Solved: The temperature coefficient of resistance in Eq.

Chapter 25, Problem 25.67

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The temperature coefficient of resistance in Eq. (25.12) equals the temperature coefficient of resistivity in Eq. (25.6) only if the coefficient of thermal expansion is small. A cylindrical column of mercury is in a vertical glass tube. At 20C, the length of the mercury column is 12.0 cm. The diameter of the mercury column is 1.6 mm and doesnt change with temperature because glass has a small coefficient of thermal expansion. The coef- ficient of volume expansion of the mercury is given in Table 17.2, its resistivity at 20C is given in Table 25.1, and its temperature coefficient of resistivity is given in Table 25.2. (a) At 20C, what is the resistance between the ends of the mercury column? (b) The mercury column is heated to 60C. What is the change in its resistivity? (c) What is the change in its length? Explain why the coeffi- cient of volume expansion, rather than the coefficient of linear expansion, determines the change in length. (d) What is the change in its resistance? (Hint: Since the percentage changes in and L are small, you may find it helpful to derive from Eq. (25.10) an equation for in terms of and (e) What is the temperature coefficient of resistance for the mercury column, as defined in Eq. (25.12)? How does this value compare with the temperature coefficient of resistivity? Is the effect of the change in length important?