A $240$ V line$-$to$-$line rms delta connected $100$ hp $60$ Hz $6-$pole $3$ phase synchronous motor is operating

with a developed power $($including losses$)$ of $50$ horsepower and a power factor of $90\%$ leading. The

synchronous reactance is $=0\mathrm{.}5.$

a$)$ Find the motor speed in rad$/$sec and the developed torque.

b$)$ Calculate phasor values for armature current, $,$ and induced rotor voltage, $.$ What is the

torque angle? $($Hints: Don$$t forget that phasors need both magnitude and angle! If $$ includes

losses, $=)$

c$)$ Suppose that the excitation remains constant, and the load torque increases until the developed

power is $100$ horsepower. Calculate the new phasor values for $,$ and torque angle. $($Hint:

remember that torque is proportional to sin $())$