Physics E & M Question about a powerline

[Brandon Hawi]

Homework Statement

A high voltage powerline operates at a 500000 V-rms and carries an rms current of 500 A. If the resistance of the cable is 0.05Ω/km, what is the resistive power loss in 200 km of the powerline.

V = 500000 V-rms
I_rms = 500 A
R/x = 0.05Ω/km
x = 200 km

Homework Equations

P = I²R
P = V²/R
P = IV

The Attempt at a Solution

I attempted to use V²/R at first, and that gave me 2.5 x 10¹⁰ Watts, however the given answer is 2.5 x 10⁶ Watts. I get that answer when I use I²R, but I was wondering why V²/R could not be used?
EDIT: Fixed to V²/R

 

[TSny]

Hello and welcome to PF!

Your formula P = V/R is incorrect. Did you mistype the formula?

Even when you have the correct formula, you have to be careful. The 500,000 V of the powerline probably represents the voltage of the line relative to ground at one end of the line. It does not represent the potential drop as you go from one end of the line to the other end of the line.

You can calculate the potential drop V and then use the (corrected) power formula that involves V and R.

 

[Brandon Hawi]

Hello and welcome to PF!

Your formula P = V/R is incorrect. Did you mistype the formula?

Even when you have the correct formula, you have to be careful. The 500,000 V of the powerline probably represents the voltage of the line relative to ground at one end of the line. It does not represent the potential drop as you go from one end of the line to the other end of the line.

You can calculate the potential drop V and then use the (corrected) power formula that involves V and R.

Sorry, I meant to type V²/R. How would one then go about calculating the potential drop V?

 

[TSny]

Sorry, I meant to type V²/R. How would one then go about calculating the potential drop V?

You're making Georg Ohm feel neglected today.

 

[Brandon Hawi]

You're making Georg Ohm feel neglected today.

Alright then, so V = IR. So I get V = 5000 V. Then I used V²/R and got 2.5 MW as my answer. Thanks !

 

[TSny]

Looks good!