Concept explainers
The resistivity ρ of a conducting wire is the reciprocal of the conductivity and is measured in units of ohm-meters (Ω-m). The resistivity of a given metal depends on the temperature according to the equation
ρ(t) = ρ20 eα(t−20)
where t is the temperature in °C. There are tables that list the values of α (called the temperature coefficient) and ρ20 (the resistivity at 20°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 ρ(t) by its first- or second-degree Taylor polynomial at t = 20.
- (a) Find expressions for these linear and quadratic approximations.
- (b) For copper, the tables give α = 0.0039/°C and ρ20 = 1.7 × 10−8 Ω-m. Graph the resistivity of copper and the linear and quadratic approximations for −250°C ≤ t ≤ 1000°C.
- (c) For what values of t does the linear approximation agree with the exponential expression to within one percent?
Trending nowThis is a popular solution!
Chapter 11 Solutions
Bundle: Multivariable Calculus, 8th + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Single-Term
- Find the intensities of earthquakes whose magnitudes are (a) R=6.0 and (b) R=7.9.arrow_forwardThe resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?arrow_forwardThe kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning