SM_chapter32

SM_chapter32 - 32 Inductance CHAPTER OUTLINE 32.1 32.2 32.3...

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32 Inductance CHAPTER OUTLINE 32.1 Self-Induction and Inductance 32.2 RL Circuits 32.3 Energy in a Magnetic Field 32.4 Mutual Inductance 32.5 Oscillations in an LC Circuit 32.6 The RLC Circuit ANSWERS TO QUESTIONS Q32.1 The coil has an inductance regardless of the nature of the current in the circuit. Inductance depends only on the coil geometry and its construction. Since the current is con- stant, the self-induced emf in the coil is zero, and the coil does not affect the steady-state current. (We assume the resistance of the coil is negligible.) Q32.2 The inductance of a coil is determined by (a) the geometry of the coil and (b) the “contents” of the coil. This is similar to the parameters that determine the capacitance of a capacitor and the resistance of a resistor. With an inductor, the most important factor in the geometry is the number of turns of wire, or turns per unit length. By the “contents” we refer to the material in which the inductor establishes a magnetic F eld, notably the magnetic properties of the core around which the wire is wrapped. *Q32.3 The emf across an inductor is zero whenever the current is constant, large or small. Answer (d). *Q32.4 The F ne wire has considerable resistance, so a few seconds is many time constants. The F nal current is not affected by the inductance of the coil. Answer (c). *Q32.5 The inductance of a solenoid is proportional to the number of turns squared, to the cross-sectional area, and to the reciprocal of the length. Coil A has twice as many turns with the same length of wire, so its circumference must be half as large as that of coil B. Its radius is half as large and its area one quarter as large. ±or coil A the inductance will be different by the factor 2 2 (1/4)(1/2) = 1/2. Answer (e). Q32.6 When it is being opened. When the switch is initially standing open, there is no current in the circuit. Just after the switch is then closed, the inductor tends to maintain the zero-current condition, and there is very little chance of sparking. When the switch is standing closed, there is current in the circuit. When the switch is then opened, the current rapidly decreases. The induced emf is created in the inductor, and this emf tends to maintain the original current. Sparking occurs as the current bridges the air gap between the contacts of the switch. *Q32.7 Just before the switch is thrown, the voltage across the twelve-ohm resistor is very nearly 12 V. Just after the switch is thrown, the current is nearly the same, maintained by the inductor. The voltage across the 1 200- resistor is then much more than 12 V. By Kirchhoff's loop rule, the voltage across the coil is larger still: V L > V 1 200 > 12.0 V > V 12 . 225

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226 Chapter 32 *Q32.8 (i) (a) The bulb glows brightly right away, and then more and more faintly as the capacitor charges up. (b) The bulb gradually gets brighter and brighter, changing rapidly at F rst and then more and more slowly. (c) The bulb gradually gets brighter and brighter. (d) The bulb glows brightly right away, and then more and more faintly as the inductor starts carrying more and more current.
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This note was uploaded on 01/19/2012 for the course PHY 232 taught by Professor Williams,frank during the Spring '11 term at Ohio State.

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SM_chapter32 - 32 Inductance CHAPTER OUTLINE 32.1 32.2 32.3...

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