ism_chapter_29

ism_chapter_29 - Chapter 29 Alternating-Current Circuits...

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705 Chapter 29 Alternating-Current Circuits Conceptual Problems *1 Determine the Concept Because the rms current through the resistor is given by R I rms rms ε = and both rms and R are independent of frequency, correct. is ) ( b 2 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 max rms V V = Express the doubled rms voltage in terms of the new peak voltage max V' : 2 2 max rms V' V = Divide the second of these equations by the first and simplify to obtain: 2 2 2 max max rms rms V V' V V = or max max 2 V V' = Solve for max V' : max max 2 V V' = and correct. is ) ( a 3 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. correct. is ) ( b 4 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 . correct. is ) ( a
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Chapter 29 706 *5 Determine the Concept The capacitive reactance of an capacitor varies with the frequency according to . 1 C X C ω = Hence, doubling will halve X C . correct. is ) ( c 6 Determine the Concept Yes to both questions. While the current in the inductor is increasing, the inductor absorbs power from the generator. When the current in the inductor reverses direction, the inductor supplies power to the generator. 7 Determine the Concept Yes to both questions. While charge is accumulating on the capacitor, the capacitor absorbs power from the generator. When the capacitor is discharging, it supplies power to the generator. 8 Picture the Problem We can use the definitions of the capacitive reactance and inductive reactance to find the SI units of LC . Use its definition to express the inductive reactance: fL X L π 2 = Solve for L : f X L L 2 = Use its definition to express the capacitive reactance: fC X C 2 1 = Solve for C : C fX C 2 1 = Express the product of L and C : C L C L X f X fX f X LC 2 2 4 2 1 2 = = Because the units of X L and X C cancel, the units of LC are those of 1/ f 2 or s 2 . correct. is ) ( a *9 •• Determine the Concept To make an LC circuit with a small resonance frequency requires a large inductance and large capacitance. Neither is easy to construct.
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Alternating-Current Circuits 707 10 ( a ) True. The Q factor and the width of the resonance curve at half power are related according to ω = 0 Q ; i.e., they are inversely proportional to each other. ( b ) True. The impedance of an RLC circuit is given by () 2 2 C L X X R Z + = . At resonance X L = X C and so Z = R . ( c ) True. The phase angle δ is related to X L and X C according to R X X C L = 1 tan . At resonance X L = X C and so = 0.
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ism_chapter_29 - Chapter 29 Alternating-Current Circuits...

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