<\/b>3<\/b><\/sub>\u00a0,\u00a0<\/b>as follows:<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"\u00a0A very sensitive ammeter (galvanometer) is connected between B and D.<\/span><\/b><\/p>\n

\"\"\u00a0<\/b>The rheostat (variable resistance) R X<\/span><\/b><\/sub>\u00a0is varied\u00a0<\/b><\/span>\u00a0until the\u00a0<\/span><\/b>\u00a0current intensity i\u00a0<\/b><\/span>A<\/span><\/b><\/sub>\u00a0in the ammeter becomes\u00a0<\/b>zero (i\u00a0<\/b>A<\/b><\/sub>\u00a0= 0).<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

<\/b>\u00a0In this situation, the bridge\u00a0<\/span><\/b>is said\u00a0<\/b><\/span>to be in equilibrium\u00a0<\/span><\/b>.\u00a0<\/span><\/b>Since\u00a0\u00a0<\/span><\/b>the current in the ammeter is zero, there is no potential difference between points B and D.<\/span><\/b><\/p>\n

\"\"<\/p>\n

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Wire bridge<\/span><\/b><\/p>\n

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 <\/p>\n

What you should know, information and tips<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0If the\u00a0<\/span><\/b>bridge is in balance,\u00a0<\/span><\/b>that is, if\u00a0<\/span><\/b>R\u00a0<\/span><\/b>1<\/span><\/b><\/sub>\u00a0. R\u00a0<\/span><\/b>X<\/span><\/b><\/sub>\u00a0= R\u00a0<\/span><\/b>2<\/span><\/b><\/sub>\u00a0. R\u00a0<\/span><\/b>3<\/span><\/b><\/sub>\u00a0,\u00a0<\/span><\/b>you can\u00a0<\/span><\/b>touch points B and D\u00a0<\/span><\/b>with your\u00a0<\/span><\/b>hands and not get a shock\u00a0<\/span><\/b>and also\u00a0<\/span><\/b>any electrical device placed between B and D will not work, since V\u00a0<\/span><\/b>B<\/span><\/b><\/sub>\u00a0= V\u00a0<\/span><\/b>D<\/span><\/b><\/sub>\u00a0and no electrical current passes through this section.<\/span><\/b><\/p>\n

\"\"<\/p>\n

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Check out the suggested exercises!<\/span><\/a><\/h3>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

WHEATSTONE BRIDGE Galvanometer as Ammeter and as Voltmeter \u2013 Wheatstone Bridge   Galvanometer \u00a0The\u00a0galvanometer is a device that measures low-intensity currents\u00a0and is composed, in a very simple way, of\u00a0many straight conductors running an\u00a0electric current,\u00a0the same principle used in the construction of electric motors. Symbol of a galvanometer Galvanometer adapted for ammeter \u00a0When\u00a0you want the\u00a0galvanometer to measure currents greater than its<\/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-11316","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11316","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=11316"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11316\/revisions"}],"predecessor-version":[{"id":12012,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11316\/revisions\/12012"}],"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=11316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}