1. Lesson 2: Resistance and Ohm’s Law

2. Learning Objectives  Describe the concept of resistance. Given a color code table, determine the value and tolerance of fixed resistors using their color codes. Use Ohm’s law to calculate current, voltage, and resistance values in a circuit. Discuss the difference between an open circuit and a short circuit. Demonstrate how to measure current, voltage, and resistance in a circuit.

3. Resistance of conductors Resistance is the opposition to charge movement. As electrons move through a material, they constantly collide with atoms in the material and with other electrons. These collisions cause some of the energy carried by the charge to be released as heat. So resistance is dependent on type of material, length of the conductor, cross-sectional area and temperature.

4. Resistance of conductors Type of material: Atomic differences of materials cause variations in how electron collisions affect resistance Differences produce resistivity. The higher the resistivity, the greater is the resistance of the conductor. Represented by the symbol  (Greek letter rho) Units of  : Ohms x meters (Ω∙m)

5. Resistance of conductors Length of conductor: Directly proportional to its length. The longer the conductor, the greater is the resistance.  If you double the length of the wire, the resistance will double  = length  In meters or feet

6. Resistance of conductors Cross-sectional area:  Inversely proportional to cross-sectional area of the conductor. The greater the area of the conductor, the less is the resistance.  If cross-sectional area is doubled, resistance will be one half as much  A =Cross-sectional area, in m 2

7. Resistance of conductors Temperature: for most conductors, a temperature increase causes an increase in resistance. Increase is relatively linear In semiconductors and insulators, increase in temperature results in decrease in resistance

8. Resistance of conductors Resistance of a conductor at a given temperature can be expressed mathematically A(CM) 1x10 -3 inches = 1 mil & A CM = (diameter mils ) 2

9. Example Problem 1 Need to measure length of this copper coil but don’t want to unroll. Resistance measured is 103.7 Ohms. Diameter is 0.01 inches 1x10 -3 inches = 1 mil & A CM = (diameter mils ) 2

10. Fixed resistors To provide control of electrical circuits.

11. Variable resistors Variable resistors have an adjustable value of resistance and have two principle functions  Potentiometers are used to adjust voltage.  Rheostats are used to adjust current.  Used to adjust volume, set level of lighting, adjust temperature,… a c b R ab R bc

12. Resistors usually have 4, 5 or 6 color bands. 4 color bands: Band 1: First Digit Band 2: Second Digit Band 3: Multiplier (10 X ) Band 4: Tolerance Sometimes a 5th or 6th band is added (Reliability) to meet MILSPEC requirements. Resistor color coding 5 color bands: Band 1: First Digit Band 2: Second Digit Band 3: Third Digit Band 4: Multiplier (10 X ) Band 5: Tolerance

13. Resistor color coding MULTIPLIER 4=10 4 5=10 5 IF THIRD BAND Read left To right

14. Example Problem 2 Determine the resistance of a carbon resistors having the color codes shown in the figure below. Brown = 1 Black = 0 Brown = 10X Gold = 5% tolerance = ± 5 Ω 10 x 10 = 100 Ω Green = 5 Blue = 6 Yellow = 4 Green = 100000X Silver = 10% tol = ±5.6 MΩ 565 x 10k = 56.4 MΩ

15. OHM’S LAW Every conversion of energy from one form to another can be related to this equation. In electric circuits, the effect we are trying to establish is the flow of charge, or current. The potential difference, or voltage, between two points is the cause (“pressure”), and the opposition is the resistance encountered.

16. Ohm’s law Ohm discovered experimentally that voltage and current in a wire were linearly related to each other by a constant (Resistance) Current in a resistive circuit  Directly proportional to its applied voltage  Inversely proportional to its resistance

17. Ohm’s law Two different symbols are commonly used to represent voltage.  E for sources  V for loads (such as the voltage drop across a resistor)

18. OHM’S LAW In summary, therefore, the absence of an applied “pressure” such as voltage in an electric circuit will result in no reaction in the system and no current in the electric circuit. Current is a reaction to the applied voltage and not the factor that gets the system in motion. EXAMPLE: The greater the pressure in a hose, the greater is the rate of water flow through the hose, just as applying a higher voltage to the same circuit results in a higher current.

19. Example Problem 3 Determine the current provided by the source.

20. Open circuits Current can only exist where there is a conductive path. Since current is zero, the circuit has an infinite resistance. This is called an open circuit.

21. Short circuits A very low (or near zero) resistance is placed across a circuit Since resistance is near zero, all current will bypass the rest of circuit and go through the short. With zero resistance, current draw will approach the limits of the power source (infinite current), frequently causing damage to wiring or the power source

22. Measuring voltage Voltage and current is measured using voltmeters and ammeters, or a Digital Multi-Meter (DMM). Measure voltage by placing the voltmeter leads across the component whose voltage you wish to measure. Polarity can be determined by probe placement. “Auto-polarity”

23. Meter Symbol: Voltmeter

24. Current representation The current depicted in the following circuits is identical.

25. Measuring current The current that you wish to measure must pass through the meter. Be careful that the meter’s maximum current rating is not exceeded!

26. Meter Symbol: Ammeter

27. Voltage polarity and current direction For the voltage across a resistor, always place the plus sign at the tail of the current reference arrow. To ensure the correct voltage sign on the DMM, place the red lead where you think the “+” sign should be For correct current polarity, the current should enter the red lead of the DMM.

28. Example Problem 4 Determine the readings, magnitude and polarity for the measurements taken below:

29. Measuring resistance An ohmmeter is a device used to measure the resistance of a component. Resistance cannot be measured when voltage is supplied to the circuit.

30. Measuring component resistance You must isolate the component that you are measuring from the circuit!

31. Measuring Total Resistance You must remove the power source prior to measuring total resistance!

32. Lesson 3: Power, and Energy

33. Learning Objectives Describe the relationship between battery capacity, current drain and battery’s useful life. Calculate the total cost given a rate of energy consumption. Calculate power supplied/dissipated in a circuit. Calculate the power efficiency of a circuit.

34. POWER In general, the term power is applied to provide an indication of how much work (energy conversion) can be accomplished in a specified amount of time; that is, power is a rate of doing work.

35. Power Power is defined as the rate of doing work or as the rate of energy transfer. The SI unit of power is the watt (W) or joules per second. The English unit of power is horsepower (hp).

36. Power in electrical systems We need to express power in terms of voltage and current, recall that Combining them we have

37. Power in electrical systems Applying Ohm’s law ( V = IR and I = V/R ) we can also express power as

38. Power Calculate the power to the heater using all three electrical formulas

39. Power Power is defined as the rate of doing work or as the rate of energy transfer. The greater the power rating of a light, the more light energy it can produce each second The greater the power rating of a heater, the more heat energy it can produce The greater the power rating of a motor, the more mechanical work it can do per second Power is related to energy. Is the capacity to do work

40. Example Problem 1 A resistor draws 3 amps from a 12V battery. How much power does the battery deliver to the resistor? I = 3 A E=12V

41. ENERGY For power, which is the rate of doing work, to produce an energy conversion of any form, it must be used over a period of time. The energy (W) lost or gained by any system is therefore determined by:

42. Energy We can rearrange our formula for power to solve for energy The unit of energy is joules (J), but is also expressed as watt-hours (Wh) or kilowatt-hours (kWh). Cost = Power × time × cost per unit The residential energy cost from BGE is 14.8 cents per kWh.

43. Energy Cost = Energy × cost per unit or Cost = Power × time × cost per unit

44. Example Problem 2 Suppose you are at home and use 3 100-W lamps for 3 hours and An Xbox 500W for 2,5 hours. The TV consumes 180 W. At $0.148 per kilowatt-hour, how much will this cost you?

45. Efficiency In the process of converting energy, energy losses inevitably occur. The measure of output energy (or power) to input energy (or power) is called efficiency. Thermal energy out

46. Efficiency Poor efficiency in energy transfers results in wasted energy An inefficient piece of equipment generates more heat. As heat must be removed to guarantee a proper function, it means more $$.

47. Efficiency Efficiency is usually expressed in percent and denoted by the symbol . Since P in = P out + P losses, efficiency can also be expressed as

48. Efficiency To find the total efficiency of a system  Obtain product of individual efficiencies of all subsystems:  Total =  1 ×  2 ×  3 × ∙∙∙

49. Efficiency Suppose a power amplifier delivers 400 W to its speaker system. If the power loss is 509 W, what is the efficiency?

50. A 120 V dc motor drives a pump through a gearbox. The power output to the pump is 1100 W. Gearbox efficiency is 75%. Power input to the motor is 1600W. What is Overall efficiency? Hp output and efficiency of the motor? Example Problem 3

51. Fuses A fuse is a device that prevents excessive current to protect against overloads or possible fires. A fuse literally “blown” can not be reset.

52. Digital Multimeter Dual Voltage Source Lab Bench

53. Measuring Voltage Push “DCV” button to measure DC volts

54. Measuring Current Push “SHIFT” + “DCV” button to measure amps X

55. Measuring resistance Push “Ω 2W” button to measure resistance

56. Quad Board Four Terminals Connected Together

57. Laboratory Voltage Source Functions as an ideal voltage source- maintains desired output voltage regardless of load (within limits) Verify V1/V2 knob on power supply is turned CCW before turning power on!