(D) For a conducting sphere of radius $R$, the capacitance $C$ in free space is given by $C = 4\pi\epsilon_0R$.The volume $V$ of the sphere is $V = (4

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(D) For a conducting sphere of radius $R$, the capacitance $C$ in free space is given by $C = 4\pi\epsilon_0R$.The volume $V$ of the sphere is $V = (4/3)\pi R^3$.The surface area $A$ of the sphere is $A = 4\pi R^2$.Dividing the volume by the surface area, we get $V/A = [(4/3)\pi R^3] / [4\pi R^2] = R/3$.Therefore, $R = 3V/A$.Substituting this value of $R$ into the capacitance formula:$C = 4\pi\epsilon_0(3V/A) = 12\pi\epsilon_0V/A$.

Class 12 Physics Electric Potential and Capacitance Basic of Capacitor and type of capacitor (Spherical, Cylindrical)

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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 $(\epsilon_0 = \text{permittivity of free space})$

MHT CET 2026 All MHT CET

A
$2\pi\epsilon_0V/A$
B
$4\pi\epsilon_0V/A$
C
$8\pi\epsilon_0V/A$
D
$12\pi\epsilon_0V/A$

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Electric Potential and Capacitance

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Basic of Capacitor and type of capacitor (Spherical, Cylindrical)

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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 $(\epsilon_0 = \text{permittivity of free space})$

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