Chapter 24
Capacitance
Conceptual Problems
1
•
If the voltage across a parallelplate capacitor is doubled, its
capacitance (
a
) doubles (
b
) drops by half (
c
) remains the same.
Determine the Concept
The capacitance of a parallelplate capacitor is a
function of the surface area of its plates, the separation of these plates, and the
electrical properties of the matter between them. The capacitance is, therefore,
independent of the voltage across the capacitor.
)
(
c
is correct.
2
•
If the charge on an isolated spherical conductor is doubled, its self
capacitance (
a
) doubles (
b
) drops by half (
c
) remains the same.
Determine the Concept
The capacitance of an isolated spherical capacitor is
given by
R
C
0
4
∈
π
=
, where
R
is its radius. The capacitance is, therefore,
independent of the charge of the capacitor.
)
(
c
is correct.
3
•
True or false: The electrostatic energy density is uniformly distributed
in the region between the conductors of a cylindrical capacitor.
Determine the Concept
False.
The electrostatic energy density is not uniformly
distributed because the magnitude of the electric field strength is not uniformly
distributed,
4
•
If the distance between the plates of a charged and isolated parallel
plate capacitor is doubled, what is the ratio of the final stored energy to the initial
stored energy?
Determine the Concept
The energy stored in the electric field of a parallelplate
capacitor is related to the potential difference across the capacitor by
.
2
1
QV
U
=
If
Q
is constant,
U
is directly proportional to
V
and doubling
V
doubles
U
. Hence the
ratio of the initial stored energy to the final stored energy is
2
.
5
•
[SSM]
A parallelplate capacitor is connected to a battery. The space
between the two plates is empty. If the separation between the capacitor plates is
tripled while the capacitor remains connected to the battery, what is the ratio of
the final stored energy to the initial stored energy?
Determine the Concept
The energy stored in a capacitor is given by
QV
U
2
1
=
and the capacitance of a parallelplate capacitor by
.
0
d
A
C
=
We can
2287
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combine these relationships, using the definition of capacitance and the condition
that the potential difference across the capacitor is constant, to express
U
as a
function of
d.
Express the energy stored in the
capacitor:
QV
U
2
1
=
(1)
Use the definition of capacitance to
express the charge of the capacitor:
CV
Q
=
Express the capacitance of a
parallelplate capacitor in terms of
the separation
d
of its plates:
d
A
C
0
∈
=
where
A
is the area of one plate.
Substituting for
Q
and
C
in equation
(1) yields:
d
AV
U
2
2
0
=
Because
d
U
1
∝
, tripling the separation of the plates will reduce the energy stored
in the capacitor to onethird its previous value. Hence the ratio of the final stored
energy to the initial stored energy is
3
/
1
.
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 Summer '08
 Wei
 Capacitance

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