Hello,

If dθ  is change in the deflection produced used by a small change in the current dI, sensitivity (S) of galvanometer is given by

S = dθ /dI

The current ( I ) flowing through the moving coil galvanometer is given by

I = k/NAB × θ

where θ  is the angle of deflection, N is it turns, is A is area, B is magnetic induction and k is the couple per unit twists.

Sp, θ = NAB / k × I

So, dθ /dI = NAB / k

Hence, S = NAB / k

Best Wishes