Question

Capacitor #1 with capacitance C and initial charge Q is connected in parallel across an initially uncharged capacitor with capacitance 2C (#2). After the system comes to equilibrium, what is the charge on capacitor #1?

Answer 1

After the two capacitors are connected their charges must satisify 

Q₁ + Q₂ = Q

Q₁/C = Q₂/2C

whre the first condition comes from charge conservation and the second comes from the fact that the potential drop across each capacitor is the same since they are connected in parallel. Solving for Q₁ yields

Q₁ = Q/3