Torque Equation for PMMC

The equation for the developed torque of the PMMC can be obtained from the basic law of electromagnetic torque. The deflecting torque is given by,

                                           Td = NBAI

Where,

Td = deflecting torque in N-m

B = flux density in air gap, Wb/m2

N = Number of turns of the coils

A = effective area of coil m2

I = current in the moving coil, amperes

Therefore, Td = GI

Where, G = NBA = constant

The controlling torque is provided by the springs and is proportional to the angular deflection of the pointer.

                                               Tc = KØ

Where,

Tc = Controlling Torque

K = Spring Constant Nm/rad or Nm/deg

Ø = angular deflection

For the final steady state position,

                        Td = Tc

Therefore GI = KØ

So,                      Ø = (G/K)I               or            I = (K/G) Ø

Thus the deflection is directly proportional to the current passing through the coil. The pointer deflection can therefore be used to measure current.