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

Neglecting all losses, the developed torque $$(T)$$ of $$d.c.$$ separately excited motor, operating under constant terminal voltage, is related to its output power $$(P)$$ as under

A separately excited $$d.c.$$ motor has an armature resistance of $$0.5$$ $$ohm.$$ It runs off a $$250$$ $$V$$ $$d.c.$$ supply drawing an armature current of $$20$$ $$A$$ at $$1,500$$ $$rpm.$$ The torque developed for an armature current of $$10$$ $$A$$ will be __________ for the same field current.

Two transformers of the same type, using the same grade of iron and conductor materials, are designed to work at the same flux and current densities; but the linear dimensions of one are two times those of the other in all respects. The ratio of $$kVA$$ of the two transformers closely equals