The speed of a $$4$$-pole induction motor is controlled by varying the supply frequency while maintaining the ratio of supply voltage to supply frequency $$(V/f)$$ constant. At rated frequency of $$50$$ $$Hz$$ and rated voltage of $$400$$ $$V$$ its speed is $$1440$$ $$rpm$$. Find the speed at $$30$$ $$Hz,$$ if the load torque is constant

A $$4$$ pole, $$50$$ $$Hz,$$ synchronous generator has $$48$$ slots in which a double layer winding is house. Each coil has $$10$$ turns and is short pitched by an angle to $$36$$ degrees electrical. The fundamental flux per pole is $$0.025$$ $$Wb$$

The line to line induced $$emf$$, for a three phase star connection is approximately

A $$3$$-phase $$4000$$ $$V,$$ $$5$$ $$kW,$$ star connected synchronous motor having an internal reactance of $$10$$ $$ohms$$ is operating at $$50\% $$ load, unity power factor. Now, the excitation is increased by $$1\% $$, what will be the new load in percent, if the power factor is to be kept same? Neglect all losses and consider linear magnetic circuit.

A $$220V$$ $$DC$$ machine supplies $$20$$ $$A$$ at $$200V$$ as a generator. The armature resistance is $$0.2$$ ohm. If the machine is now operated as a motor at same terminal voltage and current but with the flux increased by $$10\% ,$$ the ratio of motor speed to generator speed is