$5\mathrm{.}25$ A $3$ induction machine is mechanically coupled to a dc shunt machine. The rating and parameters

of the machines are as follows:

Induction machine:

$3$$,5$ kVA, $208$ V$,60$ Hz$,$ four$-$pole, $1746$ rpm

R$1=0$:$25,$ X$1=0$:$55,$ R$02=0$:$35,$ X$02$

$=1$:$1,$ Xm $=38$

DC machine:

$220$ V$,5$ kW$,1750$ rpm

Ra $=0$:$4,$ Rfw $=100,$ Rfc $=100$

The induction machine is connected to a $3$$,208$ V$,60$ Hz supply, and the dc machine is connected

to a $220$ V dc supply. The rotational loss of each machine of theM$$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.

$($e$)$ Determine the armature current $($and its direction$)$ of the dc machine.