Question

Why does the charge of capacitor 2 go down?

Answer 1

So I get that:
a) Q3 goes up (obviously, that's given in the problem)


b) Q1 goes up, because $$C1 = C2+C3 $$ and since C3 has increased, C1 must now increase to make up for the difference.


c) So for Q2, I don't understand why it goes down. I know the potential difference for capacitors in parallel is the same, but the potential difference does not change due to C3 increasing, so why would that effect $$Q2 = C\Delta V $$ ?

Answer 2

All of those capacitors are acting like one large capacitor. Charge will build up on C1, and an equal amount will be spread over C2 and C3. That is, Q1 = Q2+Q3

The amount that builds up on C2 and C3 depends on their capacitance. The higher the capacitance, the more charge it will get. So, if C3 is increased, the total capacitance increases (thus increasing the charge on Q1), and the ratio shifts toward C3 between it and C2.