A multirange voltmeter can be constructed by using a galvanometer… - Vidyadip

Question

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

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Answer

Key concept: 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 $I_g(G + R)$ 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 $2V$ range
For $I_g(G + R_1 + R_2) = 20$ for $20V$ range
And For $I_g(G + R_1 + R_2 + R_3) = 200$ for $200V$ range
By solving, we get
$R_1 = 1990\Omega , R_2 = 18k\Omega$ and $R_3 = 180k\Omega .$

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