A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants K₁, K₂, K₃, K₄ arranged as shown in the figure. The effective dielectric constant K will be
(A) K = [(K₁ + K₃) (K₂ + K₄)] ÷ (K₁ + K₂ + K₃ + K₄)
(B) K = [(K₁ + K₂) (K₃ + K₄)] ÷ 2(K₁ + K₂ + K₃ + K₄)
(C) K = [(K₁ + K₂) (K₃ + K₄)] ÷ (K₁ + K₂ + K₃ + K₄)
(D) K = [(K₁ + K₄) (K₂ + K₃)] ÷ 2(K₁ + K₂ + K₃ + K₄)
(A) K = [(K₁ + K₃) (K₂ + K₄)] ÷ (K₁ + K₂ + K₃ + K₄)
(B) K = [(K₁ + K₂) (K₃ + K₄)] ÷ 2(K₁ + K₂ + K₃ + K₄)
(C) K = [(K₁ + K₂) (K₃ + K₄)] ÷ (K₁ + K₂ + K₃ + K₄)
(D) K = [(K₁ + K₄) (K₂ + K₃)] ÷ 2(K₁ + K₂ + K₃ + K₄)
Answers & Comments
Verified answer
Answer:
Correct option is D)
C
12
=
C
1
+C
2
C
1
C
2
=
(k
1
+K
2
)
⎣
⎢
⎢
⎡
d/2
∈
0
.
2
L
×L
⎦
⎥
⎥
⎤
d/2
k
1
∈
0
2
L
×L
.
d/2
k
2
[∈
0
2
L
×L]
C
12
=
k
1
+k
2
k
1
k
2
d
∈
0
L
2
in the same way we get , C
34
=
k
3
+k
4
k
3
k
4
d
∈
0
L
2
∴C
eq
=C
12
+C
34
=[
k
1
+k
2
k
1
k
2
+
k
3
+k
4
k
3
k
4
]
d
∈
0
L
2
Now if k
eq
−k,C
eq
=
d
k∈
0
L
2
on comparing equation (i) to equation (ii) , we get
k
eq
=
(k
1
+k
2
)(k
3
+k
4
)
k
1
k
2
(k
3
+k
4
)+k
3
K
4
(k
1
+k
2
)
This does not match with any of the options so probably they have assumed the wrong combination
C
13
=
d/2
k
1
∈
0
L
2
L
+k
3
∈
0
d/2
L.
2
L
=(k
1
+k
3
)
d
∈
0
L
2
C
24
=(k
2
+k
4
)
d
∈
0
L
2
C
eq
=
C
13
C
24
C
13
C
24
=
(k
1
+k
2
+k
3
+k
4
)
(K
1
+K
3
)(k
2
+k
4
)
d
∈
0
L
2
=
d
k∈
0
L
2
k=
(k
1
+k
2
+k
3
+k
4
)
(k
1
+k
3
)(k
2
+k
4
)
Step-by-step explanation:
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Answer:1
Step-by-step explanation: