If we double the number of turns in a moving coil galvanometer, the voltage sensitivity of the galvanometer
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → does not change
The voltage sensitivity of a moving coil galvanometer is the deflection per unit voltage:
\( \displaystyle \frac{\theta}{V} = \frac{N B A}{k R} \)
where \( N \) is the number of turns, \( B \) the magnetic field, \( A \) the area of the coil, \( k \) the torsion constant and \( R \) the resistance of the coil.
Doubling \( N \) doubles the numerator. The coil now has twice as much wire, so its resistance \( R \) also doubles. The two doublings cancel, so the voltage sensitivity does not change; only the current sensitivity \( NBA/k \) doubles.
NCERT (2026-27):
The Moving Coil Galvanometer – “… We define the voltage sensitivity as the deflection per unit voltage.”
The Moving Coil Galvanometer – “… If N → 2N, i.e., we double the number of turns, then
\( \displaystyle \frac{\phi}{I} \rightarrow 2\frac{\phi}{I} \)
Thus, the current sensitivity doubles. However, the resistance of the galvanometer is also likely to double, since it is proportional to the length of the wire. In Eq. (4.28), N →2N, and R →2R, thus the voltage sensitivity,
\( \displaystyle \frac{\phi}{V} \rightarrow \frac{\phi}{V} \)
remains unchanged.”