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Chapter 25 Current and Resistance

Chapter 25 Current and Resistance. Scalar Sense determined by the movement of the positive charge carrier. Average Electric Current. Instantaneous Electric Current. Units:. Microscopic view of current. +. +. A. +. +. +. +. Isn’t E = 0?.

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Chapter 25 Current and Resistance

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  1. Chapter 25 Current and Resistance • Scalar • Sense determined by the movement of the positive charge carrier Average Electric Current Instantaneous Electric Current Units:

  2. Microscopic view of current + + A + + + + Isn’t E = 0? Current density, j, is the electric current per unit cross sectional area. Current density is a vector. Charge carriers experience a force and accelerate. They collide with the atoms in the metal and are slowed down eventually reaching a terminal velocity called the drift velocity

  3. Resistance model – Why doesn’t the electron accelerate?

  4. Counting the charge flow + + A + + + + Let:

  5. Current density for electrons - - A - - - - vd E For non-uniform current density

  6. Ohm’s Law + + + + + +

  7. Scalar form of Ohm’s Law + + + + + + a b

  8. Units of resistance, resistivity, and conductivity

  9. Temperature effect on resistivity

  10. Superconductors • A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, TC • TC is called the critical temperature • The graph is the same as a normal metal above TC, but suddenly drops to zero at TC

  11. Superconductor Application • An important application of superconductors is a superconducting magnet • The magnitude of the magnetic field is about 10 times greater than a normal electromagnet • Used in MRI units

  12. V Electrical energy and power The power transformed in an electric device is then: Using Ohm’s Law

  13. Example Problem Given: Copper wire transmission line length = 1500 m diameter = 0.1cm current = 50 A rcu = 1.67 x 10-6W-cm Find: Power loss due to heating the wire

  14. Example P27.6 The quantity of charge q (in coulombs) that has passed through a surface of area 2.00 cm2 varies with time according to the equation q = 4t3 + 5t + 6, where t is in seconds. (a) What is the instantaneous current through the surface at t = 1.00 s? (b) What is the value of the current density?

  15. Example P27.15 A 0.900-V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of 0.600 mm2. What is the current in the wire?

  16. Example P27.29 A certain lightbulb has a tungsten filament with a resistance of 19.0 Ω when cold and 140 Ω when hot. Assume that the resistivity of tungsten varies linearly with temperature even over the large temperature range involved here, and find the temperature of the hot filament. Assume the initial temperature is 20.0°C.

  17. Resistor Values • Values of resistors are commonly marked by colored bands

  18. I The Lead Acid Electric Battery Sulfuric Acid Electrolyte: - + Terminals Oxidation at the Negative Plate (Electrode:Anode): Sulfuric Acid Solution H2SO4 Spongy Lead (Pb) Lead Oxide (PbO2) Reduction at the Positive Plate (Electrode:Cathode): Cell: 2 V Battery: Multiple cells

  19. Batteries

  20. Kirchoff’s Rules • Conservation of charge • Junction (Node) Rule: At any junction point, the sum of all currents entering the junction must equal the sum of the currents leaving the junction. • Conservation of energy • Loop Rule: The some of the changes in potential around any closed path of a circuit must be zero.

  21. Energy in a circuit

  22. Series Circuit Apply the Loop Rule +

  23. Parallel Circuits + Apply the Junction Rule

  24. Rule Set – Problem Solving Strategy • A resistor transversed in the direction of assumed current is a negative voltage (potential drop) • A resistors transversed in the opposite direction of assumed current is a positive voltage (potential rise) • A battery transversed from – to + is a positive voltage. • A battery transversed from + to - is a negative voltage. • Ohm’s Law applies for resistors. • Both the loop rule and junction rule are normally required to solve problems.

  25. More about the Loop Rule • Traveling around the loop from a to b • In (a), the resistor is traversed in the direction of the current, the potential across the resistor is – IR • In (b), the resistor is traversed in the direction opposite of the current, the potential across the resistor is is + IR

  26. Loop Rule, final • In (c), the source of emf is traversed in the direction of the emf (from – to +), and the change in the electric potential is +ε • In (d), the source of emf is traversed in the direction opposite of the emf (from + to -), and the change in the electric potential is -ε

  27. Example Problem 1 Given: V = 3 Volts Find: current in each resistor

  28. Example Problem 2 Given: Find: current in the 20 W resistor

  29. Alternating Current

  30. AC Power ?

  31. Root Mean Square (rms)

  32. The Wheatstone bridgea simple Ohmmeter

  33. Charging a capacitor in an RC circuit Same Symbol At t = 0, Qo = 0 and

  34. Solving the charging differential equation Kirchoff’s loop rule Convert to a simple equation in Current by taking the first derivative w.r.t. time Separate variables

  35. Integrate the results

  36. Charge buildup

  37. Discharging the capacitor in an RC circuit At t = 0, Q = Qo

  38. Solving the discharging differential equation Kirchoff’s loop rule Separate variables Integrate

  39. Charge and current decay

  40. Charge and current decay

  41. More on microscopic picture of conduction (See Ch 38)

  42. Mean Free Path What is vav for an electron? (M-B)

  43. Evaluation of classical conduction theory • Resistivity does not depend on the electric field. • Temperature dependence of resistivity does not agree with • laboratory measurement. • Calculated resistivities calculated from M-B average velocities and • path lengths are 6x greater than measured.

  44. Quantum theory of free electrons • Electrons are fermions not bosons • There can be at most 2 electrons with the same set of values for their spatial quantum numbers • The energy level of the last filled (highest) energy level at T=0 K is found from quantum mechanics

  45. Fermi Energies

  46. Fermi-Dirac Distribution At room temperature ~ 300K kT=.026 eV Only a few electrons can be taken to higher energy levels at room temperature. If the temperature is very high k=8.62x10-5 eV/K kT More electrons might be in higher energy states, but for typical temperatures below this FermiTemperature, the electrons have energy like the T=0 K case

  47. Correcting the classical picture Use Fermi Speed Correct the mean path length Area is not physical size of lattice ion but vibration amplitude of oscillation E~r2~A~T

  48. Electrical Safety • Current kills, not voltage (70 mA) • Normal body resistance = 105W But could be less than 1000 W • Take advantage of insulators, remove conductors • Work with one hand at a time • Shipboard is more dangerous • Electrical safety is an officer responsibility

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