A parallel-plate capacitor of area A, plate
separation d and capacitance C is filled with four
dielectric materials having dielectric constants ka,
k. Ky and , as shown in the figure below. If a
single dielectric material is to be used to have the
same capacitance C in this capacitor, then its
dielectric constant k is given by
[NEET (Phase-2)-2016]
A/3 A/3 A/3
d/2
А
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Answer:
Answer
Correct option is
B
K
1
=
K
1
+K
2
1
+
2K
3
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
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