Question:

The deflection in a moving coil galvanometer is reduced to half when it is shunted with $ X \, \Omega $ coil. The relation between $ X $ and resistance of galvanometer $ G $ is

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When a galvanometer is shunted, the deflection depends on the ratio of the resistance of the shunt and the galvanometer. The deflection reduces when the current is split between the two.

Updated On: Jan 30, 2026

$ 2X = G $
$ 4X = G $
$ X = 2G $
$ X = G $

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The Correct Option is D

Solution and Explanation

Step 1: Understanding the effect of shunting.
When a galvanometer is shunted with a resistor $ X $, the total current is shared between the galvanometer and the shunt. The deflection in the galvanometer is directly proportional to the current passing through it. When the deflection is reduced to half, the current passing through the galvanometer is halved.
Step 2: Applying the relation between the resistances.
The current through the galvanometer and the shunt are related by the formula: \[ \frac{G}{X} = 2 \quad \Rightarrow \quad X = G \]
Step 3: Conclusion.
Thus, the resistance of the shunt is equal to the resistance of the galvanometer, $ X = G $, which corresponds to option (D).

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