Chapter 31. Current and Resistance. What quantity is represented by the symbol J?

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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.

1 Topics:

• The Electron Current

• Creating a Current

• Current and Current Density

Chapter 31. Chapter 31. Current and Resistance

Current and Resistance

• Conductivity and Resistivity

• Resistance and Ohm’s Law

2 Chapter 31. Reading Quizzes

Chapter 31. Reading Quizzes

What quantity is represented by the

symbol

J

_?

A. Resistivity

B. Conductivity

C. Current density

D. Complex impedance

E. Johnston’s constant

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A. Resistivity

What quantity is represented by the

symbol

J

_?

A. Resistivity

B. Conductivity

C. Current density

D. Complex impedance

E. Johnston’s constant

5 The electron drift speed in a typical

current-carrying wire is

A. extremely slow (

_≈

10 –4

_m/s).

A. extremely slow (

_≈

10 m/s).

B. moderate (

_≈

1 m/s).

C. very fast (

_≈

10

4 _m/s).

D. Could be any of A, B, or C.

E. No numerical values were provided.

6 A. extremely slow (

_≈

10 –4

_m/s).

The electron drift speed in a typical

current-carrying wire is

A. extremely slow (

_≈

10 m/s).

B. moderate (

_≈

1 m/s).

C. very fast (

_≈

10

4 _m/s).

D. Could be any of A, B, or C.

E. No numerical values were provided.

7 All other things being equal, current will

be larger in a wire that has a larger value

of

A. conductivity.

B. resistivity.

C. the coefficient of current.

D. net charge.

E. potential.

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All other things being equal, current will

be larger in a wire that has a larger value

of

A. conductivity.

B. resistivity.

C. the coefficient of current.

D. net charge.

E. potential.

9 The equation

I =

_∆

V/R

is called

A. Ampère’s law.

B.Faraday’s law.

C. Ohm’s law.

D. Weber’s law.

10 The equation

I =

_∆

V/R

_{is called}

A. Ampère’s law.

B. Farady’s law.

C. Ohm’s law.

D. Weber’s law.

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

_.

electron current are s .

t

i

(4)

The Electric Current

t

nAv

x

nA

nV

N

=

∆

=

∆

13 t

nAv

x

nA

nV

N

_e

=

∆

=

_d

∆

d

nAv

i

=

The drift speed v

_d

is the net speed with which the

electrons move, not the speed at which any one

electron is bouncing around.

t

nAv

t

i

N

_e

=

∆

=

_d

∆

The Electron Current

d

nAv

i

=

Typical V is about 10

-4

_m/s.

14 Typical V

d

is about 10

-4

m/s.

The Law of Conservation of Current: the electron

current is the same at all points in a

current-carrying wire.

15 The electron current at A is exactly equal to the electron current at B.

How long does it take to discharge

a capacitor?

0.2 [m] /10

-4

_{[m/s] = 2000 s?}

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How long does it take to discharge

a capacitor?

t

nAv

t

i

N

_e

=

∆

=

_d

∆

e

nAv

N

t

=

∆

17 s

s

m

t

10 4 2 6 3 28 11

10

9 ]

/

[

10 ]

[

10

4

14 .

3 ]

[

10

5 .

8

10

− − − −

=

⋅

=

∆

d

nAv

t

=

∆

Establishing the Electric Field in a

Wire

18 A Model of Conduction

m

eE

m

F

a

_x

=

t

m

eE

v

t

a

v

_x

=

_ix

+

_x

∆

=

_ix

+

∆

The energy transfer is

the “friction” that raises

the temperature of the

wire.

A Model of Conduction

t

m

eE

v

t

a

v

_x

=

_ix

+

_x

∆

=

_ix

+

∆

τ

m

eE

v

_d

=

_ix

+

_m

τ

eE

v

_d

=

(6)

A Model of Conduction

τ

m

eE

v

_d

=

d

nAv

i

=

21 m

AE

ne

i

=

τ

The electron current is

directly proportional to the

electric field strength.

Current and Current Density

)

,

(

in

the

direction

of

E

dt

dQ

I

r

≡

1 Ampere = 1 A = 1 coulomb per second = 1 C/s

22 ei

t

eN

t

Q

I

e

₌

∆

=

∆

=

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.

Conservation of Current

∑

I

_in

=

I

_out

23 The Current Density in a Wire

A

nev

ei

I

=

_d

d

nev

A

I

density

current

J

=

24 d

nev

A

density

current

J

=

JA

I

=

(7)

Conductivity and Resistivity

ne

E

e

τ

2 τ

=

E

J

=

σ

25 E

m

ne

m

E

e

ne

nev

J

=

_d

=

(

τ

)

=

τ

m

ne

ty

conductivi

τ

σ

2 =

=

τ

σ

ρ

1 ₂

ne

m

y

resistivit

=

Conductivity and Resistivity

26 Resistance and Ohm’s Law

The resistance of a long, thin conductor of length

L

and

cross=sectional area

A

is

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:

Ohm’s Law

• 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

.

called

ohmic

.

• The current through an ohmic material is

directly proportional to the potential difference. Doubling

the potential difference doubles the current.

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29 Chapter 31. Summary Slides

Chapter 31. Summary Slides

30 General Principles

General Principles

31 General Principles

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General Principles

33 Important Concepts

34

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Applications

37 Chapter 31. Questions

Chapter 31. Questions

38 These four wires are made of the same metal. Rank

in order, from largest to smallest, the electron

currents

i

_a

to

i

_d

.

A. i

_d

>

i

_a

>

i

_b

>

i

_c

B. i

_b

=

i

_d

>

i

_a

=

i

_c

C. i

_c

>

i

_b

>

i

_a

>

i

_d

D. i

_c

>

i

_a

=

i

_b

>

i

_d

E. i

_b

=

i

_c

>

i

_a

=

i

_d

39 These four wires are made of the same metal. Rank

in order, from largest to smallest, the electron

currents

i

_a

to

i

_d

.

A. i

_d

>

i

_a

>

i

_b

>

i

_c

B. i

_b

=

i

_d

>

i

_a

=

i

_c

C. i

_c

>

i

_b

>

i

_a

>

i

_d

D. i

_c

>

i

_a

=

i

_b

>

i

_d

E. i

_b

=

i

_c

>

i

_a

=

i

_d

40

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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.

41 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.

42 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

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