The temperature coefficient of resistance a in Eq. (25.12) equals the temperature coefficient of resistivity a in Eq. (25.6) only if 1he coefficient of Thermal expansion is small. A cylindrical column of mercury is in a vertical glass tube. At 20oC, 1he length of the mercury column is 12.0 cm. The diameter of the mercury column is 1.6 mm and doesn't change with temperature because glass has a small coefficient of thermal expansion. The coefficient of volume expansion of the mercury is given in Table 17.2, its Resistivity at 20°C is given in Table 25.1, and its temperature coefficient of resistivity is given in Table 25.2.
(a) At 20°C, what is the resistance between the ends of the mercury column?
(b) The mercury column is heated to 60°C. What is the change in its resistivity?
(c) What is the change in its length? Explain why the coefficient of volume expansion, rather than the coefficient of linear expansion, determines the change in length.
(d) What is the change in its resistance?
(e) What is the temperature coefficient of resistance a 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?