The current sensitivity of a moving coil galvanometer depends on

The correct answer is Option (3) → torsional constant of the spring

The current sensitivity of a galvanometer is its deflection per unit current, \( \phi/I \). In equilibrium the magnetic torque \( NIAB \) on the coil is balanced by the spring torque \( k\phi \). This gives \( \phi/I=NAB/k \).

Option (1) angle of deflection — Incorrect. The deflection \( \phi \) grows in proportion to the current, so the ratio \( \phi/I \) stays the same. It is fixed by \( N \), \( A \), \( B \) and \( k \) of the instrument.

Option (2) earth’s magnetic field — Incorrect. The field \( B \) in \( NAB/k \) is the radial field of the permanent magnet, made stronger by the soft iron core. The weak field of the earth plays no part.

Option (3) torsional constant of the spring — Correct. \( k \) is in the denominator of \( NAB/k \). A spring with a smaller torsional constant twists more for the same torque, so the galvanometer becomes more sensitive.

NCERT (2026-27):
The Moving Coil Galvanometer – “We define the current sensitivity of the galvanometer as the deflection per unit current. … this current sensitivity is,”

    \( \displaystyle \frac{\phi}{I}=\left(\frac{NAB}{k}\right) \)\( \qquad (4.27) \)

The Moving Coil Galvanometer – “where k is the torsional constant of the spring; i.e. the restoring torque per unit twist. …”