Question:
A moving coil galvanometer, having a resistance G, produces full scale deflection when a current \(I_g\) flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to \(I_0\ (I_0 \gt I_g)\) by connecting a shunt resistance \(R_A\) to it and (ii) into a voltmeter of range 0 to V \((V = GI_0)\) by connecting a series resistance \(R_V\) to it. Then,
A moving coil galvanometer, having a resistance G, produces full scale deflection when a current \(I_g\) flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to \(I_0\ (I_0 \gt I_g)\) by connecting a shunt resistance \(R_A\) to it and (ii) into a voltmeter of range 0 to V \((V = GI_0)\) by connecting a series resistance \(R_V\) to it. Then,
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Get \(R_A\) from the shunt condition \(I_gG = (I_0-I_g)R_A\) and \(R_V\) from \(V = I_g(G+R_V) = GI_0\); then form the product and ratio.
Updated On: Nov 11, 2026
- \(R_AR_V = G^2\) and \(\frac{R_A}{R_V} = \frac{I_g}{(I_0 - I_g)}\)
- \(R_AR_V = G^2\left(\frac{I_g}{I_0 - I_g}\right)\) and \(\frac{R_A}{R_V} = \left(\frac{I_0 - I_g}{I_g}\right)^2\)
- \(R_AR_V = G^2\left(\frac{I_0 - I_g}{I_g}\right)\) and \(\frac{R_A}{R_V} = \left(\frac{I_g}{I_0 - I_g}\right)^2\)
- \(R_AR_V = G^2\) and \(\frac{R_A}{R_V} = \left(\frac{I_g}{I_0 - I_g}\right)^2\)
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The Correct Option is D
Solution and Explanation
Ammeter: the shunt carries \(I_0 - I_g\) at the same potential difference as the galvanometer, so \(I_gG = (I_0-I_g)R_A\Rightarrow R_A = \frac{I_gG}{I_0-I_g}\).
Voltmeter: \(V = I_g(G+R_V) = GI_0\Rightarrow G + R_V = \frac{GI_0}{I_g}\Rightarrow R_V = \frac{G(I_0-I_g)}{I_g}\).
Product: \(R_AR_V = \frac{I_gG}{I_0-I_g}\cdot\frac{G(I_0-I_g)}{I_g} = G^2\).
Ratio: \(\frac{R_A}{R_V} = \frac{I_gG}{I_0-I_g}\cdot\frac{I_g}{G(I_0-I_g)} = \left(\frac{I_g}{I_0-I_g}\right)^2\).
Answer: (4) \(R_AR_V = G^2\) and \(\frac{R_A}{R_V} = \left(\frac{I_g}{I_0 - I_g}\right)^2\)
Voltmeter: \(V = I_g(G+R_V) = GI_0\Rightarrow G + R_V = \frac{GI_0}{I_g}\Rightarrow R_V = \frac{G(I_0-I_g)}{I_g}\).
Product: \(R_AR_V = \frac{I_gG}{I_0-I_g}\cdot\frac{G(I_0-I_g)}{I_g} = G^2\).
Ratio: \(\frac{R_A}{R_V} = \frac{I_gG}{I_0-I_g}\cdot\frac{I_g}{G(I_0-I_g)} = \left(\frac{I_g}{I_0-I_g}\right)^2\).
Answer: (4) \(R_AR_V = G^2\) and \(\frac{R_A}{R_V} = \left(\frac{I_g}{I_0 - I_g}\right)^2\)
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