A synchronous motor operates at $$0.8$$ $$p.f.$$ lagging. If the field current of the motor is continuously increased

$$(1)$$ the power factor decreases upto a certain value of field current and thereafter it increases
$$(2)$$ the armature current increases upto a certain value of field current and thereafter it decreases
$$(3)$$ the power factor increases upto a certain value of field current and thereafter it decreases
$$(4)$$ the armature current decreases upto a certain value of field current and thereafter it increases. From these the correct one is

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