Question

Two single phase, (11000/400) V transformers have kVA ratings of 200 kVA and 100 kVA respectively. The equivalent resistance and reactance of the 200 KVA transformer are respectively 1.0 and 5.0 ohms, when referred to the 11000 V side. The equivalent reactance of 100 KVA transformer to the 11000 V side is 9 $\Omega$. The value of equivalent resistance of 100 KVA transformer when each transformer is to supply load in proportion to its kVA rating when operated in parallel is _______ $\Omega$. (Answer upto 3 decimal places)

• A. 4.795

Answer 1

The correct option is A 4.795
$\text{For load to be shared proportion to its load rating}$

$kVA\propto \frac{1}{Z_{eq}}$

So, $\frac{kV{A}_1}{kV{A}_2}=\frac{Z_{eq.2}}{Z_{eq.1}}$

$\frac{200}{100}=\frac{\sqrt{r_{eb}^2+9^2}}{\sqrt{26}}$

$2=\frac{\sqrt{r_{eb}^2+9^2}}{\sqrt{26}}$

$r_{e{b}^2}+81=4\times 26$

$r_{e{b}^2}=23$

$r_{eb}=4.795\Omega$