If a 400 V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply?

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 $$415$$ $$V,$$ $$2$$ 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.