chapter_21 - Arecibo a large radio telescope in Puerto Rico...

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693 21 CHAPTER Alternating Current Circuits and Electromagnetic Waves O U T L I N E 21.1 Resistors in an AC Circuit 21.2 Capacitors in an AC Circuit 21.3 Inductors in an AC Circuit 21.4 The RLC Series Circuit 21.5 Power in an AC Circuit 21.6 Resonance in a Series RLC Circuit 21.7 The Transformer 21.8 Maxwell’s Predictions 21.9 Hertz’s Confirmation of Maxwell’s Predictions 21.10 Production of Electromagnetic Waves by an Antenna 22.11 Properties of Electromagnetic Waves 21.12 The Spectrum of Electromagnetic Waves 21.13 The Doppler Effect for Electromagnetic Waves © Bettmann/Corbis Every time we turn on a television set, a stereo system, or any of a multitude of other electric appliances, we call on alternating currents (AC) to provide the power to operate them. We begin our study of AC circuits by examining the characteristics of a circuit containing a source of emf and one other circuit element: a resistor, a capacitor, or an inductor. Then we examine what happens when these elements are connected in combination with each other. Our discussion is limited to simple series configurations of the three kinds of elements. We conclude this chapter with a discussion of electromagnetic waves , which are composed of fluctuating electric and magnetic fields. Electromagnetic waves in the form of visible light enable us to view the world around us; infrared waves warm our environment; radio-frequency waves carry our television and radio programs, as well as information about processes in the core of our galaxy. X-rays allow us to perceive structures hidden inside our bodies, and study properties of distant, collapsed stars. Light is key to our understanding of the universe. 21.1 RESISTORS IN AN AC CIRCUIT An AC circuit consists of combinations of circuit elements and an AC generator or an AC source, which provides the alternating current. We have seen that the output of an AC generator is sinusoidal and varies with time according to v V max sin 2 ft [21.1] where v is the instantaneous voltage, V max is the maximum voltage of the AC gen- erator, and f is the frequency at which the voltage changes, measured in hertz (Hz). (Compare Equations 20.7 and 20.8 with Equation 21.1.) We first consider a simple Arecibo, a large radio telescope in Puerto Rico, gathers electromagnetic radiation in the form of radio waves. These long wavelengths pass through obscuring dust clouds, allowing astronomers to create images of the core region of the Milky Way Galaxy, which can't be observed in the visible spectrum.
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694 Chapter 21 Alternating Current Circuits and Electromagnetic Waves circuit consisting of a resistor and an AC source (designated by the symbol ), as in Active Figure 21.1. The current and the voltage across the resistor are shown in Active Figure 21.2. To explain the concept of alternating current, we begin by discussing the current-versus-time curve in Active Figure 21.2. At point a on the curve, the cur- rent has a maximum value in one direction, arbitrarily called the positive direc- tion. Between points a and b , the current is decreasing in magnitude but is still in the positive direction. At point
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