Two identical parallel plate capacitors are connected in series to a battery of $100\,V$. $A$ dielectric slab of dielectric constant $4.0$ is inserted between the plates of the second capacitor. The potential difference across the capacitors will now be respectively:

Two insulated spheres of radii $R_1$ and $R_2$ having charges $Q_1$ and $Q_2$ respectively are connected to each other. There is:

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After some time, $S_2$ is released and then $S_3$ is pressed. After some time, which of the following statements are correct?

The energy stored in a capacitor is $U$. If an uncharged capacitor of the same capacity is connected in parallel with it,then the energy stored in each capacitor is:

Two capacitors $C_1$ and $C_2$ are connected in parallel. If a charge $Q$ is given to the combination,the charge gets shared. Then the ratio of charge on $C_1$ to charge on $C_2$ is . . . . . . .

Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12\, \mu C$ and $-3\, \mu C$ charges,respectively,and are at a large distance from each other. They are now connected by a conducting wire. $A$ long time after this is done,the charges on $S_{1}$ and $S_{2}$ are respectively: