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-

Options

A. `(6 in_(0)R)/(5d+3vt)`
B. `((15d+9vt)in_(0)R)/(2d^(2)-3dvi-9v^(2)t^(2))`
C. `(6 in_(0)R)/(5d-3vt)`
D. `((15d-9vt)epsilon_(0)R)/(2d^(2)+3dvt-9v^(2)t^(2))`

Answer

A

Explanation

`tau=RC^(C=(epsilon_(0)A)/((d-x)+(x)/(k))k=2 x=(d)/(3)-vt)`.