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26 January, 16:03

A high-voltage transmission line with aresistance of 0.29 Ω/km carries a current of 1040 A. The lineis at a potential of 730 kV at the power station and carries thecurrent to a city located 163 km from the station.

(a) What is the power loss due to resistance inthe line?

(b) What fraction of the transmitted power does this lossrepresent?

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  1. 26 January, 18:49
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    Resistance per unit length = 0.29 ohm/km

    Current, i = 1040 A

    Voltage, V = 730 kV = 730000 V

    distance, l = 163 km

    (a) Total resistance of wire, R = length of wire x resistance per unit length

    R = 0.29 x 163

    R = 47.27 ohm

    power, P = i²R

    P = 1040 x 1040 x 47.27

    P = 51127232 W

    (b) Transmitted power, P' = V x i

    P' = 730000 x 1040

    P' = 759200000 W

    P / P' = 51127232 / 759200000

    P/P' = 0.067
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