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32 - Inductance

# 32 - Inductance - Chapter 32 Inductance CHAPTE R OUTLI N E...

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1003 Inductance CHAPTER OUTLINE 32.1 Self-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 Chapter 32 ± An airport metal detector contains a large coil of wire around the frame. This coil has a property called inductance. When a passenger carries metal through the detector, the inductance of the coil changes, and the change in inductance signals an alarm to sound. (Jack Hollingsworth/Getty Images)

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1004 I n Chapter 31, we saw that an emf and a current are induced in a circuit when the magnetic ﬂux through the area enclosed by the circuit changes with time. This phenomenon of electromagnetic induction has some practical consequences. In this chapter, we ﬁrst describe an effect known as self-induction, in which a time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current. Self-induction is the basis of the inductor, an electrical circuit element. We discuss the energy stored in the magnetic ﬁeld of an inductor and the energy density associated with the magnetic ﬁeld. Next, we study how an emf is induced in a circuit as a result of a changing magnetic ﬂux produced by a second circuit; this is the basic principle of mutual induction . Finally, we examine the characteristics of circuits that contain inductors, resistors, and capaci- tors in various combinations. 32.1 Self-Inductance In this chapter, we need to distinguish carefully between emfs and currents that are caused by batteries or other sources and those that are induced by changing magnetic ﬁelds. When we use a term without an adjective (such as emf and current ) we are describing the parameters associated with a physical source. We use the adjective induced to describe those emfs and currents caused by a changing magnetic ﬁeld. Consider a circuit consisting of a switch, a resistor, and a source of emf, as shown in Figure 32.1. When the switch is thrown to its closed position, the current does not immediately jump from zero to its maximum value ± / R . Faraday’s law of electromag- netic induction (Eq. 31.1) can be used to describe this effect as follows: as the current increases with time, the magnetic ﬂux through the circuit loop due to this current also increases with time. This increasing ﬂux creates an induced emf in the circuit. The direction of the induced emf is such that it would cause an induced current in the loop (if the loop did not already carry a current), which would establish a magnetic ﬁeld opposing the change in the original magnetic ﬁeld. Thus, the direction of the induced emf is opposite the direction of the emf of the battery; this results in a gradual rather than instantaneous increase in the current to its ﬁnal equilibrium value. Because of the direction of the induced emf, it is also called a back emf , similar to that in a motor, as discussed in Chapter 31. This effect is called self-induction because the changing ﬂux through the circuit and the resultant induced emf arise from the circuit itself. The emf
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32 - Inductance - Chapter 32 Inductance CHAPTE R OUTLI N E...

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