Question

A capacitor is made of two square plates each of side ‘ $a$ ’ making a very small angle $\alpha$ between them, as shown in figure. The capacitance will be close to:

JEE Main 2020 (08 Jan Shift 2)

Options

• A: $\frac{{\in }_0{a}^2}{d}\left(1-\frac{\alpha a}{2d}\right)$
• B: $\frac{{\in }_0{a}^2}{d}\left(1-\frac{\alpha a}{4d}\right)$
• C: $\frac{{\in }_0{a}^2}{d}\left(1+\frac{\alpha a}{d}\right)$
• D: $\frac{{\in }_0{a}^2}{d}\left(1-\frac{3\alpha a}{2d}\right)$

Question

A parallel plate capacitor has plate of length $l$, width $w$ and separation of plates is $d$. It is connected to a battery of emf $V$. A dielectric slab of the same thickness $d$ and of dielectric constant $K=4$ is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

JEE Main 2020 (05 Sep Shift 2)

Options

• A: $\frac{2l}{3}$
• B: $\frac{l}{3}$
• C: $\frac{l}{4}$
• D: $\frac{l}{2}$

Question

For the given input voltage waveform ${\mathrm{V}}_{\text{in }}\left(\mathrm{t}\right),$ the output voltage waveform ${\mathrm{V}}_0\left(\mathrm{t}\right),$ across the capacitor is correctly depicted by :

JEE Main 2020 (06 Sep Shift 1)

Options

• A:   
• B:    
• C:   
• D:  

Question

A capacitor is connected to a $20 \mathrm{V}$ battery through a resistance of $10\mathrm{\Omega }.$ It is found that the potential difference across the capacitor rises to $2 \mathrm{V}$ in $1 \mathrm{\mu s}.$ The capacitance of the capacitor is $\_\_\_\_\_\_\_\_\mathrm{\mu F}.$
Given In $\left(\frac{10}{9}\right)=0.105$

JEE Main 2021 (01 Sep Shift 2)

Options

• A: $0.95$
• B: $9.52$
• C: $1.85$
• D: $0.105$

Question

Calculate the amount of charge on capacitor of $4 \mathrm{\mu F}.$ The internal resistance of battery is $1\mathrm{\Omega }:$

JEE Main 2021 (27 Aug Shift 1)

Options

• A: $4 \mathrm{\mu C}$
• B: $8 \mathrm{\mu C}$
• C: $16 \mathrm{\mu C}$
• D: zero

Question

In a parallel plate capacitor set up, the plate area of capacitor is $2{ \mathrm{m}}^2$ and the plates are separated by $1 \mathrm{m}$. If the space between the plates are filled with a dielectric material of thickness $0.5 \mathrm{m}$ and are $2{ \mathrm{m}}^2$ (see figure) the capacitance of the set-up will be ${\epsilon }_0$ ________.

(Dielectric constant of the material $=3.2$)

(Round off to the Nearest Integer)

JEE Main 2021 (16 Mar Shift 2)

Enter your answer

Question

A parallel plate capacitor with plate area '$A$' and distance of separation '$d$' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:

$\epsilon \left(x\right)={\epsilon }_0+kx$, for $\left(0<x\le \frac{d}{2}\right)$

$\epsilon \left(x\right)={\epsilon }_0+k\left(d-x\right)$, for $\left(\frac{d}{2}\le x\le d\right)$

JEE Main 2021 (25 Jul Shift 1)

Options

• A: ${\left({\epsilon }_0+\frac{kd}{2}\right)}^{2/kA}$
• B: $\frac{kA}{2ln\left(\frac{2{\epsilon }_0+kd}{2{\epsilon }_0}\right)}$
• C: $0$
• D: $\frac{kA}{2}\ln \left(\frac{2{\epsilon }_0}{2{\epsilon }_0-kd}\right)$

Question

A parallel-plate capacitor with plate area $A$ has separation $d$ between the plates. Two dielectric slabs of dielectric constant $K_1$ and $K_2$ of same area $\frac{A}{2}$ and thickness $\frac{d}{2}$ are inserted in the space between the plates. The capacitance of the capacitor will be given by :

JEE Main 2021 (26 Aug Shift 2)

Options

• A: $\frac{{\epsilon }_0 A}{ d}\left(\frac{1}{2}+\frac{K_1{ K}_2}{{ K}_1+K_2}\right)$
• B: $\frac{{\epsilon }_0 A}{ d}\left(\frac{1}{2}+\frac{2\left({ K}_1+K_2\right)}{K_1{ K}_2}\right)$
• C: $\frac{{\epsilon }_0 A}{ d}\left(\frac{1}{2}+\frac{K_1+K_2}{{ K}_1{ K}_2}\right)$
• D: $\frac{{\epsilon }_0 A}{ d}\left(\frac{1}{2}+\frac{K_1{ K}_2}{2\left({ K}_1+K_2\right)}\right)$

Question

A condenser of $2 \mu \mathrm{F}$ capacitance is charged steadily from $0$ to $5 \mathrm{C}$. Which of the following graph represents correctly the variation of potential difference$\left(V\right)$ across its plates with respect to the charge $\left(Q\right)$ on the condenser?

JEE Main 2022 (25 Jul Shift 1)

Options

• A:
• B:
• C:
• D:

Question

Two metallic plates form a parallel plate capacitor. The distance between the plate is '$d$'. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

JEE Main 2022 (25 Jun Shift 2)

Options

• A: $1:2$
• B: $2:1$
• C: $1:4$
• D: $4:1$

Question

A force of $10 \mathrm{N}$ acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.

JEE Main 2022 (27 Jun Shift 1)

Options

• A: $5 \mathrm{N}$
• B: $10 \mathrm{N}$
• C: $20 \mathrm{N}$
• D: Zero

Question

Two capacitors, each having capacitance $40\mu \mathrm{F}$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $K$ such that the equivalence capacitance of the system became $24\mu \mathrm{F}$. The value of $K$ will be :

JEE Main 2022 (28 Jul Shift 1)

Options

• A: $1.5$
• B: $2.5$
• C: $1.2$
• D: $3$

Question

The equivalent capacitance between points $A$ and $B$ in below shown figure will be _____ $\mu \mathrm{F}$.

JEE Main 2022 (25 Jun Shift 1)

Enter your answer

Question

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($t_1$ and $t_2$) as shown in figure. The two different dielectric material are separated by a conducting foil $F$. The voltage of the conducting foil is _____ $\mathrm{V}$.

JEE Main 2022 (26 Jul Shift 1)

Enter your answer

Question

In the circuit shown, the energy stored in the capacitor is $n \mathrm{\mu J}$. The value of $n$ is _____.

JEE Main 2023 (13 Apr Shift 2)

Enter your answer

Question

A parallel plate capacitor of capacitance $12.5 \mathrm{pF}$ is charged by a battery connected between its plates to potential difference of $12.0 \mathrm{~V}$. The battery is now disconnected and a dielectric slab $\left(\epsilon_{\mathrm{r}}=6\right)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _____ $10^{-12} \mathrm{~J}$.

JEE Main 2024 (04 Apr Shift 2)

Enter your answer

Question

Three capacitors of capacitances $25 \mu \mathrm{F}, 30 \mu \mathrm{F}$ and $45 \mu \mathrm{F}$ are connected in parallel to a supply of $100 \mathrm{~V}$. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{x} \mathrm{E}$. The value of $x$ is _____.

JEE Main 2024 (05 Apr Shift 1)

Enter your answer

Question

The electric field between the two parallel plates of a capacitor of $1.5 \mu \mathrm{F}$ capacitance drops to one third of its initial value in $6.6 \mu \mathrm{s}$ when the plates are connected by a thin wire. The resistance of this wire is _____$\Omega$. (Given, $\log 3=1.1$ )

JEE Main 2024 (05 Apr Shift 1)

Enter your answer

Question

A $16 \mathrm{\Omega }$ wire is bend to form a square loop. A $9 \mathrm{V}$ battery with internal resistance $1 \mathrm{\Omega }$ is connected across one of its sides. If a $4 \mathrm{\mu F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \mathrm{\mu J}$, where $x=$______.

JEE Main 2024 (29 Jan Shift 1)

Enter your answer

Question

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is :

JEE Main 2024 (09 Apr Shift 1)

Options

• A: $\frac{13 \epsilon_o A}{17 d}$
• B: $\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{18 \mathrm{~d}}$
• C: $\frac{18 \epsilon_{\mathrm{o}} \mathrm{A}}{11 \mathrm{~d}}$
• D: $\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{20 \mathrm{~d}}$