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SM_PDF_chapter21 - Current and Direct Current Circuits...

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577 Current and Direct Current Circuits CHAPTER OUTLINE 21.1 Electric Current 21.2 Resistance and Ohm’s Law 21.3 Superconductors 21.4 A Structural Model for Electrical Conduction 21.5 Electric Energy and Power 21.6 Sources of emf 21.7 Resistors in Series and in Parallel 21.8 Kirchhoff’s Rules 21.9 RC Circuits 21.10 Context Connection The Atmosphere as a Conductor ANSWERS TO QUESTIONS Q21.1 Consider all of the eastbound lanes on a highway, taken together. Individual vehicles correspond to bits of charge. The number of vehicles that pass a certain milepost, divided by the time during which they go past, corresponds to the value of the current. Q21.2 Geometry and resistivity. In turn, the resistivity of the material depends on the temperature. Q21.3 The radius of wire B is 3 times the radius of wire A, to make its cross–sectional area 3 times larger. Q21.4 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, and a current steadily increasing in time. On the other hand, 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. Q21.5 The amplitude of atomic vibrations increases with temperature. Atoms can then scatter electrons more efficiently. Q21.6 A current will continue to exist in a superconductor without voltage because there is no resistance loss. Q21.7 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 field everywhere in the wire nearly instantaneously, to make electrons start drifting everywhere all at once. Q21.8 The 25 W bulb has a higher resistance. The 100 W bulb carries more current. Q21.9 One ampere–hour is 3 600 coulombs. The ampere–hour rating is the quantity of charge that the battery can lift though its nominal potential difference.
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578 Current and Direct Current Circuits Q21.10 In series, the current is the same through each resistor. Without knowing individual resistances, nothing can be determined about potential differences or power. Q21.11 In parallel, the potential difference is the same across each resistor. Without knowing individual resistances, nothing can be determined about current or power. Q21.12 A short circuit can develop when the last bit of insulation frays away between the two conductors in a lamp cord. Then the two conductors touch each other, opening a low-resistance branch in parallel with the lamp. The lamp will immediately go out, carrying no current and presenting no danger. A very large current exists in the power supply, the house wiring, and the rest of the lamp cord up to the contact point. Before it blows the fuse or pops the circuit breaker, the large current can quickly
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