Question

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

• A. \( 30 \, \mu\text{A} \)
• B. \( 120 \, \mu\text{A} \)
• C. \( 60 \, \mu\text{A} \)
• D. \( 180 \, \mu\text{A} \)

Hint:

The deflection angle in a moving coil galvanometer is proportional to the current passing through it. Always use the proportionality relation \( \frac{I_2}{I_1} = \frac{\theta_2}{\theta_1} \) to calculate unknown currents when deflection angles are given.

Answer 1

The Correct Option is C

The deflection of a moving coil galvanometer is proportional to the current passing through it: \[ I \propto \theta. \] Given: \[ I_1 = 200 \, \mu\text{A}, \quad \theta_1 = 60^\circ, \quad \theta_2 = \frac{\pi}{10}. \] Convert \( 60^\circ \) to radians: \[ \theta_1 = 60^\circ = \frac{\pi}{3}. \] Using the proportionality relation: \[ \frac{I_2}{I_1} = \frac{\theta_2}{\theta_1}. \] Substituting the values: \[ \frac{I_2}{200} = \frac{\frac{\pi}{10}}{\frac{\pi}{3}}. \] Simplify the equation: \[ \frac{I_2}{200} = \frac{3}{10}. \] Solve for \( I_2 \): \[ I_2 = 200 \cdot \frac{3}{10} = 60 \, \mu\text{A}. \] Final Answer: \[ \boxed{60 \, \mu\text{A}} \]