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Question

(A) The capacitance $C$ of a spherical capacitor with inner radius $a$ and outer radius $b$ filled with a dielectric of constant $K$ is given by the f

Vedclass · Accepted Answer

$400 \ pF$

Vedclass · Answer

(A) The capacitance $C$ of a spherical capacitor with inner radius $a$ and outer radius $b$ filled with a dielectric of constant $K$ is given by the formula:$C = \frac{4 \pi \epsilon_0 K ab}{b - a}$Given:$a = 8 \ cm = 8 	imes 10^{-2} \ m$$b = 9 \ cm = 9 	imes 10^{-2} \ m$$K = 5$$\frac{1}{4 \pi \epsilon_0} = 9 	imes 10^9 \ N \cdot m^2/C^2$Substituting the values:$C = \frac{5 	imes 8 	imes 10^{-2} 	imes 9 	imes 10^{-2}}{(9 	imes 10^{-2} - 8 	imes 10^{-2}) 	imes 9 	imes 10^9}$$C = \frac{360 	imes 10^{-4}}{10^{-2} 	imes 9 	imes 10^9}$$C = \frac{360 	imes 10^{-4}}{9 	imes 10^7} = 40 	imes 10^{-11} \ F$$C = 400 	imes 10^{-12} \ F = 400 \ pF$Therefore,the correct option is $A$.

The radii of the inner and outer spheres of a spherical capacitor are $8 \ cm$ and $9 \ cm$ respectively. The outer sphere is earthed and the inner sphere is charged. If the space between the concentric spheres is filled with a liquid of dielectric constant $5$,the capacitance of the capacitor is:

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