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

For a $$1.8$$ degree, $$2$$-phase bipolar stepper motor, the stepping rate is $$100$$ steps/second. The rotational speed of the motor in $$rpm$$ is

A $$500$$ $$MW$$ $$3$$-phase $$Y$$-connected synchronous generator has a rated voltage of $$21.5kV$$ at $$0.85$$ $$pf.$$ The line current when operating at full load rated conditions will be

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