Kapoor (mk9499) – homework12 – Turner – (60230)
1
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001
10.0 points
A capacitor network with airflled capacitors
as shown below.
29
.
7 V
70
.
2
μ
±
70
.
2
μ
±
70
.
2
μ
±
70
.
2
μ
±
b
a
c
d
When the top righthand capacitor is flled
with a material oF dielectric constant
κ
, the
charge on this capacitor is increases by a Fac
tor oF 1
.
43.
±ind the dielectric constant
κ
oF the mate
rial inserted into the top righthand capaci
tor.
Correct answer: 2
.
50877.
Explanation:
Let :
C
1
=
C
= 70
.
2
μ
±
,
C
2
=
C
= 70
.
2
μ
±
,
C
3
=
C
= 70
.
2
μ
±
,
C
4
=
C
= 70
.
2
μ
±
,
E
B
= 29
.
7 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 specifc values
are immaterial. ±urthermore, 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 fnal charges on
C
2
and
Q
′
Q
≡
α
=ratio oF fnal 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
.
43
.
Solving For
κ
, we have
κ
=
α
2

α
=
1
.
43
2

1
.
43
=
2
.
50877
.
002
10.0 points
Consider the two cases shown below. In Case
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View Full DocumentKapoor (mk9499) – 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
Flls 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.
C
′
12
C
12
=
κ
2
.
2.
C
′
12
C
12
= 1 +
κ .
3.
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 Fall '08
 Turner
 Physics, Electrostatics, Work, Electric charge, Kapoor, C12 C12 C12

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