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Energy in an RC Circuit?

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data

    I have an RC Circuit. There's the EMF (voltage supplier; battery), a resistor, and a capacitor. They are all in series. I need to prove that

    --the energy stored in the capacitor through it charging equals 1/2 the energy supplied by the EMF

    Then I need to show

    --how much energy is lost by the resistor (which should be the other 1/2 of the energy supplied by the EMF by conservation of energy) and I need to prove it other than just using conservation of energy.

    Since this problem is all ratios, you can use whatever variables you want (E, i, Q, V, etc) so long as they cancel

    2. Relevant equations

    P = dW/dt

    P = IV = I^2R = V^2/R

    q = Q(1-e^(-t/(RC)))

    There may be more I need.. I really don't know..

    3. The attempt at a solution

    I'm thinking to use power, which is dW/dt, and integrate indefinitely. I don't know how to incorporate the charging equation, but I'm pretty sure its part of determining the energy of the capacitor?
  2. jcsd
  3. Mar 18, 2010 #2


    User Avatar
    Science Advisor

    You're on the right track. Use I = dQ/dt, calculate the current through the resistor, use this to calculate the power, and integrate.
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