A parallel plate capacitor has plates of area A separated by distance d between them. It is filled with a…

A parallel plate capacitor has plates of area A separated by distance $d$ between them. It is filled with a dielectric which has a dielectric constant that varies as $K\left(x\right)=K_0\left(1+\alpha x\right)$ where $x$ is the distance measured from one of the plates. If $\left(\alpha d\right)<<1,$ the total capacitance of the system is best given by the expression:

1. $\frac{A{K}_0{\epsilon }_0}{d}\left(1+\frac{\alpha d}{2}\right)$
2. $\frac{A{K}_0{\epsilon }_0}{d}\left[1+{\left(\frac{\alpha d}{2}\right)}^2\right]$
3. $\frac{A{K}_0{\epsilon }_0}{d}\left(1+\frac{{\alpha }^2{d}^2}{2}\right)$
4. $\frac{A{K}_0{\epsilon }_0}{d}\left(1+\alpha d\right)$

Solution

Asked in: JEE Main 2020 (07 Jan Shift 1)

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