Question

a parallel plate capacitor filled with three different dielectric constant k1,k2,k3 as shown in figure. The resultant capacitance is ------​

Answer 1

Let C

1

= Capacity of capacitor with dielectric K

1

C

2

= Capacity of capacitor with dielectric K

2

C

3

= Capacity of capacitor with dielectric K

3

C

1

=K

q

(

2

A

)

d

ε

o

×2

=

d

Aε

o

K

1

C

2

=

d/2

K

2

ε

o

(

2

A

)

=

d

K

2

ε

o

A

C

3

=

d/2

K

3

ε

o

(A)

=

d

2K

3

ε

o

A

C

1

and C

2

are in parallel

C

eq

−

d

ε

o

A

(K

1

+K

2

)

C

eq

andC

3

are in series

C

1

=

C

eq

1

+

C

3

1

K

A

ε

o

d

=

Aε

o

(K

1

+K

2

)

d

+

2Aε

o

K

3

d

K

1

=

K

1

+K

2

1

+

2K

3

1