The self and mutual inductances of a machine with two windings are given by L 11 = (1 + sin ? ),…

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).

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