293
Chapter 24
Capacitance
Conceptual Problems
1
•
If the voltage across a parallel-plate capacitor is doubled, its
capacitance (
a
) doubles (
b
) drops by half (
c
) remains the same.
Determine the Concept
The capacitance of a parallel-plate 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 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 parallel-plate
capacitor is related to the capacitance of the capacitor and the potential difference
across the capacitor by
.
2
1
QV
U
=
Because the capacitor is isolated,
Q
is constant
and
U
is directly proportional to
V
. Because, for a parallel-plate capacitor,
Ed
V
=
and
E
is constant,
U
is directly proportional to
d
. Hence doubling the
distance between the plates doubles the stored energy and the ratio of the initial
stored energy to the final stored energy is
2
.
5
•
[SSM]
A parallel-plate 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?

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