Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 26, Problem 42AP
(a)
To determine
To show: The resistance between the ends of the wire under strain is given by
(b)
To determine
Whether the result is exact or approximate, if assumptions are precisely true.
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The strain in a wire can be monitored and computed by measuring the resistance of the wire. Let Li represent the original length of the wire, Ai its original cross-sectional area, Ri = ρLi /Ai the original resistance between its ends, and δ = ΔL/Li = (L - Li )/Li the strain resulting from the application of tension. Assume the resistivity and the volume of the wire do not change as the wire stretches. (a) Show that the resistance between the ends of the wire under strain is given by R = Ri (1 + 2δ + δ2). (b) If the assumptions are precisely true, is this result exact or approximate? Explain your answer.
Two conductors are made of the same material and have the same length.
Conductor A is a solid wire of diameter 1.9 mm. Conductor B is a hollow tube of
outside diameter 2.9 mm and inside diameter 1.9 mm. What is the resistance ratio
RA/RB, measured between their ends?
A copper transmission line is to be replaced by one of aluminum having the same total resistance. If the cross-sectional area of the copper wire is 500 MCM, what would be the cross-sectional area of the new aluminum wire?
Chapter 26 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 26.1 - Consider positive and negative charges of equal...Ch. 26.2 - Prob. 26.2QQCh. 26.2 - Prob. 26.3QQCh. 26.4 - When does an incandescent lightbulb carry more...Ch. 26 - Prob. 1PCh. 26 - A small sphere that carries a charge q is whirled...Ch. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - Prob. 5PCh. 26 - Figure P26.6 represents a section of a conductor...
Ch. 26 - The quantity of charge q (in coulombs) that has...Ch. 26 - Prob. 8PCh. 26 - Prob. 9PCh. 26 - A wire 50.0 m long and 2.00 mm in diameter is...Ch. 26 - Prob. 11PCh. 26 - Prob. 12PCh. 26 - Prob. 13PCh. 26 - Prob. 14PCh. 26 - Prob. 15PCh. 26 - Prob. 16PCh. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - An aluminum wire with a diameter of 0.100 mm has a...Ch. 26 - Prob. 20PCh. 26 - At what temperature will aluminum have a...Ch. 26 - You are working in a laboratory that studies the...Ch. 26 - Assume that global lightning on the Earth...Ch. 26 - The Van de Graaff generator, diagrammed in Figure...Ch. 26 - Prob. 25PCh. 26 - The potential difference across a resting neuron...Ch. 26 - Prob. 27PCh. 26 - Prob. 28PCh. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - Prob. 32PCh. 26 - Prob. 33PCh. 26 - Prob. 34APCh. 26 - Prob. 35APCh. 26 - You are working with an oceanographer who is...Ch. 26 - A charge Q is placed on a capacitor of capacitance...Ch. 26 - Prob. 38APCh. 26 - Prob. 39APCh. 26 - Prob. 40APCh. 26 - Review. An office worker uses an immersion heater...Ch. 26 - Prob. 42APCh. 26 - A close analogy exists between the flow of energy...Ch. 26 - The dielectric material between the plates of a...Ch. 26 - Review. A parallel-plate capacitor consists of...Ch. 26 - Prob. 46APCh. 26 - Prob. 47APCh. 26 - Prob. 48CPCh. 26 - Prob. 49CPCh. 26 - Material with uniform resistivity is formed into...
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- Two conductors are made of the same material and have the same length. Conductor 1 is asolid wire of diameter 2.0 m. Conductor 2 is a hollow tube of outside diameter 3.0 m andinside diameter 2.0 m. The ratio of their resistance, R1/R2, is: CHOICES: 1.5/4.3/2.3.8. Which of the following wires has the least resistance? (Assume that they have the sameresistivity.) Choices: Thin, long, and hot.Thin, short, and hot.Thin, short, and cool.Thick, long, and hot.arrow_forwardA straight, cylindrical wire lying along the x axis has a length of 0.515 m and a diameter of 0.195 mm. It is made of a material described by Ohm's law with a resistivity of ? = 4.00 ✕ 10−8 Ω · m. Assume a potential of 4.00 V is maintained at the left end of the wire at x = 0. Also assume V = 0 at x = 0.515 m. (a) Find the magnitude (in V/m) and direction of the electric field in the wire. (b) Find the resistance of the wire (in Ω). (c) Find the magnitude (in A) and direction of the electric current in the wire. (d) Find the current density in the wire (in MA/m2). See image for the full question.arrow_forwardA straight, cylindrical wire lying along the x axis has a length of 0.500 m and a diameter of 0.200 mm. It is made of a material described by Ohm’s law with a resistivity of ρ = 4.00 x 10-8 Ω ⋅ m. Assume a potential of 4.00 V is maintained at the left end of the wire at x = 0. Also assume V = 0 at x = 0.500 m. Find (a) the magnitude and direction of the electric field in the wire, (b) the resistance of the wire, (c) the magnitude and direction of the electric current in the wire, and (d) the current density in the wire. (e) Show that E = ρJ.arrow_forward
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