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Unformatted text preview: 33 CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors in an AC Circuit 33.5 The RLC Series Circuit 33.6 Power in an AC Circuit 33.7 Resonance in a Series RLC Circuit 33.8 The Transformer and Power Transmission 33.9 Rectifiers and Filters Alternating Current Circuits ANSWERS TO QUESTIONS Q33.1 If the current is positive half the time and negative half the time, the average current can be zero. The rms current is not zero. By squaring all of the values of the current, they all become positive. The average (mean) of these positive values is also positive, as is the square root of the average. Q33.2 ∆ ∆ V V avg = max 2 , ∆ ∆ V V rms = max 2 Q33.3 AC ammeters and voltmeters read rms values. With an oscilloscope you can read a maximum voltage, or test whether the average is zero. Q33.4 Suppose the voltage across an inductor varies sinusoidally. Then the current in the inductor will have its instantaneous peak positive value 1 4 cycle after the voltage peaks. The voltage is zero and going positive 1 4 cycle (90°) before the current is zero and going positive. Q33.5 If it is run directly from the electric line, a fluorescent light tube can dim considerably twice in every cycle of the AC current that drives it. Looking at one sinusoidal cycle, the voltage passes through zero twice. We don’t notice the flickering due to a phenomenon called retinal imaging. We do not notice that the lights turn on and off since our retinas continue to send information to our brains after the light has turned off. For example, most TV screens refresh at between 60 to 75 times per second, yet we do not see the evening news flickering. Home video cameras record information at frequencies as low as 30 frames per second, yet we still see them as continuous action. A vivid display of retinal imaging is that persistent purple spot you see after someone has taken a picture of you with a flash camera. Q33.6 The capacitive reactance is proportional to the inverse of the frequency. At higher and higher frequencies, the capacitive reactance approaches zero, making a capacitor behave like a wire. As the frequency goes to zero, the capacitive reactance approaches infinity—the resistance of an open circuit. Q33.7 The second letter in each word stands for the circuit element. For an inductor L , the emf ε leads the current I —thus ELI. For a capacitor C , the current leads the voltage across the device. In a circuit in which the capacitive reactance is larger than the inductive reactance, the current leads the source emf—thus ICE. 265 266 Alternating Current Circuits Q33.8 The voltages are not added in a scalar form, but in a vector form, as shown in the phasor diagrams throughout the chapter. Kirchhoff’s loop rule is true at any instant, but the voltages across different circuit elements are not simultaneously at their maximum values. Do not forget that an inductor can induce an emf in itself and that the voltage across it is 90°...
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 Spring '08
 Shannon
 Current, Power, Alternating Current, Ω, tan φ, ∆Vrms

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