Question $3[14$ Marks$]$

Design a $5$ kVA $,$ single$-$phase transformer with a voltage rating of $\frac{3300}{230}V.$ The frequency of the supply is $50$ Hz $.$ Use maximum flux density $=1\mathrm{.}4T$ and circular core limbs of $110$ mm diameter. During the testing of the transformer, the copper loss was $781$ Watts at a winding temperature of $67C,$ the measured winding resistances were $1\mathrm{.}2$ and $96$ for both LV and HV windings respectively. Calculate:

$($a$)$ the number of turns for the HV winding.

$[3]$

$($b$)$ the number of turns for the LV winding.

$[3]$

$($c$)$ th full load current of HV and LV windings.

$[2]$

$($d$)$ the copper losses at $75C$

$[6]$

Reference equations: