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: $Image$
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]
- A
$\frac{6 \varepsilon_0 \mathrm{R}}{5 \mathrm{~d}+3 \mathrm{Vt}}$
- B
$\frac{(15 \mathrm{~d}+9 \mathrm{Vt}) \varepsilon_0 \mathrm{R}}{2 \mathrm{~d}^2-3 \mathrm{dVt}-9 \mathrm{~V}^2 \mathrm{t}^2}$
- C
$\frac{6 \varepsilon_0 \mathrm{R}}{5 \mathrm{~d}-3 \mathrm{Vt}}$
- D
$\frac{(15 \mathrm{~d}-9 \mathrm{Vt}) \varepsilon_0 \mathrm{R}}{2 \mathrm{~d}^2+3 \mathrm{dVt}-9 \mathrm{~V}^2 \mathrm{t}^2}$
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