We connect a capacitor $C_1=8F$ to a power supply, charge it to a potential difference $V_0=120V,$ then we dis connect the power supply as shown $($Switch S is open during this time$).$

$($a$)$ What is the charge $Q_0$ on $C_1?$

$($b$)$ Calculate the energy stored on $C_1$

After disconnecting the power supply we close $S_1$ and $C_2$ starts charging.

$($C$)$ What is the potential difference across $C_1$ and $C_2?$

Show me all the steps to solve this problem and explain your ansewer