A $$230V,$$ $$50Hz,$$ $$4$$ pole, single phase induction motor is rotating in the clockwise (forward) direction at a speed of $$1425$$ $$rpm.$$ If the rotor resistance at standstill is $$7.8\,\,\Omega ,$$ then the effective rotor resistance in the backward branch of the equivalent circuit 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:

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 $$3$$-phase, $$440$$ $$V,$$ $$50$$ $$Hz,$$ $$4$$ pole, slip ring induction motor is feed from the rotor side through an auto transformer and the stator is connected to a variable resistance as shown in the figure.

The motor is coupled to a $$220$$ $$V$$, separately excited $$d.c.$$ generator feeding power to fixed resistance of $$10\Omega .$$ Two watt-meter method is used to measure the input power to induction motor. The variable resistance is adjusted such that motor recorded
$${W_1} = 1800\,W,\,\,{W_2} = - 200\,W.$$

The Speed of rotation of stator magnetic field with respect to rotor structure will be