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How long does it take for energy stored in the capacitor to reach its maximal value?

  1. Oct 15, 2012 #1
    1. The problem statement, all variables and given/known data
    An RC circuit has EMF=12.0V, R=15 kΩ and C=3.8 μF. How long does it take for energy stored in the capacitor to reach 65% of its maximal value?


    2. Relevant equations
    1) Q = Cε
    2) Q X .65 = desired charge
    3) q(t) = Q(1 - e-t/RC)


    3. The attempt at a solution
    This is fairly straightforward to be honest, but I just don't know how to isolate for t in formula 3.

    1) Q = 12v X 3.8μf = 4.56 X 10-5 C
    2) Q X .65 = 4.56 X 10-5 C X .65 = 2.964 X 10-5
    3) q(t) = 2.964 X 10-5(1 - e-t/0.057)

    First question: Is that how I have to write down the formula with the known values?
    Second question: How do I isolate for t?


    Thank you!

    Edit: Here is what I found by browsing on the Internet:

    0.65Q = Q(1 - e-t/RC, or 0.65 = 1 - e-t/RC
    -.35 = -e-t/RC
    .35 = e-t/RC
    ln .35 = -t/RC
    t = -ln(.35) * RC
    t = 1.0498 * 0.057
    t = 0.0598 seconds
     
    Last edited: Oct 15, 2012
  2. jcsd
  3. Oct 15, 2012 #2

    CWatters

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    Re: How long does it take for energy stored in the capacitor to reach its maximal val

    Deleted as you found the answer.
     
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