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.

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

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

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=IR

Water Flow Analogy

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

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

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)

Radial current leakage in a coaxial cable

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

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.

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

“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

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,

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?

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

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