A $30$ induction machine is mechanically coupled to a dc shunt machine. The rating and para$-$ meters of the machines are as follows:

Induction machine:

$30,5$ kVA, $208$ V$,60$ Hz$,$ four$-$pole, $1746$ rpm R$\_\{1\}=0\mathrm{.}25$Omega X$\_\{1\}=0\mathrm{.}55$Omega R$\_\{2\}\text{'}=0\mathrm{.}35$Omega X$\_\{2\}\text{'}=1\mathrm{.}1$Omega X$\_\{$m$\}=38$Omega

DC machine:

$220$ V$,5$ kW$,1750$ rpm R$\_\{$a$\}=0\mathrm{.}4$Omega Rfw $=100\backslash$Omega $,$ Rfc $=100\backslash$Omega

The induction machine is connected to a $30,208$ V$,60$ Hz supply, and the de machine is con$-$ nected to a $220$ V dc supply. The rotational loss of each machine of the M$-$G set may be considered constant at $225$ W$.$

The system rotates at $1710$ rpm in the direction of the rotating field of the induction machine.

$($a$)$ Determine the mode of operation of the induction machine.

$($b$)$ Determine the current taken by the induction machine.

$($c$)$ Determine the real and reactive power at the terminals of the induction machine and indicate their directions.

$($d$)$ Determine the copper loss in the rotor circuit.