(D) The capacitance $C$ of a spherical capacitor consisting of two concentric conducting spheres of radii $R_1$ and $R_2$ $(R_2 > R_1)$ is given by th

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(D) The capacitance $C$ of a spherical capacitor consisting of two concentric conducting spheres of radii $R_1$ and $R_2$ $(R_2 > R_1)$ is given by the formula:$C = 4\pi \varepsilon_0 \frac{R_1 R_2}{R_2 - R_1}$Since $4\pi \varepsilon_0$ is a constant,the capacitance is proportional to the term $\frac{R_1 R_2}{R_2 - R_1}$.Therefore,the correct option is $D$.

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

Medium

$A$ solid conducting sphere of radius $R_1$ is surrounded by another concentric hollow conducting sphere of radius $R_2$. The capacitance of this assembly is proportional to

A
$\frac{R_2 - R_1}{R_1 R_2}$
B
$\frac{R_2 + R_1}{R_1 R_2}$
C
$\frac{R_1 R_2}{R_1 + R_2}$
D
$\frac{R_1 R_2}{R_2 - R_1}$

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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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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 $\left(\frac{R_{2}}{R_{1}}\right)$ is:

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

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$1000$ small water drops,each of capacitance $C$,join together to form one large spherical drop. The capacitance of the bigger sphere is ......... $C$.

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$A$ solid conducting sphere of radius $R_1$ is surrounded by another concentric hollow conducting sphere of radius $R_2$. The capacitance of this assembly is proportional to

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$A$ drop of capacitance $1 \ \mu F$ is divided into $8$ identical drops. The capacitance of each small drop is .... $\mu F$.

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