The area of the plates of a parallel plate capacitor is $A$ and the gap between them is $d$. The gap is filled with a non-homogeneous dielectric whose dielectric constant varies with the distance $‘y’$ from one plate as : $K = \lambda \ sec(\pi y/2d)$, where $\lambda $ is a dimensionless constant. The capacitance of this capacitor is

  • A

    $\pi \varepsilon_0\lambda A / 2d$

  • B

    $\pi \varepsilon_0\lambda A /d$

  • C

    $2\pi \varepsilon_0\lambda A /d$

  • D

    none

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