JEE Physics 2024 Question with Solution

Given: A current of $200 \, \mu A$ produces a deflection of $60^\circ$.

Find: The current required for a deflection of $\pi/10$ radians.

In a moving coil galvanometer, deflection is directly proportional to current:

$$\theta \propto I$$

So,

$$\frac{I_1}{I_2} = \frac{\theta_1}{\theta_2}$$

Convert $60^\circ$ into radians:

$$60^\circ = \frac{\pi}{3}$$

Now use

$$\frac{I_1}{200} = \frac{\frac{\pi}{10}}{\frac{\pi}{3}}$$

Thus,

$$\frac{I_1}{200} = \frac{3}{10}$$

So,

$$I_1 = 200 \times \frac{3}{10} = 60 \, \mu A$$

Therefore, the current required is $60 \, \mu A$. The correct option is C.

Given: Deflection is proportional to current.

Find: Current for deflection $\pi/10$ when $200 \, \mu A$ gives $\pi/3$.

Because current and deflection are directly proportional, the current scales by the same factor as the angle:

$$I_1 = 200 \times \frac{\pi/10}{\pi/3}$$

Cancel $\pi$ and simplify:

$$I_1 = 200 \times \frac{3}{10} = 60 \, \mu A$$

Therefore, the required current is $60 \, \mu A$. The correct option is C.