A $$3$$ phase, $$10$$ $$kW$$, $$400$$ $$V,$$ $$4$$ pole, $$50$$ $$Hz$$, star connected induction motor draws $$20$$ A on full load. Its no load and blocked rotor test data are given below.
No Load Test: $$400V$$ $$6A$$ $$1002W$$
Blocked Rotor Test: $$90V$$ $$15A$$ $$762W$$
Neglecting copper loss in No Load Test and core loss in Blocked Rotor Test, estimate motor's full load efficiency.

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.