I am asked to find the charge on each cap in this circuit when S1 is closed:
I am given that C1=1μF, C2=2μF, C3=3μF, and C4=4μF. V=12V
Caps in series have an equivalent capacitance of Ceq=C1C2/(C1+C2), and caps in parallel have an equivalent capacitance of Ceq=C1+C2. The capacitance equals the voltage across the cap times the charge "held" in the cap. Parallel capacitors have the same voltage, whereas caps in series have the same charge.
The Attempt at a Solution
I found the equivalent capacitance of the circuit to be 2.083μF, and using that and C=QV, found that the total charge on the circuit is 25μC. I worked backwards from there, knowing that caps in parallel have the same V, and found the charge on each equivalent cap for the series to be 9μC for C13 and C24. This is where I get lost. The book has the answer to be 9μC on both C1 and C3 and 16μC for C2 and C4. Assuming that I found the correct charge on the circuit, 25μC, this violates the law of charge conservation, doesn't it? Any help is appreciated, thanks.