Chapter 3

1. Chapter 3 Resistance

2. FIG. 3.1 Resistance symbol and notation.

3. Resistance of Conductors • Resistance of material is dependent on several factors: • Type of Material • Length of the Conductor • Cross-sectional area • Temperature

4. Type of Material • Differences at the atomic level of various materials will cause variations in how the collisions affect resistance. • These differences are called the resistivity. • We use the symbol (Greek letter rho). • Units are ohm-meters.

5. Length • The resistance of a conductor is directly proportional to the length of the conductor. • If you double the length of the wire, the resistance will double. •  = length, in meters.

6. Area • The resistance of a conductor is inversely proportional to the cross-sectional area of the conductor. • If the cross-sectional area is doubled, the resistance will be one half as much. • A = cross-sectional area, in m2.

7. Resistance Formula • At a given temperature, • This formula can be used with both circular and rectangular conductors.

8. FIG. 3.2 Factors affecting the resistance of a conductor.

9. FIG. 3.3 Cases in which R2 > R1. For each case, all remaining parameters that control the resistance level are the same.

10. Electrical Wire Tables • The American Wire Gauge is the primary system to denote wire diameters. • The higher the AWG number, the smaller the diameter. • A given length of AWG 22 wire will have more resistance than the same length of AWG 14 wire. • Larger gauge wires can handle more current.

11. Circular Mils (CM) • Diameter is expressed in circular mils. • 1 CM is defined as the area of a circle having a diameter of 1 mil (0.001 inch). • A square mil is the area of a square having sides 1 mil long. • 1 CM = /4 square mils

12. FIG. 3.4 Defining the circular mil (CM).

13. FIG. 3.5 Verification of Eq. (3.2): ACM = (dmils)2.

14. FIG. 3.8 Popular wire sizes and some of their areas of application.

15. Temperature Effects • For most conductors, an increase in temperature causes an increase in resistance. • This increase is relatively linear. • In many semiconductors, an increase in temperature results in a decrease in resistance.

16. Temperature Effects • The rate of change of resistance with temperature is called the temperature coefficient. • Represented by  (Greek letter alpha). • Any material for which the resistance increases as temperature increases is said to have a positive temperature coefficient. If it decreases, it has a negative coefficient.

17. FIG. 3.12 Demonstrating the effect of a positive and a negative temperature coefficient on the resistance of a conductor.

18. FIG. 3.13 Effect of temperature on the resistance of copper.

19. Fixed Resistors • Resistances essentially constant. • Rated by amount of resistance, measured in ohms. • Also rated by power ratings, measured in watts.

20. Fixed Resistors • Different types of resistors are used for different applications. • Molded carbon composition • Carbon film • Metal film • Metal Oxide • Wire-Wound • Integrated circuit packages

21. FIG. 3.16 (continued) Film resistors: (a) construction; (b) types.

22. FIG. 3.16 Film resistors: (a) construction; (b) types.

23. FIG. 3.17 Fixed composition resistors: (a) construction; (b) appearance.

24. FIG. 3.17 (continued) Fixed composition resistors: (a) construction; (b) appearance.

25. FIG. 3.18 Fixed metal-oxide resistors of different wattage ratings.

26. FIG. 3.19 Various types of fixed resistors.

27. FIG. 3.19 (continued) Various types of fixed resistors.

28. Variable Resistors • Used to adjust volume, set level of lighting, adjust temperature. • Have three terminals. • Center terminal connected to wiper arm. • Potentiometers • Rheostats

29. FIG. 3.20 Potentiometer: (a) symbol; (b) and (c) rheostat connections; (d) rheostat symbol.

30. FIG. 3.21 Molded composition-type potentiometer.

31. FIG. 3.23 Variable resistors: (a) 4 mm (≈5/32”) trimmer (courtesy of Bourns, Inc.); (b) conductive plastic and cermet elements (courtesy of Honeywell Clarostat); (c) three-point wire-wound resistor.

32. FIG. 3.24 Potentiometer control of voltage levels.

33. Color Code • Colored bands on a resistor provide a code for determining the value of resistance, tolerance, and sometimes the reliability.

34. FIG. 3.25 Color coding for fixed resistors.

35. FIG. 3.29 Five-band color coding for fixed resistors.

36. FIG. 3.26 Color coding.

37. FIG. 3.30 Guaranteeing the full range of resistor values for the given tolerance: (a) 20%; (b) 10%.

38. FIG. 3.27 Example 3.13.

39. FIG. 3.28 Example 3.14.

40. Measuring Resistance • Remove all power sources to the circuit. • Component must be isolated from rest of the circuit. • Connect probes across the component. • No need to worry about polarity. • Useful to determine shorts and opens.

41. FIG. 3.22 Resistance components of a potentiometer: (a) between outside terminals; (b) between wiper arm and each outside terminal.

42. Thermistors • A two-terminal transducer in which the resistance changes with change in temperature. • Applications include electronic thermometers and thermostatic control circuits for furnaces. • Many have negative temperature coefficients.

43. FIG. 3.35 Thermistor: (a) characteristics; (b) symbol.

44. FIG. 3.36 NTC (negative temperature coefficient) and PTC (positive temperature coefficient) thermistors.

45. Photoconductive Cells • Two-terminal transducers which have a resistance determined by the amount of light falling on them. • May be used to measure light intensity or to control lighting. • Used as part of security systems.

46. FIG. 3.37 Photoconductive cell: (a) characteristics. (b) symbol.

47. FIG. 3.38 Photoconductive cells.

48. Varistors • Resistors which are sensitive to voltage. • Have a very high resistance when the voltage is below the breakdown value. • Have a very low resistance when the voltage is above the breakdown value. • Used in surge protectors.

49. FIG. 3.39 Varistors available with maximum dc voltage ratings between 18 V and 615 V.

50. FIG. 3.39 (continued) Varistors available with maximum dc voltage ratings between 18 V and 615 V.