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Question
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 10Ω and that produces maximum deflection for current of 1 mA. Find R1, R2 and R3 that have to be used.
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Solution
The galvanometer can also be used as a voltmeter to measure the voltage across a given section of the circuit. For this, a very high resistance wire is to be connected in series with galvanometer. The relationship is given by Ig (G + R) – V where Ig is the range of galvanometer, G is the resistance of galvanometer and R is the resistance of wire connected in series with galvanometer.
Applying expression in different situations
For `i_G (G + R_1)` = 2 for 2 V range
For `i_G (G + R_1 + R_2)` = 20 for 20 V range
And For `i_G (G + R_1 + R_2 + R_3)` = 200 for 200 V range
By solving, we get
R1 = 1990 Ω R2 = 18 kΩ and R3 = 180 kΩ.
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