For a $$1.8$$ degree, $$2$$-phase bipolar stepper motor, the stepping rate is $$100$$ steps/second. The rotational speed of the motor in $$rpm$$ is

A $$400$$ $$V,$$ $$50$$ $$kVA,$$ $$0.8$$ $$pf$$ leading delta connected, $$50$$ $$Hz$$ synchronous machine has a synchronous reactance of $$2$$ $$ohm$$ and negligible armature resistance. The friction and windage losses are $$2$$ $$kW$$ and the core loss is $$0.8$$ $$kW.$$ The shaft is supplying $$9$$ $$kW$$ load at a power factor of $$0.8$$ leading. The line current drawn is

Two $$3$$-phase, $$Y$$-connected alternators are to be paralleled to a set of common bus bars. The armature has a per phase synchronous reactance of $$1.7\Omega $$ and negligible armature resistance. The line voltage of the first machines is adjusted to $$3300$$ $$V$$ and that of the second machine is adjusted to $$3200$$ $$V.$$ the machine voltages are in phase at the instant they are paralleled. Under this condition, the synchronizing current per phase will be

A $$4$$-pole, $$3$$-phase, double layer winding is housed in a $$36$$-slot stator for an $$ac$$ machine with $$60$$ degree phase spread. Coil span is $$7$$ slot pitches. Number of slots in which top and bottom layers belong to different phases is.