CK-12-Physics - Intermediate

http://www.ck12.org Chapter 17. Circuits

A quantity called the conductivity expressed using the Greek letter sigmaσis defined as the reciprocal of the
resistivityσ=^1 ρ. The greater the conductivity is, the smaller amount of resistance in the circuit; and therefore, the
greater current in the circuit.

The resistivity is determined experimentally. When the same voltage is applied to wires of different materials, but
of identical cross section and length, different currents are measured.

For example, under identical conditions, a copper wire conducts almost 60 times the current than a nichrome wire
(an alloy of nickel, iron, and chromium). Which wire do you think has greater resistivity?

Table17.1 gives resistivity values for some common conducting materials at 20◦C. Resistivity values are sensitive
to changes in temperature and differ for different materials.

TABLE17.1:

Material Resistivity,ρ(Ω∗m)× 10 −^8

Silver 1.59

Copper 1.68

Gold 2.44

Aluminum 2.65

Tungsten 5.60

Nichrome 100

Illustrative Example 18.2.1

A copper wire is to replace an aluminum wire of length 1. 20 × 10 −^1 min an electrical circuit. The copper wire has a
cross-sectional area which is 80% of the aluminum wire. The resistance of the circuit must remain the same. What
length of copper wire must be used? Assume the temperature remains constant at 20◦Cin the circuit.

Answer:

Raluminum=ρalLAalalandRco p per=ρcLAcc

Since the resistances must be equal,

ρal

Lal

Aal

=ρc

Lc

Ac

→Lc=

ρal

ρc

Ac

Aal

Lal→

Lc=

(

2. 65 × 10 −^8 Ω∗m

1. 68 × 10 −^8 Ω∗m

)(

0. 80 Aal

Aal

)

( 1. 20 × 10 −^1 m) = 1. 514 × 10 −^1 m= 1. 51 cm

Semiconductors

As we mentioned earlier, charges move readily in conductors and do not move at all in insulators (nonconductors).
There are materials, however, that fall in between these two extremes. They are calledsemiconductors. Semicon-
ductors permit a limited amount of electron flow and are very useful in constructing electronic devices. Common
semiconductors are silicon, germanium, and carbon. The resistors discussed below are often made from carbon.
Semiconductors are used in the construction of electronic components such as transistors and diodes, to name just
two.

Superconductors

In the early 20th century, it was discovered that when certain materials were cooled to near absolute zero, they
lost all their resistance. Materials displaying this attribute are calledsuperconductors. Superconductors hold great