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RC Circuit discharge question - please help

  1. Nov 1, 2009 #1
    RC Circuit discharge question - test prep for tomorrow

    1. The problem statement, all variables and given/known data

    A charged 6[tex]\mu[/tex]F capacitor is discharged across a 2[tex]\Omega[/tex] resistor. How long does it take to lose half its stored energy?

    2. Relevant equations
    ....so many:

    Q = CV
    V = IR
    W = I2R
    U = 1/2 QV
    V = V0e-t/RC

    3. The attempt at a solution

    I'm not really sure where to start on this one. I'm trying to find a way to resolve Q and V where I only have one unknown, given C and R, but I'm having trouble. This is prep for an exam tomorrow, so any help is greatly appreciated.
     
    Last edited: Nov 1, 2009
  2. jcsd
  3. Nov 1, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    Hi jemitu, welcome to PF.
    Energy stored in the capacitor is given by
    E = 1/2*C*Vo^2.
    In the expression C remains constant.
    To change E to E/2, what should be the value of V in terms of Vo?
     
  4. Nov 1, 2009 #3
    Thanks for responding so quickly, I'm getting a little overwhelmed here.

    Given the energy equation you get Vo = sqrt(2E/C).
    plugging in to V(t), V= sqrt(2E/C) e^(-t/RC)

    But when you do the math, you don't have the original E so you can't solve it. The question is multiple choice with values, not expressions, hence my severe confusion. I think I need a little more hand-holding.
     
  5. Nov 1, 2009 #4

    rl.bhat

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    Homework Helper

    V0 = sqrt(2E/C)
    When E changes to E/2
    V(t) = sqrt(2*E/2*1/C) = 1/Sqrt(2)*sqrt(2E/C) = V0/sqrt(2)
    Substitute this in the equation and solve for t
     
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