Short Version : 24. Electric Current. 24.1. Electric Current Current (I) = Net rate of (+) charge crossing an area.[ I ] = Ampere Electronics: I ~ mA.

Short Version : 24. Electric Current

24.1. Electric Current

Current (I) = Net rate of (+) charge crossing an area. [ I ] = Ampere

Electronics: I ~ mA Biomedics: I ~ A

Steady current:

QI

t

Instantaneous current:

d QI

d t

+ charges moving right

charges moving left Both charges moving right

Net current

Zero net current

Curent: A Microscopic Look

v of charge carriers in media with E = 0 is

thermal ( random with v = 0 ).

For E 0, vd = v 0.

drift velocity

QI

t

/ d

n A L q

L v

n = number of carriers per unit volumeq = charge on each carrier

Charge in this volume is Q = n A L q.

dI n A q v

Example 24.1. Copper Wire

A 5.0-A current flows in a copper wire with cross-sectional area 1.0

mm2,

carried by electrons with number density n = 1.11029 m3.

Find the electron’s drift speed.d

Iv

n A q

29 3 6 2 19

5.0

1.1 10 1.0 10 1.6 10

A

m m C

42.8 10 / m s

0.28 / mm s

TIP: Big difference between vd ~ mm/s and signal speed ~ c.

Current Density

Current can flow in ill-defined paths ( vd depends on position ),

e.g., in Earth, chemical solutions, ionized gas, …

Better description of such flows is by

current density ( J ) = current per unit area

dn qJ v [ J ] = A /m2

Charge densityd v

Example 24.2. Cell Membrane

Ion channels are narrow pores that allow ions to pass through cell membranes.

A particular channel has a circular cross section 0.15 nm in radius;

it opens for 1 ms and passes 1.1104 singly ionized potassium ions.

Find both the current & the current density in the channel.

Q

It

121.8 10 A

12

29

1.8 10

0.15 10

A

m

4 19

3

1.1 10 1.6 10

1 10

C

s

1.8 pA

I

JA

6 225 10 / A m 225 / MA m

~ 4 times max. safe current density in household wirings

Lipid molecules

ion channels

~0.3 nm

AWG 10 :

22

305.7 /

5.26

AJ MA m

mm

24.2. Conduction Mechanism

E 0 in conductor non-electrostatic equilibrium charges accelerated

Collisions steady state

J E Ohm’s law, microscopic version

conductivity

Ohmic material: independent of E

1

J E resistivity

[] Vm/A

m

[] (m)1

No band gap

Large band gap

Small band gap

Material Resistivity (m)

Metallic conductors (20C)

Aluminum 2.65108

Copper 1.68108

Gold 2.24108

Iron 9.71108

Mercury 9.84107

Silver 1.59108

Ionic solutions ( in water, 18C)

1-molar CuSO4 3.9104

1-molar HCl 1.7102

1-molar NaCl 1.4104

H2 O 2.6105

Blood, human 0.70

Seawater (typical) 0.22

Semiconductors (pure, 20C)

Germanium 0.47

Silicon 23.0

Insulators

Ceramics 1011 1014

Glass 1010 1014

Polystyrene 1015 1017

Rubber 1013 1016

Wood (dry) 108 1014

Example 24.3. Household Wiring

A 1.8-mm-diameter copper wires carries 15 A to a household appliance.

Find E in the wire.

E J

8

23

15 1.68 10

0.90 10

A m

m

I

A

99 /mV m

Conduction in Metals

Metal: ~ 108 106 m

Atomic structure: polycrystalline.

Carriers: sea of “free” electrons, v ~ 106 m/s

E = 0: equal # of e moving directions v = 0.

E 0: Collisions between e-ph vd ~ const.d v m

m v eEd t

Steady state:

0d v

d t d

eEv

m

dJ n e v 2ne

Em

E Ohm’s law

= relaxation time

T Due to high T Bose statistics of phonons.Cu

c.f., vth T

Ionic Solutions

Electrolyte: Carriers = e + ions ~ 104 105 m

Examples:

Ions through cell membranes.

Electric eels.

Batteries & fuel cells.

Electroplating.

Hydrolysis.

Corrosion of metal.

Plasmas

Plasma: Ionized gas with e & ions as carriers.

Examples:

Fluorescent lamps.

Plasma displays.

Neon signs.

Ionosphere.

Flames.

Lightning.

Stars.

Rarefied plasma (collisionless) can sustain large I with minimal E.

E.g., solar corona.

Semiconductor

Pure semiC: T = 0, no mobile charge carriers.T 0, thermally excited carriers, e & holes.

increases with T

Doped semiC: Mobile charge carriers from impurities.N-type: carriers = e. Impurities = Donors. E.g. P in Si.P-type: carriers = h. Impurities = Acceptors. E.g. B in Si.

Thermal motion dislodges an e ...

… leaving a hole behind.

e & h move oppositely in E

Bound e jumps left, h moved to right

Phosphorous with 5 e

P fits into Si lattice, leaving 1 free e

PN Junction

Current flows in only 1 direction

No battery:e & h diffuse across junction & recombine.Junction depleted of carriers.

Depletion region

Reverse bias:e & h pulled away from junction.Depletion region widens.I ~ 0.

Forward bias:e & h drawn to junction.Depletion region vanishes.I 0.

Application: Transistor

Large current change controlled by small signal (at gate): Amplifier, orDigital switch.

Normally channel is closed ( I = 0 ) as one of the junctions is reverse biased.

+ V applied to gate attracts e to channel: I 0

Superconductor

Onnes (1911): Hg = 0 below 4.2K.

Muller et al (1986): TC ~ 100K.

Current record: TC ~ 160K.

YBaCuO

TC =

Applications:

Electromagnets for strong B:

Labs, MRI, LHC, trains …

SQUIDS for measuring weak B.

24.3. Resistance & Ohm’s LawV

IR

Ohm’s Law macrscopic version

Open circuit: R I = 0 V

Short circuit: R = 0 I V

EJ I J A

EA

V

AL

LR

A

Resistor: piece of conductor made to have specific resistance.

All heating elements are resistors.

So are incandescent lightbulbs.

Table 24.2. Micrscopic & Macroscopic Quantities in Ohm’s Law

Microscopic Macroscopic Relation

V d E r

I d J A

LR

A

1

J E

VI

R

E L

J A

E

J

V

I

R

24.4. Electric Power

I VElectric Power : dP q V

d t for time independent V

P I V 2I R2V

R V I R

Power increase with R( for fixed I )

Power decrease with R( for fixed V )

No contradiction

Conceptual Example 24.1. Electric Power Transmission

Power P = I V.

Transmission loss PW = I 2 RW = P2 RW / V2

Low I , i.e., high V , lowers PW for same P.

PW = (V VL )2 / RW

= (V P RL / V )2 / RW

see Prob 56VL < V because of power loss in wire

Long distance power transmission lines operate at very high voltages – often hundreds of kVs.

Why?

Making the Connection

What is the current in a typical 120 V, 100 W lightbulb?

What’s the bulb’s resistance?

PI

V

100

120

W

V 0.833 A

VR

I

120

0.833

V

A 144

24.5. Electrical Safety

Typical human resistance ~ 105 .

Fatal current ~ 100 mA = 0.1 A. 50.1 10V A 10,000V

A wet person can be electrocuted by 120V.

TABLE 24.3. Effects of Externally Applied Current on Humans

Current Range Effect --------------------------------------------------------------------------------------------------

0.5 2 mA Threshold of sensation

10 15 mA Involuntary muscle contractions; can’t let go

15 100 mA Severe shock; muscle control lost; breathing difficult

100 200 mA Fibrillation of heart; death within minutes

> 200 mA Cardiac arrest; breathing stops; severe burns

Ground fault interupter

Large current thru operator

No current thru operator

Large current blows fuse