Q$1.$ A $220$V$,1000$rpm$,60$ A separately excited dc motor has an armature resistance of $0\mathrm{.}1.$ it is fed from a single phase full converter with an ac source voltage of $230$V$,50$ Hz$.$ Assuming continuous conduction, compute

$($i$)$ firing angle for rated torque at $600$ rpm

$($ii$)$ firing angle for rated motor torque at $(-500$ rpm$)$

$($iii$)$ motor speed for $=150$ and half rated torque