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Chap 25 SM - Chapter 25 Electric Current and Direct-Current...

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385 Chapter 25 Electric Current and Direct-Current Circuits Conceptual Problems 1 In our study of electrostatics, we concluded that no electric field exists within the material of a conductor in electrostatic equilibrium. Why can we discuss electric fields within the material of conductors in this chapter? Determine the Concept In earlier chapters the conductors are constrained to be in electrostatic equilibrium. In this chapter this constraint is no longer in place. 2 Figure 25-12 shows a mechanical analog of a simple electric circuit. Devise another mechanical analog in which the current is represented by a flow of water instead of marbles. In the water circuit, what would be analogous to the battery? What would be analogous to the wire? What would be analogous to the resistor? Determine the Concept The analog is a wind-up water pump that pumps water through a tube with a necked down section. One end of the tube is connected to the output port of the pump, and the other end of the tube is connected to the input port of the pump. The pump, including the spring, is analogous to the battery. The tube is analogous to the wires. The necked down section is analogous to the resistor. 3 Wires A and B are both made of copper. The wires are connected in series, so we know they carry the same current. However, the diameter of wire A is twice the diameter of wire B. Which wire has the higher number density (number per unit volume) of charge carriers? ( a ) A, ( b ) B, ( c ) They have the same number density of charge carriers. Determine the Concept Equation 25-3 ( d qnAv I = ) relates the current I in a wire to the charge q of the charge carriers, the number density n of charge carriers, the cross-sectional area A of the wire, and the drift speed v d of the charge carriers. Both the number density of the charge carriers and the resistivity are properties of the substance, and do not depend on the current. Because the number density of carriers may, like resistivity, vary slowly with temperature and the drift speeds are not equal in the two wires, the correct answer is ( ) c . 4 The diameters of copper wires A and B are equal. The current carried by wire A is twice the current carried by wire B. In which wire do the charge carriers have the higher drift speed? ( a ) A ( b ) B ( c ) They have the same drift speed.
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Chapter 25 386 Determine the Concept Equation 25-3 ( d qnAv I = ) relates the current I in a wire to the charge q of the charge carriers, the number density n of charge carriers, the cross-sectional area A of the wire, and the drift velocity v d of the charge carriers. Both the number density of the charge carriers and the resistivity are properties of the substance, and do not depend on the current. Because the cross-sectional areas, the charge of the charge carriers, and the number densities of the charge carriers are the same for the two wires, the drift speed of the charge carriers will be higher in the wire carrying the larger current. Because wire A carries the larger current, ( ) a is correct.
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