A dielectric is completely filled between the space of a parallel plate capacitor. The separation between plates of capacitor is ‘ $d$ ’ and dielectric constant is given by $k = k_{0} e^{λ x}$ where ' $k_{0}$ ' and ' $λ$ ' are positive constants and $x$ is distance from one plate of capacitor. If distance between plate (d) increases slowly then graph between capacitance of capacitor and distance between plate is given by

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Detailed Solution

$d C = \frac{k ε_{0} A}{d x}$

$\frac{1}{C_{e q v}} = \int \frac{1}{d C}$

$= \int \frac{1}{k ε_{0} A} d x = \int_{0}^{d} \frac{1}{k_{0} e^{λ x} ε_{0} A} d x,$

$C_{e q} = \frac{λ k_{0} ε_{0} A}{1 - e^{- λ d}}$

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