1. You must return your reworked exams today
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.

2. Current, Drift Velocity, Current Density
Current density J, is a vector
while total current I is not

3. 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
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

4. 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

5. Resistance of a straight wire
V=IR

6. Water Flow Analogy

7. Interpreting Resistance
ohmic
(linear)
nonohmic
(non-linear)
I-V curves
Resistivity and Temperature
r(T) = r0[1+a(T-T0)]

8. Electrical Shock Current (A) Effect 0.001 Can be felt 0.005 Is painful
“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

9. EVA Suit Specified to –40 V
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
Display and Control Module (DCM)
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 Tether
 Surface of spacesuit could charge to high voltage leading to subsequent discharge.
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)

10. Radial current leakage in a coaxial cable

11. 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

12. 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.

13. As charges move through the circuit they loose their potential energy
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

14. “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

15. Evolution of the electric potential in the circuit with a load
Internal Resistance
In ideal situation,
Evolution of the electric potential in the circuit with a load
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,

16. We measure voltages with voltmeters We measure currents 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?

17. Examples Bulb B is taken away, will the bulb A glow differently?
Which bulb glows brighter?
Which bulb glows brighter?

18. Potential gain in the battery
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