Question$-1$:

$[$CLO$-3,4$; Tax$-1$; $05$ marks$]$

Three similar coils, each having a resistance of $4\mathrm{.}0$ and an inductive reactance of $3\mathrm{.}46,$ are connected $($a$)$ in star and $($b$)$ in delta across a $400V,3-$phase supply. Calculate for each connection the readings on each of the two wattmeters connected to measure the power by the two$-$wattmeter method.

Question$-2$:

$[$CLO$-3,4$; Tax$-1$; $05$ marks$]$

A $440V,3-$phase AC motor has a power output of $11\mathrm{.}25$ kW and operates at a power factor of $0\mathrm{.}8$ lagging and with an efficiency of $84\%.$ If the motor is delta$-$connected, determine $($a$)$ the power input, $($b$)$ the line current, and $($c$)$ the phase current.

Question$-3$:

$[$CLO$-4,5,6$; Tax$-2$; $05$ marks$]$

A $20-$kVA$\frac{8000}{480}-V$ distribution transformer has the following resistances and reactances: $R_P=32,R_S=0\mathrm{.}05,x_P=45,x_S=0\mathrm{.}06,x_C=250k,x_M=30k$ The excitation branch impedances are referred to as the high$-$voltage side of the transformer.

$($a$)$ Find the equivalent circuit of this transformer referred to the high$-$voltage side.

$($b$)$ Assume that this transformer supplies a rated load $(20$kVA$)$ at $480$ V and $0\mathrm{.}8$ PF lagging. What is this transformer's input voltage? What is the voltage regulation?

$($c$)$ What is the transformer's efficiency under part $($b$)$ conditions?

Question$-4$:

$[$CLO$-4,5,6$; Tax$-2$; $05$ marks$]$

A $15-$KVA $8000/230-$V distribution transformer has an impedance referred to as the primary of $80+j300.$ The components of the excitation branch referred to on the primary side are $R_c=350k$ and $x_m=70k.$

$($a$)$ If the primary voltage is $7967$ V and the load impedance is $Z_L=3\mathrm{.}2+j1\mathrm{.}5,$ what is the secondary voltage of the transformer? What is the voltage regulation of the transformer? $($b$)$ If the load is disconnected and a capacitor of $-j3\mathrm{.}5$ is connected in its place, what is the secondary voltage of the transformer? What is its voltage regulation under these conditions?