A $$5MVA$$, $$11kV$$, $$3$$-phase star connected alternator is synchronized to the bus bars and is operating with an induced $$EMF$$ of $$125\% $$ of the rated voltage. If the load current is $$500$$ $$A,$$ what is the power factor of operation? The machine has a synchronous reactance of $$5\,\,\Omega $$ and negligible resistance per phase.

The per unit voltage of two synchronous machines connected through a lossless line are $$0.95\,\,\angle \,{10^0}\,\,$$ and $$1.0\,\,\angle \,{0^0}\,\,$$. Match the two sides in the following
$$(a)$$ Real power of Machine $$1$$
$$(b)$$ Reactive power of machine $$1$$
$$(c)$$ Power factor of Machine $$1$$

$$(P)$$ Positive real power
$$(Q)$$ Positive reactive power
$$(R)$$ Negative real power
$$(S)$$ Negative reactive power
$$(T)$$ Leading power factor
$$(U)$$ Lagging power factor

The distribution factor for a $$36$$ slot stator with three-phase, $$8$$-pole winding, having $${120^ \circ }$$ phase Spread, is _________

Figure depicts the load characteristics of an constant speed. Match the following sets of operating conditions with the given characteristics. Disregard the effects of saliency, saturation and stator resistance.

$$(a)$$ Constant excitation and non-zero leading power-factor
$$(b)$$ Constant excitation and zero power-factor, leading
$$(c)$$ Constant terminal voltage and zero power-factor, leading
$$(d)$$ Constant terminal voltage and non-zero leading power-factor