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SM_chapter27 - 27 Current and Resistance CHAPTER OUTLINE...

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27 Current and Resistance CHAPTER OUTLINE 27.1 Electric Current 27.2 Resistance 27.3 A Model for Electrical Conduction 27.4 Resistance and Temperature 27.5 Superconductors 27.6 Electrical Power 101 ANSWERS TO QUESTIONS Q27.1 Voltage is a measure of potential difference, not of current. “Surge” implies a fl ow—and only charge, in coulombs, can fl ow through a system. It would also be correct to say that the victim carried a certain current, in amperes. Q27.2 Geometry and resistivity. In turn, the resistivity of the material depends on the temperature. *Q27.3 (i) We require r L / A A = 3 r / A B . Then A A / A B = 1/3, answer (f ). (ii) π r A 2 / π r B 2 = 1/3 gives r A / r B = 1/ 3, answer (e). *Q27.4 Originally, R A = ρ l . Finally, R AA R f == = ρρ (/) . ll 3 39 9 Answer (b). Q27.5 The conductor does not follow Ohm’s law, and must have a resistivity that is current-dependent, or more likely temperature-dependent. Q27.6 The amplitude of atomic vibrations increases with temperature. Atoms can then scatter electrons more ef± ciently. Q27.7 (i) The current density increases, so the drift speed must increase. Answer (a). (ii) Answer (a). Q27.8 The resistance of copper increases with temperature, while the resistance of silicon decreases with increasing temperature. The conduction electrons are scattered more by vibrating atoms when copper heats up. Silicon’s charge carrier density increases as temperature increases and more atomic electrons are promoted to become conduction electrons. *Q27.9 In a normal metal, suppose that we could proceed to a limit of zero resistance by lengthening the average time between collisions. The classical model of conduction then suggests that a constant applied voltage would cause constant acceleration of the free electrons. The drift speed and the current would increase steadily in time. It is not the situation envisioned in the question, but we can actually switch to zero resistance by substituting a superconducting wire for the normal metal. In this case, the drift velocity of electrons is established by vibrations of atoms in the crystal lattice; the maximum current is limited; and it becomes impossible to establish a potential difference across the superconductor. Q27.10 Because there are so many electrons in a conductor (approximately 10 28 electrons/m 3 ) the average velocity of charges is very slow. When you connect a wire to a potential difference, you establish an electric ± eld everywhere in the wire nearly instantaneously, to make electrons start drifting everywhere all at once.
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102 Chapter 27 *Q27.11 Action (a) makes the current three times larger. (b) causes no change in current. (c) corresponds to a current 3 times larger. (d) R is 1/4 as large, so current is 4 times larger. (e) R is 2 times larger, so current is half as large. (f) R increases by a small percentage as current has a small decrease.
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SM_chapter27 - 27 Current and Resistance CHAPTER OUTLINE...

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