p212c26: 1

Charge carrier motion in a conductor in two parts

Constant Acceleration

Randomizing Collisions (momentum, energy)

=>Resulting Motion

Average motion = Drift Velocity = vd ~10-4 m/s

Typical speeds ~ 106 m/s

Chapter 26: Current, Resistance and Electromotive Force

F ma qE

p212c26: 2

Current Flow = net motion of charges = Charge carriers

charge qspeed vd

I = Current = rate at which charge passes the area

vd

IdQ

dt

C

SAmp A units:

1

11 1

I

vdI

Negative charge carriers move in opposite direction of conventional current.

p212c26: 3

Connection with microscopic picture:

vd

E

v dtd

A

q

IdQ

dtnqv Ad

Current Density:

JI

Anqv

J nqv

d

d

J n q v n q vd d 1 1 1 2 2 2

dQ = charge that passes through A= number that pass through A charge on each= (n A vd dt) q, n = number density = number/volume

(works for negative charge carriers, multiple types of charge carriers as well)

p212c26: 4

Example: 18 gauge copper wire (~1.02 mm in diameter) -constant current of 2A-n = 8.5x1028 m-3 (property of copper)

find J, vd

p212c26: 5

Current as a response to an applied electric field

J J E

E

E

JV m

A m

V

Am m

( )

= conductivity

resistivity

units = =

1

2

p212c26: 6

depends upon•material•E•Temperature

If does not depend on E, the material is said to obey “Ohm’s Law”

J

E

slope = 1/

linear responseOhm’s Law

J

E

nonlinear response

J

E

diodenonlinear response

direction dependence!

p212c26: 7

For a cylindrical conductor

E J I

a b

E J

V V E

J IA

RV

I AV IR

ab

resistance

Example: 50 meter length of 18 gauge copper wire (~1.02 mm in diameter) constant current of 2A = 1.72x10-8 .mfind E,V, R

see also example 28-3 re: alternate geometries

p212c26: 8

Temperature Dependence of

TMetallic Conductor

TSuperconductor

TSemiconductor

T o o

T o o

T T

R R T T

[ ( )]

[ ( )]

1

1

temperature coefficient of resistivity

For small changes in temperature:

p212c26: 9

Resistor Color Codes

Color number color rangeblack 0 none ±20%brown 1 silver ±10%red 2 gold ±5%orange 3yellow 4 value: n1n2x10n3±x%green 5blue 6violet 7gray 8white 9 10x102±5%

p212c26: 10

Electromotive Force and Circuits

Steady currentrequires a complete circuitpath cannot be only resistance

cannot be only potential drops in direction of current flow

Electromotive Force (EMF)provides increase in potential converts some external form of energy into electrical energy

Single emf and a single resistor:

I

V = IR

+ - V = IR =

p212c26: 11

Measurements

Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device.

V

Ammeters measure current through a device by being placed in series with the device.

A

p212c26: 12

Real Sources and Internal Resistance

r

a b

Ideal emf determined by how energy is converted into electrical energy

Internal Resistance r unavoidable “internal” lossesaging batteries => increasing internal resistance

p212c26: 13

A

V

A

r

a b

Open Circuit I=0Vr=0Vab=

r

a b

Short Circuit Vr = Ir = Vab= 0

V

p212c26: 14

A r

a b

Complete Circuit V

RI

IrVrR

I

IRIr

ab

r

a b

Charging Battery

IIrVab

V

A

p212c26: 15

Energy and Power

V=IR

I + -a b

V=

+ -a b

dW dQV V Idt

PdW

dtIV

ab ab

ab

Resistance

P IV I RV

R 2

2

battery +) of into ( or to

+) ofout (by deliverdPower

emf Ideal

I

I

IP

p212c26: 16

Power and Real Sources

r

a bDischarging Battery

I

rIIIV

IrV

ab

ab

2 :externally deliveredPower

I

r

a bCharging Battery

I

rIIIV

IrV

ab

ab

2 :source externalby deliveredPower

I

p212c26: 17RrPP

eff

RrR

RIP

rrR

rIP

rRIP

RrrRR

IRV

rRI

R

R

r

R

11

1

22

22

2

E

E

Real Battery with Load

I

A r

a b

V

R

max

"Impedance Matching"

P

dP

dRR r

R

R 0

p212c26: 18

Complete Circuit Example

A =12V r = 2

a b

V

R = 4

I

V

P

P

P

P

ab

r

R

Vab

E

p212c26: 19

Theory of Metallic ConductionConstant Acceleration between randomizing

collisions (momentum, velocity randomized)

E

JJ nqv

aF

m

qE

mv v a

v aqE

mv

J nqvnq

mE

m

nq

d

o

avg d

d

2

2

E

mean time between

collisions

mean free path

= (

vo avg)

p212c26: 20

Example: What is the mean time between collisions and the mean free path for conduction electrons in copper?

127 10

8 5 10

9 1 10

16 10

1 10

8

28 3

31

19

6

.

.

.

.

m

n m

m kg

q e C

v xm

so

p212c26: 21

Physiological Effects of Current

Nerve action involves electrical pulses

currents can interfere with nervous system

~.1A can interfere with essential functions

(heartbeat, e.g.)

currents can cause involuntary convulsive muscle action

~.01 A

Joule Heating (I2R)

With skin resistance

dry skin: R ~ 500k

wet skin: R ~ 1000