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Ohm’s Law and Power

Ohm’s Law and Power. Al Penney VO1NO. Chapter 3. Voltage and Current. Current In Amps. Voltage in Volts. As Voltage is increased, Current also increases. Ohm’s Law. Relationship between Voltage, Current and Resistance can be expressed mathematically as: E = I x R Where

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Ohm’s Law and Power

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  1. Ohm’s Law and Power Al Penney VO1NO Chapter 3

  2. Voltage and Current Current In Amps Voltage in Volts As Voltage is increased, Current also increases.

  3. Ohm’s Law • Relationship between Voltage, Current and Resistance can be expressed mathematically as: E = I x R Where E is measured in Volts; I is measured in Amps; and R is measured in Ohms.

  4. Ohm’s Law The equation can be re-written to determine any of the 3 variables if the other two are known: I = E / R And R = E / I

  5. Ohms Law Triangle Remember the Units: - E is measured in VOLTS - I is measured in AMPS - R is measured in OHMS

  6. Ohms Law Triangle(Okay – Circle!)

  7. Ohms Law Problem #1 What is the current? 12 Volts 96 Ohms

  8. Ohms Law Problem #1 What is the current? 12 Volts 96 Ohms Consult the Ohms Law Triangle:

  9. Ohms Law Problem #1 What is the current? 12 Volts 96 Ohms I = E / R Consult the Ohms Law Triangle:

  10. Ohms Law Problem #1 What is the current? 12 Volts 96 Ohms I = E / R I = 12 Volts / 96 Ohms I =

  11. Ohms Law Problem #1 What is the current? 12 Volts 96 Ohms I = E / R I = 12 Volts / 96 Ohms I = 0.125 Amps

  12. Ohms Law Problem #2 What is the voltage? 1.5 Amps 15 Ohms

  13. Ohms Law Problem #2 What is the voltage? 1.5 Amps 15 Ohms Consult the Ohms Law Triangle:

  14. Ohms Law Problem #2 What is the voltage? 1.5 Amps 15 Ohms E = I x R Consult the Ohms Law Triangle:

  15. Ohms Law Problem #2 What is the voltage? 1.5 Amps 15 Ohms E = I x R = 1.5 Amps x 15 Ohms

  16. Ohms Law Problem #2 What is the voltage? 1.5 Amps 15 Ohms E = I x R = 1.5 Amps x 15 Ohms = 22.5 Volts

  17. Ohms Law Problem #3 What is the resistance? 30 milliamps 150 millivolts

  18. Ohms Law Problem #3 What is the resistance? 30 milliamps 150 millivolts Consult the Ohms Law Triangle:

  19. Ohms Law Problem #3 What is the resistance? 30 milliamps 150 millivolts R = E / I Consult the Ohms Law Triangle:

  20. Ohms Law Problem #3 What is the resistance? 30 milliamps 150 millivolts R = E / I = 150 millivolts / 30 milliamps

  21. Ohms Law Problem #3 • REMEMBER the UNITS! • 150 millivolts = 150 / 1000 volts = 0.15 volts • 30 milliamps = 30 / 1000 amps = 0.03 amps

  22. Ohms Law Problem #3 What is the resistance? 30 milliamps 150 millivolts R = E / I = 150 millivolts / 30 milliamps = 0.15 Volts / 0.03 Amps

  23. Ohms Law Problem #3 What is the resistance? 30 milliamps 150 millivolts R = E / I = 150 millivolts / 30 milliamps = 0.15 Volts / 0.03 Amps = 5 Ohms

  24. Resistors in Series • When resistors are in SERIES, the total resistance is the SUM of the individual resistances. RTotal = R1 + R2 + R3 + ….. + RN

  25. Resistors in Series 5 Ω 15 Ω 25 Ω

  26. Resistors in Series 5 Ω 15 Ω 25 Ω RTotal = R1 + R2 + R3

  27. Resistors in Series 5 Ω 15 Ω 25 Ω RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 25 Ω

  28. Resistors in Series 5 Ω 15 Ω 25 Ω RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 25 Ω RTotal = 45 Ω

  29. Resistors in Parallel • When resistors are in Parallel, the total resistance is given by the following equation: 1/RTotal = 1/R1 + 1/R2 + 1/R3 + ….. + 1/RN

  30. Resistors in Parallel A 75 Ω 50 Ω 25 Ω 25 Ω B

  31. Resistors in Parallel A 75 Ω 50 Ω 25 Ω 25 Ω B 1/RTotal = 1/R1 + 1/R2 + 1/R3 + 1/R4

  32. Resistors in Parallel A 75 Ω 50 Ω 25 Ω 25 Ω B 1/RTotal = 1/R1 + 1/R2 + 1/R3 + 1/R4 1/RTotal = 1/25 + 1/75 + 1/50 + 1/25

  33. Resistors in Parallel A 75 Ω 50 Ω 25 Ω 25 Ω B 1/RTotal = 1/R1 + 1/R2 + 1/R3 + 1/R4 1/RTotal = 1/25 + 1/75 + 1/50 + 1/25 = 6/150 + 2/150 + 3/150 + 6/150

  34. Resistors in Parallel A 75 Ω 50 Ω 25 Ω 25 Ω B 1/RTotal = 1/R1 + 1/R2 + 1/R3 + 1/R4 1/RTotal = 1/25 + 1/75 + 1/50 + 1/25 = 6/150 + 2/150 + 3/150 + 6/150 1/RTotal = 17/150 Ω

  35. Resistors in Parallel A 75 Ω 50 Ω 25 Ω 25 Ω B 1/RTotal = 1/R1 + 1/R2 + 1/R3 + 1/R4 1/RTotal = 1/25 + 1/75 + 1/50 + 1/25 = 6/150 + 2/150 + 3/150 + 6/150 1/RTotal = 17/150 Ω RTotal = 150/17 Ω = 8.82 Ω

  36. Current in a Series Circuit • The current through each resistor in a Series Circuit is identical. ITotal = IR1 = IR2 = IR3

  37. Voltage in Series Circuits • The sum of all the voltages across each resistor in a Series Circuit will equal the source voltage. 5 Ω 20 Volts 15 Ω 20 Ω Esource = ER1 + ER2 + ER3

  38. To Calculate Voltage Drop… 5 Ω 20 Volts 15 Ω 20 Ω

  39. 1. Determine Total Resistance RTotal = R1 + R2 + R3 RTotal = 5 Ω 20 Volts 15 Ω 20 Ω

  40. 1. Determine Total Resistance RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 20 Ω RTotal = 40 Ω 5 Ω 20 Volts 15 Ω 20 Ω

  41. 2. Determine Current RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 20 Ω RTotal = 40 Ω I = E / R I = 5 Ω 20 Volts 15 Ω 20 Ω

  42. 2. Determine Current RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 20 Ω RTotal = 40 Ω I = E / R I = 20 Volts / 40 Ohms I = 0.5 Amps 5 Ω 20 Volts 15 Ω 20 Ω

  43. 3. Determine Voltage Drops RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 20 Ω RTotal = 40 Ω I = E / R I = 20 Volts / 40 Ohms I = 0.5 Amps 5 Ω 20 Volts 15 Ω 20 Ω ER3 = I x R3 ER3 = ER2 = I x R2 ER2 = ER1 = I x R1 ER1 =

  44. 3. Determine Voltage Drops RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 20 Ω RTotal = 40 Ω I = E / R I = 20 Volts / 40 Ohms I = 0.5 Amps 5 Ω 20 Volts 15 Ω 20 Ω ER3 = I x R3 ER3 = 0.5 Amps x 20 Ω ER3 = 10 Volts ER2 = I x R2 ER2 = 0.5 Amps x 15 Ω ER2 = 7.5 Volts ER1 = I x R1 ER1 = 0.5 Amps x 5 Ω ER1 = 2.5 Volts

  45. 4. Check Your Results! RTotal = R1 + R2 + R3 RTotal = 5 Ω + 15 Ω + 20 Ω RTotal = 40 Ω I = E / R I = 20 Volts / 40 Ohms I = 0.5 Amps 5 Ω 20 Volts 15 Ω 20 Ω ER3 = I x R3 ER3 = 0.5 Amps x 20 Ω ER3 = 10 Volts ER2 = I x R2 ER2 = 0.5 Amps x 15 Ω ER2 = 7.5 Volts ER1 = I x R1 ER1 = 0.5 Amps x 5 Ω ER1 = 2.5 Volts Esource = ER1 + ER2 + ER3 Esource = 2.5V + 7.5V+ 10V = 20V

  46. Voltage in Parallel Circuits • The voltage applied to each resistor in a Parallel Circuit is the same as the source voltage. Esource = ER1 = ER2 = ER3 = ER4

  47. Current in a Parallel Circuit • The total current in a Parallel Circuit is divided among the resistors. • The sum of the currents through each resistor equals the total current. ITotal = IR1 + IR2 + IR3

  48. To Calculate Currents… 100 Volts 500 Ω 500 Ω 1KΩ

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