Two capacitors of capacitance $3 \ \mu F$ and $6 \ \mu F$ are charged to a potential of $12 \ V$. They are then connected by joining their positive plates together and their negative plates together. What will be the potential difference across each capacitor in $V$?

$A$ conducting body $1$ has some initial charge $Q$,and its capacitance is $C$. There are two other conducting bodies,$2$ and $3$,having capacitances $C_2 = 2C$ and $C_3 \rightarrow \infty$. Bodies $2$ and $3$ are initially uncharged. Body $2$ is touched with body $1$. Then,body $2$ is removed from body $1$ and touched with body $3$,and then removed. This process is repeated $N$ times. The charge on body $1$ at the end must be:

$A$ $20 \mu F$ capacitor is charged to $5 V$ and isolated. It is then connected in parallel with an uncharged $30 \mu F$ capacitor. The decrease in the energy of the system will be (in $\text{J}$)

$A$ capacitor of capacitance $C$ is charged to a potential $V$. It is then disconnected and connected in parallel with an identical uncharged capacitor. Find the charge on each capacitor.

$A$ $0.2 \, F$ capacitor is charged to $600 \, V$ by a battery. After removing the battery,it is connected to another uncharged parallel plate capacitor of $1 \, F$. The potential decreases to $V$ equal to:

$A$ capacitor of capacity $C_1$ is charged up to $V$ volt and then connected to an uncharged capacitor of capacity $C_2$. The final potential difference across each will be: