Capacitance — JEE Main PYQs

A capacitor $P$ with capacitance $10\times 10^{-6}\mathrm{F}$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20\times 10^{-6}\mathrm{F}$. The char …

The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants ${\mathrm{K}}_1=2,{\mathrm{K}}_2=3$, and ${\mathrm{K}}_3=5$ (as shown in the figure). If new capacitance is …

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25\%$ more charge from the battery. The dielectric con …

Three parallel plate capacitors each with area A and separation d are filled with two dielectric (k₁ and k₂) in the following fashion. Which of the following is true? (k₁ > k₂)

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of c …

A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates.
A sheet having thickness ${\left(\frac{1}{3}\right)}^{\text{rd }}$ of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitan …

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If x is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^{\alpha }$, where …

From the circuit given below, the capacitance between terminals A and B shown in the circuit is
$\_\_\_\_$ $\mu \mathrm{F}$. (take ${\mathrm{C}}_1={\mathrm{C}}_2={\mathrm{C}}_3=1\mu \mathrm{F}$ and ${\mathrm{C}}_4=2\mu \mathrm{F}$.)

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7}\mathrm{J}$. The valu …

A parallel plate capacitor is having separation between plates 0.885 mm . It has a capacitance of $1\mu \mathrm{F}$ when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\Omega \mathrm{m}$ and resistance …

A parallel plate air capacitor has a capacitance C. When it is half filled as show in figure with a dielectric constant $\mathrm{K}=5$, the percentage increase in the capacitance is ____.

A parallel-plate capacitor of capacitance $40\mu \mathrm{F}$ is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant $\mathrm{K}=2$. Due to the introduction of dielectric material, the extra …

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

At steady state the charge on the capacitor, as shown in the circuit below, is $\_\_\_\_$ $\mu \mathrm{C}$.

A capacitor, ${\mathrm{C}}_1=6\mu \mathrm{F}$ is charged to a potential difference of ${\mathrm{V}}_0=5\mathrm{V}$ using a 5 V battery. The battery is removed and another capacitor, ${\mathrm{C}}_2=12\mu \mathrm{F}$ is inserted in place of the battery. When the switch ' S ' …

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is $7\times 10^8\mathrm{V}/\mathrm{s}$ then the integer value of the distance bet …

A parallel plate capacitor of capacitance $1\mu \mathrm{F}$ is charged to a potential difference of 20 V . The distance between plates is $1\mu \mathrm{m}$. The energy density between plates of capacitor is :

Two capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_1$ and $U_2$, respectively. Which of the given statements is true ?

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and ${\epsilon }_0$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is :-

A parallel plate capacitor was made with two rectangular plates, each with a length of $l=3\mathrm{cm}$ and breath of $b=1\mathrm{cm}$. The distance between the plates is $3\mu \mathrm{m}$. Out of the following, which are the ways to increase the capacitance by a factor of …

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant ${\epsilon }_1$ and ${\epsilon }_2$, as shown in figures. The distance between the plates is d and area of each plate is A . If capacitance in first configuration and second config …

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)

Four capacitor each of capacitance $16\mu \text{F}$ are connected as shown in the figure. The capacitance between points A and B is : ______ (in $\mu \text{F}$).

A parallel plate capacitor has charge $5\times 10^{-6}\mathrm{C}$. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4\times 10^{-6}$ C then the dielectric constant of the slab …

Space between the plates of a parallel plate capacitor of plate area $4{\mathrm{cm}}^2$ and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in par …

Three parallel plate capacitors ${\mathrm{C}}_1,{\mathrm{C}}_2$ and ${\mathrm{C}}_3$ each of capacitance $5\mu \mathrm{F}$ are connected as shown in figure. The effective capacitance between points A and B , when the space between the parallel plates of …

A capacitor of $10\mu \mathrm{F}$ capacitance whose plates are separated by 10 mm through air and each plate has area $4{\mathrm{cm}}^2$ is now filled equally with two dielectric media of ${\mathrm{K}}_1=2,{\mathrm{K}}_2=3$ respectively as shown in figure. If new force betw …

A parallel plate capacitor of capacitance 12.5 pF is charged by a battery connected between its plates to potential difference of 12.0 V . The battery is now disconnected and a dielectric slab ( ${ϵ}_r=6$ ) is inserted between the plates. The change in its potential ener …

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 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored ene …

A capacitor has air as dielectric medium and two conducting plates of area $12{\mathrm{cm}}^2$ and they are 0.6 cm apart. When a slab of dielectric having area $12{\mathrm{cm}}^2$ and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be …

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 $\frac{\mathrm{A}}{3}$ and the height is d, the capacitance of the arrangement is:

In the given figure, the charge stored in $6\mu \mathrm{F}$ capacitor, when points A and B are joined by a connecting wire is ______ $\mu \mathrm{C}$.

A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric c …

A galvanometer ( G ) of $2\Omega$ resistance is connected in the given circuit. The ratio of charge stored in ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is :

In an electrical circuit drawn below the amount of charge stored in the capacitor is ______ $\mu \mathrm{C}$.

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2C and potential 2V. Then the loss of energy is $\frac{x}{3}E$, where x is ______.

A 600 pF capacitor is charged by 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is $\_\_\_\_$ $\mu \mathrm{J}$.

In this figure the resistance of the coil of galvanometer G is $2\Omega$. The emf of the cell is 4 V. The ratio of potential difference across ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is:

As shown in the figure, two parallel plate capacitors having equal plate area of $200{\mathrm{cm}}^2$ are joined in such a way that $\mathrm{a}\ne \mathrm{b}$. The equivalent capacitance of the combination is $\mathrm{x}{\in }_0\mathrm{F}$. The value of $x$ is ______.

The distance between two plates of a capacitor is d and its capacitance is ${\mathrm{C}}_1$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2\mathrm{d}}{3}$ and of same area as plate is introduced between the plates, the capacitance of the c …

The equivalent capacitance of the combination shown is

A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is ${\mathrm{E}}_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The …

In the network shown below, the charge accumulated in the capacitor in steady state will be :

In the given figure the total charge stored in the combination of capacitors is 100 μC. The value of 'x' is ______.

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant $\mathrm{K}=4$. The thickness of the dielectric material is x, where $\mathrm{x}<\mathrm{d}$.

Let ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ be the capacita …

In the given circuit,
${\mathrm{C}}_1=2\mu \mathrm{F},{\mathrm{C}}_2=0.2\mu \mathrm{F},{\mathrm{C}}_3=2\mu \mathrm{F},{\mathrm{C}}_4=4\mu \mathrm{F}$, ${\mathrm{C}}_5=2\mu \mathrm{F},{\mathrm{C}}_6=2\mu \mathrm{F}$, the charge stored on capacitor ${\mathrm{C}}_4$ …

A parallel plate capacitor with air between the plate has a capacitance of 15 pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $\frac{\mathrm{X}}{4}$ pF. The value of …

A parallel plate capacitor has plate area $40{\mathrm{cm}}^2$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is:

A capacitor has capacitance $5\mu \mathrm{F}$ when it's parallel plates are separated by air medium of thickness d . A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates. Capacitance of the …