Electrical power

Question

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

Easy

Solution

Here,

Distance between two cities = 150 km

Resistance of the wire, R = (0.5 $\Omega $$k{m}^{-1}$) (150 km) = 75 $\Omega $

Voltage drop across the wire

V = (8 V $k{m}^{-1}$) (150 km) = 1200 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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