Question

1
62. A parallel plate capacitor with air between the
plates has a capacitance of 9pf. The separation
between its plates is d'. The space between the plates
is now filled with two dielectrics. One of the dielectrics
has dielectric constant k = 3 and thickness d/3 while
the other one has dielectric constant k, = 6 and
thickness 2d/3. Capacitance of the capacitor is now
1) 1.8pF 2) 45pF 3) 40.5pF 4) 20.25pF
​

Answer 1

Answer:

The air filled capacitance , C=

d

Aϵ

0

=9pF

According to question there are two capacitor with capacitances C

1

and C

2

. and they are in series .

Here, C

1

= (d/3)Ak 1

ϵ 0

=9 d

Aϵ

0

=9C as k 1

=3 and C 2

= (2d/3)Ak 2

ϵ

0

=9 dAϵ 0

=9C as k 2

=6

The equivalent capacitance, C

eq

= C 1 +C 2

C 1 C 2

= 9C+9C

(9C)(9C)

= 29

C=(9/2)9=40.5pF