Chapter 29

Chapter 29 - Chapter 29 Alternating-Current Circuits...

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Chapter 29 Alternating-Current Circuits Conceptual Problems 1 A coil in an ac generator rotates at 60 Hz. How much time elapses between successive peak emf values of the coil? Determine the Concept Successive peaks are one-half period apart. Hence the elapsed time between the peaks is () ms .33 8 s 60 2 1 2 1 2 1 1 - = = = f T . 2 If the rms voltage in an ac circuit is doubled, the peak voltage is ( a ) doubled, ( b ) halved, ( c ) increased by a factor of 2 , ( d ) not changed. Picture the Problem We can use the relationship between V and V peak to decide the effect of doubling the rms voltage on the peak voltage. Express the initial rms voltage in terms of the peak voltage: 2 peak rms V V = Express the doubled rms voltage in terms of the new peak voltage : peak V' 2 2 peak rms V' V = Divide the second of these equations by the first and simplify to obtain: 2 2 2 peak peak rms rms V V' V V = peak peak 2 V V' = Solving for yields: peak V' peak peak 2 V V' = ) ( a is correct. 3 [SSM] If the frequency in the circuit shown in Figure 29-27 is doubled, the inductance of the inductor will ( a ) double, ( b ) not change, ( c ) halve, ( d ) quadruple. Determine the Concept The inductance of an inductor is determined by the details of its construction and is independent of the frequency of the circuit. The inductive reactance, on the other hand, is frequency dependent. ) ( b is correct. 4 If the frequency in the circuit shown in Figure 29-27 is doubled, the inductive reactance of the inductor will ( a ) double, ( b ) not change, ( c ) halve, ( d ) quadruple. 2739
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Chapter 29 2740 Determine the Concept The inductive reactance of an inductor varies with the frequency according to . L X L ω = Hence, doubling will double X L . ) ( a is correct. 5 If the frequency in the circuit in Figure 29-28 is doubled, the capacitive reactance of the circuit will ( a ) double, ( b ) not change, ( c ) halve, ( d ) quadruple. Determine the Concept The capacitive reactance of an capacitor varies with the frequency according to . 1 C X C = Hence, doubling will halve X C . ) ( c is correct. 6 ( a ) In a circuit consisting solely of a ac generator and an ideal inductor, are there any time intervals when the inductor receives energy from the generator? If so, when? Explain your answer. ( b ) Are there any time intervals when the inductor supplies energy back to the generator? If so when? Explain your answer. Determine the Concept Yes to both questions. ( a ) While the magnitude of the current in the inductor is increasing, the inductor absorbs power from the generator. ( b ) When the magnitude of the current in the inductor decreases, the inductor supplies power to the generator. 7 [SSM] ( a ) In a circuit consisting of a generator and a capacitor, are there any time intervals when the capacitor receives energy from the generator? If so, when? Explain your answer. ( b ) Are there any time intervals when the capacitor supplies power to the generator? If so, when? Explain your answer.
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Chapter 29 - Chapter 29 Alternating-Current Circuits...

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