Capacitance — JEE Main PYQs

A capacitor of capacitance $900\mu$F is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capaci …

Two parallel plate capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ each having capacitance of $10\mu \mathrm{F}$ are individually charged by a 100 V D.C. source. Capacitor ${\mathrm{C}}_1$ is kept connected to the source and a dielectric slab is inserted between it plates. Cap …

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charg …

Two identical thin metal plates has charge ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ respectively such that ${\mathrm{q}}_1>{\mathrm{q}}_2$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

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 …

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}\mathrm{d}$, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be …

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

A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is $E_1$. Now key 'K' is opened and dielectric of dielectric constant 5 is introduced betw …

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capac …

Capacitance of an isolated conducting sphere of radius $R_1$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_2$ connected to earth. The ratio of their radii $\left(\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}\right)$ is:

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric …

The total charge on the system of capacitance ${\mathrm{C}}_1=1\mu \mathrm{F},{\mathrm{C}}_2=2\mu \mathrm{F},{\mathrm{C}}_3=4\mu \mathrm{F}$ and ${\mathrm{C}}_4=3\mu \mathrm{F}$ connected in parallel is
(Assume a battery of 20 V is connected to the combination)

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 ______ V.

A capacitor ${\mathrm{C}}_1$ of capacitance $5\mu \mathrm{F}$ is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor ${\mathrm{C}}_2$ of capacitance $10\mu \mathrm{F}$ as shown in …

A paralle plate capacitor is made up of stair like structure with a palte area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{{\epsilon }_{0}A}{b}$. The value of $x$ is ______.

The displacement current of $4.425\mu \mathrm{A}$ is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of $10^6{\mathrm{Vs}}^{-1}$. The area of each plate of the capacitor is 40 ${\mathrm{cm}}^2$. The distance between each …

The charge on capacitor of capacitance $15\mu \mathrm{F}$ in the figure given below is :

A parallel plate capacitor with plate area A and plate separation $\mathrm{d}=2\mathrm{m}$ has a capacitance of $4\mu \mathrm{F}$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant …

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :

Two capacitors having capacitance ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ respectively are connected as shown in figure. Initially, capacitor ${\mathrm{C}}_1$ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor …

A force of 10 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 :

A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ______ nJ.

A parallel plate capacitor is formed by two plates each of area $30\pi {\mathrm{cm}}^2$ separated by 1 mm. A material of dielectric strength $3.6\times 10^7{\mathrm{Vm}}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without caus …

If the charge on a capacitor is increased by 2 C, the energy stored in it increases by $44\%$. The original charge on the capacitor is (in C) :

Two metallic plates form a parallel plate capacitor. The distance between the plates 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 capacita …

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

The material filled between the plates of a parallel plate capacitor has resistivity $200\Omega \mathrm{m}$. The value of capacitance of the capacitor is 2 pF . If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current …

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ of same area $\mathrm{A}/2$ and thickness $\mathrm{d}/2$ are inserted in the space between the plates. The capac …

Consider the combination of 2 capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$, with ${\mathrm{C}}_2>{\mathrm{C}}_1$, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series, Calculate the r …

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

A parallel plate capacitor of capacitance $200\mu \mathrm{F}$ is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in …

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given area of plate $=\mathrm{A}$)

Two capacitors of capacities 2C and C are joined in parallel and charge up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be:

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference $\mathrm{V}=12\mathrm{V}$ between its plates. The charging battery is now disconnected and a porcelain plate with $\mathrm{k}=7$ is inserted between the plates, then th …

Four identical rectangular plates with length, $\ell =2\mathrm{cm}$ and breadth, $\mathrm{b}=\frac{3}{2}\mathrm{cm}$ are arranged as shown in figure. The equivalent capacitance between $A$ and $C$ is $\frac{X{\epsilon }_0}{d}$. The value of $x$ is ⋯------. (Roun …

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

If $q_f$ is the free charge on the capacitor plates and $q_b$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge $q_b$ can be expressed as :

A simple pendulum of mass '$m$', length '$\ell$' and charge '$+q$' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be:

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4}d$, where ' $d$ ' is the separation between t …

In a parallel plate capacitor set up, plate area of capacitor is $2{\mathrm{m}}^2$ and the plates are separated by 1 m . If the space between the plates are filled with a dielectric material of thickness 0.5 m and area $2{\mathrm{m}}^2$ (See fig) the capacitance of the set- u …

A $2\mu \mathrm{F}$ capacitor ${\mathrm{C}}_1$ is first charged to a potential difference of 10 V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor ${\mathrm{C}}_2$ of $8\mu \mathrm{F}$. The charge in ${\mathrm{C}}_2$ on equ …

A parallel plate capacitor has plate area $100{\mathrm{m}}^2$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.
The value of …

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as $k(x)=K(1+\alpha x)$ where 'x' is the distance measured from one of the plates.

If $(\alpha d)\ll 1$, the total …

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) __ …

Effective capacitance of parallel combination of two capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is $10\mu \mathrm{F}$. When these capacitor are individually connected to a voltage source of 1 V , the energy stored in the capacitor ${\mathrm{C}}_2$ is 4 times that of …

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

In the circuit shown, charge on the $5\mu \mathrm{F}$ capacitor is:

A parallel plate capacitor has plate of length '$\ell$', width '$w$' and separation of plates is '$d$'. It is connected to a battery of emf V. A dielectric slap of the same thickness 'd' and of dielectric constant $\mathrm{k}=4$ is being, inserted between the plates of the capaci …

In the circuit shown in the figure, the total charge is 750 $\mu \mathrm{C}$ and the voltage across capacitor ${\mathrm{C}}_2$ is 20 V. Then the charge on capacitor ${\mathrm{C}}_2$ is