Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-12 GTBL042-Callister-v2 August 13, 2007 18:22

462 • Chapter 12 / Electrical Properties

Ammeter

Variable resistor

Battery

Specimen

Voltmeter

Cross-sectional

area, A

V

I

l

Figure 12.1 Schematic

representation of the

apparatus used to measure

electrical resistivity.

wherelis the distance between the two points at which the voltage is measured, and

Ais the cross-sectional area perpendicular to the direction of the current. The units

forρare ohm-meters (-m). From the expression for Ohm’s law and Equation 12.2,

ρ=

VA

Il

(12.3)

Electrical

resistivity—

dependence on

applied voltage,

current, specimen

cross-sectional area,

and distance between

measuring points

Figure 12.1 is a schematic diagram of an experimental arrangement for measuring

electrical resistivity.

12.3 ELECTRICAL CONDUCTIVITY

electrical Sometimes,electrical conductivityσis used to specify the electrical character of a

conductivity material. It is simply the reciprocal of the resistivity, or

σ=

1

ρ

(12.4)

Reciprocal

relationship between

electrical

conductivity and

resistivity and is indicative of the ease with which a material is capable of conducting an elec-

tric current. The units forσare reciprocal ohm-meters [(-m)−^1 , or mho/m]. The

following discussions on electrical properties use both resistivity and conductivity.

In addition to Equation 12.1, Ohm’s law may be expressed as

J=σe (12.5)

Ohm’s law

expression—in terms

of current density,

conductivity, and

applied electric field

in whichJis the current density, the current per unit of specimen areaI/A, andeis

the electric field intensity, or the voltage difference between two points divided by

the distance separating them; that is,

e=

V

l

Electric field (12.6)

intensity

The demonstration of the equivalence of the two Ohm’s law expressions (Equations

12.1 and 12.5) is left as a homework exercise.

Solid materials exhibit an amazing range of electrical conductivities, extending

over 27 orders of magnitude; probably no other physical property experiences this

breadth of variation. In fact, one way of classifying solid materials is according to