Chapter 20
Resistance
Suppose we apply a potential differenceVacross the ends of a conductor. If the conductor were to allow
the free, unimpeded flow of electrons, then the resulting current in the conductor would be unlimited. But
in a real conductor, there is always some electricalresistanceto the flow of electric current due to the free
electrons constantly bumping into their neighbors. This electrical resistance is measured in units ofohms
(), after German physicist Georg Simon Ohm. One ohm is defined to be that resistance that produces a
current of 1 ampere in the presence of a potential difference of 1 volt: 1D 1 V/A.
Resistance is often introduced deliberately into electrical devices by electronic components calledresis-
tors. A resistor is typically a small cylindrical device with metal wires protruding from each end. The cylinder
is decorated with color bands, which are acolor code(Figure 20.1) that indicates the value of the resistance.
In a four-band color code, the first two bands are the first two significant digits of the resistance, and the
third band is the power of 10 by which the first two bands are to be multiplied. A fourth band indicates the
tolerance—how far the resistor is allowed to be from its marked value.
20.1 Resistivity
Even a plain conductor—like a copper wire—contain some small amount of resistance. The resistance of a
conductor is related to its dimensions and to a quantity called itsresistivity. If the resistance inR, and the
resistivity is , then the two are related by
RD
L
A
; (20.1)
whereRis the resistance (), is the resistivity (m),Lis the length of the conductor (in the direction of
the flow of current), andAis the cross-sectional area of the conductor (perpendicular to the direction of the
flow of current). It’s important to recognize that the resistivity is an intrinsic property of the material: for
example, you can look up the resistivity of copper in a physics handbook. The resistanceR, though, depends
on the geometry—the length and diameter of the conductor, as well as its resistivity.
It turns out that the resistivity depends on temperature. You can compute the temperature correction using
the equation
D 0 Œ1C ̨.TT 0 /: (20.2)Here 0 is the resistivity at temperatureT 0 , is the resistivity at temperatureT, and ̨is called thetempera-
ture coefficient of resistivity. You can find 0 ,T 0 and ̨for a particular conductor in a physics handbook (e.g.
Table 20-1); then for any given temperatureT, you can find the resistivity at that temperature.