Capacitance — CBSE Class 12 board PYQs

\textit{Case study — dielectrics in capacitors:} A dielectric slab placed in an external field develops opposite bound charges on its faces, setting up an internal field; this raises a capacitor's capacitance and alters its stored energy. Which of the following is a polar molecul …

Which of the following statements about dielectrics is correct?

When a dielectric slab is inserted between the plates of an \emph{isolated} charged capacitor, the energy stored in it

An air-filled capacitor with plate area $A$ and plate separation $d$ has capacitance $C_0$. A slab of dielectric constant $K$, area $A$ and thickness $\frac{d}{5}$ is inserted between the plates. The capacitance becomes

Two capacitors of capacitances $2C_0$ and $6C_0$ are first connected in series and then in parallel across the same battery. The ratio of the energy stored in the series combination to that in the parallel combination is

Define the term 'dielectric constant' of a medium in terms of capacitance of a capacitor.

Sketch a graph to show how the charge $Q$ acquired by a capacitor of capacitance $C$ varies with the increase in potential difference between its plates.

A parallel plate capacitor (A) of capacitance $C$ is charged by a battery to voltage $V$. The battery is disconnected and an uncharged capacitor (B) of capacitance $2C$ is connected across A. Find the ratio of (i) final charges on A and B, and (ii) total electrostatic energy stor …

The space between the plates of a parallel plate capacitor is completely filled in two ways. In the first case, it is filled with a slab of dielectric constant $K$. In the second case, it is filled with two slabs of equal thickness and dielectric constants $K_1$ and $K_2$ respect …

A capacitor of unknown capacitance is connected across a battery of $V$ volt. A charge of $360\mu \text{C}$ is stored in it. When the potential across the capacitor is reduced by 120 V, the charge stored in the capacitor becomes $120\mu \text{C}$. Calculate $V$ and the unknown …

A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6 pF is connected in series with it with the same battery connected across the combination, find the charge stored and potential difference across e …

Two parallel plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates while Y contains a dielectric medium of ${\epsilon }_r=4$. (i) Calculate the capacitance of each capacitor if the equivalent capacitance of the comb …

Two capacitors of unknown capacitances $C_1$ and $C_2$ are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of $C_1$ and $C_2$. Also calculate the charge …

A parallel plate capacitor of capacitance $C$ is charged to a potential $V$. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

A slab of material of dielectric constant $K$ has the same area as that of the plates of a parallel plate capacitor but has the thickness $\frac{2d}{3}$, where $d$ is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between …

Net capacitance of three identical capacitors in series is $1\mu \text{F}$. What will be their net capacitance if connected in parallel? Find the ratio of energy stored in the two configurations if they are both connected to the same source.

A parallel-plate capacitor is charged to a potential difference $V$ by a dc source. The capacitor is then disconnected from the source. If the distance between the plates is doubled, state with reason how the following change:
(i) electric field between the plates,
(ii) capacitan …

The equivalent capacitance of the combination between A and B in the given figure is $4\mu \text{F}$, where the $20\mu \text{F}$ capacitor is in series with a capacitor C. (i) Calculate the capacitance of the capacitor C. (ii) Calculate the charge on each capacitor if a 12 V ba …

A parallel plate capacitor, each with plate area $A$ and separation $d$, is charged to a potential difference $V$. The battery used to charge it is then disconnected. A dielectric slab of thickness $d$ and dielectric constant $K$ is now placed between the plates. What change, if …

The given graph shows the variation of charge $q$ versus potential difference $V$ for two capacitors $C_1$ and $C_2$. The two capacitors have the same plate separation but the plate area of $C_2$ is double that of $C_1$. Which of the lines in the graph corresponds to $C_1$ and …

Two capacitors of capacitance $6\mu \text{F}$ and $12\mu \text{F}$ are connected in series with a battery. The voltage across the $6\mu \text{F}$ capacitor is 2 V. Compute the total battery voltage.

A parallel plate capacitor with air between the plates has a capacitance of 8 pF. The separation between the plates is now reduced by half and the space between them is filled with a medium of dielectric constant 5. Calculate the value of capacitance in the second case.

(a) Why does the electric field inside a dielectric decrease when it is placed in an external electric field?
(b) A parallel plate capacitor with air between the plates has a capacitance of 8 pF. What will be the capacitance if the distance between the plates is reduced by half a …

A $5\mu \text{F}$ capacitor is charged by a 100 V supply. The supply is then disconnected and the charged capacitor is connected to another uncharged $3\mu \text{F}$ capacitor. How much electrostatic energy of the first capacitor is lost in the process of attaining the steady s …

A $4\mu \text{F}$ capacitor is charged by a 200 V supply. The supply is then disconnected and the charged capacitor is connected to another uncharged $2\mu \text{F}$ capacitor. How much electrostatic energy of the first capacitor is lost in the process of attaining the steady s …

A parallel plate capacitor is to be designed with a voltage rating 1 kV, using a material of dielectric constant 3 and dielectric strength about $10^7{\text{V m}}^{-1}$. For safety we would like the field never to exceed, say, 10% of the dielectric strength. What minimum area …

A $20\mu \text{F}$ capacitor is charged by a 30 V dc supply and then connected across an uncharged $50\mu \text{F}$ capacitor. Calculate
(i) the final potential difference across the combination, and
(ii) the initial and final energies. How will you account for the difference i …

(a) Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.
(b) A parallel plate capacitor is charged by a battery to a potential differenc …

(a) Distinguish, with the help of a suitable diagram, the difference in the behaviour of a conductor and a dielectric placed in an external electric field. How does polarised dielectric modify the original external field? (b) A capacitor of capacitance $C$ is charged fully by con …

(a) Derive an expression for the energy stored in a parallel plate capacitor $C$, charged to a potential difference $V$.
(b) Obtain the equivalent capacitance of the network given below ($C_1=100\text{pF}$ with $200\text{pF}$ capacitors on either side, $C_2$ and $C_3$ of …