A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region
between the plates is filled with N dielectric layers, parallel to its plates, each with thickness ???? = d
N
The dielectric constant of the mth layer is Km = K ( 1+ m/N). For a very large N (>10³) the capacitance C is
????(K????₀A/d In2). The value of ???? will be ___________.
[∊₀ is the permittivity of free space]
Answers
Answered by
0
Answer:
m
x
=
N
D
d(
C
1
) =
K
m
ε
0
A
dx
=
Kε
0
A(1+
N
m
)
dx
=
Kε
0
A(1+
D
x
)
dx
C
eq
1
=∫d(
C
1
)=∫
0
D
Kε
0
A(D+x)
Ddx
C
eq
1
=
Kε
0
A
D
ln2
C
eq
=
Dln2
Kε
0
A
.
Therefore α=1.
Explanation:
m
x
=
N
D
d(
C
1
) =
K
m
ε
0
A
dx
=
Kε
0
A(1+
N
m
)
dx
=
Kε
0
A(1+
D
x
)
dx
C
eq
1
=∫d(
C
1
)=∫
0
D
Kε
0
A(D+x)
Ddx
C
eq
1
=
Kε
0
A
D
ln2
C
eq
=
Dln2
Kε
0
A
.
Therefore α=1.
Answered by
0
Answer:
m = thcickness of mth layer of dx
x = distance
δ = d / N = x / m
Km = K (1 + m /N )
Km = K (1 + x /d )
for mth layer we can write ,
dC = KmAε₀ / dx
1 / Ceq = ∫dx / KmAε₀∫ dx / (1 + x/d)
1/Ceq = d / KAε₀[ ln (1 + x /d)]
1/Ceq = KAε₀/dln2 ⇒ α = 1
Attachments:
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