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  4. A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2 The level of liquid is dl 3 initially. Suppose the liquid level decreases at a constant speed v , the time constant as a function of time t is

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Q. A parallel plate capacitor $C$ with plates of unit area and separation d is filled with a liquid of dielectric constant $K = 2$ The level of liquid is dl $3$ initially. Suppose the liquid level decreases at a constant speed $v$ , the time constant as a function of time $t$ isPhysics Question Image

IIT JEEIIT JEE 2008Electrostatic Potential and Capacitance

Solution:

After time $t$, thickeness of liquid will remain $\left(\frac {d}{3}-vt \right). $
Now, time constant as function of time
$\tau_c=CR= \frac {\varepsilon_0(1).R}{(d- \frac {d}{3}+vt)+ \frac {d/3-vt}{2}} $
(Applying $C= \frac {\varepsilon_0A}{d-t+ \frac {t}{k}}$)
$= \frac {6 \varepsilon_0R}{5d+3vt} $