When a resistance of $5\Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of 250 mA, however when $1050\Omega$ resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is ______ $\Omega$.

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Current Electricity

When a resistance of

5Ω

is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of 250 mA, however when

1050Ω

resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is ______

Ω

Answer: 50

For the shunt configuration, the current through the galvanometer at full scale deflection is:

i_{g} = \frac{250 \times 1 0 ^{- 3} \times 5}{5 + R _{G}}

For the series configuration:

i_{g} = \frac{25}{1050 + R _{G}}

Equating the two expressions:

\frac{1.25}{5 + R _{G}} = \frac{25}{1050 + R _{G}}

Cross-multiplying:

1.25 (1050 + R_{G}) = 25 (5 + R_{G})

1312.5 + 1.25 R_{G} = 125 + 25 R_{G}

1187.5 = 23.75 R_{G}

R_{G} = 50Ω

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Integer answer