Chapter 3 Resistance. 2 FIG. 3.1 Resistance symbol and notation.

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

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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.

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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.

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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.

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Resistance Formula

• At a given temperature,

• This formula can be used with both circular and rectangular conductors.

AR

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FIG. 3.2 Factors affecting the resistance of a conductor.

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

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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.

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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

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FIG. 3.4 Defining the circular mil (CM).

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

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

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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.

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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.

TRR 11

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

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

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Fixed Resistors

• Resistances essentially constant.• Rated by amount of resistance, measured in

ohms.• Also rated by power ratings, measured in

watts.

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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

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

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

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

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

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

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FIG. 3.19 Various types of fixed resistors.

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

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Variable Resistors

• Used to adjust volume, set level of lighting, adjust temperature.

• Have three terminals.• Center terminal connected to wiper arm.• Potentiometers• Rheostats

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

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FIG. 3.21 Molded composition-type potentiometer.

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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.

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FIG. 3.24 Potentiometer control of voltage levels.

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Color Code• Colored bands

on a resistor provide a code for determining the value of resistance, tolerance, and sometimes the reliability.

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FIG. 3.25 Color coding for fixed resistors.

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

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FIG. 3.26 Color coding.

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

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FIG. 3.27 Example 3.13.

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FIG. 3.28 Example 3.14.

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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.

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

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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.

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

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

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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.

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

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FIG. 3.38 Photoconductive cells.

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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.

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

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

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

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FIG. 3.41 Dashboard dimmer control in an automobile.

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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.

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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.

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FIG. 3.14 Rising temperatures of superconductors.

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FIG. 3.15 Defining the critical temperature Tc.