Short Version : 24. Electric Current. 24.1. Electric Current Current (I) = Net rate of (+) charge...
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Transcript of Short Version : 24. Electric Current. 24.1. Electric Current Current (I) = Net rate of (+) charge...
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