The particle $P$ shown in the figure has a mass of $10 \mathrm{mg}$ and a charge of $-0.01 \mathrm{\mu C}$. Each plate has a surface area of ${10}^{-2}{ \mathrm{m}}^2$ on one side. What potential difference $V$ should be applied to the combination to hold the particle $P$ in equilibrium?

The figure shows two identical parallel plate capacitors connected to a battery through a switch $S$. Initially, the switch is closed so that the capacitors are completely charged. The switch is now open and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant $3$. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.

In the circuit shown, a capacitor of capacitance $3 \mu \mathrm{F}$ is charged from a battery of emf $6 \mathrm{V}$ with a switch connected to terminal $P$. The switch is now connected to $Q$. This charges the $6 \mu \mathrm{F}$ capacitor from the $3 \mu \mathrm{F}$ one. What is the new potential difference across combinations?

In the given arrangement of capacitors, $6 \mu \mathrm{C}$ charge is added to point $A$. Find the charge on the upper capacitor.

Two capacitors $A$ and $B$ with capacities $C_1$ and $C_2$ are charged to a potential difference of $V_1$ and $V_2$, respectively. The plates of the capacitors are connected as shown in the figure. The upper plate of $A$ is positive and that of $B$ is negative. An uncharged capacitor of capacitance $C$ and falls on the free ends to complete the circuit, then

In the circuit shown in the figure, the charge stored on a capacitor of capacitance $3 \mathrm{\mu F}$ is

Find the equivalent capacitance between $A$ and $B$. [Assume each conducting plate is having same dimensions and neglect the thickness of the plate, $\frac{{\epsilon }_{\sigma }A}{d}=7 \mathrm{\mu F}$, where $A$ is area of plates and $A\gg d]$.