A $$415$$ $$V,$$ $$2$$ pole, $$3$$ phase, $$50$$ $$Hz,$$ star connected, non-salient pole synchronous motor has synchronous reactance of $$2\,\Omega $$ per phase and negligible stator resistance. At a particular field excitation, it draws 20 A at unity power factor from a $$415$$ $$V,$$ $$3$$ phase, $$50$$ $$Hz$$ supply. The mechanical load on the motor is now increased till the stator current is equal to $$50$$ $$A.$$ The field excitation remains unchanged. Determine:
$$(a)$$ the per phase open circuit voltage $${E_0}$$
$$(b)$$ the developed power for the new operating condition and corresponding power factor.

The flux per pole in a synchronous motor with the field circuit ON and the stator disconnected from the supply is found to be $$25$$ $$mWb.$$ When the stator is connected to the rated supply with the field excitation unchanged, the flux per pole in the achine is found to be $$20$$ $$mWb$$ while the motor is running on no load. Assuming no load losses to be zero, the no load current down by the motor from the supply

A single phase $$6300$$ $$kVA,$$ $$50$$ $$Hz,$$ $$3300V/400V$$ distribution transformer is connected between two $$50$$ $$Hz$$ supply systems, $$A$$ and $$B$$ as shown in Fig. The transformer has $$12$$ and $$99$$ turns in the low and high voltage windings respectively. The magnetizing reactance of the transformer referred to the high voltage side is $$500\Omega .$$ The leakage reactance of the high and low voltage windings are $$1.0\Omega $$ and $$0.012\Omega $$ respectively. Neglect the winding resistance and core losses of the transformer. The Thevenin voltage of system $$A$$ is $$3300V$$ while that of system $$B$$ is $$400V.$$ the short circuit reactance of systems $$A$$ and $$B$$ are $$0.5\Omega $$ and $$0.010\Omega $$ respectively. If no power is transferred between $$A$$ and $$B,$$ so that the two system voltages are in phase, find the magnetizing ampere turns of the transformer.

In a single phase $$3$$ winding transformer the turns ratio for primary: secondary: tertiary windings is $$20:4:1.$$ With the lagging currents of $$50A$$ at a power factor of $$0.6$$ in the tertiary winding find the primary current and power factor.