Unformatted text preview: 70 111 RESISTANCE
TEMPERATURE EFFECTS 111 71
34 TEMPERATURE EFFECTS
Temperature has a significant effect on the resistance of conductor
semiconductors, and insulators.
with an increase in temperature. Since temperature can have such a pro-
nounced effect on the resistance of a conductor, it is important that we
have some method of determining the resistance at any temperature
within operating limits. An equation for this purpose can be obtained by
Conductors have a generous number of free electrons, and any introdu
approximationg the curve in Fig. 3.1 1 by the straight dashed line that in-
tion of thermal energy will have little impact on the total number of fro
tersects the temperature scale at - 234.5.C. Although the actual curve
carriers. In fact, the thermal energy only increases the intensity of
extends to absolute zero (-273.15.C, or ( K), the straight-line approx-
imation is quite accurate for the normal operating temperature range. At
random motion of the particles within the material and makes it increat
two temperatures 71 and 72, the resistance of copper is R1 and R2, re-
ingly difficult for a general drift of electrons in any one direction to
established. The result is that
spectively, as indicated on the curve. Using a property of similar trian-
gles, we may develop a mathematical relationship between these values
Demonstrating the effect of a positive and a negative
for good conductors, an increase in temperature results in an
of resistance at different temperatures. Let x equal the distance from
temperature coefficient on the resistance of a
increase in the resistance level. Consequently, conductors have a
-234.5'C to 71 and y the distance from -234.5.C to 72, as shown in
positive temperature coefficient.
Fig. 3.11. From similar triangles,
nferred absolute temperatures (T;).
The plot in Fig. 3.10(a) has a positive temperature coefficient.
R1 - R 2
234.5 + 71 _234.5 + 12
In semiconductors, an increase in temperature imparts a measure of there
mal energy to the system that results in an increase in the number of free
carriers in the material for conduction. The result is that
for semiconductor materials, an increase in temperature results in a
The temperature of - 234.5.C is called the inferred absolute tempera-
decrease in the resistance level. Consequently, semiconductors have
negative temperature coefficients.
ture of copper. For different conducting materials, the intersection of the
straight-line approximation occurs at different temperatures. A few typi-
The thermistor and photoconductive cell discussed in Sections 3.12
cal values are listed in Table 3.3.
and 3.13, respectively, are excellent examples of semiconductor devices
The minus sign does not appear with the inferred absolute tempera-
with negative temperature coefficients. The plot in Fig. 3.10(b) has a
negative temperature coefficient.
ure on either side of Eq. (3.5) because x and y are the distances from
-234.5.C to 7, and T2, respectively, and therefore are simply magni-
tudes. For 71 and T2 less than zero, x and y are less than -234.5.C, and
the distances are the differences between the inferred absolute tempera-
As with semiconductors, an increase in temperature results in a
ture and the temperature of interest.
decrease in the resistance of an insulator. The result is a negative
Eq. (3.5) can easily be adapted to any material by inserting the
proper inferred absolute temperature. It may therefore be written as
Inferred Absolute Temperature
Fig. 3.11 reveals that for copper (and most other metallic conductors),
the resistance increases almost linearly (in a straight-line relationship)
where |7, | indicates that the inferred absolute temperature of the material
involved is inserted as a positive value in the equation. In general, there-
fore, associate the sign only with T, and T2 .
EXAMPLE 3.7 If the resistance of a copper wire is 50 2 at 20 C, what
is its resistance at 100 C (boiling point of water)?
Inferred absolute zero
Solution: Eq. (3.5):
Effect of temperature on the meine-
234.5.C + 20 C 234.50C + 100'C
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- Fall '19
- SK Abid