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Electrical Power Related

  1. Apr 12, 2009 #1
    I am studying DC circuits and trying to derive formula for power; that is in fact
    [tex]P = I.Vab[/tex]

    where Vab is the potential difference between two terminals of a circuit element.

    From my previous studies, I know that.

    [tex] P = dW / dt [/tex]

    I assume that for a small interval, dt, a single charge q has a small displacement , dx.

    Then;

    [tex]dW = E q dx[/tex]

    where E is magnitude of the electric field.

    Hence, from the formula above,

    [tex] P = E q dx / dt [/tex]

    This is all I could come up with. I want to go on with this idea to prove

    [tex] P = I Vab [/tex]


    I know I need to substitute dq somewhere (to get I ) , somehow.. Simply replacing q with dq does not seem to work; it leads to an incorrect formula. (I find P = I dV ; I guess, if I do that.)
     
  2. jcsd
  3. Apr 13, 2009 #2

    MATLABdude

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    Science Advisor

    It would be more advantageous to assume that you have a differential charge dq moving a distance x in the electric field E. (And does dq/dt ring a bell?) Also I believe this approach is more correct, since you have numerous charges (instead of a single one) and you're attempting to find their aggregate behaviour when you use Ohm's law.

    This derivation is also a very macroscopic one; the standard first-principles approach is given at Wikipedia:
    http://en.wikipedia.org/wiki/Ohm's_law
     
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