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

2[ / ]

Concentration of mobile charge

carriers per unit volume:

Average speed in the direction

of current (drift speed):

For a variety of charge carriers:

| |

d

d

d

di ii

Q qnAv t

I QJ qn v A m

A A t

n

v

J q n v

Current density J, is a vector while total current I is not

I d

J S

Electric current in solution of NaCl is due to both positive Na+ and negative Cl- charges flow

Example: An 18-gauge copper wire has nominaldiameter of 1.02 mm and carries a constant currentof 1.67 A to 200W lamp. The density of free electronsis 8.5*1026 el/m3. Find current density and drift velocity

6 22

42 10 /

I IJ A m

A d

4; 1.5 10 /d dJ nev v m s

Why, then, as we turn on the switch, light comesimmediately from the bulb?

E-field acts on all electrons at once (E-fieldpropagates at ~2 108 m/s in copper)

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/

with E-independent conductivity σ=1/

This is Ohm’s law

(empirical and restricted)

Ohm’s Law

Conductors, Insulators and Semiconductors

Resistance of a straight wire

1 ( )

Resistance

1 VoltUnit: 1 Ohm ( )

1 Ampere

1Resistivity

Unit: 1 m

b a b a

VI J A E A A

L

I V V V VR

LR

A

LR

A

V=IR

Water Flow Analogy

Interpreting Resistance

ohmic

(linear)

nonohmic

(non-linear)

I-V curves

Resistivity and Temperature

(T) = 0[1+(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

– EVA Suit Specified to –40 V• anodized coating arcing occurred

at –68V in MSFC test– Possible Sneak-Circuit

• 1 mA safety threshold

Safety Tether

Display and Control Module (DCM)

Body Restraint Tether (BRT)

Mini Work Station (MWS)

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 getswrapped around astronaut.

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.

Charging on Astronaut Space Suit in Auroral Zone: Potentially hazardous situation

Radial current leakage in a coaxial cable

€

J(r) =I

2πrL

V = E(r)dr =a

b

∫ ρJ(r)a

b

∫ dr =ρI

2πLln

b

a

R =ρ

2πLln

b

a

Consider electrons as classical particles – no quantum mechanical properties for now

Simplest model – each atom gives one electron to the “pool” of conductive electrons

Microscopic model for drift velocity and conduction

6

4

14

Conduction electrons in metals move in

random directions with average speeds

~ 10 m/s

Overall average velocity (when 0)

0

When 0,

~ (typically) ~ 10 m/s

~ 10 s is the average time betw

d

d

v

v

qa

m

E

E

Ev

8

2

2

een

random collisions with ions, impurities etc

Mean free path ~ 10 m

1

d

d

l v

nqJ nq v E

m

nqv nq

E m

Temperature dependence of resistivity

Conductors – quantum mechanics says that at T=0, atoms do not vibrate – no collisionsat all (electrons scatter elastically). At T>0 – atoms vibrate, collisions intensify

Superconductors – there are certain quantum states where there are only elasticcollisions – no energy is transferred to the ions in the crystal

Semiconductor have very different electric properties. As T increases, concentration ofFree electrons goes up dramatically, decreasing resistivityMost 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

IrV

rRI

IrIR

R

r

terminals

between Voltage

resistance Load

resistance Internal

Internal Resistance

Evolution of the electric potential

in the circuit with a load

In ideal situation, abV IR

As the charge flows through the circuit, the potentialrise as it passes through the ideal source is equal to potential drop via the resistance,

abV IR

Example: What are voltmeter and ammeter readings?

We measure currents

with ammeters

An ideal ammeter would have a zero

resistance

We measure voltages with voltmeters

An ideal voltmeter would have an infinite

resistance

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 resistanceincreases enormously