Question

A single phase transformer is rated as 3 kVA, 400/230 V, 50 Hz. Open circuit test is conducted by placing instruments at LV side. Open circuit test readings are
$V_{OC}=230V$, $I_{OC}=1.3A$, $P_{OC}=100W$
The resistance and reactance of exciting branch referred to high voltage side are respectively

• A. $529\Omega ,j187.73\Omega$
• B. $1600\Omega ,j567.8\Omega$
• C. $1900\Omega ,j422\Omega$
• D. $174.9\Omega ,j62.07\Omega$

Answer 1

The correct option is B $1600\Omega ,j567.8\Omega$

$\text{Given that,}$
$V_{OC}=230V,$
$I_{OC}=1.3A,$
$P_{OC}=100W$
$R_C=\frac{V_{OC}^2}{P_{OC}}=\frac{{230}^2}{100}=529\Omega$

$\text{Power factor angle,}$
${\varphi }_{OC}=co{s}^{-1}\left(\frac{P_{OC}}{V_{OC}{I}_{OC}}\right)=co{s}^{-1}\left(\frac{100}{230\times 13}\right)={70.46}^{\circ }$

$X_{\varphi }=\frac{R_c}{\tan {\varphi }_{OC}}=\frac{529}{\tan {70.46}^{\circ }}=187.73\Omega$

$\text{Referred to high voltage side,}$

$R_C=529\times {\left(\frac{400}{230}\right)}^2=1600\Omega$

$X_{\varphi }=187.73\times {\left(\frac{400}{230}\right)}^2=567.8\Omega$