IMG_20191022_095709.jpg - 70 111 RESISTANCE TEMPERATURE EFFECTS 111 71 34 TEMPERATURE EFFECTS omo Temperature has a significant effect on the resistance

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Unformatted text preview: 70 111 RESISTANCE TEMPERATURE EFFECTS 111 71 34 TEMPERATURE EFFECTS omo 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 Conductors have some method of determining the resistance at any temperature within operating limits. An equation for this purpose can be obtained by R Temperature 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- + Temperature 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 coefficient coefficient 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 Temperature 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- (2) Temperature ingly difficult for a general drift of electrons in any one direction to (6) established. The result is that spectively, as indicated on the curve. Using a property of similar trian- FIG. 3.10 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 conductor positive temperature coefficient. Fig. 3.11. From similar triangles, TABLE 3.3 nferred absolute temperatures (T;). The plot in Fig. 3.10(a) has a positive temperature coefficient. Material .C Semiconductors R1 - R 2 Silver - 243 234.5 + 71 _234.5 + 12 Copper -234.5 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 R2 (3.5) Gold -274 Aluminum -236 carriers in the material for conduction. The result is that Tungsten - 204 for semiconductor materials, an increase in temperature results in a - 147 The temperature of - 234.5.C is called the inferred absolute tempera- Nickel decrease in the resistance level. Consequently, semiconductors have - 162 negative temperature coefficients. ture of copper. For different conducting materials, the intersection of the Iron straight-line approximation occurs at different temperatures. A few typi- Nichrome 2.250 Constantan - 125,000 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- Insulators 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 temperature coefficient. proper inferred absolute temperature. It may therefore be written as follows: Inferred Absolute Temperature Fig. 3.11 reveals that for copper (and most other metallic conductors), (3.6) the resistance increases almost linearly (in a straight-line relationship) R 1 R 2 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 . Absolute zero EXAMPLE 3.7 If the resistance of a copper wire is 50 2 at 20 C, what 273.15 C/ -234.5.C is its resistance at 100 C (boiling point of water)? Inferred absolute zero Solution: Eq. (3.5): FIG. 3.11 Effect of temperature on the meine- 234.5.C + 20 C 234.50C + 100'C 50 0 R2...
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