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

Q: 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 $E=\frac{\sigma}{K \in_{o}}$ $\frac{d v}{d y}=\frac{\sigma}{K \in_{o}}$ $\int_{0}^{v} d v=\frac{\sigma}{\lambda \in_{o}} \int_{0}^{d} \cos \left(\frac{\pi y}{2 d}\right) d y V$ $=\frac{\sigma}{\lambda \in_{o}} \times \frac{2 d}{\pi}\left[\sin \frac{\pi y}{2 d}\right]_{0}^{d}$ $=\frac{\sigma}{\lambda \in_{o}} \times \frac{2 d}{\pi}$ $C=\frac{Q}{V}=\frac{A \lambda \in_{o} \pi}{2 d}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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

Advanced

STD 11 Science
NEET
STD 12 - 2. Electric potential and capacitance
Physics

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