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Lesson 5

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. Electrical Resistance.

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Lesson 5

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  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

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