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A three-phase induction motor delivers 500 hp at an efficiency of 0.91, the operating power factor...

A three-phase induction motor delivers 500 hp at an efficiency of 0.91, the operating power factor being 0.76 lagging. A loaded synchronous motor with a power consumption of 100 kW is connected in parallel with the induction motor.
Calculate the necessary kVA and the operating power factor of the synchronous motor if the overall power factor is to be unity.
Answer should be 365 kVA, 0.274
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