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Air filled capacitor of capacitance $2 μ F$ is filled with the dielectric material of dielectric constant $K_{1} = 4, K_{2} = 4$ and $K_{3} = 6$ as shown in the figure. The new capacitance of the capacitor is

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$50 μ F$

$2 μ F$

$20 μ F$

$10 μ F$

answer is D.

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Detailed Solution

$c_{e q} = \frac{k_{3} \in_{0} A / 2}{d / 2} + \frac{\in_{0} A}{\frac{d}{2 k_{1}} + \frac{d}{2 k_{2}}} = 10 μ F w h e r e \frac{\in_{0} A}{d} = 2 μ F$

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