A high-voltage transmission line that connects a city to a power plant consists

Question

A high-voltage transmission line that connects a city to a power plant consists of a pair of aluminum cables, each with a resistance of 4.0 ohms. The current flows to the city alone one wire and back along the other.

1. The transmission line delivers 1.7*105 kW of power at 2.3*105 to the city. What is the current in the transmission line? How much power is lost as Joule heat in the line?

2. If the transmission line were to deliver the same power at 115 V, how much power would be lost as Joule heat? Is it more or less efficient to transmit power at high voltage or low voltage?

Explanation / Answer

1. I = V / R = (2.3 x 10^5) / 4

I = 5.75 x 10^4 A

P_loss = I^2 R = 1.32 x 10^10 W

2. I = 115/4 = 28.75 A

P_loss = I^2 R = 3306.25 W

more efficient at low voltage.

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