Question

What is the capacitance if an insulator with dielectric constant κ and thickness d/2 is slipped between the electrodes? assume plate separation is unchanged?

Answer 1

may this answer help you

Answer 2

Solution:

let, A be the are of cross section of the electrodes.

C be the capacitance.

E be the electric field between electrodes.

sigma be the charge per unit area.

∉ be the permittivity of free space

and given in the question that

K is the dielectric constant of insulator.

d/2 is slipped between the electrodes.

now, electric filed between electrodes.

E = sigma /2∉+ sigma /2∉

E = sigma /∉    ------1

we know,  

E = V /(d/2)

V = E d/2

V = sigma /∉*d/2       ( from equation 1)

V = sigma d/2∉    ------2

again we know

C = Q/V

C = sigma A/ (sigma d/2∉ )      (from equation 2 and Q = sigma A)

C =   2∉A/d

for insulator with dielectric constant K.

C =   2K∉A/d