A motor control center (MCC) has three induction motors each rated at 40 HP and 480 V and four induction motors each rated at 30 HP and 480 V. Each 40 HP motor has an energy efficiency of 0.92 , a rated speed of 1772 rpm, and a power factor of 0.85 . Each 30 HP motor has an energy efficiency of 0.90, and a power factor of 0.90. Determine

(a) The number of poles, the slip (%), and the torque delivered by each 40 HP motor.

(b) The induction motors (by specifying their HP and their number) that needs to be replaced by synchronous motors so that the overall power factor of the MCC is as close to unity as possible without changing the total kW load of the MCC nor the HP ratings of the motors. Assume that the power factor for any synchronous motor is 0.90 leading.