Power loss at Different Voltages?

Question

Please help to explain to me the following question!

A power station delivers 520 kW of power to a factory through wires with a total resistance of 3Ω. How much power is wasted if the electricity is delivered at 50 kV vs. 12kV.

Thanks in advance! I will give my best answer to the person who can best explain the correct answer and how to get there, not the fastest person.

I can handle the algebra easily, so don't worry about spoon feeding the algebra. I just would like help with the equation part of it.

Thanks in advance!

Answer 1

Knowing the total power you can calculate the current for each voltage. Using P = I * V

Once you know the current then the power lost would be P = I^2 * R where R = 3 Ohms

Obviously the current would be higher at the lower voltage and therefore the power lost would be higher.

Answer 2

At 50 kV, 520 kW represents 520/50 = 10.4 Amps
10.4 Amps through 3 ohm will dissipate
3ohm*(10.4 Amps)^2 = 324.4 W
which is 324.4/520 000 = 0.06% of total power

At 12 kV, 520 kW represents 520/12 = 43.3 Amps
43.4 Amps through 3 ohm will dissipate
3ohm*(43.3 Amps)^2 = 5 625 W
which is 5 625/520 000 = 1.08% of total power

Bottom line is you lose 17 time more power through the lower voltage lines.
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Oups just read the part about spoon feeding... oh well sue me!