Understanding Current, Resistance, and Electrical Power in Conductors

1. Lesson 5 Lesson 5 Current and Resistance • Batteries • Current Density • Electron Drift Velocity • Conductivity and Resistivity • Resistance and Ohms’ Law • Temperature Variation of Resistance • Electrical Power and Joules Law • Classical Model of Conduction in Metals

2. Electrical Resistance • Electrical Resistance is • “friction” to the flow of electric charge • Observed in Conductors and • Non Conductors • Not found in Super Conductors

3. Charge Pump I Capacitor will send current through load resistance and loose charge Load Resistance I - +

4. Charge Pump I Battery will send current through load resistance and not loose charge Charge in battery is regenerated by Chemical reactions Load Resistance I - +

5. Flow of Charge

6. Current Picture I

7. Current Picture Definition I Current is the rate of Flow of positive charge through whole cross sectional area of conductor

8. Current Picture Definition II

9. Conservation of Current Current is Conserved I1 I1+I2 I2 I1

10. Driving force for Current • Flowing charge experiences friction • Work must be done to overcome friction • Need driving force, hence need • Electric Field • Potential Difference

11. SI units Potential Difference Electrical Resistance = Current V = R I [ ] V V [ ] = = = W R ( Ohm ) [ ] I A

12. V-I plots I-V plots slope constant = 1/R slope not constant I I V V Ohmic Material Non Ohmic Material

13. Resistance I Ohmic Materials = V RI Ohms Law V = = R constant I

14. Resistance II Non Ohmic Materials R is not Constant, but varies with current and voltage

15. Power Power = rate of doing work by applied force dU dQ = = Power = V IV dt dt C Nm Nm [ ] [ [ ] ] = = = = Power I V AV s C s J = ) W ( Watts s

16. Ohmic Materials I

17. Ohmic Materials II For Ohmic Materials • Resistance is proportional to length of conductor • Resistance is inversely proportional to the cross sectional area of the conductor

18. Resistivity

19. Picture l I a V- V+ E

20. Current Density = - = |V| V V El + - V El Ea = = = I l r R r a Divide by Area Current Densitymagnitude=Current percross sectional area I E J s E = = = r a 1 s = = conductivity r

21. Integral Formula

22. Electrical Conduction Classical Microscopic Theory of Electrical Conduction

23. Random Walk

24. Picture

25. Definition of Variables Charge in Volume D V D Q nA x q nAv t q = D = D d n number of charge carriers = per unit volume A cross sectional area = q amount of charge on = each carrier D x average distance moved in = D time t after collision = v drift velocity d

26. Equations I D Q D x = nA q D t D t dQ q Þ = I = nAv dt d Þ J = nv q d J Þ = v nq d

27. Equations II acceleration of charge q in field E q = a E m • Let t = average time between collisions • at each collision charge carrier forgets drift velocity , so we can take initial drift \ velocity = 0 and just before collisions æ ö q q = t = t = t ç ÷ v a E E è ø d m m J q = = t v E d nq m t 2 nq Þ = J E m 2 t nq Þ s = m

28. Temperature Effects Temperature Effects 1 m r = = s nq t 2 As temperature increases t decreases thus r increases [ ] ( ) ( ) r T = r 1 + a T - T 0 0 1 d r a = = Temperature Coefficient of Resistivity r dT 0

29. Temperature Effects [ ] ( ) ( ) r T = r 1 + a T - T 0 0 1 d r a = = Temperature Coefficient of Resistivity r dT Equation 0 Thus [ ] ( ) ( ) = + a - T T R T R 1 0 0