A star-connected 440 V, 50 Hz alternators has per phase synchronous reactance of 10 Ω. It supplies a balanced capacitive load current of 20 A, as shown in the per phase equivalent circuit of Figure. It is desirable to have zero voltage regulation. The load power factor should be

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.

Two identical synchronous generators, each of $$100$$ $$MVA,$$ are working in parallel supplying $$100$$ $$MVA$$ at $$0.8$$ lagging $$p.f.$$ at rated voltage. Initially the machines are sharing load equally. If the field current of first generator is reduced by $$5\% $$ and of the second generator increased by $$5\% ,$$ find the sharing of load ($$MW$$ and $$MVAR$$) between the generators.
Assume$${X_d} = {X_q} = 0.8\,\,p.u.$$ no field saturation and rated voltage across load. Reasonable approximations may be made.

In a $$dc$$ motor running at $$2000$$ $$rpm,$$ the hysteresis and eddy current losses are $$500$$ $$W$$ and $$200$$ $$W$$ respectively. If the flux remains constant, calculate the speed at which the total iron losses are halved.