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A multirange voltmeter can be constructe...

A multirange voltmeter can be constructed by using a galvanometer circuit as shown in figure. We want to construct a voltmeter that can measure 2V, 20V and 200V using a galvanometer of resistance `10Omega` and that produces maximum deflection for current of `1mA`. Find `R_1`, `R_2` and `R_3` that have to be used.

Text Solution

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Here, `G=10Omega`, `I_g=1mA=10^-3A`
Case (i), `V=2V`, `R_1=?`
`R_1=(V)/(I_g)-G=(2)/(10^-3)-10=1990Omega~~2Omega`
Case(ii), `V=20V, (R_1+R_2)=?`
`(R_1+R_2)=(20)/(10^-3)-10=20,000-10~~20kOmega`
`:. R_2=20kOmega-2kOmega=18kOmega`
Case (iii), `V=200V, (R_1+R_2+R_3)=?`
`R_1+R_2+R_3=(200)/(10^-3)-10~~200kOmega :. R_3=200 k Omega-20 k Omega~~180 k Omega`.
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