Ch31 Electromagnetic Oscillations And Alternating Test Bank - Physics Extended 11e | Test Bank by Halliday by David Halliday. DOCX document preview.
Chapter: Chapter 31
Learning Objectives
LO 31.1.0 Solve problems related to LC oscillations.
LO 31.1.1 Sketch an LC oscillator and explain which quantities oscillate and what constitutes one period of the oscillation.
LO 31.1.2 For an LC oscillator, sketch graphs of the potential differences across the capacitor and the current through the inductor as functions of time, and indicate the period T on each graph.
LO 31.1.3 Explain the analogy between a block-spring oscillator and an LC oscillator.
LO 31.1.4 For an LC oscillator, apply the relationships between the angular frequency ω (and the related frequency f and period T) and the values of the inductance and capacitance.
LO 31.1.5 Starting with the energy of a block-spring system, explain the derivation of the differential equation for charge q in an LC oscillator and then identify the solution for q(t).
LO 31.1.6 For an LC oscillator, calculate the charge q on the capacitor for any given time and identify the amplitude Q of the charge oscillations.
LO 31.1.7 Starting from the equation giving the charge q(t) on the capacitor in an LC oscillator, find the current i(t) in the inductor as a function of time.
LO 31.1.8 For an LC oscillator, calculate the current i in the inductor for any given time and identify the amplitude I of the current oscillations.
LO 31.1.9 For an LC oscillator, apply the relationship between the charge amplitude Q, the current amplitude I, and the angular frequency ω.
LO 31.1.10 From the expressions for the charge q and the current i in an LC oscillator, find the magnetic field energy UB (t) and the electric field energy UE (t) and the total energy.
LO 31.1.11 For an LC oscillator, sketch graphs of the magnetic field energy UB(t), the electric field energy UE(t), and the total energy, all as functions of time.
LO 31.1.12 Calculate the maximum values of the magnetic field energy UB and the electric field energy UE and also calculate the total energy.
LO 31.2.0 Solve problems related to damped oscillations in an RLC circuit.
LO 31.2.1 Draw the schematic of a damped RLC circuit and explain why the oscillations are damped.
LO 31.2.2 Starting with the expressions for the field energies and the rate of energy loss in a damped RLC circuit, write the differential equation for the charge q on the capacitor.
LO 31.2.3 For a damped RLC circuit, apply the expression for charge q(t).
LO 31.2.4 Identify that in a damped RLC circuit, the charge amplitude and the amplitude of the electric field energy decrease exponentially with time.
LO 31.2.5 Apply the relationship between the angular frequency ω' of a given damped RLC oscillator and the angular frequency ω of the circuit if R is removed.
LO 31.2.6 For a damped RLC circuit, apply the expression for the electric field energy UE as a function of time.
LO 31.3.0 Solve problems related to forced oscillations of three simple circuits.
LO 31.3.1 Distinguish alternating current from direct current.
LO 31.3.2 For an ac generator, write the emf as a function of time, identifying the emf amplitude and driving angular frequency.
LO 31.3.3 For an ac generator, write the current as a function of time, identifying its amplitude and its phase constant with respect to the emf.
LO 31.3.4 Draw a schematic diagram of a (series) RLC circuit that is driven by a generator.
LO 31.3.5 Distinguish driving angular frequency ωd from natural angular frequency ω.
LO 31.3.6 In a driven (series) RLC circuit, identify the conditions for resonance and the effect on the current amplitude.
LO 31.3.7 For each of the three basic circuits (purely resistive load, purely capacitive load, and purely inductive load), draw the circuit and sketch graphs and phasor diagrams for voltage v(t) and current i(t).
LO 31.3.8 For the three basic circuits, apply equations for voltage v(t) and current i(t).
LO 31.3.9 On a phasor diagram for each of the basic circuits, identify angular speed, amplitude, projection on the vertical axis, and rotation angle.
LO 31.3.10 For each basic circuit, identify the phase constant, interpret it in terms of the relative orientations of the current phasor and voltage phasor and also in terms of leading and lagging.
LO 31.3.11 Apply the mnemonic “ELI positively is the ICE man.”
LO 31.3.12 For each basic circuit, apply the relationships between the voltage amplitude V and the current amplitude I.
LO 31.3.13 Calculate capacitive reactance XC and inductive reactance XL.
LO 31.4.0 Solve problems related to the series RLC circuit.
LO 31.4.1 Draw the schematic diagram of a series RLC circuit.
LO 31.4.2 Identify the conditions for a mainly inductive circuit, a mainly capacitive circuit, and a resonant circuit.
LO 31.4.3 For a mainly inductive circuit, a mainly capacitive circuit, and a resonant circuit, sketch graphs for voltage v(t) and current i(t) and sketch phasor diagrams, indicating leading, lagging, or resonance.
LO 31.4.4 Calculate impedance Z.
LO 31.4.5 Apply the relationship between current amplitude I, impedance Z, and emf amplitude m.
LO 31.4.6 Apply the relationships between phase constant φ and voltage amplitudes VL and VC, and also between phase constant φ, resistance R, and reactances XL and XC .
LO 31.4.7 Identify the values of the phase constant φ corresponding to a mainly inductive circuit, a mainly capacitive circuit, and a resonant circuit.
LO 31.4.8 For resonance, apply the relationship between the driving angular frequency ωd, the natural angular frequency ω, the inductance L, and the capacitance C.
LO 31.4.9 Sketch a graph of current amplitude versus the ratio ωd/ω, identifying the portions corresponding to a mainly inductive circuit, a mainly capacitive circuit, and a resonant circuit and indicating what happens to the curve for an increase in the resistance.
LO 31.5.0 Solve problems related to power in alternating-current circuits.
LO 31.5.1 For the current, voltage, and emf in an ac circuit, apply the relationship between the rms values and the amplitudes.
LO 31.5.2 For an alternating emf connected across a capacitor, an inductor, or a resistor, sketch graphs of the sinusoidal variation of the current and voltage and indicate the peak and rms values.
LO 31.5.3 Apply the relationship between average power Pavg, rms current Irms, and resistance R.
LO 31.5.4 In a driven RLC circuit, calculate the power of each element.
LO 31.5.5 For a driven RLC circuit in steady state, explain what happens to (a) the value of the average stored energy with time and (b) the energy that the generator puts into the circuit.
LO 31.5.6 Apply the relationship between the power factor cos φ, the resistance R, and the impedance Z.
LO 31.5.7 Identify what power factor is required in order to maximize the rate at which energy is supplied to a resistive load.
LO 31.6.0 Solve problems related to transformers.
LO 31.6.1 For power transmission lines, identify why the transmission should be at low current and high voltage.
LO 31.6.2 Identify the role of transformers at the two ends of a transmission line.
LO 31.6.3 Calculate the energy dissipation in a transmission line.
LO 31.6.4 Identify a transformer’s primary and secondary.
LO 31.6.5 Apply the relationship between the voltage and number of turns on the two sides of a transformer.
LO 31.6.6 Distinguish between a step-down transformer and a step-up transformer.
LO 31.6.7 Apply the relationship between the current and number of turns on the two sides of the transformer.
LO 31.6.8 Apply the relationship between the power into and out of an ideal transformer.
LO 31.6.9 Identify the equivalent resistance as seen from the primary side of a transformer.
LO 31.6.10 Apply the relationship between the equivalent resistance and the actual resistance.
LO 31.6.11 Explain the role of a transformer in impedance matching.
Multiple Choice
1. An LC circuit has an inductance of 15 mH and a capacitance of 10 F. At one instant the charge on the capacitor is 25 C. At that instant the current is changing at the rate:
A) 0 A/s
B) 1.7 10–7 A/s
C) 5.9 10–3 A/s
D) 3.8 10–2 A/s
E) 170 A/s
Difficulty: M
Section: 31-1
Learning Objective 31.1.0
2. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the voltage across the inductor is a maximum is:
A) T/4
B) T/2
C) T
D) 3T/2
E) 2T
Difficulty: M
Section: 31-1
Learning Objective 31.1.1
3. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the energy stored in the magnetic field of the inductor is a maximum is:
A) T/4
B) T/2
C) T
D) 3T/2
E) 2T
Difficulty: M
Section: 31-1
Learning Objective 31.1.1
4. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the energy stored in the electric field of the capacitor is a maximum is:
A) T/4
B) T/2
C) T
D) 3T/2
E) 2T
Difficulty: E
Section: 31-1
Learning Objective 31.1.1
5. The electrical analog of a spring constant k is:
A) L
B) 1/L
C) C
D) 1/C
E) R
Difficulty: E
Section: 31-1
Learning Objective 31.1.3
6. Consider the mechanical system consisting of two springs and a block, as shown. Which one of the five electrical circuits (I, II, III, IV, V) is the analog of the mechanical system?
A) I
B) II
C) III
D) IV
E) V
Difficulty: E
Section: 31-1
Learning Objective 31.1.3
7. A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the initial charge on the capacitor is:
A) 0.15 C
B) 0.25 C
C) 8.8 C
D) 15 C
E) 35 C
Difficulty: M
Section: 31-1
Learning Objective 31.1.3
8. A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the maximum charge on the capacitor is 0.25 C. The maximum current in the LC circuit is:
A) 0.025 A
B) 0.12 A
C) 3.8 A
D) 5.3 A
E) 40 A
Difficulty: M
Section: 31-1
Learning Objective 31.1.3
9. Which of the following has the greatest effect in decreasing the oscillation frequency of an LC circuit? Using instead:
A) L/2 and C/2
B) L/2 and 2C
C) 2L and C/2
D) 2L and 2C
E) none of these
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
10. We desire to make an LC circuit that oscillates at 100 Hz using an inductance of 2.5 H. We also need a capacitance of:
A) 1 F
B) 1 mF
C) 1 F
D) 1 nF
E) 1 pF
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
11. An LC circuit consists of a 1 F capacitor and a 4 mH inductor. Its oscillation frequency is approximately:
A) 0.025 Hz
B) 25 Hz
C) 60 Hz
D) 2500 Hz
E) 16,000 Hz
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
12. An LC circuit has an oscillation frequency of 105 Hz. If C = 0.1 F, then L must be about:
A) 10 mH
B) 1 mH
C) 25 H
D) 2.5 H
E) 1 pH
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
13. In the circuit shown, switch S is first pushed up to charge the capacitor. When S is then pushed down, the current in the circuit will oscillate at a frequency of:
A) 0.010 Hz
B) 12.5 Hz
C) 320 Hz
D) 2000 Hz
E) depends on V0
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
14. Radio receivers are usually tuned by adjusting the capacitor of an LC circuit. If C = C1 for a frequency of 600 kHz, then for a frequency of 1200 kHz one must adjust C to:
A) C1/2
B) C1/4
C) 2C1
D) 4C1
E)
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
15. An LC series circuit with an inductance L and a capacitance C has an oscillation frequency f. If we now take two of those inductors, each with inductance L, and two of the capacitors, each with capacitance C, and wire them all in series to make a new circuit, its oscillation frequency will be:
A) f/4
B) f/2
C) f
D) 2f
E) 4f
Difficulty: M
Section: 31-1
Learning Objective 31.1.4
16. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the charge on the capacitor is a maximum is:
A) T/4
B) T/2
C) T
D) 3T/2
E) 2T
Difficulty: E
Section: 31-1
Learning Objective 31.1.6
17. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the current is a maximum is:
A) T/4
B) T/2
C) T
D) 3T/2
E) 2T
Difficulty: E
Section: 31-1
Learning Objective 31.1.8
18. An LC circuit has an inductance of 20 mH and a capacitance of 5.0 F. If the charge amplitude is 40 C, what is the current amplitude?
A) 0.025 A
B) 0.13 A
C) 1.0 A
D) 7.9 A
E) 400 A
Difficulty: M
Section: 31-1
Learning Objective 31.1.9
19. A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 J. At a certain instant the energy in the capacitor is 40 J. At that instant what is the potential difference across the capacitor?
A) 0 V
B) 5 V
C) 10 V
D) 15 V
E) 20 V
Difficulty: M
Section: 31-1
Learning Objective 31.1.10
20. A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 J. At a certain instant the energy in the capacitor is 40 J. At that instant what is the emf induced in the inductor?
A) 0 V
B) 5 V
C) 10 V
D) 15 V
E) 20 V
Difficulty: M
Section: 31-1
Learning Objective 31.1.10
21. In an oscillating LC circuit, the total stored energy is U. The maximum energy stored in the capacitor during one cycle is:
A) U/2
B)
C) U
D) U/(2)
E) U/
Difficulty: M
Section: 31-1
Learning Objective 31.1.10
22. In an oscillating LC circuit, the total stored energy is U and the maximum charge on the capacitor is Q. When the charge on the capacitor is Q/2, the energy stored in the inductor is:
A) U/2
B) U/4
C) (4/3)U
D) 3U/2
E) 3U/4
Difficulty: M
Section: 31-1
Learning Objective 31.1.10
23. An LC circuit has an inductance of 20 mH and a capacitance of 5.0 F. At time t = 0 the charge on the capacitor is 3.0 C and the current is 7.0 mA. The total energy is:
A) 4.1 10–7 J
B) 4.9 10–7 J
C) 9.0 10–7 J
D) 1.4 10–6 J
E) 2.8 10–6 J
Difficulty: M
Section: 31-1
Learning Objective 31.1.10
24. The total energy in an LC circuit is 5.0 10–6 J. If C = 15 F the maximum charge on the capacitor is:
A) 0.82 C
B) 8.5 C
C) 12 C
D) 17 C
E) 24 C
Difficulty: M
Section: 31-1
Learning Objective 31.1.12
25. The total energy in an LC circuit is 5.0 10–6 J. If L = 25 mH the maximum current is:
A) 10 mA
B) 14 mA
C) 20 mA
D) 28 mA
E) 40 mA
Difficulty: M
Section: 31-1
Learning Objective 31.1.12
26. At time t = 0 the charge on the 50-F capacitor in an LC circuit is 15 C and there is no current. If the inductance is 20 mH the maximum current is:
A) 15 nA
B) 15 A
C) 6.7 mA
D) 15 mA
E) 15 A
Difficulty: M
Section: 31-1
Learning Objective 31.1.12
27. An LC circuit has a capacitance of 30 F and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 C and the current is 20 mA. The maximum charge on the capacitor is:
A) 8.9 C
B) 10 C
C) 12 C
D) 17 C
E) 24 C
Difficulty: M
Section: 31-1
Learning Objective 31.1.12
28. An LC circuit has a capacitance of 30 F and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 C and the current is 20 mA. The maximum current is:
A) 15 mA
B) 20 mA
C) 25 mA
D) 35 mA
E) 42 mA
Difficulty: M
Section: 31-1
Learning Objective 31.1.12
29. An RLC circuit has a resistance of 200 and an inductance of 15 mH. Its oscillation frequency is 7000 Hz. At time t = 0 the current is 25 mA and there is no charge on the capacitor. After five complete cycles the current is:
A) 0 A
B) 1.8 10–6 A
C) 2.1 10–4 A
D) 2.3 10–3 A
E) 2.5 10–2 A
Difficulty: M
Section: 31-2
Learning Objective 31.2.0
30. The rapid exponential decay in just a few cycles of the charge on the plates of capacitor in an RLC circuit might due to:
A) a large inductance
B) a large capacitance
C) a small capacitance
D) a large resistance
E) a small resistance
Difficulty: M
Section: 31-2
Learning Objective 31.2.3
31. An RLC circuit has a capacitance of 12 F, an inductance of 25 mH, and a resistance of 60 . The current oscillates with an angular frequency of:
A) 1.2 103 rad/s
B) 1.4 103 rad/s
C) 1.8 103 rad/s
D) 2.2 103 rad/s
E) 2.6 103 rad/s
Difficulty: M
Section: 31-2
Learning Objective 31.2.5
32. An RLC circuit has a resistance of 200 an inductance of 15 mH, and a capacitance of 34 nF. At time t = 0 the charge on the capacitor is 25 µC and there is no current flowing. After five complete cycles the energy stored in the capacitor is:
A) 0.64 µJ
B) 77 µJ
C) 0.49 mJ
D) 1.8 mJ
E) 9.2 mJ
Difficulty: H
Section: 31-2
Learning Objective 31.2.6
33. The angular frequency of a certain RLC series circuit is 0. A source of sinusoidal emf, with angular frequency 20, is inserted into the circuit. After transients die out the angular frequency of the current oscillations is:
A) 0/2
B) 0
C) 1.50
D) 20
E) 30
Difficulty: E
Section: 31-3
Learning Objective 31.3.0
34. The angular frequency of a certain RLC series circuit is 0. A source of sinusoidal emf, with angular frequency , is inserted into the circuit and is varied while the amplitude of the source is held constant. For which of the following values of is the amplitude of the current oscillations the greatest?
A) 0/5
B) 0/2
C) 0
D) 20
E) None of them (they all produce the same current amplitude)
Difficulty: E
Section: 31-3
Learning Objective 31.3.6
35. A 35-F capacitor is connected to an ac source of emf with a frequency of 250 Hz and a maximum emf of 20 V. If the voltage across the capacitor is zero at time t = 0, what is the voltage at time t = 3.0 ms? Assume the phase constant is zero.
A) −20 V
B) −10 V
C) 0 V
D) 10 V
E) 20 V
Difficulty: E
Section: 31-3
Learning Objective 31.3.8
36. A 45-mH inductor is connected to an ac source of emf with a frequency of 250 Hz and a maximum emf of 20 V. If the voltage across the inductor is zero at time t = 0, what is the voltage at time t = 2.0 ms? Assume the phase constant is zero.
A) −20 V
B) −10 V
C) 0 V
D) 10 V
E) 20 V
Difficulty: E
Section: 31-3
Learning Objective 31.3.8
37. A 35-F capacitor is connected to an ac source of emf with a frequency of 400 Hz and a maximum emf of 20 V. The maximum current is:
A) 0 A
B) 0.28 A
C) 1.8 A
D) 230 A
E) 1400 A
Difficulty: M
Section: 31-3
Learning Objective 31.3.12
38. A 45-mH inductor is connected to an ac source of emf with a frequency of 400 Hz and a maximum emf of 20 V. The maximum current is:
A) 0 A
B) 0.18 A
C) 1.1 A
D) 360 A
E) 2300 A
Difficulty: M
Section: 31-3
Learning Objective 31.3.12
39. The reactance of a 35-F capacitor connected to a 400-Hz generator is:
A) 0 Ω
B) 0.014 Ω
C) 0.088 Ω
D) 11 Ω
E) 71 Ω
Difficulty: M
Section: 31-3
Learning Objective 31.3.13
40. In the diagram, the function y(t) = ymsin(t) is plotted as a solid curve. The other three curves have the form y(t) = ymsin(t + ), where is between –/2 and +/2. Rank the curves according to the value of , from the most negative to the most positive.
A) 1, 2, 3
B) 2, 3, 1
C) 3, 2, 1
D) 1, 3, 2
E) 2, 1, 3
Difficulty: M
Section: 31-4
Learning Objective 31.4.0
41. A resistor, an inductor, and a capacitor are connected in parallel to a sinusoidal source of emf. Which of the following is true?
A) The currents in all branches are in phase.
B) The potential differences across all branches are in phase.
C) The current in the capacitor branch leads the current in the inductor branch by 1/4 cycle.
D) The potential difference across the capacitor branch leads the potential difference across the inductor branch by 1/4 cycle.
E) The current in the capacitor branch lags the current in the inductor branch by 1/4 cycle.
Difficulty: E
Section: 31-4
Learning Objective 31.4.0
42. The impedance of an RLC series circuit is definitely increased if:
A) C decreases
B) L increases
C) L decreases
D) R increases
E) R decreases
Difficulty: E
Section: 31-4
Learning Objective 31.4.4
43. The impedance of the circuit shown is:
A) 21
B) 50
C) 63
D) 65
E) 98
Difficulty: M
Section: 31-4
Learning Objective 31.4.4
44. When the frequency of the oscillator in a series RLC circuit is doubled:
A) the capacitive reactance is doubled
B) the capacitive reactance is halved
C) the impedance is doubled
D) the current amplitude is doubled
E) the current amplitude is halved
Difficulty: E
Section: 31-4
Learning Objective 31.4.4
45. In an RLC series circuit, the source voltage is leading the current at a given frequency f. If f is lowered slightly, then the circuit impedance will:
A) increase
B) decrease
C) remain the same
D) cannot answer without knowing the amplitude of the source voltage
E) cannot answer without knowing whether the phase angle is larger or smaller than 45
Difficulty: E
Section: 31-4
Learning Objective 31.4.4
46. An RLC series circuit has R = 4 , XC = 3 , and XL = 6 . The impedance of this circuit is:
A) 5
B) 7
C) 7.8
D) 9.8
E) 13
Difficulty: M
Section: 31-4
Learning Objective 31.4.4
47. A coil has a resistance of 60 and an impedance of 100 . Its reactance is:
A) 40
B) 60
C) 80
D) 117
E) 160
Difficulty: M
Section: 31-4
Learning Objective 31.4.4
48. When the amplitude of the oscillator in a series RLC circuit is doubled:
A) the impedance is doubled
B) the voltage across the capacitor is halved
C) the capacitive reactance is halved
D) the power factor is doubled
E) the current amplitude is doubled
Difficulty: E
Section: 31-4
Learning Objective 31.4.5
49. An electric motor, under load, has an effective resistance of 30 and an inductive reactance of 40 . When powered by a source with a maximum voltage of 420 V, the maximum current is:
A) 6.0 A
B) 8.4 A
C) 10.5 A
D) 12 A
E) 14 A
Difficulty: M
Section: 31-4
Learning Objective 31.4.5
50. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- resistor, a 400-mH inductor, and a 200-F capacitor. The rms current is:
A) 0.125 A
B) 0.135 A
C) 0.18 A
D) 0.20 A
E) 0.40 A
Difficulty: M
Section: 31-4
Learning Objective 31.4.5
51. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- resistor, a 400-mH inductor, and a 200-F capacitor. The rms voltage across the resistor is:
A) 2.5 V
B) 3.4 V
C) 6.7 V
D) 10.0 V
E) 10.8 V
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
52. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- resistor, a 400-mH inductor, and a 200-F capacitor. The rms voltage across the capacitor is:
A) 2.5 V
B) 3.4 V
C) 6.7 V
D) 10.0 V
E) 10.8 V
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
53. An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- resistor, a 400-mH inductor, and a 200-F capacitor. The rms voltage across the inductor is:
A) 2.5 V
B) 3.4 V
C) 6.7 V
D) 10.0 V
E) 10.8 V
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
54. An RL series circuit is connected to an ac generator with a maximum emf of 20 V. If the maximum potential difference across the resistor is 16 V, then the maximum potential difference across the inductor is:
A) 2 V
B) 4 V
C) 12 V
D) 26 V
E) 36 V
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
55. In an RLC series circuit, which is connected to a source of emf mcos(t), the current lags the voltage by 45 if:
A) R = 1/C – L
B) R = 1/L – C
C) R = L – 1/C
D) R = C – 1/L
E) L = 1/C
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
56. An RLC series circuit has L = 100 mH and C = 1 F. It is connected to a 1000-Hz source emf, and the voltage is found to lead the current by 75. The value of R is:
A) 12.6
B) 126
C) 175
D) 1750
E) 1810
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
57. An RLC series circuit is connected to an oscillator with a maximum emf of 100 V. If the voltage amplitudes VR, VL, and VC are all equal to each other, then VR must be:
A) 33 V
B) 50 V
C) 67 V
D) 87 V
E) 100 V
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
58. An ac generator produces 10 V (rms) at 400 rad/s. It is connected to a series RL circuit (R = 17.3 , L = 0.025 H). The rms current is:
A) 0.50 A and leads the emf by 30
B) 0.71 A and lags the emf by 30
C) 1.4 A and lags the emf by 60
D) 0.50 A and lags the emf by 30
E) 0.58 A and leads the emf by 90
Difficulty: M
Section: 31-4
Learning Objective 31.4.6
59. In a purely capacitive circuit the current:
A) leads the voltage by one-fourth of a cycle
B) leads the voltage by one-half of a cycle
C) lags the voltage by one-fourth of a cycle
D) lags the voltage by one-half of a cycle
E) is in phase with the potential difference across the plates
Difficulty: E
Section: 31-4
Learning Objective 31.4.7
60. In a purely resistive circuit the current:
A) leads the voltage by 1/4 cycle
B) leads the voltage by 1/2 cycle
C) lags the voltage by 1/4 cycle
D) lags the voltage by 1/2 cycle
E) is in phase with the voltage
Difficulty: E
Section: 31-4
Learning Objective 31.4.7
61. In a purely inductive circuit, the current lags the voltage by:
A) 0 (they are in phase)
B) one-fourth of a cycle
C) one-half of a cycle
D) three-fourths of a cycle
E) one cycle
Difficulty: E
Section: 31-4
Learning Objective 31.4.7
62. A series RL circuit is connected to an emf source of angular frequency . The current:
A) leads the applied emf by tan–1(L/R)
B) lags the applied emf by tan–1(L/R)
C) lags the applied emf by tan–1(R/L)
D) leads the applied emf by tan–1(R/L)
E) is zero
Difficulty: M
Section: 31-4
Learning Objective 31.4.7
63. An RC series circuit is connected to an emf source having angular frequency . The current:
A) leads the source emf by tan–1(1/CR)
B) lags the source emf by tan–1(1/CR)
C) leads the source emf by tan–1(CR)
D) lags the source emf by tan–1(CR)
E) leads the source emf by /4
Difficulty: M
Section: 31-4
Learning Objective 31.4.7
64. An RLC series circuit is driven by a sinusoidal emf with angular frequency d. If d is increased without changing the amplitude of the emf, the current amplitude increases. If L is the inductance, C is the capacitance, and R is the resistance, this means that:
A) dL > 1/dC
B) dL < 1/dC
C) dL = 1/dC
D) dL > R
E) dL < R
Difficulty: M
Section: 31-4
Learning Objective 31.4.8
65. In a sinusoidally driven series RLC circuit, the inductive resistance is XL = 200 , the capacitive reactance is XC = 100 , and the resistance is R = 50 . The current and applied emf would be in phase if:
A) the resistance is increased to 100 , with no other changes
B) the resistance is increased to 200 , with no other changes
C) the inductance is reduced to zero, with no other changes
D) the capacitance is doubled, with no other changes
E) the capacitance is halved, with no other changes
Difficulty: E
Section: 31-4
Learning Objective 31.4.8
66. An RLC series circuit, connected to a source , is at resonance. Then:
A) the voltage across R is zero
B) the voltage across R equals the applied voltage
C) the voltage across C is zero
D) the voltage across L equals the applied voltage
E) the applied voltage and current differ in phase by 90
Difficulty: E
Section: 31-4
Learning Objective 31.4.8
67. The ideal meters shown read rms current and voltage. The average power delivered to the load is:
A) definitely not equal to VI
B) perhaps more than VI
C) possibly equal to VI even if the load contains an inductor and a capacitor
D) definitely less than VI
E) zero as is the average of any sine wave
Difficulty: E
Section: 31-5
Learning Objective 31.5.0
68. The units of the power factor are:
A) ohm
B) watt
C) radian
D) ohm1/2
E) none of these
Difficulty: E
Section: 31-5
Learning Objective 31.5.0
69. The rms value of a sinusoidal voltage is , where V0 is the amplitude. What is the rms value of its fully rectified wave? Recall that Vrect(t) = V(t).
A)
B)
C)
D)
E)
Difficulty: E
Section: 31-5
Learning Objective 31.5.1
70. A sinusoidal voltage V(t) has an rms value of 100 V. Its maximum value is:
A) 70.7 V
B) 100 V
C) 141 V
D) 200 V
E) 707 V
Difficulty: M
Section: 31-5
Learning Objective 31.5.1
71. In a series RLC circuit the rms value of the generator emf is and the rms value of the current is i. The current lags the emf by . The average power supplied by the generator is given by:
A) (i/2)cos
B) i
C) i2/Z
D) i2Z
E) i2R
Difficulty: M
Section: 31-5
Learning Objective 31.5.3
72. In a sinusoidally driven series RLC circuit the current lags the applied emf. The rate at which energy is dissipated in the resistor can be increased by:
A) decreasing the capacitance and making no other changes
B) increasing the capacitance and making no other changes
C) increasing the inductance and making no other changes
D) increasing the driving frequency and making no other changes
E) decreasing the amplitude of the driving emf and making no other changes
Difficulty: E
Section: 31-5
Learning Objective 31.5.4
73. An RLC circuit has a sinusoidal source of emf. The average rate at which the source supplies energy is 5 nW. This must also be:
A) the average rate at which energy is stored in the capacitor
B) the average rate at which energy is stored in the inductor
C) the average rate at which energy is dissipated in the resistor
D) twice the average rate at which energy is stored in the capacitor
E) three times the average rate at which energy is stored in the inductor
Difficulty: E
Section: 31-5
Learning Objective 31.5.5
74. The rms value of an ac current is:
A) its peak value
B) its average value
C) that steady current that produces the same rate of heating in a resistor
D) that steady current that will charge a battery at the same rate
E) zero
Difficulty: E
Section: 31-5
Learning Objective 31.5.5
75. The average power supplied to the circuit shown passes through a maximum when which one of the following is increased continuously from a very low to a very high value?
A) source emf
B) R
C) C
D) source frequency f
E) none of these
Difficulty: M
Section: 31-5
Learning Objective 31.5.6
76. A series circuit consists of a 15- resistor, a 25-mH inductor, and a 35-F capacitor. If the frequency is 100 Hz the power factor is:
A) 0
B) 0.20
C) 0.45
D) 0.65
E) 1.0
Difficulty: M
Section: 31-5
Learning Objective 31.5.6
77. In order to maximize the rate at which energy is supplied to a resistive load, the power factor of an RLC circuit should be as close as possible to:
A) 0
B) 0.5
C) 1
D) infinity
E) cannot tell without knowing R, L, C, and the driving frequency
Difficulty: E
Section: 31-5
Learning Objective 31.5.7
78. The main reason that alternating current replaced direct current for general use is:
A) ac generators do not need slip rings
B) ac voltages may be conveniently transformed
C) electric clocks do not work on dc
D) a given ac current does not heat a power line as much as the same dc current
E) ac minimizes magnetic effects
Difficulty: E
Section: 31-6
Learning Objective 31.6.0
79. Iron, rather than copper, is used in the core of transformers because iron:
A) can withstand a higher temperature
B) has a greater resistivity
C) has a very high permeability
D) makes a good permanent magnet
E) insulates the primary from the secondary
Difficulty: E
Section: 31-6
Learning Objective 31.6.0
80. The core of a transformer is made in a laminated form to:
A) facilitate easy assembly
B) reduce i2R losses in the coils
C) increase the magnetic flux
D) save weight
E) prevent eddy currents
Difficulty: E
Section: 31-6
Learning Objective 31.6.0
81. For a power transmission line, the transmission should be at low current and high voltage because:
A) this is the least dangerous to electrical workers
B) this gives the least dose of electromagnetic radiation to the public
C) this minimizes transmission losses
D) low current and high voltage is easier to transform than high current and low voltage
E) household appliances run at low current and high voltage
Difficulty: E
Section: 31-6
Learning Objective 31.6.1
82. A power transmission line carries 400A of current at a voltage of 765 kV. If the line has a resistance of 29 µΩ/m, what is the rate at which energy is being dissipated in 800 km of line?
A) 0 W
B) 3.7 kW
C) 310 kW
D) 3.7 MW
E) 310 MW
Difficulty: M
Section: 31-6
Learning Objective 31.6.3
83. A generator supplies 100 V to the primary coil of a transformer. The primary has 50 turns and the secondary has 500 turns. The secondary voltage is:
A) 1000 V
B) 500 V
C) 250 V
D) 100 V
E) 10 V
Difficulty: M
Section: 31-6
Learning Objective 31.6.5
84. A step-down transformer is used to:
A) increase the power
B) decrease the power
C) increase the voltage
D) decrease the voltage
E) change ac to dc
Difficulty: E
Section: 31-6
Learning Objective 31.6.6
85. The resistance of the primary coil of a well-designed, 1:10 step-down transformer is 1 . With the secondary circuit open, the primary is connected to a 12 V ac generator. The primary current is:
A) essentially zero
B) about 12 A
C) about 120 A
D) depends on the actual number of turns in the primary coil
E) depends on the core material
Difficulty: M
Section: 31-6
Learning Objective 31.6.7
86. The primary of an ideal transformer has 100 turns and the secondary has 600 turns. Then:
A) the power in the primary circuit is less than that in the secondary circuit
B) the currents in the two circuits are the same
C) the voltages in the two circuits are the same
D) the primary current is six times the secondary current
E) the frequency in the secondary circuit is six times that in the primary circuit
Difficulty: M
Section: 31-6
Learning Objective 31.6.7
87. The primary of a 3:1 step-up transformer is connected to a source and the secondary is connected to a resistor R. The power dissipated by R in this situation is P. If R is connected directly to the source it will dissipate a power of:
A) P/9
B) P/3
C) P
D) 3P
E) 9P
Difficulty: M
Section: 31-6
Learning Objective 31.6.8
88. In an ideal 1:8 step-down transformer, the primary power is 10 kW and the secondary current is 25 A. The primary voltage is:
A) 25,600 V
B) 3200 V
C) 400 V
D) 50 V
E) 6.25 V
Difficulty: M
Section: 31-6
Learning Objective 31.6.8
89. A source with an impedance of 100 is connected to the primary coil of a transformer and a resistance R is connected to the secondary coil. If the transformer has 500 turns in its primary coil and 100 turns in its secondary coil the greatest power will be dissipated in the resistor if R =
A) 0
B) 0.25
C) 4.0
D) 20
E) 100
Difficulty: M
Section: 31-6
Learning Objective 31.6.10