Two cities are $150\,\, km$ apart. Electric power is sent from one city to another city through copper wires. The fall of potential per $km$ is $8\,\, volt$ and the average resistance per km is $0.5 \,\,\Omega .$ The power loss in the wire is
AIPMT 2014, Medium
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Distance between two cities $=150 \,\mathrm{km}$
Resistance of the wire, $R=\left(0.5\, \Omega \mathrm{km}^{-1}\right)(150 \,\mathrm{km})=75 \,\Omega$
Voltage drop across the wire,
$V=\left(8\, \mathrm{V}\, \mathrm{km}^{-1}\right)(150 \,\mathrm{km})=1200 \,\mathrm{V}$
Power loss in the wire is
$P=\frac{V^{2}}{R}=\frac{(1200\, \mathrm{V})^{2}}{75 \,\Omega}=19200\, \mathrm{W}=19.2\, \mathrm{kW}$
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