Deck 33: Inductors and Ac Circuits

Question 1

An inductor produces a back emf in a DC series RL circuit when a switch connecting the battery to the circuit is closed. We can explain this by

A)Lenz's law.
B)increasing magnetic flux within the coils of the inductor.
C)increasing current in the coils of the inductor.
D)all of the above.
E)only (a) and (c) above.

Answer 1

all of the above.

Question 2

The magnetic field in a superconducting solenoid is 3.0 T. How much energy per unit volume is stored in the solenoid, in J/m³? μ₀ = 4π × 10−7 T ⋅ A/m

Answer 2

3.6 × 106 J/m³

Question 3

A series LC circuit contains a 100-mH inductor, a 36.0-mF capacitor and a 12-V battery. The angular frequency of the electromagnetic oscillations in the circuit is

A)36.0 × 10−4 rad/s.
B)6.00 × 10−2 rad/s.
C)2.78 rad/s.
D)16.7 rad/s.
E)277 rad/s.

Answer 3

16.7 rad/s.

Question 4

When a switch is closed, completing an LR series circuit, the time needed for the current to reach one half its maximum value is ____ time constants.

A)0.250
B)0.500
C)0.693
D)1.00
E)1.44

Question 5

The switch in the figure is closed at t = 0 when the current I is zero. When I = 15 mA, what is the potential difference across the inductor?

A)240 V
B)60 V
C)0
D)180 V
E)190 V

Question 6

Coaxial Cable A has twice the length, twice the radius of the inner solid conductor, and twice the radius of the outer cylindrical conducting shell of coaxial Cable B. What is the ratio of the inductance of Cable A to that of Cable B?

A)
B)
C)2
D)
E)

Question 7

There is no current in the circuit shown in the figure below until the switch is closed. The current through the 20-Ω resistor the instant after the switch is closed is either [1] 15 A or [2] 5.0 A, and the current through the 20-Ω resistor after the switch has been closed a long time is either [3] 5.0 A or [4] 15 A. Which combination of the above choices is correct?

A)[1] and [3]
B)[1] and [4]
C)[2] and [3]
D)[2] and [4]
E)None of these

Question 8

A series LC circuit contains a 100-mH inductor, a 36.0-mF capacitor and a 12-V battery. The frequency of the electromagnetic oscillations in the circuit is

A)5.73 × 10−4 Hz.
B)9.55 × 10−3 Hz.
C)0.442 Hz.
D)2.65 Hz.
E)44.0 Hz.

Question 9

When a switch is closed to complete a DC series RL circuit,

A)the electric field in the wires increases to a maximum value.
B)the magnetic field outside the wires increases to a maximum value.
C)the rate of change of the electric and magnetic fields is greatest at the instant when the switch is closed.
D)all of the above are true.
E)only (a) and (c) above are true.

Question 10

Before the switch is closed in the figure, the potential across the capacitor is 200 V. At some instant after the switch is closed, the instantaneous current is 0.70 A. What is the energy in the capacitor at this instant?

A)49 mJ
B)31 mJ
C)80 mJ
D)0.13 J
E)62 mJ

Question 11

A circuit contains two inductors of 6.0-mH inductance in series placed in parallel with an inductor of 8.0-mH inductance. After one of the 6.0-mH inductors burns out, the repair person wants to replace all three inductors with one inductor of equivalent inductance. Assuming inductors combine in series and parallel the same way resistors do, what inductance should she use?

A)3.0 mH
B)3.4 mH
C)4.8 mH
D)11 mH
E)20 mH

Question 12

A circuit contains two inductors of 6.0-mH inductance in parallel placed in series with an inductor of 8.0-mH inductance. After one of the 6.0-mH inductors burns out, the repairman wants to replace all three inductors with one inductor of equivalent inductance. Assuming inductors combine in series and parallel the same way resistors do, what inductance should he use?

A)3.0 mH
B)3.4 mH
C)4.8 mH
D)11 mH
E)20 mH

Question 13

A series LC circuit contains a 100-mH inductor, a 36.0-mF capacitor and a 12-V battery. The period of the electromagnetic oscillations in the circuit is

A)0.0227 s.
B)0.377 s.
C)2.26 s.
D)105 s.
E)1750 s.

Question 14

Which of the following are the units of a henry and a farad, respectively?

A)J ⋅ s²/C² and C²/J
B)V ⋅ s/A and V/C
C)V/(A ⋅ s) and C/V
D)N ⋅ m/A² and 1/J
E)None of the above

Question 15

The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed the current in the circuit and the potential difference between points a and b, Vab, are

A)0 A, 0 V
B)0 A, −240 V
C)0 A, +240 V
D)0.024 A, 0 V
E)0.024 A, +240 V

Question 16

For the circuit shown, what is the rate of change of the current in the inductor when the current in the battery is 0.50 A?

A)600 A/s
B)400 A/s
C)200 A/s
D)800 A/s
E)500 A/s

Question 17

When a switch is closed, completing an LR series circuit, the time needed for the current to reach three-quarters its maximum value is ____ time constants.

A)0.500
B)0.693
C)0.725
D)1.33
E)1.39

Question 18

After a switch is thrown to remove the battery from a DC LR circuit, but the circuit is still left complete, the time constant represents

A)the time rate of change of the current in the circuit.
B)the time rate of change of the induced emf in the circuit.
C)the magnitude of the ratio of the current to the time rate of change of the current.
D)all of the above.
E)only (a) and (b) above.

Question 19

Find the magnetic energy stored in the air gap between two very large magnetic pole pieces, one North, one South, each with an area of 100 cm². Assume the 0.05-T magnetic field is uniform within the 2-cm gap.

Question 20

What is the inductance of a series RL circuit in which R = 1.0 KΩ if the current increases to one-third of its final value in 30 μs?

A)74 mH
B)99 mH
C)49 mH
D)62 mH
E)none of the above

Question 21

A 2.0-μF capacitor in series with a 2.0-kΩ resistor is connected to a 60-Hz AC source. Calculate the impedance of the circuit.

A)1500 ohms
B)1800 ohms
C)2100 ohms
D)2400 ohms
E)8600 ohms

Question 22

An LC circuit is to have resonant oscillations at 5.0 MHz. Find the value of a capacitor which will work with a 1.0-mH inductor.

A)2.0 mF
B)1.0 μF
C)0.020 μF
D)1.0 pF
E)40 pF

Question 23

An incandescent lightbulb is rated at 100 watts when plugged into a 110 V rms household outlet. Calculate the resistance of the filament and the rms current.

A)12.2 Ω, 0.91 A (rms)
B)10 Ω, 1.0 A (rms)
C)110 Ω, 1.0 A (rms)
D)121 Ω, 0.91 A (rms)
E)11 Ω, 1.1 A (rms)

Question 24

Inductive reactance XL is given by

A)Lω.
B)L/ω.
C) .
D)ω/L.
E)ω2L.

Question 25

An AC generator with peak voltage 100 volts is placed across a 10-Ω resistor. What is the average power dissipated?

A)100 W
B)150 W
C)500 W
D)1000 W
E)2000 W

Question 26

A 10-mH inductor is connected in series with a 10-ohm resistor, a switch and a 6-volt battery. What is the time constant of the circuit? How long after the switch is closed will the current reach 99 percent of its final value?

Question 27

The voltage 8.00 sin (400t) is applied to a series RLC circuit, with R = 200 Ω, L = 0.100 H, and C = 1.00 μF. What are the impedance Z and the phase angle θ?

A)200 Ω, −37.0°
B)566 Ω, +87.0°
C)2470 Ω, −85.4°
D)2540 Ω, −88.8°
E)393 Ω, −63.0°

Question 28

The inductance of a tuning circuit of an AM radio is 4.00 mH. Find the capacitance of the circuit required for reception at 1200 kHz.

A)2.10 pF
B)4.40 pF
C)21.2 pF
D)43.4 pF
E)27.6 pF

Question 29

A 0.500-H inductor is connected into a 110 V rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the inductor?

A)0.189 A (rms)
B)0.292 A (rms)
C)0.584 A (rms)
D)1.19 A (rms)
E)0.093 A (rms)

Question 30

An electric heater draws an average power of 1100 watts when plugged into a 110 V rms outlet. Calculate the resistance of the heater and the rms current.

A)11 Ω, 10 A (rms)
B)110 Ω, 10 A (rms)
C)10 Ω, 11 A (rms)
D)10 Ω, 110 A (rms)
E)0.09 Ω, 11 A (rms)

Question 31

A high-voltage powerline operates at 500,000 V rms and carries an rms current of 500 A. If the resistance of the cable is 0.050 Ω/km, what is the resistive power loss in 200 km of the powerline?

A)250 kW
B)500 kW
C)1 megawatt
D)2.5 megawatts
E)250 megawatts

Question 32

If an R = 1.0-kΩ resistor, a C = 1.0-μF capacitor, and an L = 0.20-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source?

A)0.007 0 A
B)27 mA
C)54 mA
D)0.31 A
E)0.34 A

Question 33

A 10.0-μF capacitor is plugged into a 110 V rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor?

A)0.202 A (rms)
B)0.415 A (rms)
C)0.626 A (rms)
D)0.838 A (rms)
E)0.066 A (rms)

Question 34

Capacitive reactance XC is given by

A) .
B)ωC.
C)ω/C.
D)C/ω.
E) .

Question 35

If we wished to construct a "tank circuit" where electric charge originally stored on a capacitor flows through an inductor, then back again, what value of inductance should we place in series with a fully-charged 100-μF capacitor to get the circuit to resonate at 60.0 Hz?

Question 36

The total impedance Z of an RLC circuit driven by an AC voltage source at angular frequency ω is

A) .
B) .
C) .
D) .
E) .

Question 37

An RLC circuit has L = 250 mH, C = 0.200 μF, and R = 2.00 kΩ. What is the angular frequency of its damped oscillations?

Question 38

At what frequency will a 50.0-mH inductor have a reactance XL = 700 Ω?

A)352 Hz
B)777 Hz
C)1.25 kHz
D)2.23 kHz
E)14 kHz

Question 39

At what frequency will a 12-μF capacitor have a reactance XC = 300 Ω?

A)44 Hz
B)88 Hz
C)180 Hz
D)350 Hz
E)280 Hz

Question 40

Find the resonant frequency for a series RLC circuit where R = 10 Ω, C = 5.00 μF, and L = 2.00 mH.

A)998 Hz
B)1.59 kHz
C)2.45 kHz
D)11.3 kHz
E)2.53 kHz

Question 41

If the input to an RLC series circuit is , then the current in the circuit is

A) .
B) .​
C) .
D) .
E) .

Question 42

The impedance of the parallel RLC circuit shown is given by

A)
B)
C)
D)
E)

Question 43

What is the average power dissipation in an RLC series circuit with R = 10 Ω, L = 0.1 H, C = 10 μF when driven at resonance by a 100 V rms source?

A)100 W
B)500 W
C)1000 W
D)2 kW
E)700 W

Question 44

A current I = 3 sin (400 t) amperes flows in a series RL circuit in which L = 1 mH and R = 100 Ω. What is the average power loss?

A)225 W
B)450 W
C)980 W
D)1.12 kW
E)900 W

Question 45

Determine the rms voltage drop across the inductor in the circuit.

A)11 V
B)27.5 V
C)33 V
D)38.5 V
E)30.5 V

Question 46

Determine the resonant frequency of the circuit.

A)159 Hz
B)32 Hz
C)5 Hz
D)500 Hz
E)79.5 Hz

Question 47

A series RLC circuit has an impedance of 120 Ω and a resistance of 64 Ω. What average power is delivered to this circuit when Vrms = 90 volts?

A)36 W
B)100 W
C)192 W
D)360 W
E)12 W

Question 48

The primary winding of an electric train transformer has 400 turns and the secondary has 50. If the input voltage is 120 V (rms) what is the output voltage?

A)15 V (rms)
B)30 V (rms)
C)60 V (rms)
D)2.4 V (rms)
E)960 V (rms)

Question 49

Determine the rms voltage drop across the resistor in the circuit.

A)55 V
B)77 V
C)9.9 V
D)5.5 V
E)61 V

Question 50

Determine the rms voltage for the circuit.

A)99 V (rms)
B)140 V (rms)
C)196 V (rms)
D)70 V (rms)
E)110 V (rms)

Question 51

A transformer is to be designed to increase the 30 kV rms output of a generator to the transmission-line voltage of 345 kV rms. If the primary winding has 80 turns, how many turns must the secondary have?

A)6
B)70
C)920
D)9200
E)12

Question 52

A step-up transformer has an input voltage of 110 V (rms). There are 100 turns on the primary and 1500 on the secondary. What is the output voltage?

A)1600 V (max)
B)1650 V (rms)
C)3260 V (max)
D)165 kV (rms)
E)7.3 V (rms)

Question 53

A primary current of 6.0 A exists in an ideal iron-core transformer at a primary voltage of 100 volts. If the current in the secondary is 0.75 A, calculate the output voltage.

A)12.5 V
B)40 V
C)400 V
D)800 V
E)200 V

Question 54

Determine the impedance for the circuit. ​ ​

A)600 Ω
B)1200 Ω
C)1800 Ω
D)2300 Ω
E)1100 Ω

Question 55

Calculate Vout/Vin for the circuit if R = 2.0 kΩ, C = 0.020 μF and V = 140 V sin(50,000t). ​ ​

A)0.02
B)0.45
C)0.80
D)0.98
E)2.2

Question 56

What is the average power dissipation in a series RC circuit if R = 5.00 kΩ, C = 2.00 μF, and V = 170 cos (300t)?

A)0.930 W
B)2.60 W
C)28.2 W
D)157 W
E)5.20 W

Question 57

An RLC series circuit has R = 100 ohms, C = 25 μF, and L = 0.16 H. For what angular frequency of an AC voltage is the current flow maximum?

A)251 rad/s
B)500 rad/s
C)757 rad/s
D)884 rad/s
E)79.6 rad/s

Question 58

An ideal step-down transformer has 200 primary turns and 50 secondary turns. If 440 volts (rms) is placed across the primary, what is the current in the secondary when the load resistance is 7.00 ohms?

A)3.6 A (rms)
B)7.3 A (rms)
C)11.4 A (rms)
D)15.7 A (rms)
E)12.4 A (rms)

Question 59

Determine the rms voltage drop across the capacitor in the circuit.

A)55 V
B)77 V
C)110 V
D)154 V
E)198 V

Question 60

Determine the rms current for the circuit.

A)55 mA
B)77 mA
C)99 mA
D)0.19 A
E)61 mA

Question 61

A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. The peak current in the circuit is

A)8.24 A.
B)8.84 A.
C)11.0 A.
D)12.4 A.
E)23.5 A.

Question 62

A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. The impedance is

A)3.77 Ω.
B)9.26 Ω.
C)10.0 Ω.
D)10.7 Ω.
E)13.8 Ω.

Question 63

A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. The peak current in the circuit is

A)0.963 A.
B)10.3 A.
C)11.0 A.
D)11.9 A.
E)29.2 A.

Question 64

A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. The impedance is

A)4.68 Ω.
B)8.84 Ω.
C)10.0 Ω.
D)13.4 Ω.
E)18.8 Ω.

Question 65

An alternating current circuit has resistance R, inductance L, and capacitance C in series with a voltage source. Which statement is correct?

A)The voltage across the capacitor leads the voltage across the inductor by 90°.
B)The voltage across the inductor leads the voltage across the capacitor by 90°.
C)The voltage across the inductor leads the voltage across the resistor by 180°.
D)The voltage across the inductor is out of phase with the voltage across the capacitor by 180°.
E)Both voltages lead the voltage across the resistor by 90°.

Question 66

The graphs below show the phasors ΔVmax and Imax for five RLC series circuits. The solid arrows represent the voltage phasors, ΔV, and the dashed arrows represent the current phasors, Imax. Which graph represents a circuit where the inductive reactance is greater than the capacitive reactance?

A)
B)
C)
D)
E)

Question 67

All three circuits shown below have R = 100 Ω, L = 0.1 H and emf ε = (5.0 V) sin (377 t). Which statement regarding the angular resonance frequencies ωA, ωB, and ωC is correct? ​ ​

A)ωC > ωA = ωB
B)ωC < ωA = ωB
C)ωA = ωB = ωC
D)ωB < ωA = ωC
E)ωB > ωA = ωC

Question 68

A 10-μF capacitor in an LC circuit made entirely of superconducting materials (R = 0 Ω) is charged to 100 μC. Then a superconducting switch is closed. At t = 0 s, plate 1 is positively charged and plate 2 is negatively charged. At a later time, Vab = +10 V. At that time, Vdc is

A)0 V.
B)3.54 V.
C)5.0 V.
D)7.07 V.
E)10 V.

Question 69

The power output, Pout, of an ideal step-up transformer that receives power input, Pin, and which has N1 turns in the primary and N2 turns in the secondary coil is given by

A)Pout = Pin.
B)Pout = Pin.
C)Pout = Pin.
D)Pout = Pin.
E)Pout = Pin.

Question 70

The average power input to a series alternating current circuit is minimum when

A)there are only a resistor and capacitor in the circuit.
B)there are only a resistor and inductor in the circuit.
C)there is only a resistor in the circuit.
D)XL = XC and the circuit contains a resistor, an inductor and a capacitor.
E)there is only a capacitor in the circuit.

Question 71

Whenever the alternating current frequency in a series RLC circuit is halved,

A)the inductive reactance is doubled and the capacitive reactance is halved.
B)the inductive reactance is doubled and the capacitive reactance is doubled.
C)the inductive reactance is halved and the capacitive reactance is halved.
D)the inductive reactance is halved and the capacitive reactance is doubled.
E)the reactance of the circuit remains the same.

Question 72

In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10,000 households, we can conclude that

A)IV = I ²R.
B)I = V/R.
C)IV < I ²R.
D)IV > I ²R.
E)I ²R = 0.

Question 73

A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 Ω and L = 10.0 mH. The power factor, cos φ, is

A)−1.00.
B)−0.936.
C)+0.943.
D)+0.936.
E)+1.00.

Question 74

For driving voltage , the current through the resistor is ​
​ ​

A) .
B) .
C) .
D) .
E)

Question 75

The phase angle between V and I is

A)
B)
C)
D)
E)

Question 76

A 60.0-Hz AC generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 Ω and C = 300 μF. The power factor, cos φ, is

A)−1.00.
B)−0.749.
C)+0.749.
D)+0.834.
E)+1.00.

Question 77

The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, ΔVmax, and the dashed arrows represent the current phasors, Imax. Which graph shows the correct relationship between current and voltage phasors for a capacitor in an RC circuit?

A)
B)
C)
D)
E)

Question 78

The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, ΔV, and the dashed arrows represent the current phasors, Imax.Which graph shows the correct relationship between current and voltage phasors for an inductor in an RL circuit?

A)
B)
C)
D)
E)

Question 79

All three circuits below have R = 100 Ω, C = 1.0 mF, and emf ε = (5.0 V) sin (377 t). The inductors in (B) and (C) are placed sufficiently far apart so that they do not alter one another's inductance. Such inductors add combine like resistors. Which statement regarding the angular resonance frequencies ωA, ωB, and ωC is correct? ​ ​

A)ωC > ωA = ωB
B)ωC < ωA = ωB
C)ωA = ωB = ωC
D)ωB < ωA = ωC
E)ωB > ωA = ωC

Question 80

The graphs below show a voltage phasor at different instances of time. Which voltage phasor shows the instantaneous value of the voltage with the largest magnitude?

A)
B)
C)
D)
E)