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Which to use to calculate I: P=VI or V=IR

  1. Oct 23, 2012 #1
    Hi,

    In a power transmission cable, the power, P=24W, Voltage=12V, the resistance of the cable, R=4 ohm.

    What is the current that flows in this cable? Shall I use P=VI or V=IR to calculate the current?
    Both seems to give different answers.

    Thanks
     
  2. jcsd
  3. Oct 23, 2012 #2
    I'm fairly certain that this situation is impossible fundamentally. You should get the same answer for both.
     
  4. Oct 23, 2012 #3
    One of your given values seems to be incorrect.

    If the voltage and resistance are correct, then:
    P = V2/R = 12V2/4Ω = 36W

    If power and voltage are correct:
    R = V2/P = 122/24W = 6Ω

    If power and resistance are correct:
    V = √(P*R) = √(24W*4Ω) = 9.8V
     
    Last edited: Oct 23, 2012
  5. Oct 23, 2012 #4
    Thanks all for your response.

    Agreed with both of you.
    Somehow my gut instinct told me that the question I had was somehow flawed.

    Thanks again.
     
  6. Oct 23, 2012 #5
    In this type of situation, or power system, it is generally meant,
    the power source is a 12V source and it is delivering 24W power.
    In such case, for current flowing from the source, use
    P = VI
    Then I = 2A.



    Probably a load of 2 ohms is missing from the problem, which makes total resistance 6 ohm.
    You shouldn't use V=IR unless the problem clearly indicates 12V is dropped in the resistance R.
     
  7. Oct 24, 2012 #6
    It's also useful to remember that P = V2/R (alternatively P = I2R)

    You can of course derive both expressions.
    You can see immediately that 12*12/4 is not 24 so the question is nonsense.
     
  8. Oct 24, 2012 #7

    mfb

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    I think that is the solution to the issue.
    A power transmission cable is supposed to transmit something - using it as short circuit (with just the cable resistance) would be a bit pointless anyway.

    => Current I=24W/12V=2A

    The cable will get P=I^2*R = 4A^2*4Ω=16W of heat, and the load will receive 4A^2*2Ω=8W.
     
  9. Oct 24, 2012 #8

    CWatters

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    The question is not clear enough to be sure you can get the right answer.

    For example..

    The power is 24W but is that the transmitted power or the power dissipated in the load?
    The voltage is 12V but is that the voltage at the source or the load?

    So that's at least four possible right answers!

    In most situations a transmission system has to be designed to suit the load not the source. For example in a PC the motherboard needs defined voltages (with a tollerance) measured at the motherboard not at the power supply end of the wiring loom.

    So one valid answer would be to assume the load needs 12V delivered and will draw 24W.

    That would suggest the current through the load is 24W/12V = 2A.
    If the the cable resistance is 4 Ohms the source voltage needs to be 12+2*4 = 20V.
    The power delivered by the source would be 20V * 2A = 40W.

    but as I said that's just one of a number of possible answers that could be argued are correct given the problem statement is so loose.
     
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