Transcript PHYS_3342_100611

You must return your reworked exams today. I will be going over the answers in class
next Tuesday. This will also be your only opportunity to ask for
corrections/clarifications on any grading mistakes.
Current, Drift Velocity, Current Density
Q  qnAvd t

J

I Q

 qn v d [ A / m 2 ]
A At
Concentration of mobile charge
carriers per unit volume: n
Average speed in the direction
of current (drift speed): vd
For a variety of charge carriers:


J   | qi | ni v d
i
Current density J, is a vector
while total current I is not


I   J d S
Example: An 18-gauge copper wire has nominal
diameter of 1.02 mm and carries a constant current
of 1.67 A to 200W lamp. The density of free electrons
is 8.5*1026 el/m3. Find current density and drift velocity
J
I
4I

A d2
J  nevd ;
2  106 A / m2
vd  1.5  104
m/ s
Why, then, as we turn on the switch, light comes
immediately from the bulb?
E-field acts on all electrons at once (E-field
propagates at ~2 108 m/s in copper)
Electric current in solution of NaCl is due to
both positive Na+ and negative Cl- charges flow
Ohm’s Law
Current density J and electric field E are established inside a conductor when a
potential difference is applied –
Not electrostatics – field exists inside and charges move!
In many materials (especially metals)
over a range of conditions:
J = σE or J = E/r
with E-independent conductivity σ=1/r
This is Ohm’s law
(empirical and restricted)
Conductors, Insulators and
Semiconductors
Resistance of a straight wire
V
I  J  A E  A A
L
1
I  V (V  Vb  Va  b  a )
R
L
Resistance R 
A
1 Volt
Unit: 1 Ohm () 
1 Ampere
1
Resistivity
r

1 m
L
Rr
A
Unit:
V=IR
Water Flow Analogy
Interpreting Resistance
I-V curves
ohmic
nonohmic
(linear)
(non-linear)
Resistivity and Temperature
r(T) = r0[1+a(T-T0)]
Electrical Shock
“It’s not the voltage but the current.”
The current is what actually causes a shock - human body has resistance of ~500,000 
with dry skin - ~100  wet! Requires conducting path.
Can cause: (1) burning of tissue by heating, (2) muscle contractions, (3) disruption of
cardiac rhythms.
Current (A)
Effect
0.001
Can be felt
0.005
Is painful
0.010
Causes spasms
0.015
Causes loss of muscle control
0.070
Goes through the heart - fatal after more than
1 second
Charging on Astronaut Space Suit in Auroral Zone: Potentially hazardous situation
– EVA Suit Specified to –40 V
• anodized coating arcing occurred
at –68V in MSFC test
– Possible Sneak-Circuit
• 1 mA safety threshold
Metal waist and neck rings and other metal
portions of the suit make contact with the
sweat soaked ventilation garment providing
possible conducting path for discharge through
astronaut’s thoracic cavity.
Safety
 Surface of spacesuit could charge to high
voltage leading to subsequent discharge.
Display
and
Control
Module
(DCM)
Tether
Discharge to the station through safety tether:
• Tether is a metallic cable - connected to
astronaut via non-conducting (nylon)
housing.
• Station maintained at plasma potential arc path closed when tether gets
wrapped around astronaut.
Mini Work Station
(MWS)
Body Restraint
Tether (BRT)
Radial current leakage in a coaxial cable
I
J(r) 
2rL
V
b

a

rI b
E(r)dr   rJ(r) dr 
ln
2L a
a
r
b
R
ln
2L a
b
Microscopic model for drift velocity and conduction
Consider electrons as classical particles – no quantum mechanical properties for now
Simplest model – each atom gives one electron to the “pool” of conductive electrons
Conduction electrons in metals move in
random directions with average speeds
v ~ 106 m/s
Overall average velocity (when E  0)
vd  0
When E  0,
qE
v d  a 
 ~ (typically) ~ 104 m/s
m
 ~ 1014 s is the average time between
random collisions with ions, impurities etc
Mean free path l  v ~ 10 8 m
nq 2 
J  nq v d 
E
m
1 nqvd nq 2
 

r
E
m


Temperature dependence of resistivity
Conductors – quantum mechanics says that at T=0, atoms do not vibrate – no collisions
at all (electrons scatter elastically). At T>0 – atoms vibrate, collisions intensify
Superconductors – there are certain quantum states where there are only elastic
collisions – no energy is transferred to the ions in the crystal
Semiconductor have very different electric properties. As T increases, concentration of
Free electrons goes up dramatically, decreasing resistivity
Most importantly – current strength is not linearly proportional to voltage (diode)
Avalanche – uncontrollable stream of electrons, gaining energy as they
move through the material.
Electromotive Force and Circuits
For a conductor to have a steady current, it must be a closed loop path
If charge goes around a complete circuit and returns to a starting point –
potential energy does not change
As charges move through the circuit they loose their potential energy
due to resistance
“Electromotive force” (emf, ε) is produced by
a battery or a generator and acts as a “charge
pump”. It moves charges uphill and is equal to
the potential difference across such a device
under open-circuit conditions (no current). In
reality, batteries have some internal resistance.
Emf is measured in Volts (so it is not a “force” per say, but potential difference)
Sources of emf – batteries, electric generators, solar cells, fuel cells
Internal Resistance
In ideal situation,   Vab  IR
As the charge flows through the circuit, the potential
rise as it passes through the ideal source is equal to
potential drop via the resistance, Vab  IR

Internal resistance r
Load resistance
R
  IR  Ir
I
Evolution of the
electric potential
in the circuit
with a load

Rr
Voltage between
terminals V    Ir
We measure currents
We measure voltages
with voltmeters
with ammeters
An ideal voltmeter
would have an infinite
resistance
An ideal ammeter
would have a zero
resistance
Example: What are voltmeter
and ammeter readings?
Examples
Bulb B is taken away,
will the bulb A glow differently?
Which bulb glows brighter?
Which bulb glows brighter?
Potential changes around the circuit
Potential gain in the battery
Potential drop at all resistances
In an old, “used-up” battery emf is
nearly the same, but internal resistance
increases enormously