A $300-$hp$,440-$V$,560-$A$,863$ r$/$min shunt dc motor has been tested, and the following data were

taken:

Blocked$-$rotor test:

VA $=14\mathrm{.}9$ V exclusive of brushes

I A $=500$ A

VF $=440$ V

I F $=7\mathrm{.}52$ A

No$-$load operation:

VA $=235$ V exclusive of brushes

I A $=231$ A

I F $=7\mathrm{.}50$ A

n $=863$ r$/$min

What is this motor$$s efficiency at the rated conditions? $[$Note: Assume that: $1)$ the brush voltage drop is $2$

V; and $2)$ the core loss is to be determined at an armature voltage equal to the armature voltage under full

load; and $3)$ stray load losses are $1$ percent of full load.$]$

Q$2[25$ Marks$]$

$($a$)$ For an induction motor, explain the effect of rotor resistance on torque$-$speed characteristics.

$($b$)$ A $400$ V$,4$ pole, $60$ Hz$,$ Y$-$connected wound rotor induction motor is rated at $30$ Hp$.$ Its equivalent

circuit parameters are

R$1=1,$ R$2=1,$ X m$=20,$ X$1=0\mathrm{.}5,$ X$2=0\mathrm{.}5,$ P mech$=500,$ P core$=100$

For a slip of $0\mathrm{.}05,$ please find: a$)$ The line current; b$)$ The stator copper loss; c$)$ The air$-$gap power; d$)$ The

power converted from electrical to mechanical form; e$)$ The induced torque; and f$)$ The overall machine

efficiency.

Q$3[8$ Marks$]$

Derive the expression for the total three$-$phase power supplied to a $3-$phase load $($P$3=3$VIcos$)$

when the phase shift between the phase voltage, V and current, I is degree $($show all steps$).$