Question $3$ A $120$ V$,$ DC series motor has a field winding resistance of $0\mathrm{.}5$ and an armature winding resistance of $0\mathrm{.}7.$ When the armature current is $12$ A$,$ the motor runs at $600$ rpm$.($a$)$ Calculate $($i$)$ the power and $($ii$)$ the torque developed by the motor for the given conditions. $[6$ marks$]($b$)$ If the motor is to run at a speed of $1500$ rpm$,$ determine $($i$)$ the armature current and $($ii$)$ the motor torque. $[7$ marks$]($c$)$ Given that there are rotational losses of $50$ W for the conditions of part $($b$),$ calculate $($i$)$ the torque delivered to the load and $($ii$)$ the motor efficiency. $[7$ marks$]$