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Rearranging Exponential Curve Equation

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Hello. I'm afraid it's quite a simple and unexciting problem I have. Basically, I can't remember how to rearrange the equation for an exponential curve:

    The capacitor has a capacitance of 0.63 mF and the resistance in the discharge circuit is
    2.4 kΩ.

    (i) Calculate the time constant of the discharge circuit. This I can do: -t = RC.
    (ii) Show that it takes about 3 s to discharge the capacitor from 120 V to 15 V.

    2. Relevant equations

    V = Vo e^-t/RC

    3. The attempt at a solution

    I remember it's the above equation I need to use. And I remember it's to do with the "ln" button on my calculator. But I can't remember how, when or where I use it. I know it's meant to "get rid of" the e and make my -t/RC "un-square" themselves so I can rearrange the equation. Apologies for my terrible lack of physics vocabulary :P.

    I've tried a combination of things, enclosing the whole equation in ln( ) but I can't get the right answer (which is 3.14 seconds) as I am not rearranging it properly.

    I would appreciate any help anyone has.
  2. jcsd
  3. Jan 18, 2009 #2


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    Hi mandos! :smile:

    You're given V and V0, and you want to calculate t.

    So just "logify" the whole equation :biggrin:

    -t/RC = … ? :wink:
  4. Jan 18, 2009 #3
    Hi, am sorry to be a pain but that makes no sense to me.

    In my calculator, I try ln ((V*R*C)/(Vo)) and it gives me -1.66s.
  5. Jan 18, 2009 #4


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    But you didn't "logify" …

    ln(V) = ln(Vo e-t/RC) :wink:
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