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.