The sensitivity of a moving coil galvanometer depends on

torsional constant of the spring

The sensitivity of a moving coil galvanometer depends upon: (a) The value of n, i.e., number of turns. (b) The value of B, i.e., the intensity of the magnetic field. (c) torsional rigidity.

Current sensitivity =$\frac{nBA}{k}$​
where K is constant of torsional rigidity.