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.

Answer 1

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 I_g (G + R) – V where I_g 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.