A current tester consists of a stator winding with self-inductance L1 = 7 H., and a rotor winding with self-inductance L2 = 4 H. Their mutual inductance is given by M = 10 + 7 θ − θ 3 (H.), where θ is the rotor deflection angle of the tester in radians.
(a) Find the total magnetic energy Wm in terms of the currents i1, i2, and θ;
(b) Find the magnetic torque τm on the rotor in terms of i1, i2 and θ;
(c) If i1 = 1 and i2 = 2 both are DC in A., and the rotor torque is balanced by a torsional spring with the constant k = 5 N-m/rad., determine the deflection θ ;
(d) If now the average deflection θ = 400 under an AC current ˜I into both the stator and rotor windings, find this common AC current in rms value I.
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