Capacitance

The difference in the capacitance (in F) between the metal plates at $t=0$ and that at $t=500$ s is $(8-n)\epsilon_0$, where $\epsilon_0$ is the permittivity of free space. The value of $n$ is:

The dimensional formula of $\dfrac12\epsilon_0E^2$ ($\epsilon_0$ = permittivity of vacuum and $E$ = electric field) is $M^aL^bT^c$. The value of $2a-b+c$ = ________.

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

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 $\alpha$ is ________.

Consider a circuit consisting of a capacitor (20 μF), resistor (100 Ω) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 Ω. The time constant of the circuit is $\alpha\times10^{-3}$ s. The value of $\alpha$ is ________.

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is ________ μF.
(take $C_1=C_2=C_3=1$ μF and $C_4=2$ μF.)

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

Assertion A: In electrostatics, a conductor does not store any net charge inside.

Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.

Choose the correct answer from the options given below

Under steady state condition the potential difference across the capacitor in the circuit is ________ V.

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 $\alpha\times10^{-7}$ J. The value of $\alpha$ is ________.

(combined capacitance of spheres is 200 pF)

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity $1\times10^{13}$ Ωm and resistance $17.7\times10^{14}$ Ω. Relative permittivity of the insulating material is $\alpha\times10^7$. The value of $\alpha$ is ________.

(Take permittivity of free space $=8.85\times10^{-12}$ F/m)

The stored charge in the capacitor in steady state of the following circuit is ________ μC.

Two co-axial conducting cylinders of same length $\ell$ with radii $\sqrt2R$ and $2R$ are kept, as shown in Fig. 1. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $\kappa = 5$. Consider an imaginary plane of the same length $\ell$ at a distance $R$ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. 2. Ignoring edge effects, the flux of the electric field through the plane is ($\epsilon_0$ is the permittivity of free space):

Four identical thin, square metal sheets, $S_1$, $S_2$, $S_3$ and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d\ (\ll a)$ between them, as shown in the figure. Let $C_0 = \varepsilon_0 a^2/d$, where $\varepsilon_0$ is the permittivity of free space.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of 1 A flows through the $1\,\Omega$ resistor. The key is closed at time $t = t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1} = 0.36$]

A container has a base of $50\ \text{cm}\times5\ \text{cm}$ and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area $50\ \text{cm}\times50\ \text{cm}$. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of $250\ \mathrm{cm^3\,s^{-1}}$. What is the value of the capacitance of the container after 10 seconds?

[Given: Permittivity of free space $\epsilon_0 = 9\times10^{-12}\ \mathrm{C^2N^{-1}m^{-2}}$, the effects of the non-conducting walls on the capacitance are negligible]

In the following circuit $C_1 = 12\ \mu F$, $C_2 = C_3 = 4\ \mu F$ and $C_4 = C_5 = 2\ \mu F$. The charge stored in $C_3$ is _____ $\mu C$.

A medium having dielectric constant $K > 1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown in Figure (a). Now, both the plates are moved by a distance of $\dfrac d2$ from their original positions, as shown in Figure (b).

In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

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 $3.6\times10^7\ \mathrm{Vm^{-1}}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7\times10^{-6}$ C, the value of dielectric constant of the material is :

[Use $\dfrac1{4\pi\varepsilon_0}=9\times10^9\ \mathrm{Nm^2C^{-2}}$]

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)

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