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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.

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24 1 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

 charges moving left

Both charges moving right

curent a microscopic look
Curent: A Microscopic Look

v of charge carriers in media with E = 0 isthermal ( random with  v  = 0 ).

For E 0, vd =  v   0.

drift velocity

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

n = number of carriers per unit volume

q = charge on each carrier

example 24 1 copper wire
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 = 1.11029 m3.

Find the electron’s drift speed.

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

current density
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

[ J ] = A /m2

  Charge density

example 24 2 cell membrane
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 1.1104 singly ionized potassium ions.

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

~0.3 nm

Lipid molecules

ion channels

~ 4 times max. safe current density in household wirings

AWG 10 :

24 2 conduction mechanism
24.2. Conduction Mechanism

E 0 in conductor  non-electrostatic equilibrium

 charges accelerated

Collisions steady state

  conductivity

Ohm’s law, microscopic version

Ohmic material:  independent of E

  resistivity

[]  Vm/A

 m

[]  (m)1

slide8

No band gap

Small band gap

Large band gap

example 24 3 household wiring
Example 24.3. Household Wiring

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

Find E in the wire.

conduction in metals
Conduction in Metals

Metal:  ~ 108  106 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

Steady state:

Ohm’s law

Due to high T Bose statistics of phonons.

Cu

c.f., vth  T

ionic solutions
Ionic Solutions

Electrolyte: Carriers = e + ions

 ~ 104  105 m

Examples:

Ions through cell membranes.

Electric eels.

Batteries & fuel cells.

Electroplating.

Hydrolysis.

Corrosion of metal.

plasmas
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

Thermal motion dislodges an e ...

Semiconductor

Pure semiC:

T = 0, no mobile charge carriers.

T  0, thermally excited carriers, e & holes.

  increases with T

… leaving a hole behind.

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.

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

pn junction
PN Junction

Current flows in only 1 direction

Depletion region

No battery:

e & h diffuse across junction & recombine.

Junction depleted of carriers.

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
Application: Transistor

Large current change controlled by small signal (at gate):

Amplifier, or

Digital 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
Superconductor

Onnes (1911): Hg = 0 below 4.2K.

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

Current record: TC ~ 160K.

TC =

Applications:

Electromagnets for strong B:

Labs, MRI, LHC, trains …

SQUIDS for measuring weak B.

YBaCuO

24 3 resistance ohm s law
24.3. Resistance & Ohm’s Law

Ohm’s Law

macrscopic version

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.

24 4 electric power
24.4. Electric Power

Electric Power :

for time independent V

Power increase with R

( for fixed I )

Power decrease with R

( for fixed V )

No contradiction

conceptual example 24 1 electric power transmission
Conceptual Example 24.1. Electric Power Transmission

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

Why?

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

making the connection
Making the Connection

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

What’s the bulb’s resistance?

24 5 electrical safety
24.5. Electrical Safety

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.

slide23

Large current thru operator

No current thru operator

Large current blows fuse

Ground fault interupter