How to calculate power loss in transmission cables?

  1. Power station generates 120kW

    Electricity can be transmitted either at 240V or at 24000V using a step-up transformer.

    The cables have total resistance of 0.4W

    What is the power loss when voltage is transmitted at:

    1) 240V
    2) 24000V



    I AM SURE YOU CAN WORK THIS OUT USING I squared R (or as I have typed it: I^2R)

    Using 240V:
    P = IV, therefore I = 500A
    P = I^2R = 100000W

    Using 24000V:
    P = IV, 120000W = I24000V, therefore I = 5A
    P = I^2R = 10A

    Less power loss when using higher voltage




    My question begins with the premises called Ohm’s law and Joules’ law which lead to the textbook equations I^2R = V^2/R = P

    Power loss using I^2R works out different to power loss using V^2/R, given all text books equate I^2R with V^2/R

    THIS FAILS TO WORK WITH ABOVE QUESTION!

    Infact P=V^/R indicates greater power loss at higher voltages (for same resistance), negating the idea of stepping up voltages to reduce power loss in electrical transmission. In your solution please using the values I have used above in the question (taken from a text book)

    Please clarify - at a level for 16-18 year old physics students. Thanks.
     
  2. jcsd
  3. berkeman

    Staff: Mentor

    The thing that is confusing you is the definition of V.

    The V in V^2/R is the voltage drop across the wire, not the full voltage being transmitted. The voltage drop across the wire is V=IR, which will be much smaller than the transmitted voltage. Make sense?

    BTW, you have a typo in your question where you say the resistance is 0.4W. You meant 0.4 Ohms most likely.

    Welcome to the PF.
     
  4. If

    P = power generated at power station
    V = voltage at which power is transmitted
    R = Resisitance of transmission cable

    then

    Current in the transmission cables = P/V

    *Power loss is not equal to V^2/R because this V does not represent potential drop across the cables.

    If the cables are connected to your home then Power = V^2 / (Resistance of cables + Resistance of your house)


    Hence Power loss at the cables = I^2 R or (P/V)^2 R
     
  5. -------------------------------------------
    P = IV = I^2R = V^2/R
    -------------------------------------------
    Power loss through transmission cable is (I^2R)
    -------------------------------------------

    Example:-power station produce 500MW
    -Step up transformer is used to step up the voltage to 250KW
    -Cable has resistance of 10ohms

    P=VI
    500x10^6=250x10^3(I)

    I=500x10^6/250x10^3

    I=2000A

    Power loss is = I^2R
    Power loss is = 2000^2 x 10
    Power loss is = 4x10^7W

    Ratio: power loss/ original
    Ratio: 400x10^5/500x10^6 = 0.08 = 8% power loss
     
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