The current sensitivity of a galvanometer can be increased by : (A) decreasing the number of turns (B) increasing the magnetic field (C) decreasing the area of the coil (D) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below :

Magnetics PYQ — JEE Main 2022 · 28 Jul · Shift 1 · Q57 with Solution

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Correct answer: D

For a moving coil galvanometer,

\text{deflecting torque} = n B I A

and restoring torque is

C\theta

At equilibrium,

nBIA = C\theta

So,

\frac{\theta}{I} = \frac{nBA}{C}

Current sensitivity is

S_I = \frac{\theta}{I} = \frac{nBA}{C}

Thus, current sensitivity increases when:

(A) decreasing the number of turns

Since sensitivity is proportional to $n$ , decreasing $n$ will decrease sensitivity. So this is false.
(B) increasing the magnetic field

Since sensitivity is proportional to $B$ , increasing $B$ will increase sensitivity. So this is true.
(C) decreasing the area of the coil

Since sensitivity is proportional to $A$ , decreasing $A$ will decrease sensitivity. So this is false.
(D) decreasing the torsional constant of the spring

Since sensitivity is inversely proportional to $C$ , decreasing $C$ will increase sensitivity. So this is true.

The correct statements are:

(B) \text{ and } (D)

So the correct option is:

\boxed{\text{D}}

Stored correct answer: $\boxed{D}$

My derived answer also: $\boxed{D}$

Hence, they agree.