Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

354 Chapter 12 Electric Current and Related Parameters

The resistivity values are usually measured using samples made of a 1-cm cube or a cylinder hav-

ing a diameter of 1 mil and length of 1 ft. The resistance of the sample is then given by

(12.2)

where ris the resistivity, /is the length of the sample, andais the cross-sectional area of the

sample. The resistance for 1-ft-long wire having a diameter of 1 mil made of various materials

is given in Table 12.1. The electrical resistance of a material varies with temperature. In gen-

eral, the resistance of conductors (except for carbon) increases with increasing temperature.

Some materials exhibit near-zero resistance at very low temperatures (temperatures approach-

ing absolute zero). This behavior is commonly referred to assuperconductivity.

Ohm’s Law

Ohm’s lawdescribes the relationship among voltage,V, resistance,R, and current,I,

according to

(12.3)

Note from Ohm’s law, Equation (12.3), that current is directly proportional to voltage and

inversely proportional to resistance. As electric potential is increased, so is the current; and if

the resistance is increased, the current will decrease. The electric resistance is measured in

units of ohms (Æ). An element with 1 ohm resistance allows a current flow of 1 amp when

there exists a potential of 1 volt across the element. Stated another way, when there exists an

electrical potential of 1 volt across a conductor with a resistance of 1 ohm, then 1 ampere of

electric current will flow through the conductor.

VRI

R

r/

a

TABLE 12.1 Electrical Resistance for 1-ft-long

Wire Made of Various Metals

Having a Diameter of 1 mil at 20°C

Resistance

Metal (ohms, æ)

Aluminum 17.01

Brass 66.80

Copper 10.37

Gold 14.7

Iron 59.9

Lead 132.0

Nickel 50.8

Platinum 63.8

Silver 9.8

Tin 70.0

Tungsten 33.2

Zinc 35.58

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