Task $1$

$(25$ pts$)$

A DC series motor takes a supply current of $10$ A when its speed is $1000$ rpm$.$ The field winding is now shunted by a divertor of half of the resistance as that of the field winding. It is expected that, after mounting the divertor, the new speed will become higher.

The voltage drops due to the resistances of the windings and the brush are assumed to be negligible when compared to the back emf generated by the armature.

$($a$)$ Calculate the new speed and the new armature current if the torque of the above motor varies as the square of its speed.

$($b$)$ Calculate the new speed and the new armature current if the torque of the above motor is proportional to its speed.

$($c$)$ Explain if the above motor is suitable for driving an electric vehicle.