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Q.
An electrical cable having a resistance of $0.2\, \Omega$ delivers $10\, kW$ at $200\, V$ dc to a factory. What is the efficiency of transmission?
Current Electricity
Solution:
Let $x$ watt be the power loss in transmission line in the form of heat.
$\therefore x=\left(\frac{P}{V}\right)^{2} R=\left(\frac{10 \times 1000}{200}\right)^{2} \times 0.2=500\, W =0.5\, kW$
Efficiency of transmission
$=\frac{\text {power delivered by line}}{\text {power supplied to line}}=\frac{10\, kW }{10\, kW +x kW}$
$=\frac{10}{10+0.5}=\frac{10}{10.5}=0.95=95 \%$