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Physics E & M Question about a powerline

  1. Jul 31, 2015 #1
    1. The problem statement, all variables and given/known data
    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
    Irms = 500 A
    R/x = 0.05Ω/km
    x = 200 km

    2. Relevant equations

    P = I2R
    P = V2/R
    P = IV

    3. 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
     
    Last edited: Jul 31, 2015
  2. jcsd
  3. Jul 31, 2015 #2

    TSny

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    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.
     
  4. Jul 31, 2015 #3
    Sorry, I meant to type V2/R. How would one then go about calculating the potential drop V?
     
  5. Jul 31, 2015 #4

    TSny

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    You're making Georg Ohm feel neglected today.:wink:
     
  6. Jul 31, 2015 #5
    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 ! :smile:
     
  7. Jul 31, 2015 #6

    TSny

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    Looks good!
     
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