Consider a moving coil galvanometer (MCG) : A : The torsional constant in moving coil galvanometer has dimensions $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C : If we increase number of turns (N) to its double $(2 \mathrm{~N})$, then the voltage sensitivity doubles. D : MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E : Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below :

Current Electricity — JEE Main · 2025 · 23 Jan 2025 · Shift 1 Question with Solution

Consider a moving coil galvanometer (MCG) :
A : The torsional constant in moving coil galvanometer has dimensions

[ML^{2} T^{- 2}]

B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C : If we increase number of turns (N) to its double

(2 N)

, then the voltage sensitivity doubles.
D : MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E : Current sensitivity of MCG depends inversely on number of turns of coil.

Choose the correct answer from the options given below :

(A)A, B only✓ Correct
(B)A, D, only
(C)B, D, E only
(D)A, B, E only

Answer: (A)

Solution

A: The restoring torque in a moving coil galvanometer is

τ = C θ

, so

[C] = \frac{[ τ ]}{[ θ ]} = [M L^{2} T^{- 2}]

. True.

B: Current sensitivity is

I_{S} = \frac{θ}{I} = \frac{N B A}{C}

, and voltage sensitivity is

V_{S} = \frac{θ}{V} = \frac{N B A}{R C}

, where

R

is the coil resistance. Since

R

itself grows with

N

, a rise in current sensitivity does not automatically produce a proportional rise in voltage sensitivity. True.

C: Doubling

N

also roughly doubles the coil resistance

R

for the same wire. Since

V_{S} \propto \frac{N A B}{C R}

and

R

scales with

N

, the voltage sensitivity does not simply double. False.

D: Converting a galvanometer into an ammeter requires a shunt of *small* resistance in parallel, not large. False.

E: Current sensitivity

I_{S} \propto N

, so it is directly, not inversely, proportional to the number of turns. False.

Only statements A and B are correct.

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · One or more correct options

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Current Electricity

Solution

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