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If such a galvanometer has a 2 5- Ω size 12{2"5-" %OMEGA } {} resistance, then a voltage of only V = IR = 50 μA 25 Ω = 1 . 25 mV size 12{V= ital "IR"= left ("50" μA right ) left ("25" %OMEGA right )=1 "." "25"" mV"} {} produces a full-scale reading. By connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter that can measure a broad range of voltages or currents.

Galvanometer as voltmeter

[link] shows how a galvanometer can be used as a voltmeter by connecting it in series with a large resistance, R . The value of the resistance R size 12{R} {} is determined by the maximum voltage to be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a 2 5-Ω size 12{2"5-" %OMEGA } {} galvanometer with a 50-μA sensitivity. Then 10 V applied to the meter must produce a current of 50 μA size 12{"50" μA} {} . The total resistance must be

R tot = R + r = V I = 10 V 50 μA = 200 k Ω, or size 12{R rSub { size 8{"tot"} } =R+r= { {V} over {I} } = { {"10"" V"} over {"50" μA} } ="200"" k" %OMEGA } {}
R = R tot r = 200 kΩ 25 Ω 200 k Ω . size 12{R=R rSub { size 8{"tot"} } -r="200"k %OMEGA -"25" %OMEGA »"200"" k" %OMEGA } {}

( R size 12{R} {} is so large that the galvanometer resistance, r , is nearly negligible.) Note that 5 V applied to this voltmeter produces a half-scale deflection by producing a 2 5-μA size 12{2"5-"μA} {} current through the meter, and so the voltmeter’s reading is proportional to voltage as desired.

This voltmeter would not be useful for voltages less than about half a volt, because the meter deflection would be small and difficult to read accurately. For other voltage ranges, other resistances are placed in series with the galvanometer. Many meters have a choice of scales. That choice involves switching an appropriate resistance into series with the galvanometer.

The drawing shows a voltmeter, which is a circuit with a large resistance in series with a galvanometer, along with its internal resistance.
A large resistance R placed in series with a galvanometer G produces a voltmeter, the full-scale deflection of which depends on the choice of R size 12{R} {} . The larger the voltage to be measured, the larger R size 12{R} {} must be. (Note that r represents the internal resistance of the galvanometer.)

Galvanometer as ammeter

The same galvanometer can also be made into an ammeter by placing it in parallel with a small resistance R size 12{R} {} , often called the shunt resistance    , as shown in [link] . Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those producing a full-scale deflection of the galvanometer.

Suppose, for example, an ammeter is needed that gives a full-scale deflection for 1.0 A, and contains the same 2 5- Ω size 12{2"5-" %OMEGA } {} galvanometer with its 50-μA size 12{"50"-μA} {} sensitivity. Since R size 12{R} {} and r size 12{r} {} are in parallel, the voltage across them is the same.

These IR size 12{ ital "IR"} {} drops are IR = I G r size 12{ ital "IR"=I rSub { size 8{G} } r} {} so that IR = I G I = R r size 12{ ital "IR"= { {I rSub { size 8{G} } } over {I} } = { {R} over {r} } } {} . Solving for R size 12{R} {} , and noting that I G size 12{I rSub { size 8{G} } } {} is 50 μA size 12{"50" μA} {} and I size 12{I} {} is 0.999950 A, we have

R = r I G I = ( 25 Ω ) 50 μA 0 . 999950 A = 1 . 25 × 10 3 Ω . size 12{R=r { {I rSub { size 8{G} } } over {I} } = \( "25" %OMEGA \) { {"50" mA} over {0 "." "999950 A"} } =1 "." "25"´"10" rSup { size 8{-3} } %OMEGA } {}
A resistance R is placed in parallel with a galvanometer G having an internal resistance r to produce an ammeter.
A small shunt resistance R size 12{R} {} placed in parallel with a galvanometer G produces an ammeter, the full-scale deflection of which depends on the choice of R size 12{R} {} . The larger the current to be measured, the smaller R size 12{R} {} must be. Most of the current ( I ) flowing through the meter is shunted through R size 12{R} {} to protect the galvanometer. (Note that r represents the internal resistance of the galvanometer.) Ammeters may also have multiple scales for greater flexibility in application. The various scales are achieved by switching various shunt resistances in parallel with the galvanometer—the greater the maximum current to be measured, the smaller the shunt resistance must be.

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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