Chapter 3 Resistance

FIG. 3.1 Resistance symbol and notation.

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

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.

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.

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.

Resistance Formula 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 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 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.

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.

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.

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.

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.

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

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

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.

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

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.

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

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.

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.

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

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.

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

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

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.

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

FIG. 3.38 Photoconductive cells.

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.

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.

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.

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.

FIG. 3.14 Rising temperatures of superconductors.

FIG. 3.15 Defining the critical temperature Tc.