q the self and mutual inductances of a machine

Question

Q. The self and mutual inductances of a machine with two windings are given by L₁₁ = (1 +sin θ), L₂₂ = 2(1 + sin θ), and L₁₂ = L₂₁ = M = (1-sin θ). Assuming θ = 45°, and letting coils 1 and 2 be supplied by constant currents I₁ = 15 A and I₂ =-4 A, respectively, find the following:

(a) Magnitude and direction of the developed torque.

(b) Amount of energy supplied by each source.

(c) Rms value of the current in coil 2, if the current of coil 1 is changed to a sinusoidal current of 10 A (rms) at 60 Hz and coil 2 is short-circuited.

(d) Instantaneous torque produced in part (c).

(e) Average torque in part (c).