A $220$ V$,190$ A dc series motor has armature and field resistances of $0\mathrm{.}03$ and $0\mathrm{.}02$ ohm respectively. Running on no load as a generator with field winding connected to a separate source it gave following magnetization characteristic at $500$ rpm:

Field current, A

$40$

$80$

$120$

$160$

$200$

Terminal voltage, V

$52$

$108$

$148$

$176$

$189$

Motor is controlled by a chopper in dynamic braking with a braking resistance of $2$ ohm.

I. Calculate motor speed for a duty ratio of $0\mathrm{.}6$ and motor current of $160$ A$.$

II$.$ What will be the motor speed for a duty ratio of $0\mathrm{.}75$ and motor torque equal to half of rated torque?