1cc. Figure 30.2a shows that the charge on the capacitor in an LC
circuit is largest when the current is zero. What about the potential
difference across the capacitor?a) The potential difference across the
capacitor is largest when the current is the largest.b) The potential
difference across the capacitor is largest when the charge is the
largest.c) The potential difference across the capacitor does not
change.Figure 30.2 A single-loop circuit containing a capacitor and an
inductor. (a) The capacitor is initially completely charged when it is
connected to the circuit.(a) ... Get solution
1mcq. A 200-Ω resistor, a 40.0-mH inductor and a 3.0-µF capacitor are connected in series with a source of time-varying emf that provides 10.0 V at a frequency of 1000 Hz. What is the impedance of the circuit?a) 200 Ωb) 228 Ωc) 342 Ωd) 282 Ω Get solution
2cc. In Figure 30.3, suppose t = 0 at point (c). What is the phase constant in this case? (Define a clockwise current as positive.)a) 0b) π/2c) πd) 3π/2e) none of the aboveFigure 30.3 Variation of the charge, current, electric energy, and magnetic energy as a function of time for a simple, single-loop LC circuit. The letters along the bottom refer to the parts of Figure 30.2.... Get solution
2mcq. For which values of f is XL > XC?a) f > 2π(LC)1/2b) f > (2πLC)–1c) f > (2π(LC)1/2)–1d) f > 2πLC Get solution
3cc. What is the condition for small damping that needs to be fulfilled for equation 30.6 to be a solution for equation 30.5? (Hint: You can find this by analogy with the damped oscillation of a mass on a spring, for which the differential equation is ... and the condition for small damping is .... Alternatively, you can use dimensional analysis.)a) ...b) ...c) ...Equation 30.5...Equation 30.6... Get solution
3mcq. Which statement about the phase relation between the electric and magnetic fields in an LC circuit is correct?a) When one field is at its maximum, the other is also, and the same for the minimum values.b) When one field is at maximum strength, the other is at minimum (zero) strength.c) The phase relation, in general, depends on the values of L and C. Get solution
4cc. A circuit containing a capacitor (Figure 30.9) has a source of time varying emf that provides a voltage given by vC = VC sin ωt. What is the current, iC, through the capacitor when the potential difference across it is largest (vC = Vmax)?a) iC = 0b) iC = +Imaxc) iC = –ImaxFigure 30.9 Single-loop circuit with a capacitor and a source of time-varying emf.... Get solution
4mcq. For the band-pass filter shown in Figure 30.25, how can the width of the frequency response be increased?a) increase R1b) decrease C1c) increase R2d) increase C2e) do any of the aboveFigure 30.25 The frequency response of a low-pass filter, a high-pass filter, and a band-pass filter.... Get solution
5mcq. The phase constant, φ, between the voltage and the current in an AC circuit depends on the _______.a) inductive reactanceb) capacitive reactancec) resistanced) all of the above Get solution
6cc. The frequency response for a band-pass filter plotted in Figure 30.25 is the _________ of the frequency responses for the low-pass and high-pass filters.a) sumb) productc) differenced) ratioe) It is none of the above.Figure 30.25 The frequency response of a low-pass filter, a high-pass filter, and a band-pass filter.... Get solution
7cc. WiFi networks are installed in most coffee shops and many residences to provide access to the Internet. The most common WiFi standard is known as 802.11 g, which supports communication rates of up to 54 megabits per second. Wireless networks in the United States and Canada that follow this standard use a frequency around 2.4 GHz, in 14 different channels in the band between 2.401 GHz and 2.495 GHz. Each channel has a full width at half maximum of 22 MHz. What is the quality factor of these WiFi networks?a) 0.1b) 9.9c) 33d) 109e) 300 Get solution
7mcq. In the RLC circuit in the figure, R = 60 Ω, L = 3 mH, C = 4 mF, and the source of time-varying emf has a peak voltage of 120 V. What should the angular frequency, ω, be to produce the largest current in the resistor?a) 4.2 rad/sb) 8.3 rad/sc) 204 rad/sd) 289 rad/se) 5000 rad/sf) 20,000 rad/s... Get solution
8mcq. A standard North American wall socket plug is labeled 110 V. This label indicates the ______ value of the voltage.a) averageb) maximumc) root-mean-square (rms)d) instantaneous Get solution
9mcq. A circuit contains a source of time-varying emf, which is given by Vemf = 120.0 sin[(377 rad/s)t] V, and a capacitor with capacitance C = 5.00 µF. What is the current in the circuit at t = 1.00 s?a) 0.226 Ab) 0.451 Ac) 0.555 Ad) 0.750 Ae) 1.25 A Get solution
10mcq. A source of time-varying emf supplies Vmax = 115.0 V at f = 60.0 Hz in a series RLC circuit in which R = 374 Ω, L = 0.310 H, and C = 5.50 µF. What is the impedance of this circuit?a) 321 Ωb) 523 Ωc) 622 Ωd) 831 Ωe) 975 Ω Get solution
11cq. What is the impedance of a series RLC circuit when the frequency of time-varying emf is set to the resonant frequency of the circuit? Get solution
13cq. In a DC circuit containing a capacitor, a current will flow through the circuit for only a very short time, while the capacitor is being charged or discharged. On the other hand, a steady alternating current will flow in a circuit containing the same capacitor but powered by a source of time varying emf. Does it mean that charges are crossing the gap (dielectric) of the capacitor? Get solution
15cq. In Solved Problem 30.3, the voltage supplied by the source of time varying emf is 33.0 V, the voltage across the resistor is VR = IR = 13.1 V, and the voltage across the inductor is VL = IXL = 30.3 V. Does this circuit obey Kirchhoff’s rules? Get solution
14cq. In an RL circuit with alternating current, the current lags behind the voltage. What does this mean, and how can it be explained qualitatively, based on the phenomenon of electromagnetic induction? Get solution
16cq. Why is rms power specified for an AC circuit, not average power? Get solution
17cq. Why can’t we use a universal charger that plugs into a household outlet to charge all our electrical devices—cell phone, toy dog, can opener, and so on—rather than using a separate charger with its own transformer for each device? Get solution
18cq. If you use a parallel plate capacitor with air in the gap between the plates as part of a series RLC circuit in a generator, you can measure current flowing through the generator. Why is it that the air gap in the capacitor does not act like an open switch, blocking all current flow in the circuit? Get solution
19cq. A common configuration of wires has twisted pairs as opposed to straight, parallel wires. What is the technical advantage of using twisted pairs of wires versus straight, parallel pairs? Get solution
20cq. In a classroom demonstration, an iron core is inserted into a large solenoid connected to an AC power source. The effect of the core is to magnify the magnetic field in the solenoid by the relative magnetic permeability, κm, of the core (where κm is a dimensionless constant, substantially greater than unity for a ferromagnetic material, introduced in Chapter 28) or, equivalently, to replace the magnetic permeability of free space, µ0, with the magnetic permeability of the core, µ = κmµ0.a) The measured root-mean-square current drops from approximately 10 A to less than 1 A and remains at the lower value. Explain why.b) What would happen if the power source were DC? Get solution
22cq. A series RLC circuit is in resonance when driven by a sinusoidal voltage at its resonant frequency, ω0 = (LC)–1/2. But if the same circuit is driven by a square-wave voltage (which is alternately on and off for equal time intervals), it will exhibit resonance at its resonant frequency and at 1/3 ,1/5 , 1/7 , ... , of this frequency. Explain why. Get solution
23cq. Is it possible for the voltage amplitude across the inductor in a series RLC circuit to exceed the voltage amplitude of the voltage supply? Why or why not? Get solution
24cq. Why can’t a transformer be used to step up or step down the voltage in a DC circuit? Get solution
26cq. An RLC circuit has a capacitor, a resistor, and an inductor connected in parallel, as shown in the figure, and a source of time-varying emf providing Vrms at a frequency f. Find an expression for Irms in terms of Vrms, f, L, C, and R.... Get solution
27. For the LC circuit in the figure, L = 32.0 mH and C = 45.0 µF. The capacitor is charged to q0 = 10.0 µC, and at t = 0, the switch is closed. At what time is the energy stored in the capacitor first equal to the energy stored in the inductor?... Get solution
29. An LC circuit consists of a 1.00-mH inductor and a fully charged capacitor. After 2.10 ms, the energy stored in the capacitor is half of its original value. What is the capacitance? Get solution
30. The time-varying current in an LC circuit where C = 10.0 µF is given by i(t) = (1.00A) sin (1200.t), where t is in seconds.a) At what time after t = 0 does the current reach its maximum value?b) What is the total energy of the circuit?c) What is the inductance, L? Get solution
32. A 4.00-mF capacitor is connected in series with a 7.00-mH inductor. The peak current in the wires between the capacitor and the inductor is 3.00 A.a) What is the total electric energy in this circuit?b) Write an expression for the charge on the capacitor as a function of time, assuming the capacitor is fully charged at t = 0 s. Get solution
33. A circuit contains a 4.50-nF capacitor and a 4.00-mH inductor. If some charge is placed initially on the capacitor, an oscillating current with angular frequency ω0 is produced. By what factor does this angular frequency change if a 1.00-kΩ resistor is connected in series with the capacitor and the inductor? Get solution
34. An RLC oscillator circuit contains a 50.0-Ω resistor and a 1.00-mH inductor. What capacitance is necessary for the time constant of the circuit (the 1/e value) to be equal to the oscillation period? Plot the voltage across the resistor as a function of time. Get solution
35. A 2.00-µF capacitor was fully charged by being connected to a 12.0-V battery. The fully charged capacitor is then connected in series with a resistor and an inductor: R = 50.0 Ω and L = 0.200 H. Calculate the damped frequency of the resulting circuit. Get solution
36. An LC circuit consists of a capacitor, C = 2.50 µF, and an inductor, L = 4.00 mH. The capacitor is fully charged using a battery and then connected to the inductor. An oscilloscope is used to measure the frequency of the oscillations in the circuit. Next, the circuit is opened, and a resistor, R, is inserted in series with the inductor and the capacitor. The capacitor is again fully charged using the same battery and then connected to the circuit. The angular frequency of the damped oscillations in the RLC circuit is found to be 20.0% less than the angular frequency of the oscillations in the LC circuit.a) Determine the resistance of the resistor.b) How long after the capacitor is reconnected in the circuit will the amplitude of the damped current through the circuit be 50.0% of the initial amplitude?c) How many complete damped oscillations will have occurred in that time? Get solution
37. At what frequency will a 10.0-µF capacitor have the reactance XC = 200. Ω? Get solution
38. A capacitor with capacitance C = 5.00 · 10–6 F is connected to an AC power source having a peak value of 10.0 V and f = 100. Hz. Find the reactance of the capacitor and the maximum current in the circuit. Get solution
39. A series circuit contains a 100.0-Ω resistor, a 0.500-H inductor, a 0.400-µF capacitor, and a source of time-varying emf providing 40.0 V.a) What is the resonant angular frequency of the circuit?b) What current will flow through the circuit at the resonant frequency? Get solution
40. A variable capacitor used in an RLC circuit produces a resonant frequency of 5.0 MHz when its capacitance is set to 15 pF. What will the resonant frequency be when the capacitance is increased to 380 pF? Get solution
41. Determine the phase constant and the impedance of the RLC circuit shown in the figure when the frequency of the time-varying emf is 1.00 kHz, C = 100. µF, L = 10.0 mH, and R = 100. Ω.... Get solution
42. What is the resonant frequency of the series RLC circuit of Problem 30.41 if C = 4.00 µF, L = 5.00 mH, and R = 1.00 kΩ? What is the maximum current in the circuit if Vm = 10.0 V at the resonant frequency? Get solution
43. In a series RLC circuit, V = (12.0 V)(sin ωt), R = 10.0 Ω, L = 2.00 H, and C = 10.0 µF. At resonance, determine the amplitude of the voltage across the inductor. Is the result reasonable, considering that the voltage supplied to the entire circuit has an amplitude of 12.0 V? Get solution
44. An AC power source with Vm = 220. V and f = 60.0 Hz is connected in a series RLC circuit. The resistance, R, inductance, L, and capacitance, C, of this circuit are, respectively, 50.0 Ω, 0.200 H, and 0.0400 mF. Find each of the following quantities:a) the inductive reactanceb) the capacitive reactancec) the impedance of the circuitd) the maximum current through the circuit at this frequencye) the maximum potential difference across each circuit element Get solution
45. The series RLC circuit shown in the figure has R = 2.20 Ω, L = 9.30 mH, C = 2.27 mF, Vm = 110. V, and ω = 377 rad/s.a) What is the maximum current, Im, in this circuit?b) What is the phase constant, φ, between the voltage and the current?c) The capacitance, C, can be varied. What value of C will allow the largest current amplitude oscillations to occur, and what are the magnitudes of this current, I'm, and the phase angle, φ', between the current and the voltage?... Get solution
46. Design an RC high-pass filter that passes a signal with frequency 5.00 kHz, has a ratio Vout/Vin = 0.500, and has an impedance of 1.00 kΩ at very high frequencies.a) What components will you use?b) What is the phase of Vout relative to Vin at the frequency of 5.00 kHz? Get solution
47. Design an RC high-pass filter that rejects 60.0-Hz line noise from a circuit used in a detector. Your criteria are reduction of the amplitude of the line noise by a factor of 1000. and total impedance at high frequencies of 2.00 kΩ.a) What components will you use?b) What is the frequency range of the signals that will be passed with at least 90.0% of their amplitude? Get solution
48. What is the maximum value of the AC voltage whose root-meansquare value is (a) 110 V or (b) 220 V? Get solution
49. The quality factor, Q, of a circuit can be defined by Q = ω0(UE + UB)/P. Express the quality factor of a series RLC circuit in terms of its resistance R, inductance L, and capacitance C. Get solution
50. A label on a hair dryer reads “110V 1250W.” What is the peak current in the hair dryer, assuming that it behaves like a resistor? Get solution
52. A circuit contains a 100.-Ω resistor, a 0.0500-H inductor, a 0.400-µF capacitor, and a source of time-varying emf connected in series. The time-varying emf corresponds to Vrms = 50.0 V at a frequency of 2000. Hz.a) Determine the current in the circuit.b) Determine the voltage drop across each component of the circuit.c) How much power is drawn from the source of emf? Get solution
53. The figure shows a simple FM antenna circuit in which L = 8.22 µH and C is variable (the capacitor can be tuned to receive a specific station). The radio signal from your favorite FM station produces a sinusoidal time-varying emf with an amplitude of 12.9 µV and a frequency of 88.7 MHz in the antenna.a) To what value, C0, should you tune the capacitor in order to best receive this station?b) Another radio station’s signal produces a sinusoidal time-varying emf with the same amplitude, 12.9 µV, but with a frequency of 88.5 MHz in the antenna. With the circuit tuned to optimize reception at 88.7 MHz, what should the value, R0, of the resistance be in order to reduce by a factor of 2 (compared to the current if the circuit were optimized for 88.5 MHz) the current produced by the signal from this station?... Get solution
54. The transmission of electric power occurs at the highest possible voltage to reduce losses. By how much could the power loss be reduced by raising the voltage by a factor of 10.0? Get solution
55. Treat the solenoid and coil of Solved Problem 29.2 as a transformer.a) Find the root-mean-square voltage in the coil if the solenoid has a rootmean- square voltage of 120 V and a frequency of 60. Hz. The length of the solenoid is 12.0 cm.b) What is the voltage in the coil if the frequency is 0 Hz (DC current)? Get solution
56. A transformer has 800 turns in the primary coil and 40 turns in the secondary coil.a) What happens if an AC voltage of 100. V is across the primary coil?b) If the initial AC current is 5.00 A, what is the output current?c) What happens if a DC current at 100. V flows into the primary coil?d) If the initial DC current is 5.00 A, what is the output current? Get solution
57. A transformer contains a primary coil with 200 turns and a secondary coil with 120 turns. The secondary coil drives a current I through a 1.00-kΩ resistor. If an input voltage of Vrms = 75.0 V is applied across the primary coil, what is the power dissipated in the resistor? Get solution
58. Consider the filtered fullwave rectifier shown in the figure. If the frequency of the source of time-varying emf is 60. Hz, what is the frequency of the resulting current?... Get solution
59. A voltage Vrms = 110 V at a frequency of 60. Hz is applied to the primary coil of a transformer. The transformer has a ratio NP/NS = 11. The secondary coil is used as the source of Vemf for the filtered fullwave rectifier of Problem 30.58.a) What is the maximum voltage in the secondary coil of the transformer?b) What is the DC voltage provided to the resistor? Get solution
60. A vacuum cleaner motor can be viewed as an inductor with an inductance of 100. mH. For a 60.0-Hz AC voltage of Vrms = 115. V, what capacitance must be in series with the motor to maximize the power output of the vacuum cleaner? Get solution
61. When you turn the dial on a radio to tune it, you are adjusting a variable capacitor in an LC circuit. Suppose you tune to an AM station broadcasting at a frequency of 1000. kHz, and there is a 10.0-mH inductor in the tuning circuit. When you have tuned in the station, what is the capacitance of the capacitor? Get solution
62. A series RLC circuit has a source of time-varying emf providing 12.0 V at a frequency f0, with L = 7.00 mH, R = 100. Ω, and C = 0.0500 mF.a) What is the resonant frequency of this circuit?b) What is the average power dissipated in the resistor at this resonant frequency? Get solution
63. What are the maximum values of (a) current and (b) voltage when an incandescent 60-W light bulb (at 110 V) is connected to a wall plug labeled 110 V? Get solution
64. A 360-Hz source of emf is connected in a circuit consisting of a capacitor, a 25-mH inductor, and an 0.80-Ω resistor. For the current and the voltage to be in phase, what should the value of C be? Get solution
65. What is the resistance in an RLC circuit with L = 65.0 mH and C = 1.00 µF if the circuit loses 3.50% of its total energy as thermal energy in each cycle? Get solution
66. A transformer with 400. turns in its primary coil and 20. turns in its secondary coil is designed to deliver an average power of 1200. W with a maximum voltage of 60.0 V. What is the maximum current in the primary coil? Get solution
67. A 5.00-µF capacitor in series with a 4.00-Ω resistor is charged with a 9.00-V battery for a long time by closing the switch (position a in the figure). The capacitor is then discharged through an inductor (L = 40.0 mH) by closing the switch (position b) at t = 0.a) Determine the maximum current through the inductor.b) What is the first time at which the current is at its maximum?... Get solution
68. In the RC high-pass filter shown in the figure, R =10.0 kΩ and C = 0.0470 µF. What is the 3.00-dB frequency of this circuit (where dB means basically the same for electric current as it did for sound in Chapter 16)? That is, at what frequency does the ratio of output voltage to input voltage satisfy 20 log (Vout/Vin) = –3.00?... Get solution
69. The discussion of RL, RC, and RLC circuits in this chapter has assumed a purely resistive resistor, one whose inductance and capacitance are exactly zero. While the capacitance of a resistor can generally be neglected, inductance is an intrinsic part of the resistor. Indeed, one of the most widely used resistors, the wire-wound resistor, is nothing but a solenoid made of highly resistive wire. Suppose a wire-wound resistor of unknown resistance is connected to a DC power supply. At a voltage of V = 10.0 V across the resistor, the current through the resistor is 1.00 A. Next, the same resistor is connected to an AC power source providing Vrms = 10.0 V at a variable frequency. When the frequency is 20.0 kHz, a current, Irms = 0.800 A, is measured through the resistor.a) Calculate the resistance of the resistor.b) Calculate the inductive reactance of the resistor.c) Calculate the inductance of the resistor.d) Calculate the frequency of the AC power source at which the inductive reactance of the resistor exceeds its resistance. Get solution
70. In a certain RLC circuit, a 20.0-Ω resistor, a 10.0-mH inductor, and a 5.00-µF capacitor are connected in series with an AC power source for which Vrms = 10.0 V and f = 100. Hz. Calculatea) the amplitude of the current,b) the phase between the current and the voltage, andc) the maximum voltage across each component. Get solution
71. a) A loop of wire 5.00 cm in diameter is carrying a current of 2.00 A. What is the energy density of the magnetic field at its center?b) What current has to flow in a straight wire to produce the same energy density at a point 4.00 cm from the wire? Get solution
72. A 75,000-W light bulb (yes, there are such things!) operates at Irms = 200. A and Vrms = 440. V in a 60.0-Hz AC circuit. Find the resistance, R, and self-inductance, L, of this bulb. Its capacitive reactance is negligible. Get solution
73. Show that the power dissipated in a resistor connected to an AC power source with a frequency ω oscillates with a frequency 2ω. Get solution
74. A 300.-Ω resistor is connected in series with a 4.00-µF capacitor and a source of time-varying emf providing Vrms = 40.0 V.a) At what frequency will the potential drop across the capacitor equal that across the resistor?b) What is the rms current through the circuit when this occurs? Get solution
75. An electromagnet consists of 200 loops and has a length of 10.0 cm and a cross-sectional area of 5.00 cm2. Find the resonant frequency of this electromagnet when it is attached to the Earth (treat the Earth as a spherical capacitor). Get solution
76. Laboratory experiments with series RLC circuits require some care, as these circuits can produce large voltages at resonance. Suppose you have a 1.00-H inductor (not difficult to obtain) and a variety of resistors and capacitors. Design a series RLC circuit that will resonate at a frequency (not an angular frequency) of 60.0 Hz and will produce at resonance a magnification of the voltage across the capacitor or the inductor by a factor of 20.0 times the input voltage or the voltage across the resistor. Get solution
77. A particular RC low-pass filter has a breakpoint frequency of 200. Hz. At what frequency will the output voltage divided by the input voltage be 0.100? Get solution
78. An inductor with inductance L = 42.1 mH is connected to an AC power source that supplies Vemf = 19.1 V at f = 605 Hz. Find the reactance of the inductor. Get solution
79. An inductor with inductance L = 52.5 mH is connected to an AC power source that supplies Vemf = 19.9 V at f = 669 Hz. Find the maximum current in the circuit. Get solution
80. An inductor with inductance L is connected to an AC power source that supplies Vemf = 20.7 V at f = 733 Hz. If the reactance of the inductor is to be 81.52 Ω, what should the value of L be? Get solution
81. An inductor with inductance L is connected to an AC power source that supplies Vemf = 21.5 V at f = 797 Hz. If the maximum current in the circuit is to be 0.1528 A, what should the value of L be? Get solution
1mcq. A 200-Ω resistor, a 40.0-mH inductor and a 3.0-µF capacitor are connected in series with a source of time-varying emf that provides 10.0 V at a frequency of 1000 Hz. What is the impedance of the circuit?a) 200 Ωb) 228 Ωc) 342 Ωd) 282 Ω Get solution
2cc. In Figure 30.3, suppose t = 0 at point (c). What is the phase constant in this case? (Define a clockwise current as positive.)a) 0b) π/2c) πd) 3π/2e) none of the aboveFigure 30.3 Variation of the charge, current, electric energy, and magnetic energy as a function of time for a simple, single-loop LC circuit. The letters along the bottom refer to the parts of Figure 30.2.... Get solution
2mcq. For which values of f is XL > XC?a) f > 2π(LC)1/2b) f > (2πLC)–1c) f > (2π(LC)1/2)–1d) f > 2πLC Get solution
3cc. What is the condition for small damping that needs to be fulfilled for equation 30.6 to be a solution for equation 30.5? (Hint: You can find this by analogy with the damped oscillation of a mass on a spring, for which the differential equation is ... and the condition for small damping is .... Alternatively, you can use dimensional analysis.)a) ...b) ...c) ...Equation 30.5...Equation 30.6... Get solution
3mcq. Which statement about the phase relation between the electric and magnetic fields in an LC circuit is correct?a) When one field is at its maximum, the other is also, and the same for the minimum values.b) When one field is at maximum strength, the other is at minimum (zero) strength.c) The phase relation, in general, depends on the values of L and C. Get solution
4cc. A circuit containing a capacitor (Figure 30.9) has a source of time varying emf that provides a voltage given by vC = VC sin ωt. What is the current, iC, through the capacitor when the potential difference across it is largest (vC = Vmax)?a) iC = 0b) iC = +Imaxc) iC = –ImaxFigure 30.9 Single-loop circuit with a capacitor and a source of time-varying emf.... Get solution
4mcq. For the band-pass filter shown in Figure 30.25, how can the width of the frequency response be increased?a) increase R1b) decrease C1c) increase R2d) increase C2e) do any of the aboveFigure 30.25 The frequency response of a low-pass filter, a high-pass filter, and a band-pass filter.... Get solution
5mcq. The phase constant, φ, between the voltage and the current in an AC circuit depends on the _______.a) inductive reactanceb) capacitive reactancec) resistanced) all of the above Get solution
6cc. The frequency response for a band-pass filter plotted in Figure 30.25 is the _________ of the frequency responses for the low-pass and high-pass filters.a) sumb) productc) differenced) ratioe) It is none of the above.Figure 30.25 The frequency response of a low-pass filter, a high-pass filter, and a band-pass filter.... Get solution
7cc. WiFi networks are installed in most coffee shops and many residences to provide access to the Internet. The most common WiFi standard is known as 802.11 g, which supports communication rates of up to 54 megabits per second. Wireless networks in the United States and Canada that follow this standard use a frequency around 2.4 GHz, in 14 different channels in the band between 2.401 GHz and 2.495 GHz. Each channel has a full width at half maximum of 22 MHz. What is the quality factor of these WiFi networks?a) 0.1b) 9.9c) 33d) 109e) 300 Get solution
7mcq. In the RLC circuit in the figure, R = 60 Ω, L = 3 mH, C = 4 mF, and the source of time-varying emf has a peak voltage of 120 V. What should the angular frequency, ω, be to produce the largest current in the resistor?a) 4.2 rad/sb) 8.3 rad/sc) 204 rad/sd) 289 rad/se) 5000 rad/sf) 20,000 rad/s... Get solution
8mcq. A standard North American wall socket plug is labeled 110 V. This label indicates the ______ value of the voltage.a) averageb) maximumc) root-mean-square (rms)d) instantaneous Get solution
9mcq. A circuit contains a source of time-varying emf, which is given by Vemf = 120.0 sin[(377 rad/s)t] V, and a capacitor with capacitance C = 5.00 µF. What is the current in the circuit at t = 1.00 s?a) 0.226 Ab) 0.451 Ac) 0.555 Ad) 0.750 Ae) 1.25 A Get solution
10mcq. A source of time-varying emf supplies Vmax = 115.0 V at f = 60.0 Hz in a series RLC circuit in which R = 374 Ω, L = 0.310 H, and C = 5.50 µF. What is the impedance of this circuit?a) 321 Ωb) 523 Ωc) 622 Ωd) 831 Ωe) 975 Ω Get solution
11cq. What is the impedance of a series RLC circuit when the frequency of time-varying emf is set to the resonant frequency of the circuit? Get solution
13cq. In a DC circuit containing a capacitor, a current will flow through the circuit for only a very short time, while the capacitor is being charged or discharged. On the other hand, a steady alternating current will flow in a circuit containing the same capacitor but powered by a source of time varying emf. Does it mean that charges are crossing the gap (dielectric) of the capacitor? Get solution
15cq. In Solved Problem 30.3, the voltage supplied by the source of time varying emf is 33.0 V, the voltage across the resistor is VR = IR = 13.1 V, and the voltage across the inductor is VL = IXL = 30.3 V. Does this circuit obey Kirchhoff’s rules? Get solution
14cq. In an RL circuit with alternating current, the current lags behind the voltage. What does this mean, and how can it be explained qualitatively, based on the phenomenon of electromagnetic induction? Get solution
16cq. Why is rms power specified for an AC circuit, not average power? Get solution
17cq. Why can’t we use a universal charger that plugs into a household outlet to charge all our electrical devices—cell phone, toy dog, can opener, and so on—rather than using a separate charger with its own transformer for each device? Get solution
18cq. If you use a parallel plate capacitor with air in the gap between the plates as part of a series RLC circuit in a generator, you can measure current flowing through the generator. Why is it that the air gap in the capacitor does not act like an open switch, blocking all current flow in the circuit? Get solution
19cq. A common configuration of wires has twisted pairs as opposed to straight, parallel wires. What is the technical advantage of using twisted pairs of wires versus straight, parallel pairs? Get solution
20cq. In a classroom demonstration, an iron core is inserted into a large solenoid connected to an AC power source. The effect of the core is to magnify the magnetic field in the solenoid by the relative magnetic permeability, κm, of the core (where κm is a dimensionless constant, substantially greater than unity for a ferromagnetic material, introduced in Chapter 28) or, equivalently, to replace the magnetic permeability of free space, µ0, with the magnetic permeability of the core, µ = κmµ0.a) The measured root-mean-square current drops from approximately 10 A to less than 1 A and remains at the lower value. Explain why.b) What would happen if the power source were DC? Get solution
22cq. A series RLC circuit is in resonance when driven by a sinusoidal voltage at its resonant frequency, ω0 = (LC)–1/2. But if the same circuit is driven by a square-wave voltage (which is alternately on and off for equal time intervals), it will exhibit resonance at its resonant frequency and at 1/3 ,1/5 , 1/7 , ... , of this frequency. Explain why. Get solution
23cq. Is it possible for the voltage amplitude across the inductor in a series RLC circuit to exceed the voltage amplitude of the voltage supply? Why or why not? Get solution
24cq. Why can’t a transformer be used to step up or step down the voltage in a DC circuit? Get solution
26cq. An RLC circuit has a capacitor, a resistor, and an inductor connected in parallel, as shown in the figure, and a source of time-varying emf providing Vrms at a frequency f. Find an expression for Irms in terms of Vrms, f, L, C, and R.... Get solution
27. For the LC circuit in the figure, L = 32.0 mH and C = 45.0 µF. The capacitor is charged to q0 = 10.0 µC, and at t = 0, the switch is closed. At what time is the energy stored in the capacitor first equal to the energy stored in the inductor?... Get solution
29. An LC circuit consists of a 1.00-mH inductor and a fully charged capacitor. After 2.10 ms, the energy stored in the capacitor is half of its original value. What is the capacitance? Get solution
30. The time-varying current in an LC circuit where C = 10.0 µF is given by i(t) = (1.00A) sin (1200.t), where t is in seconds.a) At what time after t = 0 does the current reach its maximum value?b) What is the total energy of the circuit?c) What is the inductance, L? Get solution
32. A 4.00-mF capacitor is connected in series with a 7.00-mH inductor. The peak current in the wires between the capacitor and the inductor is 3.00 A.a) What is the total electric energy in this circuit?b) Write an expression for the charge on the capacitor as a function of time, assuming the capacitor is fully charged at t = 0 s. Get solution
33. A circuit contains a 4.50-nF capacitor and a 4.00-mH inductor. If some charge is placed initially on the capacitor, an oscillating current with angular frequency ω0 is produced. By what factor does this angular frequency change if a 1.00-kΩ resistor is connected in series with the capacitor and the inductor? Get solution
34. An RLC oscillator circuit contains a 50.0-Ω resistor and a 1.00-mH inductor. What capacitance is necessary for the time constant of the circuit (the 1/e value) to be equal to the oscillation period? Plot the voltage across the resistor as a function of time. Get solution
35. A 2.00-µF capacitor was fully charged by being connected to a 12.0-V battery. The fully charged capacitor is then connected in series with a resistor and an inductor: R = 50.0 Ω and L = 0.200 H. Calculate the damped frequency of the resulting circuit. Get solution
36. An LC circuit consists of a capacitor, C = 2.50 µF, and an inductor, L = 4.00 mH. The capacitor is fully charged using a battery and then connected to the inductor. An oscilloscope is used to measure the frequency of the oscillations in the circuit. Next, the circuit is opened, and a resistor, R, is inserted in series with the inductor and the capacitor. The capacitor is again fully charged using the same battery and then connected to the circuit. The angular frequency of the damped oscillations in the RLC circuit is found to be 20.0% less than the angular frequency of the oscillations in the LC circuit.a) Determine the resistance of the resistor.b) How long after the capacitor is reconnected in the circuit will the amplitude of the damped current through the circuit be 50.0% of the initial amplitude?c) How many complete damped oscillations will have occurred in that time? Get solution
37. At what frequency will a 10.0-µF capacitor have the reactance XC = 200. Ω? Get solution
38. A capacitor with capacitance C = 5.00 · 10–6 F is connected to an AC power source having a peak value of 10.0 V and f = 100. Hz. Find the reactance of the capacitor and the maximum current in the circuit. Get solution
39. A series circuit contains a 100.0-Ω resistor, a 0.500-H inductor, a 0.400-µF capacitor, and a source of time-varying emf providing 40.0 V.a) What is the resonant angular frequency of the circuit?b) What current will flow through the circuit at the resonant frequency? Get solution
40. A variable capacitor used in an RLC circuit produces a resonant frequency of 5.0 MHz when its capacitance is set to 15 pF. What will the resonant frequency be when the capacitance is increased to 380 pF? Get solution
41. Determine the phase constant and the impedance of the RLC circuit shown in the figure when the frequency of the time-varying emf is 1.00 kHz, C = 100. µF, L = 10.0 mH, and R = 100. Ω.... Get solution
42. What is the resonant frequency of the series RLC circuit of Problem 30.41 if C = 4.00 µF, L = 5.00 mH, and R = 1.00 kΩ? What is the maximum current in the circuit if Vm = 10.0 V at the resonant frequency? Get solution
43. In a series RLC circuit, V = (12.0 V)(sin ωt), R = 10.0 Ω, L = 2.00 H, and C = 10.0 µF. At resonance, determine the amplitude of the voltage across the inductor. Is the result reasonable, considering that the voltage supplied to the entire circuit has an amplitude of 12.0 V? Get solution
44. An AC power source with Vm = 220. V and f = 60.0 Hz is connected in a series RLC circuit. The resistance, R, inductance, L, and capacitance, C, of this circuit are, respectively, 50.0 Ω, 0.200 H, and 0.0400 mF. Find each of the following quantities:a) the inductive reactanceb) the capacitive reactancec) the impedance of the circuitd) the maximum current through the circuit at this frequencye) the maximum potential difference across each circuit element Get solution
45. The series RLC circuit shown in the figure has R = 2.20 Ω, L = 9.30 mH, C = 2.27 mF, Vm = 110. V, and ω = 377 rad/s.a) What is the maximum current, Im, in this circuit?b) What is the phase constant, φ, between the voltage and the current?c) The capacitance, C, can be varied. What value of C will allow the largest current amplitude oscillations to occur, and what are the magnitudes of this current, I'm, and the phase angle, φ', between the current and the voltage?... Get solution
46. Design an RC high-pass filter that passes a signal with frequency 5.00 kHz, has a ratio Vout/Vin = 0.500, and has an impedance of 1.00 kΩ at very high frequencies.a) What components will you use?b) What is the phase of Vout relative to Vin at the frequency of 5.00 kHz? Get solution
47. Design an RC high-pass filter that rejects 60.0-Hz line noise from a circuit used in a detector. Your criteria are reduction of the amplitude of the line noise by a factor of 1000. and total impedance at high frequencies of 2.00 kΩ.a) What components will you use?b) What is the frequency range of the signals that will be passed with at least 90.0% of their amplitude? Get solution
48. What is the maximum value of the AC voltage whose root-meansquare value is (a) 110 V or (b) 220 V? Get solution
49. The quality factor, Q, of a circuit can be defined by Q = ω0(UE + UB)/P. Express the quality factor of a series RLC circuit in terms of its resistance R, inductance L, and capacitance C. Get solution
50. A label on a hair dryer reads “110V 1250W.” What is the peak current in the hair dryer, assuming that it behaves like a resistor? Get solution
52. A circuit contains a 100.-Ω resistor, a 0.0500-H inductor, a 0.400-µF capacitor, and a source of time-varying emf connected in series. The time-varying emf corresponds to Vrms = 50.0 V at a frequency of 2000. Hz.a) Determine the current in the circuit.b) Determine the voltage drop across each component of the circuit.c) How much power is drawn from the source of emf? Get solution
53. The figure shows a simple FM antenna circuit in which L = 8.22 µH and C is variable (the capacitor can be tuned to receive a specific station). The radio signal from your favorite FM station produces a sinusoidal time-varying emf with an amplitude of 12.9 µV and a frequency of 88.7 MHz in the antenna.a) To what value, C0, should you tune the capacitor in order to best receive this station?b) Another radio station’s signal produces a sinusoidal time-varying emf with the same amplitude, 12.9 µV, but with a frequency of 88.5 MHz in the antenna. With the circuit tuned to optimize reception at 88.7 MHz, what should the value, R0, of the resistance be in order to reduce by a factor of 2 (compared to the current if the circuit were optimized for 88.5 MHz) the current produced by the signal from this station?... Get solution
54. The transmission of electric power occurs at the highest possible voltage to reduce losses. By how much could the power loss be reduced by raising the voltage by a factor of 10.0? Get solution
55. Treat the solenoid and coil of Solved Problem 29.2 as a transformer.a) Find the root-mean-square voltage in the coil if the solenoid has a rootmean- square voltage of 120 V and a frequency of 60. Hz. The length of the solenoid is 12.0 cm.b) What is the voltage in the coil if the frequency is 0 Hz (DC current)? Get solution
56. A transformer has 800 turns in the primary coil and 40 turns in the secondary coil.a) What happens if an AC voltage of 100. V is across the primary coil?b) If the initial AC current is 5.00 A, what is the output current?c) What happens if a DC current at 100. V flows into the primary coil?d) If the initial DC current is 5.00 A, what is the output current? Get solution
57. A transformer contains a primary coil with 200 turns and a secondary coil with 120 turns. The secondary coil drives a current I through a 1.00-kΩ resistor. If an input voltage of Vrms = 75.0 V is applied across the primary coil, what is the power dissipated in the resistor? Get solution
58. Consider the filtered fullwave rectifier shown in the figure. If the frequency of the source of time-varying emf is 60. Hz, what is the frequency of the resulting current?... Get solution
59. A voltage Vrms = 110 V at a frequency of 60. Hz is applied to the primary coil of a transformer. The transformer has a ratio NP/NS = 11. The secondary coil is used as the source of Vemf for the filtered fullwave rectifier of Problem 30.58.a) What is the maximum voltage in the secondary coil of the transformer?b) What is the DC voltage provided to the resistor? Get solution
60. A vacuum cleaner motor can be viewed as an inductor with an inductance of 100. mH. For a 60.0-Hz AC voltage of Vrms = 115. V, what capacitance must be in series with the motor to maximize the power output of the vacuum cleaner? Get solution
61. When you turn the dial on a radio to tune it, you are adjusting a variable capacitor in an LC circuit. Suppose you tune to an AM station broadcasting at a frequency of 1000. kHz, and there is a 10.0-mH inductor in the tuning circuit. When you have tuned in the station, what is the capacitance of the capacitor? Get solution
62. A series RLC circuit has a source of time-varying emf providing 12.0 V at a frequency f0, with L = 7.00 mH, R = 100. Ω, and C = 0.0500 mF.a) What is the resonant frequency of this circuit?b) What is the average power dissipated in the resistor at this resonant frequency? Get solution
63. What are the maximum values of (a) current and (b) voltage when an incandescent 60-W light bulb (at 110 V) is connected to a wall plug labeled 110 V? Get solution
64. A 360-Hz source of emf is connected in a circuit consisting of a capacitor, a 25-mH inductor, and an 0.80-Ω resistor. For the current and the voltage to be in phase, what should the value of C be? Get solution
65. What is the resistance in an RLC circuit with L = 65.0 mH and C = 1.00 µF if the circuit loses 3.50% of its total energy as thermal energy in each cycle? Get solution
66. A transformer with 400. turns in its primary coil and 20. turns in its secondary coil is designed to deliver an average power of 1200. W with a maximum voltage of 60.0 V. What is the maximum current in the primary coil? Get solution
67. A 5.00-µF capacitor in series with a 4.00-Ω resistor is charged with a 9.00-V battery for a long time by closing the switch (position a in the figure). The capacitor is then discharged through an inductor (L = 40.0 mH) by closing the switch (position b) at t = 0.a) Determine the maximum current through the inductor.b) What is the first time at which the current is at its maximum?... Get solution
68. In the RC high-pass filter shown in the figure, R =10.0 kΩ and C = 0.0470 µF. What is the 3.00-dB frequency of this circuit (where dB means basically the same for electric current as it did for sound in Chapter 16)? That is, at what frequency does the ratio of output voltage to input voltage satisfy 20 log (Vout/Vin) = –3.00?... Get solution
69. The discussion of RL, RC, and RLC circuits in this chapter has assumed a purely resistive resistor, one whose inductance and capacitance are exactly zero. While the capacitance of a resistor can generally be neglected, inductance is an intrinsic part of the resistor. Indeed, one of the most widely used resistors, the wire-wound resistor, is nothing but a solenoid made of highly resistive wire. Suppose a wire-wound resistor of unknown resistance is connected to a DC power supply. At a voltage of V = 10.0 V across the resistor, the current through the resistor is 1.00 A. Next, the same resistor is connected to an AC power source providing Vrms = 10.0 V at a variable frequency. When the frequency is 20.0 kHz, a current, Irms = 0.800 A, is measured through the resistor.a) Calculate the resistance of the resistor.b) Calculate the inductive reactance of the resistor.c) Calculate the inductance of the resistor.d) Calculate the frequency of the AC power source at which the inductive reactance of the resistor exceeds its resistance. Get solution
70. In a certain RLC circuit, a 20.0-Ω resistor, a 10.0-mH inductor, and a 5.00-µF capacitor are connected in series with an AC power source for which Vrms = 10.0 V and f = 100. Hz. Calculatea) the amplitude of the current,b) the phase between the current and the voltage, andc) the maximum voltage across each component. Get solution
71. a) A loop of wire 5.00 cm in diameter is carrying a current of 2.00 A. What is the energy density of the magnetic field at its center?b) What current has to flow in a straight wire to produce the same energy density at a point 4.00 cm from the wire? Get solution
72. A 75,000-W light bulb (yes, there are such things!) operates at Irms = 200. A and Vrms = 440. V in a 60.0-Hz AC circuit. Find the resistance, R, and self-inductance, L, of this bulb. Its capacitive reactance is negligible. Get solution
73. Show that the power dissipated in a resistor connected to an AC power source with a frequency ω oscillates with a frequency 2ω. Get solution
74. A 300.-Ω resistor is connected in series with a 4.00-µF capacitor and a source of time-varying emf providing Vrms = 40.0 V.a) At what frequency will the potential drop across the capacitor equal that across the resistor?b) What is the rms current through the circuit when this occurs? Get solution
75. An electromagnet consists of 200 loops and has a length of 10.0 cm and a cross-sectional area of 5.00 cm2. Find the resonant frequency of this electromagnet when it is attached to the Earth (treat the Earth as a spherical capacitor). Get solution
76. Laboratory experiments with series RLC circuits require some care, as these circuits can produce large voltages at resonance. Suppose you have a 1.00-H inductor (not difficult to obtain) and a variety of resistors and capacitors. Design a series RLC circuit that will resonate at a frequency (not an angular frequency) of 60.0 Hz and will produce at resonance a magnification of the voltage across the capacitor or the inductor by a factor of 20.0 times the input voltage or the voltage across the resistor. Get solution
77. A particular RC low-pass filter has a breakpoint frequency of 200. Hz. At what frequency will the output voltage divided by the input voltage be 0.100? Get solution
78. An inductor with inductance L = 42.1 mH is connected to an AC power source that supplies Vemf = 19.1 V at f = 605 Hz. Find the reactance of the inductor. Get solution
79. An inductor with inductance L = 52.5 mH is connected to an AC power source that supplies Vemf = 19.9 V at f = 669 Hz. Find the maximum current in the circuit. Get solution
80. An inductor with inductance L is connected to an AC power source that supplies Vemf = 20.7 V at f = 733 Hz. If the reactance of the inductor is to be 81.52 Ω, what should the value of L be? Get solution
81. An inductor with inductance L is connected to an AC power source that supplies Vemf = 21.5 V at f = 797 Hz. If the maximum current in the circuit is to be 0.1528 A, what should the value of L be? Get solution
