Deck 31: Electromagnetic Oscillations and Alternating Current

Question 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, 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

Answer 1

T/2

Question 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 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

Answer 2

T/4

Question 3

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

Answer 3

320 Hz

Question 4

An LC circuit consists of a 1 $\mu$ 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

Question 5

An LC circuit has an inductance of 20 mH and a capacitance of 5.0 $\mu$ F. If the charge amplitude is 40 $\mu$ 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

Question 6

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

Question 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 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

Question 8

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

A) 10 mH
B) 1 mH
C) 25 $\mu$ H
D) 2.5 $\mu$ H
E) 1 pH

Question 9

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 $\mu$ F
D) 1 nF
E) 1 pF

Question 10

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

Question 11

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

Question 12

A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 $\mu$ J. At a certain instant the energy in the capacitor is 40 $\mu$ 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

Question 13

The electrical analog of a spring constant k is:

A) L
B) 1/L
C) C
D) 1/C
E) R

Question 14

A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 $\mu$ J. At a certain instant the energy in the capacitor is 40 $\mu$ 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

Question 15

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

Question 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 current is a maximum is:

A) T/4
B) T/2
C) T
D) 3T/2
E) 2T

Question 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 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

Question 18

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

Question 19

An LC circuit has an inductance of 15 mH and a capacitance of 10 $\mu$ F. At one instant the charge on the capacitor is 25 $\mu$ 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

Question 20

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)

Question 21

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

Question 22

An RLC circuit has a capacitance of 12 $\mu$ F, an inductance of 25 mH, and a resistance of 60 $\Omega$ . 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

Question 23

An RLC circuit has a resistance of 200 $\Omega$ 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

Question 24

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

Question 25

The reactance of a 35- $\mu$ 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

Question 26

A 35- $\mu$ 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

Question 27

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

Question 28

An RLC circuit has a resistance of 200 $\Omega$ 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

Question 29

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

Question 30

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 $\pi$ )
E) U/ $\pi$

Question 31

The total energy in an LC circuit is 5.0 *10^-6 J. If C = 15 $\mu$ F the maximum charge on the capacitor is:

A) 0.82 $\mu$ C
B) 8.5 $\mu$ C
C) 12 $\mu$ C
D) 17 $\mu$ C
E) 24 $\mu$ C

Question 32

A 35- $\mu$ 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

Question 33

An LC circuit has an inductance of 20 mH and a capacitance of 5.0 $\mu$ F. At time t = 0 the charge on the capacitor is 3.0 $\mu$ 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

Question 34

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

A) 8.9 $\mu$ C
B) 10 $\mu$ C
C) 12 $\mu$ C
D) 17 $\mu$ C
E) 24 $\mu$ C

Question 35

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

Question 36

In the diagram, the function y(t) = y_msin( $\omega$ t) is plotted as a solid curve. The other three curves have the form y(t) = y_msin( $\omega$ t + $\phi$ ), where $\phi$ is between - $\pi$ /2 and + $\pi$ /2. Rank the curves according to the value of $\phi$ , 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

Question 37

The angular frequency of a certain RLC series circuit is $\omega$ ₀. A source of sinusoidal emf, with angular frequency $\omega$ , is inserted into the circuit and $\omega$ is varied while the amplitude of the source is held constant. For which of the following values of $\omega$ is the amplitude of the current oscillations the greatest?

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

Question 38

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

A) $\omega$ ₀/2
B) $\omega$ ₀
C) 1.5 $\omega$ ₀
D) 2 $\omega$ ₀
E) 3 $\omega$ ₀

Question 39

At time t = 0 the charge on the 50- $\mu$ F capacitor in an LC circuit is 15 $\mu$ C and there is no current. If the inductance is 20 mH the maximum current is:

A) 15 nA
B) 15 $\mu$ A
C) 6.7 mA
D) 15 mA
E) 15 A

Question 40

An LC circuit has a capacitance of 30 $\mu$ F and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 $\mu$ 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

Question 41

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

A) 12.6 $\Omega$
B) 126 $\Omega$
C) 175 $\Omega$
D) 1750 $\Omega$
E) 1810 $\Omega$

Question 42

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

Question 43

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 $\degree$

Question 44

An ac generator produces 10 V (rms) at 400 rad/s. It is connected to a series RL circuit (R = 17.3 $\Omega$ , L = 0.025 H). The rms current is:

A) 0.50 A and leads the emf by 30 $\degree$
B) 0.71 A and lags the emf by 30 $\degree$
C) 1.4 A and lags the emf by 60 $\degree$
D) 0.50 A and lags the emf by 30 $\degree$
E) 0.58 A and leads the emf by 90 $\degree$

Question 45

An RLC series circuit has R = 4 $\Omega$ , X_C = 3 $\Omega$ , and X_L = 6 $\Omega$ . The impedance of this circuit is:

A) 5 $\Omega$
B) 7 $\Omega$
C) 7.8 $\Omega$
D) 9.8 $\Omega$
E) 13 $\Omega$

Question 46

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

Question 47

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

Question 48

In an RLC series circuit, which is connected to a source of emf _mcos( $\omega$ t), the current lags the voltage by 45 $\degree$ if:

A) R = 1/ $\omega$ C - $\omega$ L
B) R = 1/ $\omega$ L - $\omega$ C
C) R = $\omega$ L - 1/ $\omega$ C
D) R = $\omega$ C - 1/ $\omega$ L
E) $\omega$ L = 1/ $\omega$ C

Question 49

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- $\Omega$ resistor, a 400-mH inductor, and a 200- $\mu$ 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

Question 50

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- $\Omega$ resistor, a 400-mH inductor, and a 200- $\mu$ 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

Question 51

An electric motor, under load, has an effective resistance of 30 $\Omega$ and an inductive reactance of 40 $\Omega$ . 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

Question 52

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- $\Omega$ resistor, a 400-mH inductor, and a 200- $\mu$ 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

Question 53

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

Question 54

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- $\Omega$ resistor, a 400-mH inductor, and a 200- $\mu$ 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

Question 55

A coil has a resistance of 60 $\Omega$ and an impedance of 100 $\Omega$ . Its reactance is:

A) 40 $\Omega$
B) 60 $\Omega$
C) 80 $\Omega$
D) 117 $\Omega$
E) 160 $\Omega$

Question 56

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

Question 57

An RLC series circuit is connected to an oscillator with a maximum emf of 100 V. If the voltage amplitudes V_R, V_L, and V_C are all equal to each other, then V_R must be:

A) 33 V
B) 50 V
C) 67 V
D) 87 V
E) 100 V

Question 58

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.

Question 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

Question 60

The impedance of the circuit shown is:

A) 21 $\Omega$
B) 50 $\Omega$
C) 63 $\Omega$
D) 65 $\Omega$
E) 98 $\Omega$

Question 61

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

Question 62

An RLC series circuit is driven by a sinusoidal emf with angular frequency $\omega$ _d. If $\omega$ _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) $\omega$ _dL > 1/ $\omega$ _dC
B) $\omega$ _dL < 1/ $\omega$ _dC
C) $\omega$ _dL = 1/ $\omega$ _dC
D) $\omega$ _dL > R
E) $\omega$ _dL < R

Question 63

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

Question 64

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

Question 65

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

Question 66

A series circuit consists of a 15- $\Omega$ resistor, a 25-mH inductor, and a 35- $\mu$ 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

Question 67

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 $\phi$ . The average power supplied by the generator is given by:

A) (i/2)cos $\phi$
B) i
C) i²/Z
D) i²Z
E) i²R

Question 68

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

Question 69

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

Question 70

An RC series circuit is connected to an emf source having angular frequency $\omega$ . The current:

A) leads the source emf by tan^-1(1/ $\omega$ CR)
B) lags the source emf by tan^-1(1/ $\omega$ CR)
C) leads the source emf by tan^-1( $\omega$ CR)
D) lags the source emf by tan^-1( $\omega$ CR)
E) leads the source emf by $\pi$ /4

Question 71

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 $\degree$

Question 72

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

Question 73

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

Question 74

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

Question 75

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

Question 76

A series RL circuit is connected to an emf source of angular frequency $\omega$ . The current:

A) leads the applied emf by tan^-1( $\omega$ L/R)
B) lags the applied emf by tan^-1( $\omega$ L/R)
C) lags the applied emf by tan^-1( $\omega$ R/L)
D) leads the applied emf by tan^-1( $\omega$ R/L)
E) is zero

Question 77

In a sinusoidally driven series RLC circuit, the inductive resistance is X_L = 200 $\Omega$ , the capacitive reactance is X_C = 100 $\Omega$ , and the resistance is R = 50 $\Omega$ . The current and applied emf would be in phase if:

A) the resistance is increased to 100 $\Omega$ , with no other changes
B) the resistance is increased to 200 $\Omega$ , 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

Question 78

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

Question 79

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

Question 80

The units of the power factor are:

A) ohm
B) watt
C) radian
D) ohm^1/2
E) none of these