Two $$550$$ $$kVA$$ alternators operate in parallel to supply the following loads
$$(i)$$ $$250$$ $$kW$$ at $$0.95$$ power factor lag
$$(ii)$$ $$100$$ $$kW$$ at $$0.8$$ power factor lead one machine is supplying $$200kW$$ at $$0.9$$ power factor lag. The power factor of the other machine must be

A three phase alternator has negligible stator resistance. A short circuit test is conducted on this alternator. At a particular speed a field current of $${{\rm I}_f}$$ is required to drive the rated armature current. If the speed of the alternator is reduced to half, the field current required to maintain rated armature current

A three phase slip ring induction motor is fed from the rotor side with stator winding short circuited. The frequency of the currents flowing in the short circuited stator is

The line integral of the vector potential A around the boundary of a surface S represents