benavides (jjb2356) – homework 18 – Turner – (59130)
1
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beFore answering.
001
10.0 points
An airflled cylindrical capacitor has a capac
itance oF 8 p± and is 4 cm in length.
The
coulomb
constant
is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
IF the radius oF the outside conductor is
2
.
4 cm, what is the required radius oF the
inner conductor?
Correct answer: 1
.
81722 cm.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
ℓ
= 4 cm = 0
.
04 m
,
b
= 2
.
4 cm
,
and
C
= 8 p± = 8
×
10
−
12
±
.
The capacitance oF a cylindrical capacitor
is given by
C
=
ℓ
2
k
e
ln
b
a
where
a
and
b
are the inner and outer radii,
respectively. Solving For
a
, we obtain
a
=
b e
−
ℓ/
(2
k
e
C
)
= (2
.
4 cm)
e
−
(0
.
04 m)
/
[2
k
e
(8
×
10

12
F)]
=
1
.
81722 cm
.
002
10.0 points
IF the plate separation oF an
isolated
parallel
plate capacitor is doubled,
1.
the charge density on each plate is dou
bled.
2.
None oF these
correct
3.
the charge on the each plate is halved.
4.
the electric feld is doubled.
5.
the potential di²erence is halved.
Explanation:
Q
and
A
are constant, so
E
=
Q
A ǫ
0
= constant
so that
E
′
=
2
Q
2
A ǫ
0
and
V
′
=
Q
′
C
′
=
2
Q
C
= 2
Q
C
= 2
V
′
.
003
(part 1 oF 2) 10.0 points
Consider the system oF capacitors connected
to a battery as shown below.
E
B
3
μ
±
3
μ
±
3
μ
±
3
μ
±
3
μ
±
3
μ
±
±ind the equivalent capacitance oF the cir
cuit.
1.
C
=
2
3
μ
±
2.
C
= 1
μ
±
3.
C
= 2
μ
±
correct
4.
C
=
3
2
μ
±
5.
C
=
4
3
μ
±
6.
C
= 3
μ
±
7.
C
= 4
μ
±
Explanation:
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B
C
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 Spring '08
 Turner
 Work, Electric charge, 0.04 M, Ceq, 0.82 cm, 1.64 cm

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