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the materials listed in the table, nichrome is the conductor second wire from the device carries the now low-potential fi eld
with the greatest resistance. By definition, conductors have back to the other terminal, maintaining the potential diff erence.

less electrical resistance than insulators, which have a very In an alternating-current circuit, such as a household circuit,
large electrical resistance. one wire supplies the alternating electric fi eld from the electric
2. Length. The resistance of a conductor varies directly with generator of a utility company. The second wire from the device

the length; that is, a longer wire has more resistance and a is connected to a pipe in the ground and is at the same potential
shorter wire has less resistance. The longer the wire is, the as Earth. The observation that a bird can perch on a current-

greater the resistance. carrying wire without harm is explained by the fact that there is
3. Diameter. The resistance varies inversely with the cross- no potential difference across the bird’s body. If the bird were to

sectional area of a conductor. A thick wire has a greater come into contact with Earth through a second, grounded wire,
cross-sectional area and therefore has less resistance a potential difference would be established and there would be

than a thin wire. The thinner the wire is, the greater the a current through it.
resistance. The work done by a voltage source (battery, electric gen-

4. Temperature. For most materials, the resistance increases erator) is equal to the work done by the electric field in an

with increases in temperature. This is a consequence electric device (lightbulb, electric motor) plus the energy lost

of the increased motion of electrons and ions at higher to resistance. Resistance is analogous to friction in a mechan-
temperatures, which increases the number of collisions. ical device, so low-resistance conducting wires are used to
At very low temperatures (100 K or less), the resistance of reduce this loss. Disregarding losses to resistance, electrical
some materials approaches zero, and the materials are said work therefore can be measured where the voltage source
to be superconductors. creates a potential difference by doing work (W) to move

charges (q) to a higher potential (V). From equation 6.3, this
relationship is
EXAMPLE 6.3
work = (potential)(charge)
A lightbulb in a 120 V circuit is switched on, and a current of 0.50 A

flows through the filament. What is the resistance of the bulb?

or
W = (V)(q)
SOLUTION
In units, the electrical potential is measured in joules/coulomb,

The current (I) of 0.50 A is given with a potential diff erence (V) of 120 V.

The relationship to resistance (R) is given by Ohm’s law (equation 6.5). and a quantity of charge is measured in coulombs. Th erefore,
the unit of electrical work is the joule,
V _
I = 0.50 A V = IR ∴ R =
I W = (V)(q)
V = 120 V _ _
joules
120 V _

× coulomb
R = ? = 0.50 A joule = coulomb
V _
= 240

A Recall that a joule is a unit of work in mechanics (a newton-
meter). In electricity, a joule is also a unit of work, but it is
= 240 ohms
= 240 Ω derived from moving a quantity of charge (coulomb) to higher
potential difference (joules/coulomb). In mechanics, the work

put into a simple machine equals the work output when you dis-
EXAMPLE 6.4 regard friction. In electricity, the work put into an electric circuit

What current would flow through an electrical device in a circuit with equals the work output when you disregard resistance. Th us, the

a potential difference of 120 V and a resistance of 30 Ω? (Answer: 4 A) work done by a voltage source is ideally equal to the work done
by electrical devices in the circuit.
Recall also that mechanical power (P) was defined as work

(W ) per unit time (t), or
ELECTRICAL POWER AND W _

ELECTRICAL WORK P =
t
All electric circuits have three parts in common: (1) a voltage
Since electrical work is W = Vq, then electrical power must be
source, such as a battery or electric generator that uses some
Vq
nonelectric source of energy to do work on electrons, mov- _
P =

ing them against an electric field to a higher potential; (2) an t
electric device, such as a lightbulb or electric motor, where
Equation 6.4 defined a quantity of charge (q) per unit time (t)

work is done by the electric fi eld; and (3) conducting wires that
as a current (I), or I = q/t. Therefore, electrical power is

maintain the potential difference across the electrical device. In
q
a direct-current circuit, the electric field moves from one ter- _

( )
P = (V)
minal of a battery to the electric device through one wire. Th e t
6-13 CHAPTER 6 Electricity 151