(a) Derive the expression for maximum torque (show all steps) and show that the slip at which maximum torque occurs is directly proportional to rotor resistance, but the maximum torque is independent of rotor resistance.
(b) A 230-V, 4-pole, 60-Hz, Y-connected, three-phase induction motor has the following parameters on a per phase basis:
R1 = 10.12 ohm X1 = 38.61 ohm R2 = 28.97 ohm X2 = 11.56 ohm Xm = 432.48 ohm
i. Calculate the slip at which the motor develops maximum torque.
ii. What is the maximum torque developed by the motor?
iii. What is the power developed by the motor at this slip?