Capacitance of a Conductor

A capacitor of unknown capacitance is connected across a battery of $'V'$ volt. The charge stored in it is $'Q'$ C. When potential across the capacitor is reduced by $'V_1'$ volt, the charge stored in it becomes $'Q_1'$ C. The potential $'V'$ is

Consider the earth to be a sphere, having charge $Q$. Let $R, V$ and $A$ be its radius, volume and area respectively. The capacitance of the earth is [$\varepsilon_0$ = permittivity of free space]

The earth is assumed to be a charged conducting sphere having volume 'V' and surface area 'A'. The capacitance of the earth in free space is ($\epsilon_0$ = permittivity of free space)

A capacitor of unknown capacity is connected across a battery of V volt. The charge stored in it is Q coulomb. When potential across the capacitor is reduced by $V_1$ volt, the charge stored in it becomes $Q_1$ coulomb. The potential V is

The graph shows the variation of voltage (v) across the plates of two parallel plate capacitos $A$ and $B$ versus increase of charge $Q$ stored in them. Then

The graph shows the variation of voltage ' V ' across the plates of two capacitors $A$ and $B$ versus increase in charge ' $Q$ ' stored in them. Then

The capacitance of a capacitor with charge $q$ and a potential difference $V$ depends on

The potential on the plates of capacitor are $+20\text{ V}$ and $-20\text{ V}$. The charge on the plate is $40\text{ C}$. The capacitance of the capacitor is

Given below are two statements: One is labeled as Assertion A and the other is labeled 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 charge than the hollow one.

Reason R: Capacitance of metallic spheres depends on the radii of spheres

In light of the above statements, choose the correct answer from the options given below.

Two spherical conductors of capacities $3\ \mu\text{F}$ and $2\ \mu\text{F}$ are charged to same potential having radii $3\text{ cm}$ and $2\text{ cm}$ respectively. If '$\sigma_1$ ' and '$\sigma_2$' represent surface density of charge on respective conductors then $\frac{\sigma_1}{\sigma_2}$ is

A condenser of $2\ \mu\text{F}$ capacitance is charged steadily from 0 to $5\text{ C}$. 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 R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii $\left(\frac{R_2}{R_1}\right)$ is:

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $\mu$C charge, its radius will be:

[ Take: $\frac{1}{4\pi\epsilon_0} =$ 9 $\times$ 109 N $\text{-}$ m2/C2 ]

Capacitance (in $F$) of a spherical conductor with radius $1\text{ m}$ is