A parallel plate capacitor mathrm{C} with plates of unit area and separation mathrm{d} is filled wit

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2. Electric Potential and Capacitance

normal

A parallel plate capacitor $\mathrm{C}$ with plates of unit area and separation $\mathrm{d}$ is filled with a liquid of dielectric constant $\mathrm{K}=2$. The level of liquid is $\frac{\mathrm{d}}{3}$ initially. Suppose the liquid level decreases at a constant speed $V,$ the time constant as a function of time $t$ is Figure: $Image$

$\frac{6 \varepsilon_0 \mathrm{R}}{5 \mathrm{~d}+3 \mathrm{Vt}}$

$\frac{(15 \mathrm{~d}+9 \mathrm{Vt}) \varepsilon_0 \mathrm{R}}{2 \mathrm{~d}^2-3 \mathrm{dVt}-9 \mathrm{~V}^2 \mathrm{t}^2}$

$\frac{6 \varepsilon_0 \mathrm{R}}{5 \mathrm{~d}-3 \mathrm{Vt}}$

$\frac{(15 \mathrm{~d}-9 \mathrm{Vt}) \varepsilon_0 \mathrm{R}}{2 \mathrm{~d}^2+3 \mathrm{dVt}-9 \mathrm{~V}^2 \mathrm{t}^2}$

(IIT-2008)

Solution

$ \mathrm{C}_{\text {equivulent }}=\frac{\frac{2 \varepsilon_0}{\frac{\mathrm{d}}{3}-\mathrm{vt}} \cdot \frac{\varepsilon_0}{\frac{2 \mathrm{~d}}{3}+\mathrm{vt}}}{\frac{2 \varepsilon_0}{\frac{\mathrm{d}}{3}-\mathrm{vt}}+\frac{\varepsilon_0}{\frac{2 \mathrm{~d}}{3}+\mathrm{vt}}} $

$ \therefore \tau=\mathrm{C}_{\text {equivalent }} \mathrm{R}$

Standard 12

Physics

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easy

Solution

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