11
Now if the two currents are sinusoidal and displaced by a phase angle ൫ then

1 = [ant Sin ‏اہ‎

and 1» = Imo sin (wt — $)
Ty = व [1 sin ‏ا( ۴ت) صتھ 1,.2- ہ‎ (wt)
= ( ‏گے‎ me ಫಲಾ ५
= || 12 ‏ہیں‎ SM

where ||, ‏دا‎ are the r.m.s. values of the two currents as,

Tint ‏تما‎
‎॥ = ‏كد‎ and ‏خم = را‎
i V2 2 6
As T. = KO
Hence in steady state, 1६ = Ty
|| 12 cos SM = KO

Thus the deflection is decided by the product of r.m.s. values of two currents,
cosine of the phase angle (power factor) and rate of change of mutual inductance.

For d.c. use, the deflection is proportional to square of current and the scale is
non-uniform and crowded at the ends. For a.c. use the instantaneous torque is
proportional to the square of the instantaneous current. The i? is positive and as
current varies, the deflecting torque also varies.

But moving system, due to intertia cannot follow rapid variations and thus finally
meter shows the average torque.