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Current after (1) time constant in RC circuits

  1. Oct 25, 2011 #1
    1. The problem statement, all variables and given/known data


    Maximum current:
    I max = 4.62 * 10^-4 A

    Time constant of circuit:
    T = 3.9 seconds

    2. Relevant equations

    T= RC

    3. The attempt at a solution

    I'm trying to find the current after 1 time constant. Seems simple enough, the current changes by 63%. So (Imax)-(Imax * 0.63) or basically I max * 0.37

    But the teacher just took I max * 0.63 !!! I thought it CHANGES by 63% not simply 63% of the original value!!

    I looked it up and all websites agree that the current after 1 time constant will be 0.37 of it's maximum value, hence a change of 63%!

    Has the teacher made a mistake? I have deeply confused myself over a simple thought. Please help.
    Last edited: Oct 25, 2011
  2. jcsd
  3. Oct 26, 2011 #2


    User Avatar

    Staff: Mentor

    The form of the equation is
    [tex] I(t) = I_o e^{-t/\tau}[/tex]
    You're interested in the value of I(t) for various times that are multiples of [itex]\tau[/itex]. Easy-peasy. Just divide Io by e1, e2, etc.. As you suspect, after the first time constant period the value drops to 36.8% of its initial value (1/e).
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