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Chapter 31. Current and Resistance
Chapter 31. Current and Resistance
Lights, sound systems,
microwave ovens, and
computers are all connected
by wires to a battery or an
electrical outlet. How and
why does electric current
flow through a wire?
Chapter Goal: To learn
how and why charge moves
through a conductor as what
we call a current.
Topics:
• The Electron Current
• Creating a Current
• Current and Current Density
• Conductivity and Resistivity
• Resistance and Ohm’s Law
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What quantity is represented by the
symbol J ?
Chapter 31. Reading Quizzes
A. Resistivity
B. Conductivity
C. Current density
D. Complex impedance
E. Johnston’s constant
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What quantity is represented by the
symbol J ?
The electron drift speed in a typical
current-carrying wire is
A. Resistivity
B. Conductivity
C. Current density
D. Complex impedance
E. Johnston’s constant
A.
B.
C.
D.
E.
extremely slow (≈10–4 m/s).
moderate (≈ 1 m/s).
very fast (≈104 m/s).
Could be any of A, B, or C.
No numerical values were provided.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
All other things being equal, current will
be larger in a wire that has a larger value
of
The electron drift speed in a typical
current-carrying wire is
A.
B.
C.
D.
E.
extremely slow (≈10–4 m/s).
moderate (≈ 1 m/s).
very fast (≈104 m/s).
Could be any of A, B, or C.
No numerical values were provided.
A.
B.
C.
D.
E.
conductivity.
resistivity.
the coefficient of current.
net charge.
potential.
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All other things being equal, current will
be larger in a wire that has a larger value
of
A.
B.
C.
D.
E.
The equation I = ∆V/R is called
A. Ampère’s law.
B.Faraday’s law.
C. Ohm’s law.
D. Weber’s law.
conductivity.
resistivity.
the coefficient of current.
net charge.
potential.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
The Electron Current
The electron current I is
the number of electrons
per second that pass
through a cross section
of a wire. The units of
electron current are s-1.
The equation I = ∆V/R is called
A. Ampère’s law.
B. Farady’s law.
C. Ohm’s law.
D. Weber’s law.
N e = i∆ t
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The Electric Current
The Electron Current
i = nAv d
Typical Vd is about 10-4 m/s.
N e = nV = nA∆x = nAvd ∆t
N e = i∆t = nAvd ∆t
i = nAv d
The drift speed vd is the net speed with which the
electrons move, not the speed at which any one
electron is bouncing around.
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The Law of Conservation of Current: the electron
current is the same at all points in a currentcarrying wire.
How long does it take to discharge
a capacitor?
0.2 [m] /10-4 [m/s] = 2000 s?
The electron current at A is exactly equal to the electron current at B.
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How long does it take to discharge
a capacitor?
Establishing the Electric Field in a
Wire
N e = i∆t = nAv d ∆t
∆t =
∆t =
Ne
nAv d
1011
= 9 ⋅10 −10 s
8.5 ⋅10 [m ] ⋅ 3.14 ⋅ 4 ⋅10 −6 [m 2 ] ⋅10 − 4 [m / s]
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−3
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A Model of Conduction
A Model of Conduction
ax =
v x = vix + a x ∆t = vix +
eE
∆t
m
F eE
=
m m
The energy transfer is
the “friction” that raises
the temperature of the
wire.
v x = vix + a x ∆t = vix +
eE
∆t
m
eE
vd = v = vix + τ
m
vd =
eE
τ
m
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Current and Current Density
A Model of Conduction
eE
τ
vd =
m
I ≡(
i = nAv d
neτAE
i=
m
r
dQ
, in the direction of E )
dt
1 Ampere = 1 A = 1 coulomb per second = 1 C/s
I=
The electron current is
directly proportional to the
electric field strength.
Q eN e
=
= ei
∆t
∆t
The direction of the current I in a metal is opposite
the direction of motion of the electrons.
The current direction in a wire is from the positive
terminal of a battery to the negative terminal.
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Conservation of Current
∑I
in
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The Current Density in a Wire
= ∑ I out
I = ei = nevd A
J = current density =
I
= nev d
A
I = JA
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Conductivity and Resistivity
Conductivity and Resistivity
J = σE
eτE
ne 2τ
J = nev d = ne (
)=
E
m
m
ne 2τ
σ = conductivi ty =
m
1
m
ρ = resistivit y = = 2
σ ne τ
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Resistance and Ohm’s Law
Ohm’s Law
The resistance of a long, thin conductor of length L and
cross=sectional area A is
• Ohm’s law is limited to those materials whose
resistance R remains constant—or very nearly so—during
use.
• The materials to which Ohm’s law applies are
called ohmic.
The SI unit of resistance is the ohm. 1 ohm = 1 Ω = 1 V/A.
The current through a conductor is determined by the
potential difference ∆V along its length:
• The current through an ohmic material is
directly proportional to the potential difference. Doubling
the potential difference doubles the current.
• Metal and other conductors are ohmic devices.
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Chapter 31. Summary Slides
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General Principles
General Principles
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General Principles
Important Concepts
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Important Concepts
Important Concepts
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Applications
Chapter 31. Questions
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These four wires are made of the same metal. Rank
in order, from largest to smallest, the electron
currents ia to id.
A.
B.
C.
D.
E.
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These four wires are made of the same metal. Rank
in order, from largest to smallest, the electron
currents ia to id.
id > ia > ib > ic
ib = id > ia = ic
ic > ib > ia > id
ic > ia = ib > id
ib = ic > ia = id
A.
B.
C.
D.
E.
id > ia > ib > ic
ib = id > ia = ic
ic > ib > ia > id
ic > ia = ib > id
ib = ic > ia = id
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Why does the light in a room come on
instantly when you flip a switch several meters
away?
Why does the light in a room come on
instantly when you flip a switch several meters
away?
A. Electrons travel at the speed of light through the
wire.
B. Because the wire between the switch and the bulb
is already full of electrons, a flow of electrons
from the switch into the wire immediately causes
electrons to flow from the other end of the wire
into the lightbulb.
C. The switch sends a radio signal which is received
by a receiver in the light which tells it to turn on.
D. Optical fibers connect the switch with the light, so
the signal travels from switch to the light at the
speed of light in an optical fiber.
A. Electrons travel at the speed of light through the
wire.
B. Because the wire between the switch and the
bulb is already full of electrons, a flow of
electrons from the switch into the wire
immediately causes electrons to flow from the
other end of the wire into the lightbulb.
C. The switch sends a radio signal which is received
by a receiver in the light which tells it to turn on.
D. Optical fibers connect the switch with the light, so
the signal travels from switch to the light at the
speed of light in an optical fiber.
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What are the
magnitude and the
direction of the
current in the fifth
wire?
What are the
magnitude and the
direction of the
current in the fifth
wire?
A. 15 A into the junction
B. 15 A out of the junction
C. 1 A into the junction
D. 1 A out of the junction
E. Not enough data to determine
A. 15 A into the junction
B. 15 A out of the junction
C. 1 A into the junction
D. 1 A out of the junction
E. Not enough data to determine
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