A $$50$$ $$kW$$ synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes $$800$$ $$W.$$ When the armature is short-circuited and the rated armature current of $$10$$ $$A$$ is passed through it, the driving motor requires $$2500$$ $$W.$$ On open-circuiting the armature with rated excitation, the driving motor takes $$1800$$ $$W.$$ Calculate the efficiency of the synchronous motor at $$50\% $$ load. Neglect the losses in the driving motor.

A $$2300$$ $$V,$$ $$3$$-phase synchronous motor driving a pump is provided with a line ammeter and a field rheostat. When the rheostat is adjusted such that the $$ac$$ line current is minimum. The ammeter reads $$8.8$$ $$A.$$ What is the power being delivered to the pump, neglecting losses? How should the rheostat be adjusted so that the motor operates at $$0.8$$ leading power factor? How many $$kVARs$$ is the motor supplying to the system at this new power factor?

A $$5MVA$$, $$11kV$$, $$3$$-phase star connected alternator is synchronized to the bus bars and is operating with an induced $$EMF$$ of $$125\% $$ of the rated voltage. If the load current is $$500$$ $$A,$$ what is the power factor of operation? The machine has a synchronous reactance of $$5\,\,\Omega $$ and negligible resistance per phase.

The per unit voltage of two synchronous machines connected through a lossless line are $$0.95\,\,\angle \,{10^0}\,\,$$ and $$1.0\,\,\angle \,{0^0}\,\,$$. Match the two sides in the following
$$(a)$$ Real power of Machine $$1$$
$$(b)$$ Reactive power of machine $$1$$
$$(c)$$ Power factor of Machine $$1$$

$$(P)$$ Positive real power
$$(Q)$$ Positive reactive power
$$(R)$$ Negative real power
$$(S)$$ Negative reactive power
$$(T)$$ Leading power factor
$$(U)$$ Lagging power factor