Two parallel connected, three-phase, $$50Hz,$$ $$11kV,$$ star-connected synchronous machines $$A$$ and $$B,$$ are operating as synchronous condensers. They together supply $$50$$ $$MVAR$$ to a $$11$$ $$kV$$ grid. Current supplied by both the machines are equal. Synchronous reactances of machine $$A$$ and machine $$B$$ are $$1\,\,\Omega $$ and $$3\,\,\Omega ,$$ respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine $$A$$ to that of machine $$B$$ is ____________. (Give the answer up to two decimal places).

A separately excited DC generator supplies 150 A to a 145 V DC grid. The generator is running at 800 RPM. The armature resistance of the generator is 0.1 Ω. If the speed of the generator is increased to 1000 RPM, the current in amperes supplied by the generator to the DC grid is _______.

A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4 Ω and 0.1 Ω respectively. The load torque varies as the square of the speed. The flux in the motor may be taken as being proportional to the armature current. To reduce the speed of the motor by 50% the resistance in ohms that should be added in series with the armature is _________.

A three-phase, three winding $$\triangle$$ / $$\triangle$$ / Y (1.1 kV/6.6 kV/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV winding and 300 kVA load at 0.6 power factor lag from the 400 V winding. The RMS line current in ampere drawn by the 1.1 kV winding from the mains is _______.