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 . The power loss in the wire is [2014]

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Solution

Q.
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 $Ω$ . The power loss in the wire is [2014]

1 19.2 W

2 19.2 kW

3 19.2 J

4 12.2 kW

Ans.
(2)

Here,

Distance between two cities = 150 km

Resistance of the wire, $R = (0.5 Ω {km}^{- 1}) (150 km) = 75 Ω$

Voltage drop across the wire, $V = (8 V {km}^{- 1}) (150 km) = 1200$ $V$

Power loss in the wire is

$P = \frac{V^{2}}{R} = \frac{{(1200 V)}^{2}}{75 Ω} = 19200 W = 19.2$ $kW$

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