Two windings, one mounted on a stator and the other on a rotor, have self- and mutual inductances of L11 = 4.5H L22 = 2.5H L12 = 2.8cos ? H where ? is the angle between the axes of the windings. The resistances of the windings may be neglected. Winding 2 is short-circuited, and the current in winding 1 as a function of time is il = 10 sin wt A.

a. Derive an expression for the numerical value in Newton-meters of the instantaneous torque on the rotor in terms of the angle ?.

b. Compute the time-averaged torque in Newton-meters when ? = 45°.

c. If the rotor is allowed to move, will it rotate continuously or will it tend to come to rest if the latter at what value of ?0?

Spring Coil -d- Guide ring- Cylindrical steel shell Cylindrical steel plunger Applied force, f, ato