Question

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 `d//3` initially. Suppose the liquid level decreases at a constant speed v, the time constant as a function of time t is-

A. `(6epsilon_0R)/(5d+3Vt)`
B. `((15d+9Vt)epsilon_0R)/(2d^2-3dVt - 9V^2t^2)`
C. `(6epsilon_0R)/(5d-3Vt)`
D. `((15d-9Vt)epsilon_0R)/(2d^2+3dVt-9V^2t^2)`

Answer 1

Correct Answer - A
a. `C_(eq) = ((2epsilon_0)/(d//3-Vt) xx (epsilon_0)/(2d//3+Vt))/((2epsilon_0)/(d//3-Vt)+(epsilon_0)/(2d//3+Vt)) = (6epsilon_0)/(5d + 3Vt)`
Now `tau = C_(eq) R = (6epsilon_0)/(5d+3Vt)`.