A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary wi

Question

A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5 A and its efficiency is $90 \%$. The winding of transformer is made of copper. The output current of transformer is _______ A.\

Professor PC Thomas Classes · Answer

(45) : Input power transmission, $P_{	ext {in }}$ $=V I$\ $P_{	ext {in }}=2.3 	imes 10^{3} 	imes 5$\ $P_{	ext {in }}=11.5 \mathrm{~kW}$\ As, efficiency of transformer is $90 \%$ $$ \begin{aligned} & =\frac{	ext { Output power }}{	ext { Input power }}=\frac{P_{	ext {out }}}{P_{	ext {in }}}=\frac{9}{10} \ & P_{	ext {out }}=\frac{9}{10} 	imes P_{	ext {in }}=\frac{9}{10} 	imes 11.5 	imes 10^{3} \end{aligned} $$ As, $\left[P_{	ext {out }}=V_{S} I_{S}ight.$ of secondary winding $]$\ $V_{S} I_{S}=\frac{9}{10} 	imes 11.5 	imes 10^{3}$\ $I_{S}=\frac{9 	imes 11.5 	imes 10^{3}}{10 	imes 230}=\frac{103.5 	imes 10^{3}}{23 	imes 10^{2}}$\ $I_{S}=45 \mathrm{~A}$\