Question

A high-voltage transmission line with a resistance of 0.315 Ω/km carries a current of 1.05 kA. The line is at a potential of 750 kV at the power station and carries the current to a city located 175 km from the power station. What is the power loss due to resistance in the line?

Answer 1

I got this to be 6.078×101 MW

Answer 2

but now it wants to know-->What fraction of the transmitted power does this loss represent?

Answer 3

Well, we know that \(P=IV\), then, what does this tell us?

Answer 4

So you have 60780000/750000000?

Answer 5

Around there, yes.

Answer 6

it wants it in a simplified fraction,could you help me out on that?

Answer 7

Well, work it out without solving for variables first.

We know that the energy lost is given by
\[
P_l=I^2R
\]And we know that the total power is:
\[
P_T=IR
\]Hence:
\[
\frac{P_l}{P_T}=\frac{I^2R}{IV}
\]Simplify that down and then plug in the numbers.

Answer 8

Sorry, for the second equation it should be:
\[
P_T=IV
\]