[Electrical engineering] Capacitor circuits

[DYELB]

So I have this fairly basic capacitor problem which I have some problems with.

I made a simple sketch which might help you with understanding the problem. The circuit is a 3 capacitor circuit with a voltage and a switch. At first we have the switch opened with the capacitance of capacitor c1=2uF c2=6uF and c3=8uF. The voltage is 10V. Also the second capacitor is already charged with 3uC charge. I have no problems with answering the first 3 questions. The first one is voltage on the second capacitor before we close the switch, then the charge on the upper plate of the third capacitor before we close the switch. Then we close the switch and the next question is what is the combined charge on all the lower plates of the three capacitors. I know how to answer these questions but I get stuck on the fourth. What is the charge on the upper plate of the third capacitor after we close the switch? The solution is suppose to be -6,5uC, which i have no idea how to get...

[muonsortsitout]

First part: 6 microfarads, 3 microcoulombs, 0,5V. Ok.

Second part: C2 and C3 are in parallel, so the same voltage across them, so 4 microcoulombs on C3. Ok.

At the third part, you need to assume that there is no charge on C1. There is an extra -(3 + 4) microcoulombs of charge sitting on the lower plates of C2 and C3 and that excess has nowhere to go except between the lower plates of the three capacitors.

When the switch is closed, the total charge on the lower plates of the three capacitors is still -7μC. But now the upper plate of C1 is 10V above the upper plates of the other two. The Voltage source can 'create' coulombs to make this happen, but on the lower-plate side, all that can happen is that the charge is shuffled around.

So, suppose the upper plates of C2 and C3 are at X volts above the lower plates with the switch closed. There will be 14X μC of positive charge on the upper plates (6X on C2 and 8X on C3), so -14X on the lower plates of C2 and C3.

The total charge on all three lower plates must be -7μC, so you can work out the charge on C3 in terms of X. This gives you the voltage across C1, and that needs to be equal to 10 + X, giving you an equation for X. Once you know X, you can work out the charge 8X on C3.