Two capacitors of $2\ \mu F$ and $3\ \mu F$ are charged to $300\ V$ and $500\ V$ respectively. When they are connected in parallel, the energy lost is: (in $J$)

$A$ 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:

$A$ $10 \ \mu F$ capacitor is charged to a potential difference of $50 \ V$ and connected in parallel to another uncharged capacitor. The common potential difference becomes $20 \ V$. The capacitance of the second capacitor is ........ $\mu F$.

$A$ capacitor of capacitance $C_1 = 1 \ \mu F$ is charged using a $9 \ V$ battery. $C_1$ is then removed from the battery and connected to capacitors $C_2$ and $C_3$ of $2 \ \mu F$ and $3 \ \mu F$ respectively,as shown in the figure. Find the charge on $C_3$ after equilibrium is reached.

Two metal spheres of capacitance $C_1$ and $C_2$ carry some charges. They are put in contact and then separated. The final charges $Q_1$ and $Q_2$ on them will satisfy

In the circuit shown,$C_1 = 6\,\mu F, C_2 = 3 \,\mu F$ and battery $B = 20\,V$. The switch $S_1$ is first closed. It is then opened and afterwards $S_2$ is closed. What is the charge (in $\mu C$) finally on $C_2$?