(C) The capacitance $C$ of a spherical capacitor with inner radius $a$ and outer radius $b$ is given by $C = 4\pi\epsilon_0 \frac{ab}{b - a}$.Given, t

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(C) The capacitance $C$ of a spherical capacitor with inner radius $a$ and outer radius $b$ is given by $C = 4\pi\epsilon_0 \frac{ab}{b - a}$.Given, the radius of the outer sphere $b = R$.The difference in radii is $b - a = x$, so the inner radius $a = R - x$.Substituting these values into the formula, we get $C = 4\pi\epsilon_0 \frac{(R - x)R}{x}$.Since $4\pi\epsilon_0$ is a constant, the capacity $C$ is proportional to $\frac{R(R - x)}{x}$.

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

Difficult

In a spherical condenser, the radius of the outer sphere is $R$. The difference in the radii of the outer and inner sphere is $x$. Its capacity is proportional to:

A
$\frac{xR}{R - x}$
B
$\frac{x(R - x)}{R}$
C
$\frac{R(R - x)}{x}$
D
$\frac{R}{x}$

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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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In a spherical condenser, the radius of the outer sphere is $R$. The difference in the radii of the outer and inner sphere is $x$. Its capacity is proportional to:

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