Capacitors and Capacitance

The two plates of a parallel plate capacitor are $5 \mathrm{mm}$ apart. A slab of a dielectric, of thickness $4 \mathrm{mm}$ is introduced between the plates with its faces parallel to them. The distance between the plates is adjusted so that the capacitance of the capacitor becomes equal to its original value. If the new distance between the plates equal $8 \mathrm{mm}$, what is the dielectric constant of the dielectric used?

If two similar plates, each of area $A$ having surface charge densities  $+\sigma \text{and}-\sigma$ are separated by a distance $d$ in air, write expressions for the potential difference between the plates.

Capacitance of a spherical capacitor varies with its radius $r$ as

Two plates are at potentials $-10\mathrm{V}$ and $+30\mathrm{V}$. If the separation between the plates is $2 \mathrm{cm}$ then find the electric field between them.

A parallel plate capacitor have capacitance $C$. If area of the plate doubled and distance between plates also doubled, then the capacitance will be

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$, the energy stored in the capacitor is

Consider a parallel plate capacitor filled with a dielectric of relative permittivity $2$. One of the plates has charge density $+\sigma$ while other has charge density $-\sigma$. Assume that the points are not too near the edges of the plates.The magnitudes of the electric field at points $P_1$and $P_2$ respectively are

Find the potential drop across the capacitor when the circuit given below achieves steady-state.

When the charge on a capacitor increases keeping geometry the same

A parallel plate capacitor is first charged and then disconnected from the battery and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is

Which one is the SI unit of capacitance?

Two materials of dielectric constants $k_1$ and $k_2$ are introduced to fill the space between the two parallel plates of a capacitor as shown in figure. The capacity of the capacitor is:-

Two large metal plates are placed parallel to each other. The inner surfaces of plates are charged by $+\sigma$ and $-\sigma .$ $\left(\mathrm{Coulomb} {\mathrm{m}}^{-2}\right)$ The outer surfaces are neutral. The electric field is $\dots ..$ in the region between the plates and $\dots ...$ outside the plates:-

What is the magnitude of charge that will reside in the parallel plate capacitor formed by these two plates.

Two spherical conductors $A$ and $B$ of radii $a$ and $b\left(b>a\right)$  are placed concentrically in air, The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is :-

If dielectric constant and dielectric strength be denoted by $K$ and $X$ respectively then a material suitable for use as dielectric in a capacitor must have:-

Two parallel plate capacitors are constructed one by a pair of iron plates and the second by a pair of copper plates of same area and same spacing. Then -

A thin metal plate $\mathrm{P}$ is inserted between the plates of a parallel-plate capacitor of capacitance $\mathrm{C}$ in such a way that its edges touch the two plates. The capacitance now becomes

The radii of two spherical conductors are in ratio $1:2$. The ratio of their capacitance is.

Two capacitors of capacitance $2\mathrm{ }\mathrm{\mu }\mathrm{F}$ and  $6\mathrm{ }\mathrm{\mu }\mathrm{F}$ are charged with batteries of $100 \mathrm{V}$ and $300 \mathrm{V}$ seperately. Now the capacitors are connected such that the like charged plates are joined together. The total charge on the system is:-