Current and ResistanceSunday, July 24, 2011
Current                        Convention : Current                        depicts flow of                        positive...
Current                                   Convention : Current                                   depicts flow of          ...
Current                                   Convention : Current                                   depicts flow of          ...
Current                                   Convention : Current                                   depicts flow of          ...
Current                                     Convention : Current                                     depicts flow of      ...
Current         A measure of how much charge passes through an amount of time                              +              ...
Current                        Count how many charges flow through                                    +          +        ...
Current                        Count how many charges flow through                                Expand surface to a volu...
Current                           Count how many charges flow through                                   Expand surface to ...
Current                           Count how many charges flow through                                   Expand surface to ...
Current                           Count how many charges flow through                                   Expand surface to ...
Current                           Count how many charges flow through                                   Expand surface to ...
Current                           Count how many charges flow through                                   Expand surface to ...
Current                !Q = (n A !x)*(q)                                    +         +   Total volume                    ...
Current                !Q = (n A !x)*(q)                but charges have drift velocity vd = !x/!t                        ...
Current                !Q = (n A !x)*(q)                but charges have drift velocity vd = !x/!t                        ...
Current                !Q = (n A !x)*(q)                but charges have drift velocity vd = !x/!t                        ...
Current         This is the reason why large wires are         needed to support large currentsSunday, July 24, 2011
Current         This is the reason why large wires are         needed to support large currentsSunday, July 24, 2011
Resistance     Current density (J)              current per areaSunday, July 24, 2011
Resistance     Current density (J)              current per area                         Direction of current (flow of pos...
Resistance     Current density (J)              current per area                         Direction of current (flow of pos...
Resistance     Current density (J)              current per area                         Direction of current (flow of pos...
Resistance     Current density (J)              current per area                         Direction of current (flow of pos...
Resistance         Current is proportional to conductivity but         inversely proportional to resistivity!Sunday, July ...
Resistance         Current is proportional to conductivity but         inversely proportional to resistivity!         Curr...
Resistance         Current is proportional to conductivity but         inversely proportional to resistivity!         Curr...
Resistance         Current is proportional to conductivity but         inversely proportional to resistivity!         Curr...
Resistance         Current is proportional to conductivity but         inversely proportional to resistivity!         Curr...
Resistance         Current is proportional to conductivity but         inversely proportional to resistivity!         Curr...
ResistanceSunday, July 24, 2011
Resistance    Important points:                                   same with capacitance, resistance does not              ...
Recent Equations                                        →                        →       →E                        J = σE ...
Exercise    Rank from lowest to highest amount of current    Derive the equation R = "L/A     from V = IR, J = E/" = I/A, ...
Resistance and Temperature                                        ρl                                     R=               ...
Power                     ∆U                 P =                     ∆t                            ∆(q∆V )                ...
Power                            P = I∆V                                    ∆V                                 I=         ...
Exercises     The electron beam emerging from a certain high-energy electron accelerator     has a circular cross section ...
Exercises     An electric heater is constructed by applying a potential difference of 120 V to a     Nichrome wire that ha...
Sunday, July 24, 2011
A 500-W heating coil designed to operate from 110 V is made of Nichrome wire      0.500 mm in diameter. (a) Assuming that ...
More exercises        A certain lightbulb has a tungsten filament with a resistance of 19.0 Ω when cold        and 140 Ω wh...
A certain lightbulb has a tungsten filament with a resistance of 19.0 Ω when cold       and 140 Ω when hot. Assume that the...
The cost of electricity varies widely through the United States; $0.120/kWh is             one typical value. At this unit...
Electromotive Force   The electromotive force is denoted as “ε”   A force that moves charges    The emf ε is the maximum p...
Resistors in Series                           ∆V       Recall:          I=                            R    use the equatio...
Resistors in Series                         Convert                        to simple                        equivalent    ...
Resistors in Series                                  I1            I2                                 ∆V1           ∆V2   ...
Resistors in Series                                  I1            I2                                 ∆V1           ∆V2   ...
Resistors in Series                                  I1            I2                                 ∆V1           ∆V2   ...
Resistors in Series                        I1          I2                                                      ∆V = I1 R1 ...
Resistors in Series                        I1          I2                        ∆V1        ∆V2             Conservation o...
Resistors in Parallel      1. Imagine positive charges pass first                  I1    I2         through R1 and then thr...
Resistors in Parallel                           ∆V       Recall:          I=                            R    use the equat...
Resistors in Parallel                         Convert                        to simple                        equivalent  ...
Resistors in Parallel                                        I1                                             ∆V1           ...
Resistors in Parallel                                        I1                                             ∆V1           ...
Resistors in Parallel                                        I1                                             ∆V1           ...
Resistors in Parallel                                        I1                                             ∆V1           ...
Resistors in Parallel                             I1                                  ∆V1                             I2  ...
Recall:                 Ohms Law               Capacitance                 ∆V              I=                       Q = C∆...
Exercise   Find the current passing through each resistor   Find the voltage drop (potential difference) through each resi...
Kirchhoff’s Rules       Junction Rule             “conservation of matter”       Loop Rule             “conservation of en...
Exercise   In solving complicated circuit problems   apply Junction rule first (conservation of current)   You may assign ...
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Electric Current

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Electric Current

  1. 1. Current and ResistanceSunday, July 24, 2011
  2. 2. Current Convention : Current depicts flow of positive (+) chargesSunday, July 24, 2011
  3. 3. Current Convention : Current depicts flow of positive (+) charges Area +Sunday, July 24, 2011
  4. 4. Current Convention : Current depicts flow of positive (+) charges Area + Ammeter (measures current)Sunday, July 24, 2011
  5. 5. Current Convention : Current depicts flow of positive (+) charges Area + + + Ammeter (measures current)Sunday, July 24, 2011
  6. 6. Current Convention : Current depicts flow of positive (+) charges Area + + + Ammeter (measures current)Sunday, July 24, 2011
  7. 7. Current A measure of how much charge passes through an amount of time + + + Ammeter (measures current)Sunday, July 24, 2011
  8. 8. Current Count how many charges flow through + + +Sunday, July 24, 2011
  9. 9. Current Count how many charges flow through Expand surface to a volume + + +Sunday, July 24, 2011
  10. 10. Current Count how many charges flow through Expand surface to a volume + + + Area = ASunday, July 24, 2011
  11. 11. Current Count how many charges flow through Expand surface to a volume + + + Area = A length = !xSunday, July 24, 2011
  12. 12. Current Count how many charges flow through Expand surface to a volume + + Total volume V = (A)(!x) + Area = A length = !xSunday, July 24, 2011
  13. 13. Current Count how many charges flow through Expand surface to a volume + + Total volume V = (A)(!x) + Area = A length = !x Number of charges = (charge density or charge per volume)*(volume)Number of charges = (n) * (A!x)Sunday, July 24, 2011
  14. 14. Current Count how many charges flow through Expand surface to a volume + + Total volume V = (A)(!x) + Area = A length = !x Number of charges = (charge density or charge per volume)*(volume)Number of charges = (n) * (A!x) Total amount of charge = (number of charges)*(charge) !Q = (n A !x)*(q)Sunday, July 24, 2011
  15. 15. Current !Q = (n A !x)*(q) + + Total volume V = (A)(!x) + Area = A length = !xSunday, July 24, 2011
  16. 16. Current !Q = (n A !x)*(q) but charges have drift velocity vd = !x/!t + + Total volume V = (A)(!x) + Area = A length = !x = vd !tSunday, July 24, 2011
  17. 17. Current !Q = (n A !x)*(q) but charges have drift velocity vd = !x/!t + + Total volume V = (A)(!x) + Area = A length = !x = vd !t !Q = (n A vd !t)*(q)Sunday, July 24, 2011
  18. 18. Current !Q = (n A !x)*(q) but charges have drift velocity vd = !x/!t + + Total volume V = (A)(!x) + Area = A length = !x = vd !t !Q = (n A vd !t)*(q) !Q/!t = (n A vd)*(q) I = n q vd ASunday, July 24, 2011
  19. 19. Current This is the reason why large wires are needed to support large currentsSunday, July 24, 2011
  20. 20. Current This is the reason why large wires are needed to support large currentsSunday, July 24, 2011
  21. 21. Resistance Current density (J) current per areaSunday, July 24, 2011
  22. 22. Resistance Current density (J) current per area Direction of current (flow of positive charges) is same with direction of electric fieldSunday, July 24, 2011
  23. 23. Resistance Current density (J) current per area Direction of current (flow of positive charges) is same with direction of electric field conductivitySunday, July 24, 2011
  24. 24. Resistance Current density (J) current per area Direction of current (flow of positive charges) is same with direction of electric field conductivity (material property) resistivity (material property)Sunday, July 24, 2011
  25. 25. Resistance Current density (J) current per area Direction of current (flow of positive charges) is same with direction of electric field conductivity resistivity Current is proportional to conductivity but inversely proportional to resistivity!Sunday, July 24, 2011
  26. 26. Resistance Current is proportional to conductivity but inversely proportional to resistivity!Sunday, July 24, 2011
  27. 27. Resistance Current is proportional to conductivity but inversely proportional to resistivity! Current is proportional to the electric potential (specifically potential difference)Sunday, July 24, 2011
  28. 28. Resistance Current is proportional to conductivity but inversely proportional to resistivity! Current is proportional to the electric potential (specifically potential difference) Ohm’s Law Potential difference Resistance currentSunday, July 24, 2011
  29. 29. Resistance Current is proportional to conductivity but inversely proportional to resistivity! Current is proportional to the electric potential (specifically potential difference) Ohm’s Law Potential difference Resistance current a much better form than ΔV = I RSunday, July 24, 2011
  30. 30. Resistance Current is proportional to conductivity but inversely proportional to resistivity! Current is proportional to the electric potential (specifically potential difference) Ohm’s Law Potential difference Resistance current a much better form Increasing !V increases I than ΔV = I R Increasing R decreases ISunday, July 24, 2011
  31. 31. Resistance Current is proportional to conductivity but inversely proportional to resistivity! Current is proportional to the electric potential (specifically potential difference) Ohm’s Law Potential difference Resistance current a much better form Increasing !V increases I than ΔV = I R Increasing R decreases I !V = I R Increasing R does not increase !V Current (I) is increased because !V is increasedSunday, July 24, 2011
  32. 32. ResistanceSunday, July 24, 2011
  33. 33. Resistance Important points: same with capacitance, resistance does not depend on !V and I Resistance depends on material property resistivity ", length of wire l and cross sectional area A conventional current is flowing positive (+) charges though in reality electrons flow direction of the current I is same as direction of electric fieldSunday, July 24, 2011
  34. 34. Recent Equations → → →E J = σE = ρ → → J = nq v d A → → I J = A ∆V I= R ρl R= ASunday, July 24, 2011
  35. 35. Exercise Rank from lowest to highest amount of current Derive the equation R = "L/A from V = IR, J = E/" = I/A, V = ELSunday, July 24, 2011
  36. 36. Resistance and Temperature ρl R= A ρ = ρ0 (1 + α∆T ) ∆T = T − T0 T0 is usually taken to be 25 °C T ↑ ρ↑Sunday, July 24, 2011
  37. 37. Power ∆U P = ∆t ∆(q∆V ) P = ∆t (∆q)(∆V ) P = ∆t ∆q P = ∆V ∆t P = I∆VSunday, July 24, 2011
  38. 38. Power P = I∆V ∆V I= R V2 P = P = I 2R RSunday, July 24, 2011
  39. 39. Exercises The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.00 mm. (a) The beam current is 8.00 µA. Find the current density in the beam, assuming that it is uniform throughout. (b) The speed of the electrons is so close to the speed of light that their speed can be taken as c = 3.00 x 108 m/s with negligible error. Find the electron density in the beam. (c) How long does it take for Avogadroʼs number of electrons to emerge from the accelerator? An aluminum wire having a cross-sectional area of 4.00 x 10-6 m2 carries a current of 5.00 A. Find the drift speed of the electrons in the wire. The density of aluminum is 2700 kg/m3. Assume that one conduction electron is supplied by each atom. Molar mass of Al is 27 g/mol. Four wires A, B, C and D are made of the same material but of different lengths and radii. Wire A has length L but has radius R. Wire B has length 2L but with radius ½R. Wire C has length ½L but with radius 2R. Wire D has length ½L but with radius ½R. Rank with increasing resistance 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? resistivity of tungsten is 5.6 x 10-8 Ω-mSunday, July 24, 2011
  40. 40. Exercises An electric heater is constructed by applying a potential difference of 120 V to a Nichrome wire that has a total resistance of 8.00 Ω. Find the current carried by the wire and the power rating of the heater. A 500-W heating coil designed to operate from 110 V is made of Nichrome wire 0.500 mm in diameter. (a) Assuming that the resistivity of the Nichrome remains constant at its 20.0°C value, find the length of wire used. (b) What If? Now consider the variation of resistivity with temperature. What power will the coil of part (a) actually deliver when it is heated to 1200°C? ρ = 1.50 x 10-6 Ω-mSunday, July 24, 2011
  41. 41. Sunday, July 24, 2011
  42. 42. A 500-W heating coil designed to operate from 110 V is made of Nichrome wire 0.500 mm in diameter. (a) Assuming that the resistivity of the Nichrome remains constant at its 20.0°C value, find the length of wire used. (b) What If? Now consider the variation of resistivity with temperature. What power will the coil of part (a) actually deliver when it is heated to 1200°C? ρ = 1.50 x 10-6 Ω-cmSunday, July 24, 2011
  43. 43. More exercises 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. 4.5 x 10-3 C-1 The cost of electricity varies widely through the United States; $0.120/kWh is one typical value. At this unit price, calculate the cost of (a) leaving a 40.0-W porch light on for two weeks while you are on vacation, (b) making a piece of dark toast in 3.00 min with a 970-W toaster, and (c) drying a load of clothes in 40.0 min in a 5 200-W dryer.Sunday, July 24, 2011
  44. 44. 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. 4.5 x 10-3 C-1Sunday, July 24, 2011
  45. 45. The cost of electricity varies widely through the United States; $0.120/kWh is one typical value. At this unit price, calculate the cost of (a) leaving a 40.0-W porch light on for two weeks while you are on vacation, (b) making a piece of dark toast in 3.00 min with a 970-W toaster, and (c) drying a load of clothes in 40.0 min in a 5 200-W dryer. $0.120 $0.120 1kW 1hour $3.33 × 10−8 = = 1kWh 1kWh 1000W 3600secs 1Joule ∆U ∆U 1week 1day 1hour ∆U(a) P = ∆t = 2weeks 7days 24hours 3600secs = 1209600secs ∆U 40.0W = 1209600s $3.33 × 10−8 ∆U = 48384kJ 4.84 × 107 J = $1.61 1Joule(b) $5.82 × 10− 3(c) $0.416Sunday, July 24, 2011
  46. 46. Electromotive Force The electromotive force is denoted as “ε” A force that moves charges The emf ε is the maximum possible voltage that the battery can provide. ε = ∆V in batteriesDirect current - current that is constant in direction and magnitudeSunday, July 24, 2011
  47. 47. Resistors in Series ∆V Recall: I= R use the equation to calculate the equivalent resistance ReqSunday, July 24, 2011
  48. 48. Resistors in Series Convert to simple equivalent circuitSunday, July 24, 2011
  49. 49. Resistors in Series I1 I2 ∆V1 ∆V2 Conservation of matter = Current is conserved I = I1 = I2Sunday, July 24, 2011
  50. 50. Resistors in Series I1 I2 ∆V1 ∆V2 Conservation of matter = Current is conserved I = I1 = I2 Conservation of energy ∆V = ∆V1 + ∆V2Sunday, July 24, 2011
  51. 51. Resistors in Series I1 I2 ∆V1 ∆V2 Conservation of matter = Current is conserved Ohms Law I = I1 = I2 ∆V Conservation of energy I= R ∆V = ∆V1 + ∆V2Sunday, July 24, 2011
  52. 52. Resistors in Series I1 I2 ∆V = I1 R1 + I2 R2 ∆V1 ∆V2 ∆V = IR1 + IR2 ∆V = I(R1 + R2 ) ∆V = IReq Req = R1 + R2 Conservation of matter = Current is conserved Ohms Law I = I1 = I2 ∆V Conservation of energy I= R ∆V = ∆V1 + ∆V2Sunday, July 24, 2011
  53. 53. Resistors in Series I1 I2 ∆V1 ∆V2 Conservation of matter = Current is conserved Ohms Law I = I1 = I2 ∆V Conservation of energy I= R ∆V = ∆V1 + ∆V2Sunday, July 24, 2011
  54. 54. Resistors in Parallel 1. Imagine positive charges pass first I1 I2 through R1 and then through%R2. Compared to the current in R1, the current in R2 is ∆V1 ∆V2 (a) smaller (b) larger (c) the same. 2. With the switch in the circuit of closed (left), there is no current in R2, because the current has an alternate zero-resistance path through the switch. There is current in R1 and this current is measured with the ammeter (a device for measuring current) at the right side of the circuit. If the switch is opened (right), there is current in R2. What happens to the reading on the ammeter when the switch is opened? (a) the reading goes up (b) the reading goes down (c) the reading does not change.Sunday, July 24, 2011
  55. 55. Resistors in Parallel ∆V Recall: I= R use the equation to calculate the equivalent resistance ReqSunday, July 24, 2011
  56. 56. Resistors in Parallel Convert to simple equivalent circuitSunday, July 24, 2011
  57. 57. Resistors in Parallel I1 ∆V1 I2 ∆V2 Conservation of matter = Current is conserved I = I1 + I2Sunday, July 24, 2011
  58. 58. Resistors in Parallel I1 ∆V1 I2 ∆V2 Conservation of matter = Current is conserved I = I1 + I2 Conservation of energy ∆V = ∆V1 = ∆V2Sunday, July 24, 2011
  59. 59. Resistors in Parallel I1 ∆V1 I2 ∆V2 Conservation of matter = Current is conserved Ohms Law I = I1 + I2 ∆V Conservation of energy I= R ∆V = ∆V1 = ∆V2Sunday, July 24, 2011
  60. 60. Resistors in Parallel I1 ∆V1 I = I1 + I2 ∆V ∆V1 ∆V2 I2 = + ∆V2 R R1 R2 ∆V ∆V ∆V = + R R1 R2 1 1 1 = + R R1 R2 Conservation of matter = Current is conserved Ohms Law I = I1 + I2 ∆V Conservation of energy I= R ∆V = ∆V1 = ∆V2Sunday, July 24, 2011
  61. 61. Resistors in Parallel I1 ∆V1 I2 ∆V2 Conservation of matter = Current is conserved Ohms Law I = I1 + I2 ∆V Conservation of energy I= R ∆V = ∆V1 = ∆V2Sunday, July 24, 2011
  62. 62. Recall: Ohms Law Capacitance ∆V I= Q = C∆V R Series ParallelSunday, July 24, 2011
  63. 63. Exercise Find the current passing through each resistor Find the voltage drop (potential difference) through each resistorSunday, July 24, 2011
  64. 64. Kirchhoff’s Rules Junction Rule “conservation of matter” Loop Rule “conservation of energy” Σ ∆V = 0 closed loopSunday, July 24, 2011
  65. 65. Exercise In solving complicated circuit problems apply Junction rule first (conservation of current) You may assign any direction of current as long as it is reasonable (does not violate common sense!) A Then apply the loop rule B Write down the equations for loop rules concerning loop A, B, C and the outer loop of the circuit following C clockwise direction. (there must be four equations!)Sunday, July 24, 2011

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