Synchronous Motor taking a 40 kW is working in parallel with a load of  80 kW having a power factor of 0.75 lagging. The power factor of the combined load is 0.9 lagging. Find the power factor and the  reactive KVA of the motor The answers have to be 0.96, 12.43Kvar

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Synchronous Motor

The synchronous motor is an AC electric type motor where at a steady-state the shaft rotation is synchronized with the supply current variable-frequency. To an integral number of AC cycles, the rotation period is exactly equal. The stator of the motor in the synchronous motor contains multi-phase AC electromagnets due to which a magnetic field is created that rotates in time with the oscillation of the line current. The rotor contains a permanent magnet and the rotor rotates in synchronization with the stator field at the same rate and provides the second synchronized magnetic field which is rotating in nature as a result. When the synchronous motor is supplied with independently excited multi-phase AC electromagnets on both the rotor and the stator, it is termed as a doubly-fed machine. The most widely used AC-type motors are the synchronous AC motor and the induction AC motors.