Solved: The resistivity of a conducting wire is the reciprocal of the conductivity and

Chapter 11, Problem 30

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The resistivity of a conducting wire is the reciprocal of the conductivity and is measured in units of ohm-meters ( -m). The resistivity of a given metal depends on the temperature according to the equation where is the temperature in C. There are tables that list the values of (called the temperature coefficient) and (the resistivity at C) for various metals. Except at very low temperatures, the resistivity varies almost linearly with temperature and so it is common to approximate the expression for by its first- or second-degree Taylor polynomial at . (a) Find expressions for these linear and quadratic approximations. ; (b) For copper, the tables give C and -m. Graph the resistivity of copper and the linear and quadratic approximations for 250C C. (c) For what values of does the linear approximation agreewith the exponential expression to within one percent?