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

`(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))`

Text Solution

Verified by Experts

The correct Answer is:
A
A = 1, Separation = d
`k=2, t=(d)/(3)`
Let level of liquid at any instant of time .t. be x.
`V=-(dx)/(dt)impliesdx=-Vdt`
`impliesint_((d)/(3))^(x)dx=-Vint_(0)^(t)dtimpliesx-(d)/(3)=-Vt`
`impliesx=(d)/(3)-Vt`
Now, `(1)/(C_(eq))=(1)/(C_(1))+(1)/(C_(2))`
`implies C_(eq)=(C_(1)xxC_(2))/(C_(1)+C_(2))=(((Aepsilon_(0))/(d-x))xx((epsilon_(0)Ak)/(x)))/((Aepsilon_(0))/((d-x))+(epsilon_(0)Ak)/(x))`
`implies C_(eq)=(kAepsilon_(0))/(kd+x(1-k))`
`implies C_(eq)=(2epsilon_(0))/(2d+((d)/(3)-Vt)(1-2))=(2epsilon_(0))/(2d-(d)/(3)+Vt)`
`=(6epsilon_(0))/(5d+3Vt)`
Time constant `tau=RC_(eq)=(6epsilon_(0)R)/(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