SM_chapter33

SM_chapter33 - 33 Alternating Current Circuits CHAPTER...

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33 Alternating Current Circuits 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 RectiF ers and ±ilters ANSWERS TO QUESTIONS *Q33.1 (i) Answer (d). V V avg = max 2 (ii) Answer (c). The average of the squared voltage is V V [] ( ) = ( ) 2 2 2 avg . max Then its square root is V V rms = max 2 *Q33.2 Answer (c). AC ammeters and voltmeters read rms values. With an oscilloscope you can read a maximum voltage, or test whether the average is zero. *Q33.3 (i) Answer (f). The voltage varies between + 170 V and 170 V. (ii) Answer (d). (iii) 170V/ 2 = 120 V. Answer (c). Q33.4 The capacitive reactance is proportional to the inverse of the frequency. At higher and higher frequen- cies, the capacitive reactance approaches zero, making a capacitor behave like a wire. As the frequency goes to zero, the capacitive reactance approaches inF nity—the resistance of an open circuit. Q33.5 The second letter in each word stands for the circuit element. ±or an inductor L , the emf ε leads the current I —thus ELI . ±or 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 . Q33.6 The voltages are not added in a scalar f orm, 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° ahead of the current in the circuit in phase. Q33.7 In an RLC series circuit, the phase angle depends on the source frequency. At very low frequency the capacitor dominates the impedance and the phase angle is near 90°. The phase angle is zero at the resonance frequency, where the inductive and capacitive reactances are equal. At very high frequencies f approaches + 90°. *Q33.8 (i) Inductive reactance doubles when frequency doubles. Answer (f). (ii) Capacitive reactance is cut in half when frequency doubles. Answer (b). (iii) The resistance remains unchanged. Answer (d). *Q33.9 At resonance the inductive reactance and capacitive reactance cancel out. Answer (c). 247
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248 Chapter 33 *Q33.10 At resonance the inductive reactance and capacitive reactance add to zero. tan 1 ( X L X C )/ R = 0. Answer (c). *Q33.11 (a) The circuit is in resonance. (b) 10 /20 = 0.5 (c) The resistance of the load could be increased to make a greater fraction of the emf’s power go to the load. Then the emf would put out a lot less power and less power would reach the load.
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SM_chapter33 - 33 Alternating Current Circuits CHAPTER...

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