A $750$ hp $,250$V $,1200$rpm dc shunt motor is connected to $208$V$,3-$phase, $60$Hz line using a $3-$phase semi controlled bridge converter. The full$-$load armature current is $2500$A and the armature resistance is $0\mathrm{.}004$ ohms. Assuming that conduction is continuous, calculate

$($a$)$ the firing angle required under full$-$load condition.

$($b$)$ the firing angle so that the motor would run at $600$rpm at no load

$($c$)$ the firing angle required so that motor develops itit's rated torque of $400$rpm$.$