mcconnell (kam2342) – homework12 – Turner – (60230)
1
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001
10.0 points
A capacitor network with air-filled capacitors
as shown below.
85 V
27
.
2
μ
F
27
.
2
μ
F
27
.
2
μ
F
27
.
2
μ
F
b
a
c
d
When the top right-hand capacitor is filled
with a material of dielectric constant
κ
, the
charge on this capacitor is increases by a fac-
tor of 1
.
48.
Find the dielectric constant
κ
of the mate-
rial inserted into the top right-hand capaci-
tor.
Correct answer: 2
.
84615.
Explanation:
Let :
C
1
=
C
= 27
.
2
μ
F
,
C
2
=
C
= 27
.
2
μ
F
,
C
3
=
C
= 27
.
2
μ
F
,
C
4
=
C
= 27
.
2
μ
F
,
E
B
= 85 V
,
and
Q
′
= 1
.
5
Q .
E
B
C
1
C
3
C
2
C
4
b
a
c
d
The capacitors
C
3
and
C
4
have nothing to
do with this problems. In addition, the capac-
itances are all equal and their specific values
are immaterial. Furthermore, the electric po-
tential of the battery is not required.
C
1
=
C
2
=
C
3
=
C
4
, where
Q
and
Q
′
are the initial and final charges on
C
2
and
Q
′
Q
≡
α
=ratio of final to initial charge on
C
2
.
We know the charges on
C
1
and
C
2
are the
same. Initially,
V
ab
=
V
1
+
V
2
=
Q
C
1
+
Q
C
2
=
Q
C
+
Q
C
= 2
Q
C
.
(1)
Therefore
Q
=
1
2
V
ab
C .
After the dielectric material is inserted in
C
2
,
the capacitance becomes
C
′
2
=
κ C
.
There-
fore,
V
ab
=
V
′
1
+
V
′
2
=
Q
′
C
1
+
Q
′
C
′
2
=
Q
′
C
+
Q
′
κ C
=
κ
+ 1
κ
Q
′
C
,
and using Eq. (1) and solving for
Q
′
, we have
2
Q
C
=
κ
+ 1
κ
Q
′
C
Q
′
=
κ
κ
+ 1
V
ab
C
=
κ
κ
+ 1
2
Q
Q
′
Q
≡
α
=
2
κ
κ
+ 1
= 1
.
48
.
Solving for
κ
, we have
κ
=
α
2
-
α
=
1
.
48
2
-
1
.
48
=
2
.
84615
.
002
10.0 points
Consider the two cases shown below. In Case
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mcconnell (kam2342) – homework12 – Turner – (60230)
2
One two identical capacitors are connected to
a battery with emf
V
.
In Case Two, a di-
electric slab with dielectric constant
κ
fills the
gap of capacitor
C
2
. Let
C
12
be the resultant
capacitance for Case One and
C
′
12
the resul-
tant capacitance for Case Two.
Case One
V
C
1
C
2
Case Two
V
C
1
C
′
2
κ
The ratio
C
′
12
C
12
of the resultant capacitances is
1.
None of these
2.
C
′
12
C
12
=
κ
2
.
3.
C
′
12
C
12
= 1 +
κ .
4.
C
′
12
C
12
= 2
κ .
5.
C
′
12
C
12
=
1 +
κ
2
κ
.
6.
C
′
12
C
12
=
2
1 +
κ
.
7.
C
′
12
C
12
=
2
κ
1 +
κ
.
correct
8.
C
′
12
C
12
=
κ .
9.
C
′
12
C
12
=
1 +
κ
2
.
10.
C
′
12
C
12
=
1
κ
.

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- Spring '10
- Turner
- Electrostatics, Electric charge, McConnell, μF, c12
-
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