A high-voltage transmission line with a resistance of 0.30 / km carries a current of 1040 A. The line is at a potential of 750 kV at the power station and carries the current to a city located 163 km from the station.

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?

(a) The power loss due to resistance in the line is 51.13 MW

(b) Fraction of loss power is 6.7%

Explanation:

Given;

resistance per distance = 0.29 Ω/km

distance of the city = 163 km

current in the line, I = 1040 A

voltage in the line, V = 730 kV

First, determine the resistance of the wire

R = 0.29 Ω/km x 163 km = 47.27 Ω

Part (a) the power loss due to resistance in the line

Power = I²R = (1040) ² x 47.27 = 51127232 W = 51.13 MW

Part (b) Fraction of the transmitted power the loss power represents

Total transmitted power = I x V

Total transmitted power = 1040 x 730,000 = 759200000 = 759.2 MW

Fraction of loss power = 51.13/759.2

Fraction of loss power = 0.067 = 6.7%