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MCQEasyJEE 2024Electric Current & Drift Velocity

JEE Physics 2024 Question with Solution

A current of 200 μA200 \, \mu A deflects the coil of a moving coil galvanometer through 60∘60^\circ. The current to cause deflection through π/10\pi/10 radians is:

  • A

    30 μA30 \, \mu A

  • B

    120 μA120 \, \mu A

  • C

    60 μA60 \, \mu A

  • D

    180 μA180 \, \mu A

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A current of 200 μA200 \, \mu A produces a deflection of 60∘=π/360^\circ = \pi/3 radians.

Find: The current required for deflection π/10\pi/10 radians.

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

θ∝I\theta \propto I

So,

I1I2=θ1θ2\frac{I_1}{I_2} = \frac{\theta_1}{\theta_2}

Substitute the given values:

I1200=π/10π/3\frac{I_1}{200} = \frac{\pi/10}{\pi/3} I1200=310\frac{I_1}{200} = \frac{3}{10}

Hence,

I1=200×310=60 μAI_1 = 200 \times \frac{3}{10} = 60 \, \mu A

Therefore, the current required is 60 μA60 \, \mu A. The correct option is C.

Direct Proportionality Trick

Given: Deflection in a galvanometer is proportional to current.

Find: Current for deflection π/10\pi/10 when 200 μA200 \, \mu A gives π/3\pi/3.

Since current and deflection change in the same ratio,

I1=200×π/10π/3I_1 = 200 \times \frac{\pi/10}{\pi/3} I1=200×310=60 μAI_1 = 200 \times \frac{3}{10} = 60 \, \mu A

This works because the proportionality constant of the galvanometer remains the same in both cases. Therefore, the correct option is C.

Common mistakes

  • Using 6060 directly without converting 60∘60^\circ to radians is incorrect here because the other deflection is given in radians. Convert 60∘60^\circ to π/3\pi/3 first so both angles are in the same unit.

  • Taking deflection inversely proportional to current is wrong. In a moving coil galvanometer, θ∝I\theta \propto I, so a smaller deflection must correspond to a smaller current.

  • Forming the ratio as 200I1=π/10π/3\frac{200}{I_1} = \frac{\pi/10}{\pi/3} leads to the inverse result. Keep corresponding quantities in the same order, such as I1200=θ1θ2\frac{I_1}{200} = \frac{\theta_1}{\theta_2}.

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