I have been given this problem in which one capacitor is initially charged to some voltage and then connected with another uncharged capacitor and resistor as shown in the figure. I am trying to find the charge on the capacitor as a function of time but stuck. Can anybody tell if my approach is right or wrong? 
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1 Answer
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The equation seems right. Few things you can do to confirm that any equation is correct.
- Check the units of all terms. q1, C1Vo and io(tau) have the same units. So, this is ok.
- At t=0, Q1=C1Vo. So, this is ok
- At t=inf, Q1 = C1Vo - io(tau).
io = Vo/R; tau=R*(C1C2)/(C1+C2)
If you take C1=C2, then, Q1 = C1Vo/2 at t=inf. Which makes sense because half the charge will move to the other cap so that both ends of the resistor will be at the same voltage and there will be no current in the resistor.
So, the equation seems to be correct.
