(C) The capacitance $C$ of a conducting sphere of radius $R$ is given by $C = 4 \pi \epsilon_0 R$.For a sphere,the volume $V = \frac{4}{3} \pi R^3$ an

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$\frac{12 \pi \epsilon_0 V}{A}$

(C) The capacitance $C$ of a conducting sphere of radius $R$ is given by $C = 4 \pi \epsilon_0 R$.For a sphere,the volume $V = \frac{4}{3} \pi R^3$ and the surface area $A = 4 \pi R^2$.Dividing the volume by the surface area,we get $\frac{V}{A} = \frac{\frac{4}{3} \pi R^3}{4 \pi R^2} = \frac{R}{3}$.Therefore,$R = \frac{3V}{A}$.Substituting this value of $R$ into the capacitance formula:$C = 4 \pi \epsilon_0 \left( \frac{3V}{A} \right) = \frac{12 \pi \epsilon_0 V}{A}$.Thus,the correct option is $C$.

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

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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).

MHT CET 2025 All MHT CET

A
$\frac{2 \pi \epsilon_0 V}{A}$
B
$\frac{8 \pi \epsilon_0 V}{A}$
C
$\frac{12 \pi \epsilon_0 V}{A}$
D
$\frac{4 \pi \epsilon_0 V}{A}$

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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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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).

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