Question

The gap between the plates of a parallel plate capacitor of area A and distance between plates $d$, is filled with a dielectric whose permittivity varies linearly from $\epsilon_{1}$ at one plate to $\epsilon_{2}$ at the other. The capacitance of capacitor is :

• A. $\epsilon_{0} \left(\epsilon_{1}+\epsilon_{2}\right)A/d$
• B. $\epsilon_{0} \left(\epsilon_{1}+\epsilon_{2}\right)A/2d$
• C. $\epsilon_{0}A/\left[d ln\left(\epsilon_{2}/ \epsilon_{1}\right)\right]$
• D. $\epsilon_{0}\left(\epsilon_{2}-\epsilon_{1}\right) A /\left[ d \ell n \left(\in_{2} / \epsilon_{1}\right)\right]$

Answer 1

Answer: (D)

$\varepsilon=\left(\frac{\varepsilon_{2}-\varepsilon_{1}}{d}\right) x+\varepsilon_{1} $
$d C=\frac{\varepsilon_{0} \varepsilon A}{d x} $
$C_{\text {eq }}=\int dc$