1. p212c26: 1 Charge carrier motion in a conductor in two parts Constant Acceleration Randomizing Collisions (momentum, energy) =>Resulting Motion Average motion = Drift Velocity = v d ~10 -4 m/s Typical speeds ~ 10 6 m/s Chapter 26: Current, Resistance and Electromotive Force

2. p212c26: 2 Current Flow = net motion of charges = Charge carriers charge q speed v d I = Current = rate at which charge passes the area vdvd I vdvd I Negative charge carriers move in opposite direction of conventional current.

3. p212c26: 3 Connection with microscopic picture: vdvd E A q Current Density: dQ = charge that passes through A = number that pass through A  charge on each = (n A v d dt) q,n = number density = number/volume (works for negative charge carriers, multiple types of charge carriers as well)

4. p212c26: 4 Example: 18 gauge copper wire (~1.02 mm in diameter) -constant current of 2A -n = 8.5x10 28 m -3 (property of copper) find J, v d

5. p212c26: 5 Current as a response to an applied electric field

6. p212c26: 6  depends upon material E Temperature If  does not depend on E, the material is said to obey “Ohm’s Law” J E slope = 1/  linear response Ohm’s Law J E nonlinear response J E diode nonlinear response direction dependence!

7. p212c26: 7 For a cylindrical conductor E J I a b Example: 50 meter length of 18 gauge copper wire (~1.02 mm in diameter) constant current of 2A  = 1.72x10 -8 . m find E,V, R see also example 28-3 re: alternate geometries

8. p212c26: 8 Temperature Dependence of   T Metallic Conductor   T Superconductor T Semiconductor For small changes in temperature:

9. p212c26: 9 Resistor Color Codes Colornumbercolor range black0none±20% brown1silver±10% red2gold±5% orange3 yellow4value:n 1 n 2 x10 n 3 ±x% green5 blue6 violet7 gray8 white910x10 2 ±5%

10. p212c26: 10 Electromotive Force and Circuits Steady current requires a complete circuit path cannot be only resistance cannot be only potential drops in direction of current flow Electromotive Force (EMF) provides increase in potential E converts some external form of energy into electrical energy Single emf and a single resistor: I V = IR E +- V = IR = E

11. p212c26: 11 Measurements Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device. V Ammeters measure current through a device by being placed in series with the device. A

12. p212c26: 12 Real Sources and Internal Resistance E r a b Ideal emf E determined by how energy is converted into electrical energy Internal Resistance r unavoidable “internal” losses aging batteries => increasing internal resistance

13. p212c26: 13 A V A E r a b Open Circuit I=0 V r =0 V ab = E E r a b Short Circuit V r = Ir = E V ab = 0 V

14. p212c26: 14 A E r a b Complete Circuit V R I E r a b Charging Battery I V A

15. p212c26: 15 Energy and Power V=IR I + - ab V= E +- a b

16. p212c26: 16 Power and Real Sources E r a b Discharging Battery II E r a b Charging Battery II

17. p212c26: 17 Real Battery with Load I A E r a b V R

18. p212c26: 18 Complete Circuit Example A E =12V r = 2  a b V R = 4 

19. p212c26: 19 Theory of Metallic Conduction Constant Acceleration between randomizing collisions (momentum, velocity randomized)

20. p212c26: 20 Example: What is the mean time between collisions and the mean free path for conduction electrons in copper?

21. p212c26: 21 Physiological Effects of Current Nerve action involves electrical pulses currents can interfere with nervous system ~.1A can interfere with essential functions (heartbeat, e.g.) currents can cause involuntary convulsive muscle action ~.01 A Joule Heating (I 2 R) With skin resistance dry skin: R ~ 500k  wet skin: R ~ 1000 