Calculate the power factor of the motor, Electrical Engineering

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A 3 phase 400 volt(line to line) wye connected synchronous motor has Xs= 1 ohm per phase and a negligible armature resistance. The field current is so adjusted that the internal(induced) voltage is 270volts per phase, while the motor draws 40 kw power from the source. Calculate the

(a) Power factor of the motor, and

(b) Reactive power supplied by the motor to the source.

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