A moving coil galvanometer, having a resistance G, produces full… | JEE Main 2019 (12 Apr, Shift 2)

Q166JEE Main 2019 · 12 APR · SHIFT 2Medium

Kirchhoff's Laws & Measuring Instruments

A moving coil galvanometer, having a resistance G, produces full scale deflection when a current Ig flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I0(I0 > Ig) by connecting a shunt resistance RA to it and (ii) into a voltmeter of range 0 to V (V = GI0) by connecting a series resistance RV to it. Then,

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Answer: (d)

Ammeter shunt: $R_A = \frac{I_g G}{I_0 - I_g}$
Voltmeter series resistance: $R_V = \frac{V}{I_g} - G = \frac{G I_0}{I_g} - G = \frac{G(I_0 - I_g)}{I_g}$
Product: $R_A R_V = G^2$
Ratio: $\frac{R_A}{R_V} = \left(\frac{I_g}{I_0 - I_g}\right)^2$
So the answer is (d).

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Kirchhoff's Laws & Measuring Instruments question from JEE Main 2019 (12 Apr, Shift 2)

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