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Homework Help: How is the equation for Power [U'] derived?

  1. Aug 13, 2009 #1
    1. The problem statement, all variables and given/known data

    While going through a basic electrical engineering overview, I came across the equation U = QV, which is defined to be electrical energy. For Power, which is explained in the next section, P is basically the derivative of U = QV. I tried following the derivation myself, but for some reason, what I got was different from the book.

    2. Relevant equations

    U= QV

    q = -1.6x10^-19 Coulombs ( basically a constant)

    The derivative of this turned out to be d/dt = V*d[Q]/dt. My question is HOW.

    3. The attempt at a solution

    P = d/dt = Q * d[v]/dt; treated Q as a constant, but this doesn't line up. My Calculus must be rusty. Anyway, the full statement from the book:

    P = U'= V*Q' = VI= v^2/R = I^2*R

  2. jcsd
  3. Aug 13, 2009 #2


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    Homework Helper

    Power is the rate of work done against the opposition to the flow of charges in the conductor. While doing so the voltage across the conductor is constant.
    So P = U' = V*dQ/dt.
  4. Aug 13, 2009 #3

    That makes more sense. But...I thought Q itself was just a constant, you know, an electron's charge...it must be Q in the sense that Q = u/V? :)
  5. Aug 13, 2009 #4


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    It is different. It is the energy acquired by a charge when it is accelerated the a potential difference V. It is nothing to do with the power dissipated in a resistance.
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