The following circuit is given:(adsbygoogle = window.adsbygoogle || []).push({});

[PLAIN]http://img822.imageshack.us/img822/6369/image2lz.jpg [Broken]

Switch S is closed until the charge q_{2}on C_{2}reaches its maximum, then at t=0 the switch is opened. Find q_{1}(t).

Using Kirchkoff's rules I found:

EMF= (q_{1})/(C_{1}+I_{2}R

I_{2}R= q_{2}/C_{2}

I_{1}= I_{2}+I_{3}

In order to solve for q_{1}I need to substitute [itex]I_1=\frac{dq_1}{dt}[/itex] and solve the differential equation. But I need one more equation to eliminate I_{3}and q_{2}.

I was thinking of relating the charge q_{2}to the total charge in the circuit, but after some calculation I found that the total charge isn't constant.

At t=0 the total charge q_{2}on C_{2}is EMF*C_{2}and the charge on C_{1}is zero.

At t=[itex]\inf[/itex] the total charge on both capacitors is [itex]EMFC_1C_2 / (C_1 + C_2)[/itex] (since the current is zero you can combine the two capacitors using [itex] C_3^{-1}=C_1^{-1} + C_2^{-1}[/itex])

any help is appreciated :-)

edit: I tried to put the kirchkoff equations in Latex, but for some reason the rest of the post becomes unreadable.

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# Homework Help: Finding q(t) on a capacitor in an RC circuit

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