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.

A $$230V,$$ $$250$$ $$rpm.$$ $$100A$$ separately excited $$dc$$ motor has an armature resistance of $$0.5\,\Omega .$$ The motor is connected to $$230V$$ $$dc$$ supply and rated $$dc$$ voltage is applied to the field winding. It is driving a load whose torque speed characteristic is given by $${T_L} = 500$$$$ - 10\omega ,$$ where $$\omega $$ is the rotational speed expressed in $$rad/sec$$ and $${T_L}$$ is the load torque in $$Nm.$$ Find the steady state speed at which the motor will drive the load and the armature current drawn by it from the source. Neglect the rotational losses of the machine.

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.

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.