nguyen (jmn727) – homework 18 – Turner – (59070)
1
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001
10.0 points
An airfilled cylindrical capacitor has a capac
itance of 15 pF and is 2
.
8 cm in length.
The
coulomb
constant
is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
If the radius of the outside conductor is
1
.
5 cm, what is the required radius of the
inner conductor?
Correct answer: 1
.
35204 cm.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
ℓ
= 2
.
8 cm = 0
.
028 m
,
b
= 1
.
5 cm
,
and
C
= 15 pF = 1
.
5
×
10
−
11
F
.
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
)
= (1
.
5 cm)
e
−
(0
.
028 m)
/
[2
k
e
(1
.
5
×
10

11
F)]
=
1
.
35204 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.
the charge on the each plate is halved.
3.
the electric field is doubled.
4.
None of these
correct
5.
the potential difference 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
F
3
μ
F
3
μ
F
3
μ
F
3
μ
F
3
μ
F
Find the equivalent capacitance of the cir
cuit.
1.
C
= 4
μ
F
2.
C
= 3
μ
F
3.
C
=
3
2
μ
F
4.
C
= 2
μ
F
correct
5.
C
=
4
3
μ
F
6.
C
=
2
3
μ
F
7.
C
= 1
μ
F
Explanation:
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nguyen (jmn727) – homework 18 – Turner – (59070)
2
E
B
C
1
C
2
C
3
C
4
C
5
C
6
c
a
b
c
d
Let :
C
1
=
C
= 3
μ
F
,
C
2
=
C
= 3
μ
F
,
C
3
=
C
= 3
μ
F
,
C
4
=
C
= 3
μ
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 Spring '08
 Turner
 Capacitance, Work, Potential difference, Electric charge, Dielectric, C1 C2, C1 C2 C3

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