1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Decay in Energy in an RC circuit?

  1. Apr 21, 2008 #1
    1. The problem statement, all variables and given/known data

    They want us to find T, time, when the capacitor has lost 50% of its energy. They give us voltage, capacitance, and resistance.



    2. Relevant equations

    I=I_o(e^(-t/RC))
    Q=Q_o(e^(-t/RC))

    Potential Energy = Q^2/2C

    3. The attempt at a solution

    I have no idea how to relate charge/current decay to energy in an RC circuit. Does anyone have any ideas? :(
     
  2. jcsd
  3. Apr 21, 2008 #2
    There's an additional formula for the energy stored in a capacitor in terms of the capacitance and the voltage.
     
  4. Apr 21, 2008 #3
    but even if i had that equation...how would i use it in relation to the RC equations? just because i have an energy equation in terms of capacitance and voltage doesnt mean i can find the time it takes for it to decay to 50%of its original energy.
     
  5. Apr 21, 2008 #4
    The charge on the capacitor is changing, in which the U = Q^2/2C. Since C is constant, the only variable you need to take account for is Q. If Q_o is the initial charge (and largest charge), it contributes to the highest potential energy, U_o of the capacitor. Half of U_o occors when about 1/sqr(2) of Q_o is left, in which sqr() is square root. Using Q=Q_o(e^(-t/RC)) for Q = (1/sqr(2)*Q_o, solve for t.
     
  6. Apr 21, 2008 #5
    wait how did you know that

    U_o is 1/sq(2) of Q_o?

    i know theres easy algebra involved x_x haha but i dont see how you got there
     
  7. Apr 22, 2008 #6
    He used E = Q^2/2C to find the energy at t=0 when the capacitor had a charge Q_o. that is simply E = Q_o^2/2C.
    then used the same equation to get the charge of the capacitor when it has half that energy. (1/2)E = (1/2)(Q_o^2/2C) = Q^2/2C.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Decay in Energy in an RC circuit?
  1. Decay in an RC Circuit (Replies: 5)

Loading...