Q$2$: A three$-$phase, star$-$connected, $36$hp$,400$V$,4-$pole, $50$Hz$,$ wound rotor induction motor has the following parameters per phase: R$1=0\mathrm{.}35$ X$1=0\mathrm{.}75$ XM $=40$ R$2=0\mathrm{.}3$ X$2=0\mathrm{.}75$ Mechanical losses $=2700$W Initially the rotor terminals are short$-$circuited. Calculate: a$)$ The stator supply current and power factor when supplying rated power at a slip of $8\mathrm{.}5\%.$ b$)$ Calculate the value of magnetising current, IM$,$ at this operating point. c$)$ Calculate the torque produced at this operating point. d$)$ The maximum value of torque with the rotor short$-$circuited and the speed this maximum torque occurs at$.$ e$)$ The value of extra rotor resistance required to be added in the rotor circuit to achieve maximum torque at start$-$up$,$ i$.$e$.$ the level of torque calculated in $($d$).$