$A$ capacitor of capacitance $6\ \mu F$ is charged to $100\, V$. It is then connected to another uncharged capacitor of capacitance $14\ \mu F$. Find the ratio of charges on the $6\ \mu F$ and $14\ \mu F$ capacitors and the potential across the $6\ \mu F$ capacitor.

$A$ conducting sphere $S_1$ of radius $r_1 = 3 \text{ cm}$ is connected by a conducting wire to another conducting sphere $S_2$ of radius $r_2 = 2 \text{ cm}$. Before they are connected,$S_1$ carries a charge of $10 \text{ units}$. The electric potential at a point which is at a distance $4 \text{ cm}$ from the centre of $S_1$ and a distance $3 \text{ cm}$ from the centre of $S_2$ is:

Two conducting spheres of radii $5\, cm$ and $10\, cm$ are given a charge of $15\,\mu C$ each. After the two spheres are joined by a conducting wire, the charge on the smaller sphere is.......$\mu C$.

Two capacitors $C_1$ and $C_2 = 2C_1$ are connected in a circuit with a switch $S$ between them as shown in the figure. Initially,the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state,the charge on each capacitor will be

The energy of a charged capacitor is $U$. It is removed from the battery and then connected in parallel to another uncharged capacitor having capacitance twice that of the first one. The energy of the first and second capacitors respectively is . . . . . . .

$A$ capacitor of capacitance $20 \mu F$ is charged by a battery of potential $24.3 \ V$. The capacitor is then disconnected from the battery and is connected to another uncharged capacitor of capacitance $10 \mu F$. After some time,the second capacitor is disconnected,discharged fully,and is again connected to the first capacitor. If the process is repeated several times,the charge on the first capacitor at the end of the fifth process is . . . . . . $\mu C$.