Capacitors and capacitance

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

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

Two metallic plates form a parallel plate capacitor. The distance between the plates is '$d$'. A metal sheet of thickness $\dfrac d2$ 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?

Two capacitors having capacitance $C_1$ and $C_2$ respectively are connected as shown in figure. Initially, capacitor $C_1$ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor $C_1$ is now connected to uncharged capacitor $C_2$ by closing the switch S. The amount of charge on the capacitor $C_2$, after equilibrium, is :

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 parallel plate capacitor is made up of stair like structure with a plate 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 $\dfrac x{15}\dfrac{\varepsilon_0A}b$. The value of $x$ is ______.

A capacitor $C_1$ of capacitance 5 $\mu$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 $C_2$ of capacitance 10 $\mu$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor $C_2$ is ______ $\mu$C.

A condenser of 2 $\mu$F capacitance is charged steadily from 0 to 5 C. 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 ?

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 $\left(\dfrac{R_2}{R_1}\right)$ is :

Two identical thin metal plates has charge $q_1$ and $q_2$ respectively such that $q_1>q_2$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

The magnitude of $q_1$ is ____.

The magnitude of $q_2$ is ____.

Which one of the following statements is correct?

If the capacitance of a nanocapacitor is measured in terms of a unit '$u$' made by combining the electronic charge 'e', Bohr radius '$a_0$', Planck's constant 'h' and speed of light 'c' then :

At time $t=0$, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current $I(t)=I_0\cos(\omega t)$, with $I_0=1$ A and $\omega=500\ \mathrm{rad\,s^{-1}}$ starts flowing in it with the initial direction shown in the figure. At $t=\dfrac{7\pi}{6\omega}$, the key is switched from B to D. Now onwards only A and D are connected. A total charge $Q$ flows from the battery to charge the capacitor fully. If $C=20\ \mu$F, $R=10\ \Omega$ and the battery is ideal with emf of 50 V, identify the correct statement(s).

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3\times10^4$ V/m, the charge density of the positive plate will be close to :

In the given circuit, a charge of +80 μC is given to the upper plate of the 4 μF capacitor. Then in the steady state, the charge on the upper plate of the 3 μF capacitor is