A thermal power plant produces electric power of 1000 kW at 10000 V, which is to be transmitted 20 km away from the power plant. The transmission line has resistance of 0.5 ohm per kilometre, the percentage power dissipation during transmission is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10%
The current in the line follows from the power and the transmission voltage, \( P = VI \), and the power dissipated in the line is \( I^{2}R \). The percentage loss is this loss divided by the power transmitted.
\( R = 0.5\,\Omega\,\mathrm{km^{-1}}\times20\,\mathrm{km} = 10\,\Omega \)
\( \displaystyle I = \frac{P}{V} = \frac{1000\times10^{3}\,\mathrm{W}}{10000\,\mathrm{V}} = 100\,\mathrm{A} \)
\( P_{\mathrm{loss}} = I^{2}R = (100\,\mathrm{A})^{2}\times10\,\Omega = 1\times10^{5}\,\mathrm{W} = 100\,\mathrm{kW} \)
\( \displaystyle \text{loss} = \frac{100\,\mathrm{kW}}{1000\,\mathrm{kW}}\times100 = 10\% \)