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 powe

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?

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Vân Khánh 5 years 2021-08-14T21:27:38+00:00 1 Answers 18 views 0

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  1. thucuc
    0
    2021-08-14T21:29:14+00:00
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    Answer:

    (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%

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