Deck 30: Inductance, Electromagnetic Oscillations, and Ac Circuits

Question 1

In a series LRC circuit an inductor will be dominant at higher frequencies.

Answer 1

True

Question 2

If the current increases in a solenoid, the induced emf acts to

A)decrease the flux.
B)increase the flux.
C)first increase then decrease the flux.
D)first decrease then increase the flux.
E)have no effect on the flux.

Answer 2

decrease the flux.

Question 3

A series LRC circuit connected across an ac voltage source has minimum current flowing through the circuit when operating at the resonant frequency.

Answer 3

False

Question 4

A resistor and an inductor are connected in series to an ideal battery of constant terminal voltage. At the moment contact is made with the battery, the voltage across the inductor is

A)greater than the battery's terminal voltage.
B)equal to the battery's terminal voltage.
C)less than the battery's terminal voltage, but not zero.
D)zero.

Question 5

Starting from zero, an electric current is established in a circuit made of a battery of emf E, a resistor of resistance R and an inductor of inductance L. The electric current eventually reaches its steady-state value. What would be the effect of using an inductor with a larger inductance in this circuit?

A)The steady-state value of the current would be larger, but it would take the same amount of time to reach it.
B)The steady-state value of the current would be the same, but it would take more time to reach it.
C)The steady-state value of the current would be the same, but it would take the same amount of time to reach it.
D)The steady-state value of the current would be larger, but it would take more time to reach it.
E)The steady-state value of the current would be the same, but it would take less time to reach it.

Question 6

A resistor and an inductor are connected in series to a battery. The time constant for the circuit represents the time required for the current to reach

A)25% of the maximum current.
B)37% of the maximum current.
C)50% of the original value.
D)63% of the maximum current.
E)75% of the maximum current.

Question 7

In a given LC resonant circuit,

A)the stored electric field energy is greater than the stored magnetic field energy.
B)the stored electric field energy is less than the stored magnetic field energy.
C)the stored electric field energy is equal to the stored magnetic field energy.
D)all of the given answers are possible.

Question 8

Mutual inductance can depend upon

A)the shape of the coils.
B)the number of coils.
C)the number of turns.
D)the relative position of the coils.
E)all of the above as well as other factors.

Question 9

A resistor and an inductor are connected in series to a battery. The battery is suddenly removed from the circuit. The time constant for of the circuit represents the time required for the current to decrease to

A)25% of the original value.
B)37% of the original value.
C)50% of the original value.
D)63% of the original value.
E)75% of the original value.

Question 10

The inductive reactance of an inductor is higher at low frequencies.

Question 11

The capacitive reactance is directly proportional to the frequency of the applied ac signal.

Question 12

Starting from zero, an electric current is established in a circuit made of a battery of emf E, a resistor of resistance R and an inductor of inductance L. The electric current eventually reaches its steady-state value. What would be the effect of using a resistor with a higher resistance in this circuit?

A)The steady-state value of the current would be smaller, but it would take less time to reach it.
B)The steady-state value of the current would be larger, but it would take less time to reach it.
C)The steady-state value of the current would be smaller, but it would take more time to reach it.
D)The steady-state value of the current would be larger, but it would take more time to reach it.
E)The steady-state value of the current would be smaller, but it would take the same amount of time to reach it.

Question 13

The capacitive reactance increases with the capacitance.

Question 14

A series LRC circuit connected across an ac voltage source will have a positive value of the phase angle at high frequencies.

Question 15

When a charged capacitor is connected to an inductor, the value of the charge on the capacitor oscillates and so does the current in the circuit. What changes in the current would take place if the same capacitor, with the same initial charge, is connected to a inductor with a larger inductance?

A)Both the period of oscillation of the current and its maximum value would increase.
B)The period of oscillation of the current would stay the same but its maximum value would increase.
C)The period of oscillation of the current would decrease but its maximum value would remain the same.
D)The period of oscillation of the current would increase but its maximum value would remain the same.
E)Both the period of oscillation of the current and its maximum value would decrease.

Question 16

A resistor and an inductor are connected in series to an ideal battery of constant terminal voltage. At the moment contact is made with the battery, the voltage across the resistor is

A)greater than the battery's terminal voltage.
B)equal to the battery's terminal voltage.
C)less than the battery's terminal voltage, but not zero.
D)zero.

Question 17

In a series LRC circuit a capacitor will be dominant at lower frequencies.

Question 18

Comparing the mutual inductance M₁₂ of coil 1 with respect to coil 2 with the mutual inductance M₂₁ of coil 2 with respect to coil 1, it turns out that

A)M₂₁ is always greater.
B)M₁₂ > M₂₁.
C)M₁₂ < or = M₂₁.
D)M₁₂ = M₂₁.
E)M₁₂ is always greater.

Question 19

An ac signal of a certain frequency is applied to a capacitor. The current leads the voltage by 90°.

Question 20

The capacitive reactance of a capacitor is very small at low frequencies.

Question 21

A capacitor, initially charged, and an inductor form an LC circuit. When the electric current in the circuit is equal to zero how much energy is stored on each device?

A)Inductor: zero energy. Capacitor: zero energy
B)Inductor: Half of the maximum energy. Capacitor: Half of the maximum energy
C)Inductor: maximum energy. Capacitor: zero energy
D)Inductor: zero energy. Capacitor: maximum energy
E)Inductor: maximum energy. Capacitor: maximum energy

Question 22

In a series LRC circuit, Kirchhoff's loop rule

A)is obeyed.
B)would be obeyed but the voltages are not in phase.
C)would be obeyed but the currents and voltages are not in phase.
D)is not obeyed.
E)would be obeyed but the currents are not in phase.

Question 23

In an LRC circuit, if the condition R² = L/C holds, the circuit is

A)overdamped.
B)not affected.
C)underdamped.
D)totally inundated.
E)critically damped.

Question 24

A pure capacitor is connected to an ac power supply. In this circuit, the current

A)leads the voltage by 90°.
B)lags the voltage by 90°.
C)lags the voltage by 180°.
D)is in phase with the voltage.
E)none of the given answers

Question 25

As the frequency of the ac voltage across an inductor approaches zero, the inductive reactance of that coil

A)approaches zero.
B)approaches infinity.
C)approaches unity.
D)none of the given answers

Question 26

In a pure resistive circuit, the phase angle between current and voltage is

A)0.
B)π/2 radians.
C)-π/2 radians.
D)π radians.
E)3π/4 radians.

Question 27

Consider a capacitor connected across the ac supply. The current through the capacitor will ________ as the capacitance is increased.

A)increase
B)remain constant
C)decrease

Question 28

An electric circuit consists of a resistor connected across the terminals of an ac generator. How does the power dissipated in the resistor change as the frequency in the generator decreases?

A)It decreases.
B)It increases.
C)It does not change.
D)It increases or decreases depending on the sign of the phase angle.

Question 29

What is the phase angle between the voltages of the inductor and capacitor in a LRC series circuit?

A)zero
B)45°
C)90°
D)180°
E)270°

Question 30

A pure inductor is connected to an ac power supply. In this circuit, the current

A)leads the voltage by 90°.
B)is in phase with the voltage.
C)lags the voltage by 45°.
D)lags the voltage by 90°.
E)leads the voltage by 45°.

Question 31

Consider 2 LRC circuits at critical damping. In which circuit does the initial charge on the capacitor decrease to 10% of its value the fastest?

A)in the circuit with the smallest initial charge on the capacitor
B)in the circuit with the largest resistance
C)in the circuit with the largest LC product
D)in the circuit with the smallest LC product
E)in the circuit with the largest initial charge on the capacitor

Question 32

The average energy dissipated in an inductor is

A)zero.
B)proportional to the inductance.
C)proportional to both the inductance and frequency.
D)proportional to the frequency.
E)none of the above.

Question 33

A resistor is connected to an ac power supply. On this circuit, the current

A)leads the voltage by 90°.
B)lags the voltage by 90°.
C)is in phase with the voltage.
D)leads the voltage by 45°.
E)lags the voltage by 45°.

Question 34

An LRC circuit has component values such that the circuit is initially at critical damping. Which of the following modifications would make the circuit underdamped?

A)decreasing the capacitance C, keeping the inductance L and the resistance R the same
B)reducing both the inductance and the capacitance by half, keeping the resistance R the same
C)increasing the resistance R, keeping the inductance L and the capacitance C the same
D)doubling both the inductance and the capacitance, keeping the resistance R the same
E)decreasing the inductance L, keeping the capacitance C and the resistance R the same

Question 35

The energy transformed in an inductor during a portion of a cycle

A)is always positive.
B)may be positive, negative, or zero.
C)is always negative.
D)is always zero.
E)is never zero.

Question 36

Consider an LRC circuit. The impedance of the circuit increases if X_L increases. When is this statement true?

A)always true
B)true only if X_L is equal to X_C
C)true only if X_L is less than X_C
D)true only if X_L is greater than or equal to X_C
E)never true

Question 37

An ac source of period T and maximum voltage V is connected to a single unknown element. At time t = 0 the voltage is zero. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I = - I_max where I_max is the current amplitude. What is the unknown element?

A)a resistor
B)an inductor
C)a capacitor
D)an inductor or a capacitor
E)More information is needed to identify the element.

Question 38

Consider an LRC circuit. The impedance of the circuit increases if R increases. When is this statement true?

A)always true
B)true only if X_L is less than or equal to X_C
C)true only if X_L is greater than or equal to X_C
D)true only if X_L is equal to X_C
E)never true

Question 39

In each element of a series LRC circuit

A)the currents are not in phase.
B)the currents and voltages are not in phase.
C)the voltages are in phase.
D)the currents are in phase.
E)the currents and voltages are in phase.

Question 40

As the frequency of the ac voltage across a capacitor approaches zero, the capacitive reactance of that capacitor

A)approaches zero.
B)approaches infinity.
C)approaches unity.
D)none of the given answers

Question 41

Resonance in a series LRC circuit occurs when

A)X_L is greater than X_C.
B)X_C is greater than X_L.
C)(X_L - X_C)² is greater than R².
D)(X_L - X_C)² is equal to R².
E)X_C equals X_L.

Question 42

Consider a series circuit in which the capacitive reactance equals the inductive reactance. What is the phase angle between current and voltage?

A)+180°
B)+90°
C)-180°
D)-90°
E)0°

Question 43

A coil with a self-inductance of 6 H has a constant current of 2 A flowing through it for 2 seconds. What is the emf induced in this coil?

A)6 V
B)12 V
C)0 V
D)4 V
E)8 V

Question 44

A 200-Ω resistor, a 40.0-mH inductor and a 2.00-μF capacitor are connected in series with a 120-V rms source at 1000 Hz.
(a) What is the impedance of this circuit?
(b) What is the phase angle of this circuit?

Question 45

Consider an LRC series circuit. The impedance of the circuit increases if X_C increases. When is this statement true?

A)always true
B)true only if X_L is less than or equal to X_C
C)true only if X_L is greater than X_C
D)true only if X_L is equal to X_C
E)never true

Question 46

A series circuit consists of a 0.55 H inductor with internal resistance 8.0 ohms connected in series with a 4.0-ohm resistor, a switch, and a 12-V battery.
(a) When the switch is closed, what is the initial current through the 4.0-ohm resistor?
(b) After the switch has been closed, what is the maximum current in the 4.0-ohm resistor?

Question 47

An air-filled 39.1 μH solenoid has a length 4.0 cm and cross-sectional area 0.60 cm². How many turns are in this solenoid?

A)1200
B)12
C)120
D)144
E)21000

Question 48

In a series LRC circuit, capacitive reactance and inductive reactance

A)square and subtract from one another to yield impedance.
B)combine with each other as legs of a right triangle.
C)square and add together to yield impedance.
D)add together increasing impedance.
E)subtract from one another decreasing impedance.

Question 49

An inductor has a current I = 0.5A cos[( 275 s^-1) t] . The maximum emf across the inductor is equal to 0.5 V. What is the self-inductance of the inductor?

A)4.37 mH
B)3.64 mH
C)2.75 mH
D)0.73 mH
E)1.43 mH

Question 50

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V?

A)100 A/s
B)1 A/s
C)1000 A/s
D)10,000 A/s
E)10 A/s

Question 51

A coil with a self-inductance of 6.0 H is connected to a dc source through a switch. As soon as the switch is closed at t = 0 s, the rate of change of current is 2.0 A/s. What is the emf induced in this coil at t = 0 s?

A)6.0 V
B)3.0 V
C)12 V
D)0.33 V
E)0 V

Question 52

An LRC circuit has R = 15 Ω, L = 25 mH, and C = 30 μF. The circuit is connected to a 120 V (rms) source with frequency 200 Hz.
(a) What is the average power dissipated by the circuit?
(b) What is the power factor for the circuit?

Question 53

An LRC circuit has R = 15.0 Ω, L = 25.0 mH, and C = 30.0 μF. The circuit is connected to a 120 V (rms) source with frequency 200 Hz.
(a) What is the impedance of the circuit?
(b) What is the rms current in the circuit?
(c) What is the rms voltage across the resistor?
(d) What is the rms voltage across the inductor?
(e) What is the rms voltage across the capacitor?
(f) If the current in the circuit is given by I = I₀ sin ωt, the voltage is given by

Question 54

A solenoid of length 5.0 cm has a cross sectional area of 1.0 cm² and has 300 uniformly spaced turns. The solenoid is wrapped in 180 turns of insulated wire resulting in a mutual inductance of

A)1.1 H.
B)1.4 × 10^-2 H.
C)11 H.
D)1.4 × 10^-4 H.
E)110 H.

Question 55

Consider an LRC circuit that is driven by an AC applied voltage. At resonance,

A)the peak voltage across the resistor is equal to the peak voltage across the inductor.
B)the peak voltage across the resistor is equal to the peak voltage across the capacitor.
C)the peak voltage across the capacitor is greater than the peak voltage across the inductor.
D)the current is in phase with the driving voltage.
E)the peak voltage across the inductor is greater than the peak voltage across the capacitor.

Question 56

If the inductance and the capacitance both double in an LRC series circuit, the resonant frequency of that circuit will

A)increase to twice its original value.
B)decrease to one-half its original value.
C)decrease to one-fourth its original value.
D)decrease to one-eighth its original value.
E)none of the given answers

Question 57

An LRC circuit with R = 15 Ω, L = 25 mH, and C = 30 μF, is attached to a 100 V ac (rms) power supply at the resonant frequency.
(a) What is the current (rms) in the circuit?
(b) What is the power dissipated by the circuit?

Question 58

In a LRC circuit, a second capacitor is connected in parallel with the capacitor previously in the circuit. What is the effect of this change on the impedance of the circuit?

A)It increases.
B)It decreases.
C)It does not change.
D)It increases for frequencies below resonance and decreases for frequencies above resonance.
E)It decreases for frequencies below resonance and increases for frequencies above resonance.

Question 59

In a LRC circuit, a second capacitor is connected in series with the capacitor previously in the circuit. What is the effect of this change on the impedance of the circuit?

A)It increases.
B)It decreases.
C)It does not change.
D)It increases for frequencies below resonance and decreases for frequencies above resonance.
E)It decreases for frequencies below resonance and increases for frequencies above resonance.

Question 60

What is the inductance of a solenoid 300 cm long, with 10.0 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²?

A)4.19 nH
B)4.19 pH
C)4.19 μH
D)4.19 mH
E)4.19 fH

Question 61

A current of 5 A is flowing in a 20 mH inductor. The energy stored in the magnetic field of this inductor is

A)1 J.
B)0.25 J.
C)0.50 J.
D)0.
E)dependent upon the resistance of the inductor.

Question 62

The energy stored in the earth's magnetic field with a strength of 0.5 × 10^-4 T in a room 3.0 m by 4.0 m by 2.4 m is

A)570 mJ.
B)29 mJ
C)10 mJ.
D)100 mJ.
E)zero.

Question 63

A charged capacitor is connected to an inductor. At time t = 0 the charge on the capacitor is Q = 6μC. At time t = 2 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?

A)2.38 mA
B)4.71 mA
C)0.78 mA
D)1.53 mA
E)1.19 mA

Question 64

A charged capacitor is connected to an inductor to form an LC circuit with a frequency of oscillation f = 1.6 Hz. At time t = 0 the capacitor is fully charged. At a given instant later the charge on the capacitor is measured to be Q = 3 μC and the current in the circuit is equal to 75 μA. What is the maximum charge of the capacitor?

A)6 μC
B)10 μC
C)8 μC
D)2 μC
E)4 μC

Question 65

A solenoid of inductance L = 50 mH has a magnetic energy U = 3 x 10^-4 J with a density u = 0.0042 J/ m³. What is the winding density n of the solenoid?

A)58 turns/m
B)1584 turns/m
C)1200 turns/m
D)234 turns/m
E)746 turns/m

Question 66

In an LR series circuit connected to a dc source and a switch, the inductor gets 40% of its maximum current 1.8 s after the switch is closed at t = 0 s. What is the time constant of this circuit?

A)0.80 s
B)1.5 s
C)2.5 s
D)3.5 s
E)5.5 s

Question 67

A 25-mH inductor is connected in series with a 20-Ω resistor through a 15-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the current when t = 2.0 ms?

A)0.40 A
B)0.50 A
C)0.60 A
D)0.70 A
E)0.80 A

Question 68

A 45-mH inductor is connected in series with a 60-Ω resistor through a 15-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the current after 7.0 ms?

A)250 mA
B)650 mA
C)550 mA
D)280 mA
E)850 mA

Question 69

An LC circuit with an inductance of 36 mH and a capacitance of 25 mF will oscillate with what frequency?

A)1.44 Hz
B)33 Hz
C)0.03 Hz
D)5.3 Hz
E)210 Hz

Question 70

A 25.0-mH inductor is connected in series to a 20.0-Ω resistor through a 15.0-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the time constant of this circuit?

A)0.800 × 10^-3 s
B)0.800 × 10^-2 s
C)0.500 s
D)1.25 × 10^-3 s
E)12.5 × 10^-2 s

Question 71

An LR circuit includes a resistor of resistance R, an inductor of inductance L and a battery of emf E = 10 V. At time t = 0 the current in the circuit is I = 0. At time t = 6.1 ms the current is I = 0.66 A. What are the values of L and R?

A)not enough information given
B)L = 15 mH, R = 20 Ω
C)L = 10 mH, R = 100 Ω
D)L = 50 mH, R = 150 Ω
E)L = 2 mH, R = 10 Ω

Question 72

A solenoid of length l = 0.7 m and radius R = 5 cm stores an amount of energy U = 6 × 10^-6 J when a current I = 0.4 A passes through it. What is the winding density of the solenoid?

A)865 turns /m
B)472 turns/m
C)1078 turns/m
D)104 turns/m
E)327 turns /m

Question 73

Starting from zero, the electric current takes 2 seconds to reach half its maximum possible value in an RL circuit with a resistance R, an inductance L and a battery of emf E. How long will the current take to reach 75% its maximum value (measured from the moment when I = 0)?

A)8 s
B)4 s
C)10 s
D)1 s
E)2 s

Question 74

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, a switch, and a 9.0-V power source. After the switch is closed, what is the maximum power delivered by the power supply?

A)0.40 W
B)81 W
C)0.090 W
D)8.1 W
E)0.81 W

Question 75

A capacitor of capacitance C = 5 μF and initial charge Q = 30 μC is connected to an inductor of inductance L = 20 mH. What is the electric current in the circuit when the energy stored in the capacitor is 25% of its maximum value?

A)0.001 A
B)0.08 A
C)0.04 A
D)0.02 A
E)0.01 A

Question 76

A wire of diameter d = 1 mm is wrapped around a cylindrical core of radius R = 5 cm and length l = 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.2 A passes through it?

A)1.2 × 10^-4 J
B)9.6 × 10^-4 J
C)4.8 × 10^-4 J
D)2.4 × 10^-4 J
E)0.6 × 10^-4 J

Question 77

Calculate the radius that a loop should have so that the magnetic energy density at its center is equal to 6 mJ/ m³ when a current I = 20A passes through the loop?

A)26 cm
B)10 cm
C)7 cm
D)18 cm
E)15 cm

Question 78

In an LC circuit with an inductance of 40 mH and capacitance of 1.2 mF, the maximum charge on the capacitor is 45 mC during the oscillations which occur. What is the maximum current through the inductor during the oscillations?

A)3.7 A
B)42 A
C)10 A
D)6.5 A
E)2.5 A

Question 79

An LR circuit consists of a 35-mH inductor, a resistance of 12 ohms, an 18-V battery, and a switch. What is the current 5.0 ms after the switch is closed?

A)5.0 A
B)0.27 A
C)0.053 A
D)0.75 A
E)1.2 A

Question 80

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A?

A)7.3 × 10^-5 J/ m³
B)3.7 × 10^-5 J/ m³
C)3.6 × 10^-4 J/ m³
D)1.2 × 10^-4 J/ m³
E)cannot be determined with the information given