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

Answer

A

Explanation

After time ,t thickness of liquid eill remain `(d-/3-vt)`
Now time constant as function of time `tau_e=CR(epsilon_0(1)R)/((d-d/3+vt)+(d//3-vt)/(2))("applying " c=(epsilon_0A)/(d-t+t/K))=(6epsilon_0R)/(5d+3vt)`