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:. Instantaneous current:. + charges moving right. Zero net current. Net current.
Current (I) = Net rate of (+) charge crossing an area.
[ I ] = Ampere
Electronics: I ~ mA
Biomedics: I ~ A
+ charges moving right
Zero net current
charges moving left
Both charges moving right
v of charge carriers in media with E = 0 isthermal ( random with v = 0 ).
For E 0, vd = v 0.
Charge in this volume is Q = n A L q.
n = number of carriers per unit volume
q = charge on each carrier
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.
TIP: Big difference between vd ~ mm/s and signal speed ~ c.
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
[ J ] = A /m2
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.
~ 4 times max. safe current density in household wirings
AWG 10 :
E 0 in conductor non-electrostatic equilibrium
Collisions steady state
Ohm’s law, microscopic version
Ohmic material: independent of E
Small band gap
Large band gap
A 1.8-mm-diameter copper wires carries 15 A to a household appliance.
Find E in the wire.
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.
= relaxation time
Due to high T Bose statistics of phonons.
c.f., vth T
Electrolyte: Carriers = e + ions
~ 104 105 m
Ions through cell membranes.
Batteries & fuel cells.
Corrosion of metal.
Plasma: Ionized gas with e & ions as carriers.
Rarefied plasma (collisionless) can sustain large I with minimal E. E.g., solar corona.
T = 0, no mobile charge carriers.
T 0, thermally excited carriers, e & holes.
increases with T
… leaving a hole behind.
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.
e & h move oppositely in E
Phosphorous with 5 e
Bound e jumps left, h moved to right
P fits into Si lattice, leaving 1 free e
Current flows in only 1 direction
e & h diffuse across junction & recombine.
Junction depleted of carriers.
e & h pulled away from junction.
Depletion region widens.
I ~ 0.
e & h drawn to junction.
Depletion region vanishes.
Large current change controlled by small signal (at gate):
Normally channel is closed ( I = 0 ) as one of the junctions is reverse biased.
+ V applied to gate attracts e to channel: I 0
Onnes (1911): Hg = 0 below 4.2K.
Muller et al (1986): TC ~ 100K.
Current record: TC ~ 160K.
Electromagnets for strong B:
Labs, MRI, LHC, trains …
SQUIDS for measuring weak B.
Open circuit: R I = 0 V
Short circuit: R = 0 I V
Resistor: piece of conductor made to have specific resistance.
All heating elements are resistors.
So are incandescent lightbulbs.
Electric Power :
for time independent V
Power increase with R
( for fixed I )
Power decrease with R
( for fixed V )
Long distance power transmission lines operate at very high voltages – often hundreds of kVs.
Power P = I V.
Transmission loss PW = I 2RW = P2RW / V2
Low I , i.e., high V , lowers PWfor same P.
PW = (V VL )2 / RW
= (V P RL / V )2 / RW
VL< V because of power loss in wire
see Prob 56
What is the current in a typical 120 V, 100 W lightbulb?
What’s the bulb’s resistance?
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
Typical human resistance ~ 105.
Fatal current ~ 100 mA = 0.1 A.
A wet person can be electrocuted by 120V.
No current thru operator
Large current blows fuse
Ground fault interupter