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Homework Help: Calculate the fraction of power generated that is lost in the lines

  1. Dec 23, 2004 #1
    If 30 MW of power at 45kV (rms) arrives at a town from a generator via 4-ohm transmission lines, calculate the fraction of power generated that is lost in the lines.

    okay I think I'm not completely understanding what I'm supposed to do in this question, or I'm missing something as from my calculations there is more than 100% power loss

    P/V = I

    30,000,000W/45,000V = 666.7 A

    Pl = I^2 x R

    666.7^2 x 4 = 1777955.56V = 1778kV


    probably something completely stupid that I'm doing here so would appreciate it if someone can set me straight, thnx


    ----edit-----

    sorry stupidity strikes again... forgot that the power lost comes out in W not V

    :yuck: duh! sorry again, it's fine now
     
    Last edited: Dec 23, 2004
  2. jcsd
  3. Dec 23, 2004 #2
    % Power loss = 1778/30 000 * 100 = 5.9 %


    Gamma.
     
  4. Dec 24, 2004 #3

    Andrew Mason

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    Science Advisor
    Homework Helper

    Power loss is in Watts not volts. [itex]I^2R = V_{drop}^2/R[/itex] gives you the power loss in watts. I prefer to work with the voltage drop. So:

    Voltage drop is IR = 666.7 x 4 = 2666.67 V.

    (ie. the voltage drops to 42333.3 volts at the town). So the power lost in the lines is 2666.67^2/4 = 1.78E6 Watts or 1.78 MW. As a fraction of the total power the line loss is 1.78/30 = 5.9%

    AM
     
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