If we double the number of turns in a moving coil galvanometer, the voltage sensitivity of the galvanometer

does not change

The correct answer is Option (4) → does not change

Voltage sensitivity of a moving coil galvanometer is defined as the deflection per unit voltage:

$S_v = \frac{\theta}{V}$

Using the relation between current sensitivity and voltage sensitivity:

$S_v = \frac{S_i}{R} = \frac{NAB}{kR}$

Where:

$N$ = Number of turns

$A$ = Area of the coil

$B$ = Magnetic field

$k$ = Torsional constant

$R$ = Resistance of the coil

If we double the number of turns ($N \rightarrow 2N$), the coil’s resistance also doubles approximately ($R \rightarrow 2R$).

Then,

$S_v' = \frac{2NAB}{k \cdot 2R} = \frac{NAB}{kR} = S_v$

Hence, the voltage sensitivity remains the same.