FIG. 3.1 Resistance symbol and notation.
Resistance of Conductors
• Resistance of material is dependent on
– Type of Material
– Length of the Conductor
– Cross-sectional area
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.
• 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.
• The resistance of a conductor is inversely
proportional to the cross-sectional area of the
• If the cross-sectional area is doubled, the
resistance will be one half as much.
• A = cross-sectional area, in m2.
• At a given temperature,
• This formula can be used with both circular
and rectangular conductors.
FIG. 3.2 Factors affecting the resistance of a conductor.
FIG. 3.3 Cases in which R2 > R1. For each case, all remaining parameters that control the resistance level are the same.
Electrical Wire Tables
• The American Wire Gauge is the primary
system to denote wire diameters.
• The higher the AWG number, the smaller the
• A given length of AWG 22 wire will have more
resistance than the same length of AWG 14
• Larger gauge wires can handle more current.
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
FIG. 3.4 Defining the circular mil (CM).
FIG. 3.5 Verification of Eq. (3.2): ACM = (dmils)2.
FIG. 3.8 Popular wire sizes and some of their areas of application.
• For most conductors, an increase in
temperature causes an increase in
• This increase is relatively linear.
• In many semiconductors, an increase in
temperature results in a decrease in
• The rate of change of resistance with
temperature is called the temperature
• 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.
FIG. 3.13 Effect of temperature on the resistance of copper.
• Resistances essentially constant.
• Rated by amount of resistance, measured in
• Also rated by power ratings, measured in
• Different types of resistors are used for
– Molded carbon composition
– Carbon film
– Metal film
– Metal Oxide
– Integrated circuit packages
FIG. 3.16 (continued) Film resistors: (a) construction; (b) types.
FIG. 3.16 Film resistors: (a) construction; (b) types.
FIG. 3.17 Fixed composition resistors: (a) construction; (b) appearance.
FIG. 3.17 (continued) Fixed composition resistors: (a) construction; (b) appearance.
FIG. 3.18 Fixed metal-oxide resistors of different wattage ratings.
FIG. 3.19 Various types of fixed resistors.
FIG. 3.19 (continued) Various types of fixed resistors.
• Used to adjust volume, set level of lighting,
• Have three terminals.
• Center terminal connected to wiper arm.
FIG. 3.20 Potentiometer: (a) symbol; (b) and (c) rheostat connections; (d) rheostat symbol.
FIG. 3.21 Molded composition-type potentiometer.
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.
FIG. 3.24 Potentiometer control of voltage levels.
• Colored bands
on a resistor
provide a code
the value of
FIG. 3.25 Color coding for fixed resistors.
FIG. 3.29 Five-band color coding for fixed resistors.
FIG. 3.26 Color coding.
FIG. 3.30 Guaranteeing the full range of resistor values for the given tolerance: (a) 20%; (b) 10%.
FIG. 3.27 Example 3.13.
FIG. 3.28 Example 3.14.
• Remove all power sources to the circuit.
• Component must be isolated from rest of the
• Connect probes across the component.
• No need to worry about polarity.
• Useful to determine shorts and opens.
FIG. 3.22 Resistance components of a potentiometer: (a) between outside terminals; (b) between wiper arm and each outside terminal.
• A two-terminal transducer in which the
resistance changes with change in
• Applications include electronic thermometers
and thermostatic control circuits for furnaces.
• Many have negative temperature coefficients.
FIG. 3.35 Thermistor: (a) characteristics; (b) symbol.
FIG. 3.36 NTC (negative temperature coefficient) and PTC (positive temperature coefficient) thermistors.
• 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
• Used as part of security systems.
FIG. 3.37 Photoconductive cell: (a) characteristics. (b) symbol.
FIG. 3.38 Photoconductive cells.
• 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.
FIG. 3.39 Varistors available with maximum dc voltage ratings between 18 V and 615 V.
FIG. 3.39 (continued) Varistors available with maximum dc voltage ratings between 18 V and 615 V.
FIG. 3.40 Electric baseboard: (a) 2-ft section; (b) interior; (c) heating element; (d) nichrome coil.
FIG. 3.41 Dashboard dimmer control in an automobile.
• 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.
• At very low temperatures, resistance of some
materials goes to almost zero.
• This temperature is called the critical
• Meissner Effect - When a superconductor is
cooled below its critical temperature,
magnetic fields may surround but not enter
FIG. 3.14 Rising temperatures of superconductors.
FIG. 3.15 Defining the critical temperature Tc.