A $50-$Hz $1-$kVA $2500/400-$V transformer has the following equivalent$-$circuit parameters:

$$ Primary winding resistance $60$

$$ Secondary winding resistance $2$

$$ Primary winding leakage reactance $32$

$$ Secondary winding leakage reactance $1\mathrm{.}2$

$$ Magnetizing reactance $200$ k$$

$$ Core$-$loss equivalent resistance $400$ k$$

Find the percentage regulation $(35$ marks$)$ and power efficiency $(35$ marks$)$ for the transformer for the rated

load having a lagging power factor of $0\mathrm{.}8.$ Plot phasor diagrams for the voltage and current at the source $(15$

marks$)$ and at the load $(15$ marks$)$