Question

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?

Answer 1

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

(b) Fraction of loss power is 6.7%

Step-by-step 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%