27
Current and Resistance
CHAPTER OUTLINE
27.1
Electric Current
27.2
Resistance
27.3
A Model for Electrical Conduction
27.4
Resistance and Temperature
27.5
Superconductors
27.6
Electrical Power
101
ANSWERS TO QUESTIONS
Q27.1
Voltage is a measure of potential difference, not of
current. “Surge” implies a ﬂ
ow—and only charge, in
coulombs, can ﬂ
ow through a system. It would also be
correct to say that the victim carried a certain current, in
amperes.
Q27.2
Geometry and resistivity. In turn, the resistivity of the
material depends on the temperature.
*Q27.3
(i)
We require
r
L
/
A
A
=
3
r
/
A
B
.
Then
A
A
/
A
B
=
1/3,
answer (f ).
(ii)
π
r
A
2
/
π
r
B
2
= 1/3 gives
r
A
/
r
B
= 1/
3, answer (e).
*Q27.4
Originally,
R
A
=
ρ
l
. Finally,
R
AA
R
f
==
=
ρρ
(/)
.
ll
3
39
9
Answer (b).
Q27.5
The conductor does not follow Ohm’s law, and must have a resistivity that is currentdependent,
or more likely temperaturedependent.
Q27.6
The amplitude of atomic vibrations increases with temperature. Atoms can then scatter electrons
more ef±
ciently.
Q27.7
(i) The current density increases, so the drift speed must increase. Answer (a).
(ii) Answer (a).
Q27.8
The resistance of copper
increases
with temperature, while the resistance of silicon
decreases
with increasing temperature. The conduction electrons are scattered more by vibrating atoms
when copper heats up. Silicon’s charge carrier density increases as temperature increases and
more atomic electrons are promoted to become conduction electrons.
*Q27.9
In a normal metal, suppose that we could proceed to a limit of zero resistance by lengthening the
average time between collisions. The classical model of conduction then suggests that a constant
applied voltage would cause constant acceleration of the free electrons. The drift speed and the
current would increase steadily in time.
It is not the situation envisioned in the question, but we can actually switch to zero resistance
by substituting a superconducting wire for the normal metal. In this case, the drift velocity of
electrons is established by vibrations of atoms in the crystal lattice; the maximum current is
limited; and it becomes impossible to establish a potential difference across the superconductor.
Q27.10
Because there are so many electrons in a conductor
(approximately 10
28
electrons/m
3
) the
average velocity of charges is very slow. When you connect a wire to a potential difference, you
establish an electric ±
eld everywhere in the wire nearly instantaneously, to make electrons start
drifting everywhere all at once.
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Chapter 27
*Q27.11
Action (a) makes the current three times larger.
(b) causes no change in current.
(c) corresponds to a current
3 times larger.
(d)
R
is 1/4 as large, so current is 4 times larger.
(e)
R
is 2 times larger, so current is half as large.
(f)
R
increases by a small percentage as current has a small decrease.
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 Spring '11
 williams,frank
 Current, Resistance, Energy, Power, Orders of magnitude, ρ ρ, ∆V

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