In an experiment, a $50$ Hz $,4-$pole, three$-$phase, star$-$connected synchronous generator was driven by squirrel$-$cage induction motor. A field current of $0\mathrm{.}15$ A generates an open$-$circuit $($no$-$load$)$ voltage of $279$ V line$-$to$-$line. Assume the armature resistance is $0\mathrm{.}3.$ Using the circuit diagram and the result curve shown below, calculate the following:

a$.$ The speed of rotation of the synchronous generator, $n,$ in rpm $.$

$[1$ mark$]$

b$.$ The speed of rotation of the synchronous generator, $n,ra\frac{d}{s}.$

$[2$ marks$]$

The no$-$load armature $($stator$)$ current, la$,$ A$.$

$[2$ marks$]$

The per phase terminal voltage, Vt$,$ V$.$

$[2$ marks$]$

e synchronous machine constant, Kc $,$ for a flux of $5$ mWb $.$

$[2$ marks$]$

In a LabVolt experiment, a $175$W$,50Hz,4-$pole small squirrel$-$cage induction motor was tested under load. Loading was applied using an electrodynamometer, and all wiring was completed according to the diagram shown below. The results of this experiment are presented in Table $8\mathrm{.}1.$

$[17$ Marks$]$

Table $8\mathrm{.}1$:

$\backslash$table$[[\backslash$table$[[$TORQUE$],[($ Nm $)]],h$

$(A),[b],[(a)],b$

$(a),\backslash$table$[[$w$,],[($w$)]],[w_2],[(w)],\backslash$table$[[$SPEED$],[($rimin$)]]],[0,0\mathrm{.}25,0\mathrm{.}25,0\mathrm{.}25,-23,76,1500],[0\mathrm{.}3,0\mathrm{.}27,0\mathrm{.}30,0\mathrm{.}29,-3,100,1470],[0\mathrm{.}6,0\mathrm{.}33,0\mathrm{.}35,0\mathrm{.}34,23,130,1440],[0\mathrm{.}9,0\mathrm{.}40,0\mathrm{.}43,0\mathrm{.}42,50,164,1400],[1\mathrm{.}2,0\mathrm{.}50,0\mathrm{.}51,0\mathrm{.}50,75,196,1350]]$

Using the results of Table $8\mathrm{.}1,$ and for the full$-$load condition $(1\mathrm{.}2$ N$.$m$)$ calculate the following:

a$.$ The motor slip, s$,$ in $\%.$

$[2$ marks$]$

b$.$ The average current, lav, in A$.$

$[2$ marks$]$

c$.$ The apparent power, S $,$ in VA$.$

$[3$ marks$]$

d$.$ The active power, P $,$ in W $.$

$[3$ marks$]$