Two capacitors of capacitance $2 \ \mu F$ and $5 \ \mu F$ are charged to $2 \ V$ and $10 \ V$ respectively. Find the ratio of their charges after they are connected by a wire.

$A$ 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.

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

$A$ $60\; pF$ capacitor is fully charged by a $20\; V$ supply. It is then disconnected from the supply and connected to another uncharged $60\; pF$ capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in $nJ$):

$A$ 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:

$A$ $0.2 \, F$ 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: