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Need help with basic Circuit Problem

  1. Jun 28, 2013 #1
    1. The problem statement, all variables and given/known data
    How long does it take for half the energy stored in a capacitor in an RC circuit to be dissipated?


    2. Relevant equations
    dQ(t)/dt = -Q(t)/(RC)


    3. The attempt at a solution
    So far i know Q(t) = integral(Q(t)/RC)dt
    i don't know how to evaluate this integral, and if somebody could guide me through it that'd be awesome, but i know it's suppose to come out to
    Q(t) = Qinitial * e^(-t/RC)
    and then from there i put Qinitial/2 in for Q(t) and cancel out Qinitials for 1/2 = e-t/RC which would give -RC*ln(1/2) = t but that is not the correct answer ;-( help plz
     
  2. jcsd
  3. Jun 28, 2013 #2

    gneill

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    Staff: Mentor

    You start with the differential equation and separate the variables; Gather the Q's on one side and everything else on the other. Both sides can then be integrated separately.
    You're looking for the time when the ENERGY is halved, not the charge. What an expression for the energy stored in a capacitor as a function of charge?
     
  4. Jun 28, 2013 #3
    Thanks. So i figured E is proporation to Q^2 so half the energy must mean that the charge is now Q/(sqrt(2) right?? But following this logic i get RC*ln(sqrt(2) and the answer is supposed to be (RC*Ln(2))/2

    Edit: Nevermind, they are equal, haha
     
    Last edited: Jun 28, 2013
  5. Jun 28, 2013 #4

    gneill

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    Staff: Mentor

    ## ln(\sqrt{2}) = ln(2^{1/2}) = (1/2)ln(2)##
     
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