em oscillations and ac

ELECTROMAGNETIC OSCILLATIONSAND ALTERNATING CURRENT

1. 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 aftert = 0 that the current is a maximum is:

A. TB. T/4C. T/2D. TE. 2T

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 aftert = 0 that the charge on the capacitor is a maximum is:


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 aftert = 0 that the voltage across the inductor is a maximum is:


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 aftert = 0 that the energy stored in the magnetic field of the inductor is a maximum is:


Chapter 31: ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT 455

MEDIIT GUJCET WORKSHEET

1

5. 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 aftert = 0 that the energy stored in the electric field of the capacitor is a maximum is:


6. A capacitor in an LC oscillator has a maximum potential dierence of 15V and a maximumenergy of 360J. At a certain instant the energy in the capacitor is 40J. At that instantwhat is the potential dierence across the capacitor?A. zeroB. 5VC. 10VD. 15VE. 20V

7. Which of the following has the greatest eect in decreasing the oscillation frequency of an LCcircuit? Using instead:

A. L/2 and C/2B. L/2 and 2CC. 2L and C/2D. 2L and 2CE. none of these

8. We desire to make an LC circuit that oscillates at 100Hz using an inductance of 2.5H. Wealso need a capacitance of:

A. 1FB. 1mFC. 1FD. 100FE. 1 pF

9. An LC circuit consists of a 1-F capacitor and a 4mH inductor. Its oscillation frequency isapproximately:

A. 0.025HzB. 25HzC. 60HzD. 2500HzE. 15, 800Hz

456 Chapter 31: ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT

2

10. An LC circuit has an oscillation frequency of 105 Hz. If C = 0.1F, then L must be about:

A. 10mHB. 1mHC. 25HD. 2.5HE. 1 pH

11. In the circuit shown, switch S is first pushed up to charge the capacitor. When S is then pusheddown, the current in the circuit will oscillate at a frequency of:

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A. 318HzB. 0.01HzC. 12.500HzD. 2000HzE. depends on V0

12. Radio receivers are usually tuned by adjusting the capacitor of an LC circuit. If C = C1 for afrequency of 600 kHz, then for a frequency of 1200 kHz one must adjust C to:

A. C1/2B. C1/4C. 2C1D. 4C1E.

2C1

13. An LC series circuit with an inductance L and a capacitance C has an oscillation frequency f .Two inductors, each with inductance L, and two capacitors, each with capacitance C, are allwired in series and the circuit is completed. The oscillation frequency is:

A. f/4B. f/2C. fD. 2fE. 4f


3

14. The electrical analog of a spring constant k is:

A. LB. 1/LC. CD. 1/CE. R

15. Consider the mechanical system consisting of two springs and a block, as shown. Which oneof the five electrical circuits (A, B, C, D, E) is the analog of the mechanical system?

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16. A 150-g block on the end of a spring with a spring constant of 35N/m is pulled aside 25 cmand released from rest. In the electrical analog the initial charge on the capacitor is:

A. 0.15CB. 6.67CC. 0.025CD. 40CE. 35C


4

17. A 150-g block on the end of a spring with a spring constant of 35N/m is pulled aside 25 cmand released from rest. In the electrical analog the maximum charge on the capacitor is 0.25C.The maximum current in the LC circuit is:

A. 0.38AB. 0.025AC. 40AD. 2.3AE. 5.3A

18. A capacitor in an LC oscillator has a maximum potential dierence of 15V and a maximumenergy of 360J. At a certain instant the energy in the capacitor is 40J. At that instantwhat is the potential dierence across the capacitor?A. zeroB. 5VC. 10VD. 15VE. 20V

19. A capacitor in an LC oscillator has a maximum potential dierence of 15V and a maximumenergy of 360J. At a certain instant the energy in the capacitor is 40J. At that instantwhat is the emf induced in the inductor?

A. zeroB. 5VC. 10VD. 15VE. 20V

20. In an oscillating LC circuit, the total stored energy is U . The maximum energy stored in thecapacitor during one cycle is:

A. U/2B. U/

2

C. UD. U/(2)E. U/

21. In an oscillating LC circuit, the total stored energy is U and the maximum charge on thecapacitor is Q. When the charge on the capacitor is Q/2, the energy stored in the inductor is:

A. U/2B. U/4C. (4/3)UD. 3U/2E. 3U/4

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22. The total energy in an LC circuit is 5.0 106 J. If C = 15F the charge on the capacitor is:A. 0.82CB. 8.5CC. 12CD. 17CE. 24C

23. The total energy in an LC circuit is 5.0 106 J. If L = 25mH the maximum current is:A. 10mAB. 14mAC. 20mAD. 28mAE. 40mA

24. At time t = 0 the charge on the 50-F capacitor in an LC circuit is 15C and there is nocurrent. If the inductance is 20mH the maximum current is:

A. 15 nAB. 15AC. 6.7mAD. 15mAE. 15A

25. An LC circuit has an inductance of 20mH and a capacitance of 5.0F. At time t = 0 thecharge on the capacitor is 3.0C and the current is 7.0mA. The total energy is:

A. 4.1 107 JB. 4.9 107 JC. 9.0 107 JD. 1.4 106 JE. 2.8 106 J

26. An LC circuit has a capacitance of 30F and an inductance of 15mH. At time t = 0 the chargeon the capacitor is 10C and the current is 20mA. The maximum charge on the capacitor is:

A. 8.9CB. 10CC. 12CD. 17CE. 24C


6

27. An LC circuit has an inductance of 15mH and a capacitance of 10F. At one instant thecharge on the capacitor is 25C. At that instant the current is changing at the rate of:

A. 0B. 1.7 108 A/sC. 5.9 103 A/sD. 3.8 102 A/sE. 170A/s

28. An LC circuit has a capacitance of 30F and an inductance of 15mH. At time t = 0 thecharge on the capacitor is 10C and the current is 20mA. The maximum current is:

A. 18mAB. 20mAC. 25mAD. 35mAE. 42mA

29. The graphs show the total electromagnetic energy in two RLC circuits as functions of time.Which of the following statements might be true?

t

E

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A. Circuit 1 has a smaller resistance and a larger inductanceB. Circuit 1 has a larger resistance and a smaller inductanceC. Circuit 1 has the same resistance and a larger inductanceD. Circuit 1 has a larger resistance and a larger capacitanceE. Circuit 1 has the same resistance and a smaller capacitance

30. An RLC circuit has a resistance of 200 and an inductance of 15mH. Its oscillation frequencyis 7000Hz. At time t = 0 the current is 25mA and there is no charge on the capacitor. Afterfive complete cycles the current is:

A. zeroB. 1.8 106 AC. 2.1 104 AD. 2.3 103 AE. 2.5 102 A


7

31. An RLC circuit has an inductance of 25mH and a capacitance of 5.0F. The charge on thecapacitor does NOT oscillate but rather decays exponentially to zero. The resistance in thecircuit must be:

A. greater than or equal to 20, 000B. less than 20, 000 but greater than 10, 000C. less than 10, 000 but greater than 5, 000D. less than 5, 000 but greater than 0E. 0

32. A series circuit with an inductance of 15mH, a capacitance of 35F, and a resistance of 5.0contains a sinusoidal source of emf with a frequency of 500Hz. The frequency with which thecharge on the capacitor oscillates is:

A. 500HzB. 1.4 kHzC. greater than 1.4 kHzD. less than 500HzE. between 500Hz and 1.4 kHz

33. The rapid exponential decay in just a few cycles of the charge on the plates of capacitor in anRLC circuit might be due to:

A. a large inductanceB. a large capacitanceC. a small capacitanceD. a large resistanceE. a small resistance

34. An RLC circuit has a capacitance of 12F, an inductance of 25mH, and a resistance of 60.The current oscillates with an angular frequency of:

A. 1.2 103 rad/sB. 1.4 103 rad/sC. 1.8 103 rad/sD. 2.2 103 rad/sE. 2.6 103 rad/s

35. The angular frequency of a certain RLC series circuit is 0. A source of sinusoidal emf, withangular frequency 2, is inserted into the circuit. After transients die out the angular frequencyof the current oscillations is:

A. 0/2B. 0C. 20D. 1.50E. 30

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36. The angular frequency of a certain RLC series circuit is 0. A source of sinusoidal emf, withangular frequency , is inserted into the circuit and is varied while the amplitude of thesource is held constant. For which of the following values of is the amplitude of the currentoscillations the greatest?

A. 0/5B. 0/2C. 0D. 20E. None of them (they all produce the same current amplitude)

37. An RLC circuit has a sinusoidal source of emf. The average rate at which the source suppliesenergy is 5 nW. This must also be:

A. the average rate at which energy is stored in the capacitorB. the average rate at which energy is stored in the inductorC. the average rate at which energy is dissipated in the resistorD. twice the average rate at which energy is stored in the capacitorE. three times the average rate at which energy is stored in the inductor

38. In a purely capacitive circuit the current:

A. leads the voltage by one-fourth of a cycleB. leads the voltage by one-half of a cycleC. lags the voltage by one-fourth of a cycleD. lags the voltage by one-half of a cycleE. is in phase with the potential dierence across the plates

39. In a purely resistive circuit the current:

A. leads the voltage by one-fourth of a cycleB. leads the voltage by one-half of a cycleC. lags the voltage by one-fourth of a cycleD. lags the voltage by one-half of a cycleE. is in phase with the voltage

40. In a purely inductive circuit, the current lags the voltage by:

A. zeroB. one-fourth of a cycleC. one-half of a cycleD. three-fourths of a cycleE. one cycle


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41. A series RL circuit is connected to an emf source of angular frequency . The current:A. leads the applied emf by tan1(L/R)B. lags the applied emf by tan1(L/R)C. lags the applied emf by tan1(R/L)D. leads the applied emf by tan1(R/L)E. is zero

42. A series RC circuit is connected to an emf source having angular frequency . The current:A. leads the source emf by tan1(1/CR)B. lags the source emf by tan1(1/CR)C. leads the source emf by tan1(CR)D. lags the source emf by tan1(CR)E. leads the source emf by /4

43. In an RLC series circuit, which is connected to a source of emf Em cos(t), the current lagsthe voltage by 45 if:

A. R = 1/C LB. R = 1/L CC. R = L 1/CD. R = C 1/LE. L = 1/C

44. A coil has a resistance of 60 and an impedance of 100. Its reactance, in ohms, is:A. 40B. 60C. 80D. 117E. 160

45. The reactance in ohms of a 35-F capacitor connected to a 400-Hz generator is:

A. 0B. 0.014C. 0.088D. 11E. 71


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46. A 35-F capacitor is connected to a source of sinusoidal emf with a frequency of 400Hz and amaximum emf of 20V. The maximum current is:

A. 0B. 0.28AC. 1.8AD. 230AE. 1400A

47. A 45-mH inductor is connected to a source of sinusoidal emf with a frequency of 400Hz and amaximum emf of 20V. The maximum current is:

A. 0B. 0.18AC. 1.1AD. 360AE. 2300A

48. The impedance of an RLC series circuit is definitely increased if:

A. C decreasesB. L increasesC. L decreasesD. R increasesE. R decreases

49. An RLC series circuit has R = 4, XC = 3, and XL = 6. The impedance of this circuitis:

A. 5B. 7C. 9.8D. 13E. 7.8


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50. The impedance of the circuit shown is:

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A. 21B. 50C. 63D. 65E. 98

51. An electric motor, under load, has an eective resistance of 30 and an inductive reactance of40. When powered by a source with a maximum voltage of 420V, the maximum current is:A. 6.0AB. 8.4AC. 10.5AD. 12.0AE. 14.0A

52. An RL series circuit is connected to an ac generator with a maximum emf of 20V. If themaximum potential dierence across the resistor is 16V, then the maximum potential dierenceacross the inductor is:

A. 2VB. 4VC. 12VD. 25.6VE. 36V

53. When the amplitude of the oscillator in a series RLC circuit is doubled:

A. the impedance is doubledB. the voltage across the capacitor is halvedC. the capacitive reactance is halvedD. the power factor is doubledE. the current amplitude is doubled


12

54. When the frequency of the oscillator in a series RLC circuit is doubled:

A. the capacitive reactance is doubledB. the capacitive reactance is halvedC. the impedance is doubledD. the current amplitude is doubledE. the current amplitude is halved

55. In an RLC series circuit, the source voltage is leading the current at a given frequency f . If fis lowered slightly, then the circuit impedance will:

A. increaseB. decreaseC. remain the sameD. need to know the amplitude of the source voltageE. need to know whether the phase angle is larger or smaller than 45

56. In the diagram, the function y(t) = ym sin(t) is plotted as a solid curve. The other threecurves have the form y(t) = ym sin(t + ), where is between /2 and +/2. Rank thecurves according to the value of , from the most negative to the most positive.

t

y(t)

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A. 1, 2, 3B. 2, 3, 1C. 3, 2, 1D. 1, 3, 2E. 2, 1, 3


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57. An RLC series circuit has L = 100mH and C = 1F. It is connected to a 1000-Hz source andthe source emf is found to lead the current by 75. The value of R is:

A. 12.6B. 126C. 175D. 1750E. 1810

58. An RLC series circuit is driven by a sinusoidal emf with angular frequency d. If d isincreased without changing the amplitude of the emf the current amplitude increases. If L isthe inductance, C is the capacitance, and R is the resistance, this means that:

A. dL > 1/dCB. dL < 1/dCC. dL = 1/dCD. dL > RE. dL < R

59. In a sinusoidally driven series RLC circuit, the inductive reactance is XL = 200, the capac-itive reactance is XC = 100, and the resistance is R = 50. The current and applied emfwould be in phase if:

A. the resistance is increased to 100, with no other changesB. the resistance is increased to 200, with no other changesC. the inductance is reduced to zero, with no other changesD. the capacitance is doubled, with no other changesE. the capacitance is halved, with no other changes

60. In a sinusoidally driven series RLC circuit the current lags the applied emf. The rate at whichenergy is dissipated in the resistor can be increased by:

A. decreasing the capacitance and making no other changesB. increasing the capacitance and making no other changesC. increasing the inductance and making no other changesD. increasing the driving frequency and making no other changesE. decreasing the amplitude of the driving emf and making no other changes

61. An RLC series circuit, connected to a source E, is at resonance. Then:

A. the voltage across R is zeroB. the voltage across R equals the applied voltageC. the voltage across C is zeroD. the voltage across L equals the applied voltageE. the applied voltage and current dier in phase by 90


14

62. An RLC series circuit is connected to an oscillator with a maximum emf of 100V. If thevoltage amplitudes VR, VL, and VC are all equal to each other, then VR must be:

A. 33VB. 50VC. 67VD. 87VE. 100V

63. 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 dierences across all branches are in phase.C. The current in the capacitor branch leads the current in the inductor branch by one-fourth

of a cycleD. The potential dierence across the capacitor branch leads the potential dierence across

the inductor branch by one-fourth of a cycle.E. The current in the capacitor branch lags the current in the inductor branch by one-fourth

of a cycle.

64. The rms value of an ac current is:

A. its peak valueB. its average valueC. that steady current that produces the same rate of heating in a resistor as the actual

currentD. that steady current that will charge a battery at the same rate as the actual currentE. zero

65. The rms value of a sinusoidal voltage is V0/2, where V0 is the amplitude. What is the rms

value of its fully rectified wave? Recall that Vrect(t) = |V (t)|.

t

V0

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A. V 20 /2

B. V 20 /2C.

2V0

D. V0/2

E. V0/(22)


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66. A sinusoidal voltage V (t) has an rms value of 100V. Its maximum value is:

A. 100VB. 707VC. 70.7VD. 141VE. 200V

67. An ac generator produces 10V (rms) at 400 rad/s. It is connected to a series RL circuit(R = 17.3, L = 0.025H). The rms current is:A. 0.50A and leads the emf by 30

B. 0.71A and lags the emf by 30

C. 1.40A and lags the emf by 60

D. 0.50A and lags the emf by 30

E. 0.58A and leads the emf by 90

68. An ac generator producing 10V (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 in amperes is:

A. 0.125B. 0.135C. 0.18D. 0.20E. 0.40

69. An ac generator producing 10V (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 (in volts) across the resistor is:

A. 2.5B. 3.4C. 6.7D. 10.0E. 10.8

70. An ac generator producing 10V (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 (in volts) across the capacitor is:

A. 2.5B. 3.4C. 6.7D. 10.0E. 10.8


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71. An ac generator producing 10V (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 (in volts) across the inductor is:

A. 2.5B. 3.4C. 6.7D. 10.0E. 10.8

72. The ideal meters shown read rms current and voltage. The average power delivered to the loadis:

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A. definitely equal to V IB. definitely more than V IC. possibly equal to V I even if the load contains an inductor and a capacitorD. definitely less than V IE. zero, as is the average of any sine wave

73. The average power supplied to the circuit shown passes through a maximum when which oneof the following is increased continuously from a very low to a very high value?

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CE , f

A. Source emf EB. RC. CD. Source frequency fE. None of these


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74. In a series RLC circuit the rms value of the generator emf is E and the rms value of the currentis i. The current lags the emf by . The average power supplied by the generator is given by:A. (iE/2) cos B. iEC. i2/ZD. i2ZE. i2R

75. The units of the power factor are:

A. ohmB. wattC. radianD. ohm1/2

E. none of these

76. A series circuit consists of a 15- resistor, a 25-mH inductor, and a 35-F capacitor. If thefrequency is 100Hz the power factor is:

A. 0B. 0.20C. 0.45D. 0.89E. 1.0

77. The main reason that alternating current replaced direct current for general use is:

A. ac generators do not need slip ringsB. ac voltages may be conveniently transformedC. electric clocks do not work on dcD. a given ac current does not heat a power line as much as the same dc currentE. ac minimizes magnetic eects

78. A step-down transformer is used to:

A. increase the powerB. decrease the powerC. increase the voltageD. decrease the voltageE. change ac to dc


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79. Iron, rather than copper, is used in the core of transformers because iron:

A. can withstand a higher temperatureB. has a greater resistivityC. has a very high permeabilityD. makes a good permanent magnetE. insulates the primary from the secondary

80. The core of a transformer is made in a laminated form to:

A. facilitate easy assemblyB. reduce i2R losses in the coilsC. increase the magnetic fluxD. save weightE. prevent eddy currents

81. A generator supplies 100V to the primary coil of a transformer. The primary has 50 turns andthe secondary has 500 turns. The secondary voltage is:

A. 1000VB. 500VC. 250VD. 100VE. 10V

82. The resistance of the primary coil of a well-designed, 1 : 10 step-down transformer is 1. Withthe secondary circuit open, the primary is connected to a 12V ac generator. The primarycurrent is:

A. essentially zeroB. about 12AC. about 120AD. depends on the actual number of turns in the primary coilE. depends on the core material

83. 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 circuitB. the currents in the two circuits are the sameC. the voltages in the two circuits are the sameD. the primary current is six times the secondary currentE. the frequency in the secondary circuit is six times that in the primary circuit


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em oscillations and ac

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charged capacitor

time t

f capacitor

time aftert

resulting oscillations

mh inductor

lc circuit

oscillation frequency