Expression for Deflecting Torque & Controlling torque

Expression for Deflecting Torque

Force on a coil side = BilN (Newton, N)

Torque on both coil sides = (2r) (BilN) (Nm)

                                       = Gi (Nm)

G = Constant.

Hence deflecting torque, T_d α I.

Expression for Controlling torque

Since the instrument is spring controlled, Control torque = Cθ

Hence T_c α θ.

The pointer will come to a rest when T_d = T_c

Therefore θ α  I

Thus the deflection is directly proportional to the operating current. Hence such instruments have a uniform scale.