A $$400$$ $$V,$$ $$50$$ $$Hz,$$ $$30$$ $$hp,$$ three-phase induction motor is drawing $$50$$ A current at $$0.8$$ power factor lagging. The stator and rotor copper losses are $$1.5kW$$ and $$900$$ $$W$$ respectively. The friction and windage losses are $$1050$$ $$W$$ and the core losses are $$1200$$ $$W.$$ The air-gap power of the motor will be

A $$400$$ $$V,$$ $$50$$ $$Hz$$, $$4$$ pole, $$1400$$ $$rpm$$, star connected squirrel cage induction motor has the following parameters referred to the stator:
$$R = 1.0\,\Omega ,{X_s} = X{'_r} = 1.5\,\Omega $$ Neglect stator resistance and core and rotational losses of the motor. The motor is controlled from a $$3$$-phase voltage source inverter with constant $$V/f$$ control. The stator line-to-line voltage $$(rms)$$ and frequency to obtain the maximum torque at starting will be:

The core of two-winding transformer is subjected to a magnetic flux variation as indicated in the figure.

The induced $$emf$$ $$\left( {{e_{rs}}} \right)$$ in the secondary winding as a function of time will be of the form

Three single-phase transformers are connected to form a $$3$$-phase transformer bank. The transformers are connected in the following manner.

The transformer connection will be represented by