A moving coil of a galvanometer when shunted with $2 \Omega$ resistance gives a full scale deflection for a current of 500 mA. When a resistance of $470 \Omega$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is ______ $\Omega$.

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Current Electricity

A moving coil of a galvanometer when shunted with

2Ω

resistance gives a full scale deflection for a current of 500 mA. When a resistance of

470Ω

is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is ______

Ω

Answer: 50

At full-scale deflection the coil carries its characteristic current

i_{g}

in both arrangements. With the

2 Ω

shunt, the remaining current passes through the shunt:

i_{g} R_{g} = 2 (0.5 - i_{g})

, which rearranges to

i_{g} = \frac{1}{R _{g} + 2}

. Used as a voltmeter with

470 Ω

in series, full-scale deflection at

10 V

requires

10 = (R_{g} + 470) i_{g}

. Substituting,

10 = \frac{R _{g} + 470}{R _{g} + 2}

, hence

10 R_{g} + 20 = R_{g} + 470

, so

9 R_{g} = 450

and

R_{g} = 50 Ω

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Integer answer