Question:

A galvanometer has resistance $ G $ and range $ V_g $. How much resistance is required to read voltage up to $ V $ volts?

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To extend the voltage range of a galvanometer, use a series resistor. The value of this resistor depends on the desired voltage range and the initial range of the galvanometer.

Updated On: Jan 26, 2026

$ \frac{G(V + V_g)}{V} $
$ G \left( \frac{V}{V_g} - 1 \right) $
$ \frac{G(V - V_g)}{V} $
$ G V_g $

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The Correct Option is B

Solution and Explanation

Step 1: Understanding the problem.
To extend the range of a galvanometer to measure higher voltages, a series resistance must be added. The total voltage across the galvanometer plus the series resistance is equal to the voltage $ V $ we wish to measure. Using the concept of current, the current $ I $ through the galvanometer when the maximum voltage $ V_g $ is applied is $ I = \frac{V_g}{G} $. To measure $ V $ volts, the total resistance must be such that the current remains the same.
Step 2: Using the formula.
The total resistance required to measure $ V $ volts is $ G \left( \frac{V}{V_g} - 1 \right) $, where $ G $ is the resistance of the galvanometer and $ V_g $ is the maximum voltage for which the galvanometer is calibrated.
Step 3: Conclusion.
Thus, the correct answer is (B) $ G \left( \frac{V}{V_g} - 1 \right) $.

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