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Charged Capacitors

  1. Apr 29, 2015 #1
    1. The problem statement, all variables and given/known data
    A 10nF and 20nF capacitor is independently charged to respectively 40V and 50V. The positive sides of the two capacitors are connected, and a 1kΩ resistor is connected across the negative terminals. Find equations for total voltage VT(t) across the resistor and voltages across each capacitor V1(t) and V2(t)

    2. Relevant equations
    V(t)=V0e-t/RC

    3. The attempt at a solution
    It seems VT(0) = 50-40 = 10V.
    Can we use VT(t)=V2(t)-V1(t), since the capacitors are connected positive to positive? In that case what value for R do we use for each capacitor?
     
    Last edited: Apr 29, 2015
  2. jcsd
  3. Apr 29, 2015 #2

    haruspex

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    There may be some law you can appeal to, but it isn't hard to work out from first principles. (I.e., obtain a differential equation for the current.)
     
  4. Apr 29, 2015 #3
    "work out from first principles" is a bit cryptic/generic and not really helpful. The equation I gave IS in effect a differential equation (well, the solution to one) Can you please elaborate?
     
  5. Apr 29, 2015 #4

    haruspex

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    Yes, it's the solution to a differential equation, but you don't know how to apply it because the equation was for a simpler set-up. I'm proposing writing out the differential equation for the set-up in the question and solving that in the same way. You can then be confident in how to apply it here. (It turns out to be just what you might have guessed.)
     
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