A $230$ V$,1000$ rpm$,30$ A separately excited motor has armature resistance and inductance of $0\mathrm{.}7$ and $50$ mH respectively. Motor is controlled in regenerative braking by a chopper operating at $800$ Hz from dc source of $230$ V$.$ Assuming continuous conduction.

$($i$)$Calculate duty ratio of chopper for rated torque and the speed of $800$ rpm$.($ii$)$ What will be the motor speed for duty ratio of $0\mathrm{.}6$ and rated motor torque?

$($iii$)$ What will be the maximum allowable speed of motor, if chopper has a maximum duty ratio of $0\mathrm{.}9$ and maximum allowable motor current is twice the rated current?

$($iv$)$ Calculate power fed to the source for operating conditions in $($iii$).$

$($v$)$ Motor field is also controlled along with armature voltage. Rated field current is $0\mathrm{.}5$ A$.$ Calculate field current for the duty ratio of $0\mathrm{.}9$ and motor speed of $1500$ rpm and armature current of $30$ A$.$