Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337671729
Author: SERWAY
Publisher: Cengage
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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.
A metallic wire is stretched from original length of 1 m to 5 m. If the original cross-sectional area is 4 square millimeters and original resistance
is 7 ohms, determine the new resistance (in ohms) of the metallic wire. Assume the volume of the wire is preserved.
A cylindrical conductor has resistance of R0 = 950 Ω. It has length L, radius of the cross section r, and resistivity ρ.
a) If the resistivity was restored to its original value and instead the length of the conductor decreased by a factor of 2, what would the value of the new resistance be, in ohms?
b) If the resistivity and length of the conductor were at their original values and the radius of the conductor increased by a factor of 4, what would be the value of the new resistance, in ohms?
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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