1. Ohm’s Law and Power ELPT 1311 Basic Electrical Theory Chapter 04_Ohm’s Law Introduction to Electricity by Paynter & Boydell and Pearson Illustrations

2. Objectives Describe the relationship among voltage, current and resistance Predict how either a change in voltage or resistance will affect the circuit current Use Ohm’s Law to calculate any one of the following basic electrical values, given the other two: current, voltage, resistance Describe how Ohm’s Law is used in troubleshooting Define “power” and its relationship to current and voltage Calculate power from any two of current, voltage resistance Describe the relationship between power and heat Determine minimum acceptable power rating for a resistor in a circuit Define and calculate efficiency and the kilowatt hour (kWh) unit of energy Calculate any two of the following given the other two: current, voltage, resistance, power

3. The Relationship Between Current and Voltage Current is directly proportional to voltage. Current is inversely proportional to resistance. Voltage is the force or potential difference that causes current to flow

4. Double the voltage, double the current

5. 60  120  Double the resistance, current decreases by 1/2

6. Conclusion  Increases in resistance causes decreases in current  Decreases in resistance causes increases in current  Increases in voltage causes increases in current  Decreases in voltage causes decreases in current Thus the amount of current flow through a circuit is dependent upon the amount of voltage and resistance The Relationship Between Current and Voltage

7. Using Ohm’s Law to Calculate Current The mathematical relationship between voltage, current and resistance is derived from Ohm’s Law: where I = the circuit current E = the applied voltage R = the circuit resistance Calculating current:

8. Using Ohm’s Law to Calculate Current Question: will the fuse below blow? 220 V

9. Using Ohm’s Law to Calculate Current Question: will the fuse below blow? Yes, 6.7 A exceeds 5 A 220 V

10. Using Ohm’s Law to Calculate Voltage Calculating voltage: 15 V

11. Using Ohm’s Law to Calculate Voltage Question: what is the maximum voltage that can be applied before the fuse blows?

12. Using Ohm’s Law to Calculate Circuit Values Question: what is the maximum voltage that can be applied before the fuse blows?

13. Using Ohm’s Law to Calculate Resistance Calculating resistance:

14. Using Ohm’s Law to Calculate Resistance Question: If a speaker has 10 V applied with 1.25 A flowing through the speaker, what is the resistance of the speaker?

15. Using Ohm’s Law to Calculate Resistance Question: If a speaker has 10 V applied with 1.25 A flowing through the speaker, what is the resistance of the speaker?

16. Using Ohm’s Law to Calculate Resistance Question: What is the minimum allowable setting for the rheostat below to prevent the fuse from blowing?

17. Using Ohm’s Law to Calculate Resistance Question: What is the minimum allowable setting for the rheostat below to prevent the fuse from blowing?

18. Current Relationships Question: What does current change to if voltage doubles?

19. Current Relationships Question: What does current change to if voltage doubles?

20. Current Relationships Question: What does current change to if resistance doubles?

21. Current Relationships Question: What does current change to if resistance doubles?

22. Ohm's Law Wheel - Ohm's Law Triangle

23. Troubleshooting Using Ohm’s Law Problem: What could be wrong if the circuit shows the current to be 4 A, but the drawing shows that it should be 1 A? Question: Either _________ is too high, or ________ is too low.

24. Troubleshooting Using Ohm’s Law Problem: What could be wrong if the circuit shows the current to be 4 A, but the drawing shows that it should be 1 A? Question: Either _________ is too high, or ________ is too low. voltageresistance

25. Troubleshooting Using Ohm’s Law Question: what would the voltage need to be to produce 4 A at the resistance of 10 Ω? Question: what would the resistance need to be to produce 4 A at 10 V?

26. Troubleshooting Using Ohm’s Law Question: what would the voltage need to be to produce 4 A at the resistance of 10 Ω? Question: what would the resistance need to be to produce 4 A at 10 V?

27. Power Power is the rate at which a component, circuit or system uses energy The more power a circuit consumes, the more heat it produces; example is a resistor dissipating heat Technically, power is the amount of energy consumed per unit of time Electrical power is measured in watts Some important relationships - 1 volt = 1 joule per coulomb (the joule is a measure of energy) - 1 amp = 1 coulomb per second (6.25 x 10 18 electrons per second) - 1 watt = 1 joule per second

28. Power Calculating power when current and voltage is known: 1 W

29. Power Question: How much power is being provided by the voltage source?

30. Power Question: How much power is being provided by the voltage source?

31. Power Question: How much power is being provided by the voltage source?

32. Power Question: How much power is being provided by the voltage source?

33. The Power Wheel

34. Power Calculating power when current and resistance is known:

35. Power Question: How much power is being consumed in the circuit?

36. Power Question: How much power is being consumed in the circuit?

37. Power Question: How much power is being consumed in the circuit? I = 2.25 A 6 kΩ

38. Power Question: How much power is being consumed in the circuit? I = 2.25 A 6 kΩ

39. Power Calculating power when voltage and resistance is known:

40. Power Question: How much power is being consumed in the circuit? 50 V 125 Ω

41. Power 125 Ω 50 V Question: How much power is being consumed in the circuit?

42. Power 2.75 kΩ 480 V Question: How much power is being consumed in the circuit?

43. Power Question: How much power is being consumed in the circuit? 2.75 kΩ 480 V

44. The Complete DC Ohm's Wheel

45. Power and Heat Energy cannot be created or destroyed Energy can be transferred from one part of a circuit to another - a toaster converts electrical energy to heat - a light bulb converts electrical energy to heat and light - a motor converts electrical energy to heat and motion - a speaker converts electrical energy to mechanical energy (sound) A component such as a resistor converts a given amount of energy in a unit of time.

46. Resistor Power Ratings The power rating of a resistor is a measure of its ability to dissipate heat measured in watts (W) When choosing a resister, the power rating of the resistor should be greater than the amount of power expected to be dissipated or the resistor is likely to fail.25 W.5 W 1 W 2 W 25 W ALUMINUM COOLING FINS

47. Power Question: What is the minimum power rating that the resistor should have?

48. Power Question: What is the minimum power rating that the resistor should have?

49. Efficiency Every circuit contains a variety of components that use some amount of power Therefore the output power from a circuit is always less than its input power The ratio of the a circuit’s (or component’s) output power to its input power is its efficiency where η = efficiency P out = the circuit output power P in = the circuit input power

50. Efficiency A DC power supply has the following ratings: P in = 1600 W P out = 1250 W

51. Efficiency Question: what is the efficiency of the DC to AC inverter with the following ratings: P in = 1.76 kW P out = 950 W

52. Efficiency Question: what is the efficiency of the DC to AC inverter with the following ratings: P in = 1.76 kW P out = 950 W

53. Energy Measurement

54. How much energy is required to run twenty 60 W incandescent light bulbs for six hours? - total wattage is the sum of the individual wattages If you pay 13.5 cents per kWh, what is your cost?

55. Energy Measurement Question: you keep a 150 W incandescent light on in your barn 24 hours a day, how many kilowatt hours are you using? If you pay 13.5 cents per kWh, what is your cost?

56. Question: you keep a 150 W incandescent light on in your barn 24 hours a day, how many kilowatt hours are you using? Energy Measurement If you pay 13.5 cents per kWh, what is your cost?

57. Energy Measurement Question: you replace the 150 W incandescent light with a compact florescent (CFL) with the same lumens that is rated at 32 watts. At the same 13.5 cents per kWh how much do you save?

58. Energy Measurement Question: you replace the 150 W incandescent light with a compact florescent (CFL) with the same lumens that is rated at 32 watts. At the same 13.5 cents per kWh how much do you save?

59. Energy Measurement Question: you replace the 150 W incandescent light with a LED lamp with the same lumens that is rated at 23 watts. At the same 13.5 cents per kWh how much do you save?

60. Energy Measurement Question: you replace the 150 W incandescent light with a LED lamp with the same lumens that is rated at 23 watts. At the same 13.5 cents per kWh how much do you save?

61. Energy Measurement Reading a kWh meter

62. Problems: + - 12 V R = _______ 500 mA + - 60 V R = _______ 1.25 A + - 2.75 mA 1.5 k  V = _______ + - 2.2 A 100  V = _______ + - 2.2 M  4160 V + - 250  90 V

63. Problems: + - 12 V R = _______ 500 mA + - 60 V R = _______ 1.25 A 24 Ω48 Ω + - 2.2 M  4160 V + - 250  90 V 1.89 mA360 mA + - 2.75 mA 1.5 k  V = _______ + - 2.2 A 100  V = _______ 4.125 V220 V

64. Problems: + - 35 V POWER = _______ 1.2 A + - 120 V POWER = _______ 750 mA + - 2.7 k  480 V + - 333  48 V POWER = _______ + - 1.35 k  + - 120  2.5 A POWER = _______.275 mA

65. Problems: + - 120 V POWER = _______ 750 mA 90 W + - 35 V POWER = _______ 1.2 A 42 W + - 2.7 k  480 V + - 333  48 V POWER = _______ 6.9 W85.3 W + - 1.35 k  + - 120  2.5 A POWER = _______.275 mA 750 W10.2 mW

66. Problems: + - R = _______ 60 V 2.5 A What is the minimum resistance that the circuit can have and not blow the fuse? + - __________ V 555 mA What is the maximum voltage that the circuit can have and not blow the fuse? 332 

67. Problems: 184.26 V + - R = _______ 60 V 2.5 A What is the minimum resistance that the circuit can have and not blow the fuse? + - __________ V 555 mA What is the maximum voltage that the circuit can have and not blow the fuse? 332  24 Ω

68. Problems: What is the efficiency of the circuit? 180 W 75 W How many kWh are used to cook a stuffed 30 lb turkey for 5 hours and 30 minutes in a 2,200 watt oven? How much did it cost to cook the turkey at 12.72 cents per kWh? 40 W

69. Problems: What is the efficiency of the circuit? How many kWh are used to cook a stuffed 30 lb turkey for 5 hours and 30 minutes in a 2,200 watt oven? How much did it cost to cook the turkey at 12.72 cents per kWh? 75 W 40 W 180 W