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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


    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 %

  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%

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