Question

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

• A. 30 μΑ
• B. 120 μΑ
• C. 60 μΑ
• D. 180 μΑ

Answer 1

Answer: (C)

60 μΑ

Answer 2

For a moving coil galvanometer, the deflection ($\theta$) is directly proportional to the current ($I$) passing through it.

So, $I \propto \theta$, or $I = k\theta$, where $k$ is the galvanometer constant.

Given: Initial current $I_1 = 200 \, \mu A$ Initial deflection $\theta_1 = 60^\circ$ Target deflection $\theta_2 = \frac{\pi}{10}$ radian

First, convert $\theta_1$ to radians for consistency: $\theta_1 = 60^\circ = 60 \times \frac{\pi}{180} \, \text{radian} = \frac{\pi}{3} \, \text{radian}$.

Using the proportionality: $\frac{I_1}{\theta_1} = \frac{I_2}{\theta_2}$ $I_2 = I_1 \left(\frac{\theta_2}{\theta_1}\right)$ $I_2 = 200 \, \mu A \times \left(\frac{\frac{\pi}{10}}{\frac{\pi}{3}}\right)$ $I_2 = 200 \, \mu A \times \left(\frac{\pi}{10} \times \frac{3}{\pi}\right)$ $I_2 = 200 \, \mu A \times \frac{3}{10}$ $I_2 = 20 \times 3 \, \mu A$ $I_2 = 60 \, \mu A$