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: $Image$
IIT 2008, Advanced
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$ \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}$
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