Question

A current of 200 $\mu A$ deflects the coil of a moving coil galvanometer through $60^{\circ}$. The current to cause deflection through $\frac{\pi}{10}$ radian is :

• A. 30 $\mu A$
• B. 120 $\mu A$
• C. 60 $\mu A$
• D. 180 $\mu A$

Answer 1

The Correct Option is C

Given:

- $i_2 = 200 \, \mu A$,
- $\theta_2 = 60^\circ = \frac{\pi}{3} \, \text{radians}$.

The deflection $\theta$ is proportional to the current $i$. Therefore:

$\frac{i_1}{i_2} = \frac{\theta_1}{\theta_2}.$

For $\theta_1 = \frac{\pi}{10} \, \text{radians}$:

$\frac{i_1}{200} = \frac{\frac{\pi}{10}}{\frac{\pi}{3}}.$

Simplify:

$\frac{i_1}{200} = \frac{3}{10} \implies i_1 = 200 \times \frac{3}{10} = 60 \, \mu A.$

The Correct answer is: 60 $\mu A$