p212c25: 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 25: Current, Resistance and Electromotive Force

F ma qE

p212c25: 2

Current Flow = net motion of charges = Charge carriers

charge qspeed vd

I = Current = rate at which charge passes the area

vd

I dQdt

CS

Amp A units: 11

1 1

I

vd I

Negative charge carriers move in opposite direction of conventional current.

p212c25: 3

Connection with microscopic picture:

vd

E

v dtd

A

q

I dQdt

nqv Ad

Current Density:J I

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)

p212c25: 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

p212c25: 5

Current as a response to an applied electric field

J J EE

EJ

V mA m

VA

m m

( )

= conductivity

resistivity

units = =

1

2

p212c25: 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!

p212c25: 7

For a cylindrical conductor

E J I

a b

E JV V E

J IA

R VI A

V 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

p212c25: 8

Temperature Dependence of

TMetallic Conductor

TSuperconductor

TSemiconductor

T o o

T o o

T T

R R T T

[ ( )]

[ ( )]

1

1temperature coefficient of resistivity

For small changes in temperature:

p212c25: 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%

p212c25: 10

Electromotive Force and CircuitsSteady current

requires a complete circuitpath cannot be only resistance

cannot be only potential drops in direction of current flowElectromotive 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 =

p212c25: 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

p212c25: 12

Real Sources and Internal Resistance

ra b

Ideal emf determined by how energy is converted into electrical energy

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

p212c25: 13

A

V

A

ra b

Open Circuit I=0Vr=0Vab=

ra b

Short Circuit Vr = Ir = Vab= 0

V

p212c25: 14

A r

a b

Complete Circuit V

RI

IrVrR

I

IRIr

ab

ra b

Charging Battery

IIrVab V

A

p212c25: 15

Energy and Power

V=IR

I + -a b

V=

+ -a b

ab

abab

IVdt

dWP

IdtVdQVdW

Resistance

P IV I R VR

22

battery +) of into ( or to +) ofout (by deliverdPower

emf Ideal

II

IP

p212c25: 16

Power and Real Sources

ra b

Discharging BatteryI

rIIIVIrV

ab

ab2 :externally deliveredPower

I

ra b

Charging BatteryI

rIIIVIrV

ab

ab2 :source externalby deliveredPower

I

p212c25: 17

RrPPeff

RrR

RIP

rrR

rIP

rRIP

RrrRRIRV

rRI

R

R

r

R

11

1

22

22

2

E

Real Battery with Load

I

A r

a b

V

R

max

"Impedance Matching"

PdPdR

R r

R

R 0

p212c25: 18

Complete Circuit Example

A =12V r = 2

a b

V

R = 4

IVPPPP

ab

r

R

Vab

E

p212c25: 19

Theory of Metallic ConductionConstant Acceleration between randomizing collisions

(momentum, velocity randomized)

EJ

J nqv

a Fm

qEm

v v a

v a qEm

v

J nqv nqm

E

mnq

d

o

avg d

d

2

2

E

mean time between collisions

mean free path= (

vo avg)

p212c25: 20

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

127 1085 109 1 10

16 10

1 10

8

28 3

31

19

6

.

..

.

mn mm kgq e C

v x mso

p212c25: 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