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?

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