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Here's the question I was working with:

circuit diagram with three capacitors

The switch is closed at $t=0$. Find the charges on the capacitor. The batteries are both $20\ \mathrm{V}$ and $C_1 = 2\ \mathrm{\mu F}$, $C_2 = 4\ \mathrm{\mu F}$, and $C_3 = 2\ \mathrm{\mu F}$.

So I proceeded with this solution:

I found the charge on the capacitor when the switch is open and found them to be $40\ \mathrm{\mu F}$ on both $C_1$ and $C_3$.

After the switch is closed at $t = 0$, the charges on the capacitors will change so I used Kirchoff's rule on the 2 loops but it didn't help me because there are 3 unknown charges and only 2 loops so I got stuck.

When I asked my teacher, he said that the circled plates are floating plates because these plates are isolated from the circuit so charges can't come on these plates from outside and so sum of charges on these plates would be zero, but I couldn't understand that... Isn't $C_2$ connected with the battery so charges can come from the battery?

Anyway can you tell me the reason for them to be floating plates so that I can connect the dots?

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I think what you may be forgetting is that the two plates of a capacitor are actually physically separated. There's a gap in there, filled with air or rubber or something else that charged particles can't get through. That's precisely the reason we draw capacitors with a "hole" in the middle (i.e. a break in the line): it makes it easy to see where there are these gaps that charges can't cross.

So when your teacher says the plates are "floating", what he means is that they are disconnected from the rest of the circuit. There's no way for any charge to get in or out of the circled part of the circuit.

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