# Chapter 3: Resistance

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```					Chapter 3
Resistance
FIG. 3.1   Resistance symbol and notation.

2
Resistance of Conductors
• Resistance of material is dependent on
several factors:
–   Type of Material
–   Length of the Conductor
–   Cross-sectional area
–   Temperature

3
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.

4
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.

5
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.

6
Resistance Formula
• At a given temperature,

R
A
• This formula can be used with both circular
and rectangular conductors.

7
FIG. 3.2   Factors affecting the resistance of a conductor.

8
FIG. 3.3   Cases in which R2 > R1. For each case, all remaining parameters that control the resistance level are the same.

9
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.
10
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

11
FIG. 3.4   Defining the circular mil (CM).

12
FIG. 3.5   Verification of Eq. (3.2): ACM = (dmils)2.

13
FIG. 3.8   Popular wire sizes and some of their areas of application.

14
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.

15
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.
R  R1 1  T               16
FIG. 3.12   Demonstrating the effect of a positive and a negative temperature coefficient on the resistance of a conductor.

17
FIG. 3.13   Effect of temperature on the resistance of copper.

18
Fixed Resistors
• Resistances essentially constant.
• Rated by amount of resistance, measured in
ohms.
• Also rated by power ratings, measured in
watts.

19
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
20
FIG. 3.16 (continued)   Film resistors: (a) construction; (b) types.

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

22
FIG. 3.17   Fixed composition resistors: (a) construction; (b) appearance.

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

24
FIG. 3.18   Fixed metal-oxide resistors of different wattage ratings.

25
FIG. 3.19   Various types of fixed resistors.

26
FIG. 3.19 (continued)   Various types of fixed resistors.

27
Variable Resistors
• Used to adjust volume, set level of lighting,
• Have three terminals.
• Center terminal connected to wiper arm.
• Potentiometers
• Rheostats

28
FIG. 3.20   Potentiometer: (a) symbol; (b) and (c) rheostat connections; (d) rheostat symbol.

29
FIG. 3.21   Molded composition-type potentiometer.

30
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.

31
FIG. 3.24   Potentiometer control of voltage levels.

32
Color Code
• Colored bands
on a resistor
provide a code
for determining
the value of
resistance,
tolerance, and
sometimes the
reliability.
33
FIG. 3.25   Color coding for fixed resistors.

34
FIG. 3.29   Five-band color coding for fixed resistors.

35
FIG. 3.26   Color coding.

36
FIG. 3.30   Guaranteeing the full range of resistor values for the given tolerance: (a) 20%; (b) 10%.

37
FIG. 3.27   Example 3.13.

38
FIG. 3.28   Example 3.14.

39
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.

40
FIG. 3.22   Resistance components of a potentiometer: (a) between outside terminals; (b) between wiper arm and each outside terminal.

41
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.

42
FIG. 3.35   Thermistor: (a) characteristics; (b) symbol.

43
FIG. 3.36   NTC (negative temperature coefficient) and PTC (positive temperature coefficient) thermistors.

44
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.

45
FIG. 3.37   Photoconductive cell: (a) characteristics. (b) symbol.

46
FIG. 3.38   Photoconductive cells.

47
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.

48
FIG. 3.39   Varistors available with maximum dc voltage ratings between 18 V and 615 V.

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

50
FIG. 3.40   Electric baseboard: (a) 2-ft section; (b) interior; (c) heating element; (d) nichrome coil.

51
FIG. 3.41   Dashboard dimmer control in an automobile.

52
Conductance
• The measure of a material’s ability to allow
the flow of charge.
• Conductance is the reciprocal of resistance.
• G = 1/R
• Unit is siemens.

53
Superconductors
• At very low temperatures, resistance of some
materials goes to almost zero.
• This temperature is called the critical
temperature.
• Meissner Effect - When a superconductor is
cooled below its critical temperature,
magnetic fields may surround but not enter
the superconductor.
54
FIG. 3.14   Rising temperatures of superconductors.

55
FIG. 3.15   Defining the critical temperature Tc.

56

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