ism_ch24

ism_ch24 - Chapter 24 Alternating-Current Circuits Answers...

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111 Chapter 24 Alternating-Current Circuits Answers to Even-numbered Conceptual Questions 2. Light will attain its maximum brightness 120 times per second; that is, twice per cycle. The reason for the factor of two per cycle is that the current reverses direction every cycle, and the bulb will be brightest when the current is a maximum in either direction. 4. The intensity of the light bulb will decrease if the frequency of the generator is increased. The reason is that inductors oppose any change in current, and the more rapidly the current changes the stronger the opposition. Thus, as the frequency is increased, the current in the circuit decreases, and the light bulb becomes dimmer. 6. Current and voltage are not always in phase in an ac circuit because capacitors and inductors respond not to the current itself – as a resistor does – but to the charge (capacitor) or to the rate of change of the current (inductor). The charge takes time to build up; therefore, a capacitor’s voltage lags behind the current. The rate of change of current is greatest when the current is least; therefore, an inductor’s voltage leads the current. Resistors, of course, are always in phase with the current. 8. As the frequency is increased, the inductive reactance increases as well. Therefore, at frequencies greater than the resonance frequency of an LC circuit, the inductive reactance is greater than the capacitive reactance. As a result, the inductor dominates, and the voltage leads the current. This means that the phase angle, φ , is positive. 10. No. In a dc circuit the frequency is zero, which means that the inductive reactance is zero as well. Therefore, the inductor has no effect at all on the current in the circuit, nor on the brightness of the bulb. In a dc circuit, an ideal inductor is the same as a piece of zero- resistance wire. 12. At low frequency, the capacitor is essentially the same as a break in the circuit, whereas the inductor is essentially an ideal wire. It follows, then, that more current will be supplied by the generator if the inductor and the capacitor are connected in parallel. 14. Recall that charge in an RLC circuit is the analog of position in a mass-spring system. Therefore, the current – which is the rate of change of charge – is analogous to the velocity – which is the rate of change of position. (See Table 24-2.) 16. Yes. All that is required for their resonance frequencies to be the same is for the product of L and C to be the same. (See Equation 24-18.) 18. At high frequency, we can replace the inductor with an open circuit. At low frequency, we can replace the capacitor with an open circuit. In either case, the effective resistance of the circuit is R ; therefore, the current is the same. 20. At high frequency, the capacitor behaves essentially the same as an ideal wire, which means that the effective resistance of the circuit is R /2. At low frequency, the capacitor is basically a break in the circuit. In this case, the effective resistance of the circuit is R . It follows that the current in the circuit is greater at high frequency.

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This note was uploaded on 04/08/2008 for the course PHYS 104 taught by Professor Pengyi during the Fall '08 term at UNC.

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ism_ch24 - Chapter 24 Alternating-Current Circuits Answers...

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