# What is the power loss due to resistance in the line?

## Homework Statement

A high-voltage transmission line with a resistance of 0.30ohm/km carries a current of 1050 A. The line is at a potential of 670 kV at the power station and carries the current to a city located 164 km from the station.

(a) What is the power loss due to resistance in the line? W

(b) What fraction of the transmitted power does this loss represent? %

W = AdeltaV

## The Attempt at a Solution

first i did 1050A/1000 to convert that into 1.05 kA (not sure if this is correct)

then i did 1.05 x 670 = 703.5 kW or 703500 W (still not sure if im doing this correctly)

that is when i get lost on how to do the next step, but from what i been doing i think i am doing it wrong and it will only lead me to confuse myself even more.

thanks for any help.

## Answers and Replies

Integral
Staff Emeritus
Science Advisor
Gold Member
What is the resistance of the power line?

Given that and voltage or current power loss is easy.

the resistance of the power line is .30 ohm/km and the current is 1050 A

Integral
Staff Emeritus
Science Advisor
Gold Member
You need the total resistance.

.30 ohm/km x 164 km = 49.2 ohm km (total resistance)

Integral
Staff Emeritus
Science Advisor
Gold Member
.30 ohm/km x 164 km = 49.2 ohm km (total resistance)

Think a bit about the units you have writen on the above number.

Now that you have the resistance you should be able to complete the proplem.

Okay, i been trying to figure this out and still lost on how I would go about finding the power loss due to the resistance.

I know that to get the total power its A x DeltaV = total W

so i did 1050A x 670000 = 703500000 W (which might be wrong) since i think 670 kV = 670000

that is where i am unsure what to do next or what I need to do with the total resistance