Question

If a dielectric plate of thickness t is placed between the plates of parallel plate capacitor of plate distance d the capacitance becomes half of the original value. The dielectric constant of the plate will be​

Answer 1

Explanation:

Original value of parallel plate capacitance C

o

=

d

Aϵ

o

Let the dielectric constant of material be K.

Capacitance of capacitor with material C

1

=

d/2

KAϵ

o

Capacitance of capacitor without material C

2

=

d/2

Aϵ

o

Equivalent capacitance of series combination C

eq

=

C

1

+C

2

C

1

C

2

=

K+1

2K

d

Aϵ

o

=

K+1

2K

C

o

Given, C

eq

=

3

4

C

o

∴ We get

K+1

2K

=

3

4

⟹ K=2