A hydraulic turbine having rated speed of $$250$$ $$rpm$$ is connected to a synchronous generator. In order to produce power at $$50$$ $$Hz,$$ the number of poles required in the generator are

A $$400$$ $$V,$$ $$50$$ $$kVA,$$ $$0.8$$ $$pf$$ leading delta connected, $$50$$ $$Hz$$ synchronous machine has a synchronous reactance of $$2$$ $$ohm$$ and negligible armature resistance. The friction and windage losses are $$2$$ $$kW$$ and the core loss is $$0.8$$ $$kW.$$ The shaft is supplying $$9$$ $$kW$$ load at a power factor of $$0.8$$ leading. The line current drawn is

The synchronous speed for the seventh space harmonic $$mmf$$ wave of a $$3$$-phase, $$8$$ pole, $$50$$ $$Hz$$ induction machine is

Two $$3$$-phase, $$Y$$-connected alternators are to be paralleled to a set of common bus bars. The armature has a per phase synchronous reactance of $$1.7\Omega $$ and negligible armature resistance. The line voltage of the first machines is adjusted to $$3300$$ $$V$$ and that of the second machine is adjusted to $$3200$$ $$V.$$ the machine voltages are in phase at the instant they are paralleled. Under this condition, the synchronizing current per phase will be