Question

Consider three identical ideal capacitors. The first capacitor is charged to a voltage V0 and then disconnected from the battery. The other two capacitors, initially uncharged and connected in series, are then connected across the first capacitor. What is the final voltage on the first capacitor?

Answer 1

$$Q_1=CV_0\\C_2=0.5C\\q_1+q_2=Q_1\\\frac{q_1}{C}=\frac{q_2}{0.5C}\\1_1=2q_2\\q_1=\frac{2}{3}CV_0\\V'=\frac{2}{3}V_0$$