Task $1$

$(20$ points$)$

$($a$)$ A $4$ pole DC series motor has wave connected winding with $600$ conductors. The total resistance of motor is $0\mathrm{.}8.$ When fed from $250$ V DC source, the motor takes a $50$ A with a flux per pole of $3$ mWb $.$ For these operating conditions, calculate the speed and the developed torque of this motor.

$(4$ pts$)$

$($b$)$ An external resistance of $0\mathrm{.}5$ ohm is inserted in series with the field winding of the above DC motor. Calculate the new steady state armature current and the speed if

i$.$ the load torque is to be kept constant;

$(8$ pts$)$

ii$.$ the load torque is proportional to the square of the speed.

$(8$ pts$)$