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?

Explanation:

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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