# A Galvanometer of Resistance G is Converted into a Voltmeter to Measure Upto V Volts by Connecting a Resistance R1 in Series with the Coil. - Physics

A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance R1 in series with the coil. If a resistance R2 is connected in series with it, then it can measures upto V/2 volts. Find the resistance, in terms of R1 and R2, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the galvanometer in terms of R1 and R2

#### Solution

A high resistance that is connected in series with the galvanometer to convert it into voltmeter. The value of the resistance is given by R=V/I_g-G

Here,
V = Potential difference across the terminals of the voltmeter

Ig = Current through the galvanometer

G = Resistance of the galvanometer

When resistance R1 is connected in series with the galvanometer,

R_1=V/I_g-G

When resistance R2 is connected in series with the galvanometer,

R_2=V/(2I_g)-G" .....(ii)"

From (i) and (i), we get

V/(2I_g)=R_1-R_2 " and "G=R_1-2R_2

The resistance R3 required to convert the given galvanometer into voltmeter of range 0 to 2V is given by

R_3=(2V)/I_g-G

R3=4(R1R2)(2R1R2)=3R12R2

G in terms of R1 and R2 is given by

G=R12R2

Concept: Moving Coil Galvanometer
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