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MCQEasyJEE 2024Potentiometer

JEE Physics 2024 Question with Solution

The deflection in a moving coil galvanometer falls from 2525 divisions to 55 divisions when a shunt of 24 Ω24 \, \Omega is applied. The resistance of the galvanometer coil will be:

  • A

    12 Ω12 \, \Omega

  • B

    96 Ω96 \, \Omega

  • C

    48 Ω48 \, \Omega

  • D

    100 Ω100 \, \Omega

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Initial deflection is D1=25D_1 = 25 divisions, final deflection is D2=5D_2 = 5 divisions, and shunt resistance is S=24 ΩS = 24 \, \Omega.

Find: The resistance GG of the galvanometer coil.

Deflection in a moving coil galvanometer is proportional to the current through it. Using the shunt relation:

D1D2=1+GS\frac{D_1}{D_2} = 1 + \frac{G}{S}

Substitute the given values:

255=1+G24\frac{25}{5} = 1 + \frac{G}{24}

So,

5=1+G245 = 1 + \frac{G}{24}

Rearranging,

5−1=G245 - 1 = \frac{G}{24} 4=G244 = \frac{G}{24}

Hence,

G=4×24=96 ΩG = 4 \times 24 = 96 \, \Omega

Therefore, the resistance of the galvanometer coil is 96 Ω96 \, \Omega. The correct option is B.

Current Division Method

Given: Let the current required per division be xx. Initially, for 2525 divisions, the galvanometer current is I=25xI = 25x.

Find: The galvanometer resistance GG.

After applying the shunt, the deflection becomes 55 divisions. Hence current through the galvanometer is:

Ig=5xI_g = 5x

The remaining current passes through the shunt, so current in shunt is:

I−Ig=25x−5x=20xI - I_g = 25x - 5x = 20x

Since the galvanometer and shunt are in parallel, the potential difference across both is equal:

IgG=(I−Ig)SI_g G = (I - I_g) S

Substitute Ig=5xI_g = 5x, (I−Ig)=20x(I - I_g) = 20x, and S=24 ΩS = 24 \, \Omega:

5xG=20x×245xG = 20x \times 24

Cancelling xx,

5G=20×245G = 20 \times 24 G=20×245=96 ΩG = \frac{20 \times 24}{5} = 96 \, \Omega

Therefore, the resistance of the galvanometer coil is 96 Ω96 \, \Omega. The correct option is B.

Common mistakes

  • Assuming deflection is inversely proportional to shunt resistance alone is incomplete. The correct relation comes from current division in the galvanometer-shunt combination. Always use the galvanometer-shunt formula or equal potential condition.

  • Using 25x25x as the galvanometer current after shunting is incorrect. After the shunt is connected, the galvanometer current corresponds to the reduced deflection, so it becomes 5x5x.

  • Forgetting that the galvanometer and shunt are in parallel leads to a wrong equation. The correct step is to equate potential differences: IgG=IsSI_g G = I_s S.

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