S L Arora Solutions for Chapter: Electrostatic Potential and Capacitance, Exercise 1: Problems For Practice

The two plates of a parallel plate capacitor are $4 \mathrm{mm}$ apart. A slab of dielectric constant $3$ and thickness $3 \mathrm{mm}$ is introduced between the plates with its faces parallel to them. The distance between the plates is so adjusted that the capacitance of the capacitor becomes $\frac{2}{3}$ rd of its original value. What is the new distance between the plates?

The distance between the parallel plates of a Charged capacitor is $5 \mathrm{cm}$ and the intensity of the electric field is $300 \mathrm{V} {\mathrm{cm}}^{-1}$. A slab of dielectric constant 5 and thickness, $1 \mathrm{cm}$ is inserted parallel to the plates. Determine the potential difference between the plates, before and after the slab is inserted?

Figure below shows a parallel plate capacitor of plate area $A$ and plate separation $d$. Its entire space is filled with three different dielectric slabs of the same thickness. Find the equivalent capacitance of the arrangement.

The space between the plates of a parallel plate capacitor of capacitance $C$ is filled with three dielectric slabs of equal thickness, as shown in Figure. If the dielectric constants of the three slabs are $k_1, k_2$ and $k_3$, find the new capacitance.

A parallel-plate capacitor of capacity $0.5 \mu F$ is to be constructed using paper sheets of thickness $0.04 \mathrm{mm}$ as dielectric. Find how many circular metal foils of diameter $0.1 \mathrm{m}$ will have to be used. Take the dielectric constant of paper used as $4$.

When a slab of insulating material $4 \mathrm{mm}$ thick is introduced between the plates of a parallel plate capacitor, it is found that the distance between the plates has to be increased by $3.2 \mathrm{mm}$ to restore the capacitance to the original value. Calculate the dielectric constant of the material.

A parallel plate capacitor with plate separation $5 \mathrm{mm}$ is charged by a battery. It is found that on Introducing a mica sheet $2 \mathrm{mm}$ thick, while keeping the battery connections intact, the capacitor draws $25\%$ more charge from the battery than before. Find the dielectric constant of mica.

A slab of material of dielectric constant $k$ has the same area as the plates of a parallel plate capacitor but has a thickness $\frac{d}{2}$, where $d$ is the separation between the plates. Find the expression for the capacitance when the slab is inserted between the plates.