From the principle of conservation of energy,
Energy input = Energy stored + Mechanical energy
Mechanical energy = Energy input — Energy stored
Substracting (2) from (1),
Mechanical energy = liz dL; +} 13412 i; 12 dM

The self inductances ‏ہا‎ and ‏ہا‎ are constants and hence dL,;and dL, are zero.

स Mechanical energy = i; iz dM

If Tj is the instantaneous deflecting torque and 30 is the change in the deflection
then

Mechanical energy = Mechanical work done
= Ti do
7 12 d M = Ti d 9

T; = iy ig SN

This is the expression for the instantaneous deflecting torque. Let us see its
operation on a.c. and d.c.

D.C. operation : For d.c. currents of I; and 12,

aM

Ta = 1112 a0

The controlling torque is provided by springs hence

T = KO
In steady state, Ty ടനം
dM
I, Iz ठठ = 1; 0
൫ ‏سے‎ [12 dM
K 988

Thus the deflection is proportional to the product of the two currents and the rate
of change of mutual inductance.

A.C, operation;: In a.c. operation, the total deflecting torque over a cycle must be
obtained by integrating 11. over one period.

Average deflecting torque over one cycle is,
it
Ta = பய dit

T = Time period of one cycle

dM 1. .
Ta = ‏وق‎ ٣٣ di