A parallel plate capacitor having square plate of area $a$ and separation between plates $d$ is completely…

A parallel plate capacitor having square plate of area $a$ and separation between plates $d$ is completely filled with a dielectric of dielectric constant $k$. Capacitor is connected with a battery of potential difference $V$. Now dielectric is pulled with constant speed $u$. Find the initial value of current.

1. $\frac{\varepsilon_{0} \sqrt{a} u}{2 d}(k-1)$ V
2. $\frac{\varepsilon_{0} \sqrt{a} u}{d}(k-1)$ V
3. zero V
4. $\frac{2 \varepsilon_{0} \sqrt{a} u}{d}(k-1)$ V

Solution

\(\begin{aligned} & C=\frac{k \sqrt{a}(\sqrt{a}-x) \varepsilon_0}{d^2}+\frac{\sqrt{a x} \varepsilon_0}{d} \\ & \mathrm{Q}=\mathrm{CV}=\frac{\mathrm{V}_{\sqrt{ } \varepsilon_0}}{\mathrm{~d}} \mathrm{k}_{\sqrt{\mathrm{a}}}-\mathrm{x}+\mathrm{x} \\ & \mathrm{I}=\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{V} \frac{\mathrm{dC}}{\mathrm{dt}}=\frac{\mathrm{V} \sqrt{a} \varepsilon_0}{\mathrm{~d}}-\mathrm{k}+1 \frac{\mathrm{dx}}{\mathrm{dt}} \\ & \mathrm{I}=\frac{\mathrm{v}_{\sqrt{ } \mathrm{a} u \varepsilon_0}}{\mathrm{~d}} \mathrm{k}-1 \quad \text { (constant) } \end{aligned}\) ,

Asked in: JEE Mains - Capacitance - Test 2

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