Home
Class 12
PHYSICS
A parallel plate capacitor C with plates...

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

`(6epsiolon_(0)R)/(5d+3Vt)`

B

`((15d+9Vt)epsilon_(0)R)/(2d^(2)-3dVt-9V^(2)t^(3))`

C

`(6epsilon_(0)R)/(5d-3Vt)`

D

`((15d+9Vt)epsilon_(0)R)/(2d^(2)-3dVt-9V^(2)t^(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the fall in the lavel in time `t` be `x`. Then `x=vt`.
At that time the thickness of air in the capacitor
is `d_(1) = ((2d)/(3)+vt)` and the thickness of liquid
column is `d_(2) = ((d)/(3)-vt)`. At that time the equivalent capacitance is.
`(1)/(C) =(1)/(C_(1)) +(1)/(C_(2)) =(((2d)/(3)+vt))/(in_(0)A) +(((d)/(3)-vt))/(Kin_(0)A)`
put `A = 1` and `K = 2`, we get `C = (6in_(0))/(5d+3vt)`
`tau = RC = (6in_(0)C )/(5d +3vt)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the gap between the plates of a parallel plate capacitor is filled with medium of dielectric constant k=2 , then the field between them

A parallel plate capacitor with plate area A & plate separation d is filled with a dielectric material of dielectric constant given by K=K_(0)(1+alphax). . Calculate capacitance of system: (given alpha d ltlt 1) .

A parallel plate capacitor of plate area A and separation d is filled with two materials each of thickness d/2 and dielectric constants in_1 and in_2 respectively. The equivalent capacitance will be

A parallel plate capacitor carries a harge Q. If a dielectric slab with dielectric constant K=2 is dipped between the plates, then

Figure shown a parallel-plate capacitor having square plates of edge a and plate-separation d. The gap between the plates is filled with a dielectric of dielectric constant K which varies parallel to an edge as where K and a are constants and x is the distance from the left end. Calculate the capacitance.

Two conducting plates each having area A are kept at a separation d parallel to each other. The two plates are con- nected to a battery of emf V. The space between the plates is filled with a liquid of dielectric constant K. The height (x) of the liquid between the plates increases at a uniform rate from zero to d in a time interval t_(0) . (a) Write the capacitance of the system as a function of x as the liquid beings to fill the space between the plates. (b) write the current through the cell at time t