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

Distributed winding and short chording employed in AC machines will result in

In a stepper motor, the detent torque means

A synchronous motor is connected to an infinite bus at $$1.0$$ $$p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power factor. Its synchronous reactance is $$1.0$$ $$pu$$ and resistance is negligible.

The excitation voltage and load angle will respectively be