Deck 33: Alternating-Current Circuits

Question 1

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

Answer 1

54 mA

Question 2

The inductance of a tuning circuit of an AM radio is 4.00 mH.Find the capacitance of the circuit required for reception at 1 200 kHz.

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

Answer 2

4.40 pF

Question 3

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

Answer 3

500 W

Question 4

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 5

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 6

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 7

Inductive reactance X_L is given by

A)Lω
B)L/ω
C)1/Lω
D)ω/L
E)ω²L

Question 8

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)1 500 ohms
B)1 800 ohms
C)2 100 ohms
D)2 400 ohms
E)8 600 ohms

Question 9

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

Question 10

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

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

Question 11

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)2 470 Ω,−85.4°
D)2 540 Ω,−88.8°
E)393 Ω,−63.0°

Question 12

If the input to an RLC series circuit is V = V_m cos ωt,then the current in the circuit is

A) cos ωt
B)
C)
D)
E)

Question 13

A 230000 V-rms powerline carries an average power P_avg = 250 MW a distance of 200 km.If the total resistance of the cables is 10 ohms,what is the resistive power loss?

A)1.0 MW
B)2.5 MW
C)5.4 MW
D)12 MW
E)10 kW

Question 14

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 15

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

Question 16

Capacitive reactance X_C is given by

A)1/ωC
B)ωC
C)ω/C
D)C/ω
E)1/ω²C

Question 17

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 18

A high-voltage powerline operates at 500000 V-rms and carries an rms current of 500 A.If the resistance of the cable is 0.050Ω/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 19

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

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

Question 20

Find the resonant frequency for a series RLC circuit where R = 10Ω,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 21

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 22

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)1 600 V (max)
B)1 650 V (rms)
C)3 260 V (max)
D)165 kV (rms)
E)7.3 V (rms)

Question 23

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 24

The primary winding of an electric train transformer has 400 turns and the secondary has 50.If the input voltage is 120V(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 25

For driving voltage V = V_m sin ωt,the current through the resistor is

A)V_m sin (ωt + φ)
B)V_m cos (ωt + φ)
C) sin (ωt + φ)
D) sin (ωt + φ)
E) sin ωt

Question 26

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 27

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 28

Calculate V_out/V_in for the circuit if R = 2.0 kΩ,C = 0.020 μF and V = 140V sin(50000t).
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A)0.02
B)0.45
C)0.80
D)0.98
E)2.2

Question 29

Determine the resonant frequency of the circuit.

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

Question 30

Determine the impedance for the circuit.
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​

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

Question 31

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

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

Question 32

The impedance of the parallel RLC circuit shown is given by

A)
B)
C)
D)
E)

Question 33

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 34

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 35

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 36

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

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

Question 37

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 38

What is the average power dissipation in an RLC series circuit with R = 10Ω,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 39

Determine the rms current for the circuit.

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

Question 40

The phase angle between V and I is

A)
B)
C)
D)
E)

Question 41

The graphs below represent current and voltage phasors at one instant of time.The solid arrows represent the voltage phasors,ΔV_max,and the dashed arrows represent the current phasors,I_max.The graph which shows the correct relationship between current and voltage phasors for a capacitor in an RC circuit is

A)
B)
C)
D)
E)

Question 42

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 43

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

A)P_out = P_in.
B)P_out = P_in.
C)P_out = P_in.
D)P_out = P_in.
E)P_out = P_in.

Question 44

In a parallel RLC circuit,where I_R = IR_,max sin(ωt),the current through the capacitor,I_C,is

A)I_C = −IC_,max sin(ωt).
B)I_C = IC_,max sin(ωt).
C)I_C = −IC_,max cos(ωt).
D)I_C = IC_,max cos(ωt).
E)I_C = IC_,max tan(ωt).

Question 45

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,V_ab = +10 V.At that time,V_dc is

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

Question 46

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 10000 households,we can conclude that

A)IV = I²R.
B)I = V/R.
C)IV < I²R.
D)IV > I²R.
E)I²R = 0.

Question 47

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

A)
B)
C)
D)
E)

Question 48

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)X_L = X_C and the circuit contains a resistor,an inductor and a capacitor.
E)there is only a capacitor in the circuit.

Question 49

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 50

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

A)
B)
C)
D)
E)

Question 51

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 52

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 53

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 ω_A,ω_B and ω_C is correct?

A)ω_C > ω_A = ω_B
B)ω_C < ω_A = ω_B
C)ω_A = ω_B = ω_C
D)ω_B < ω_A = ω_C
E)ω_B > ω_A = ω_C

Question 54

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 ω_A,ω_B and ω_C is correct?

A)ω_C > ω_A = ω_B
B)ω_C < ω_A = ω_B
C)ω_A = ω_B = ω_C
D)ω_B < ω_A = ω_C
E)ω_B > ω_A = ω_C

Question 55

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,I_max.The graph which shows the correct relationship between current and voltage phasors for an inductor in an RL circuit is

A)
B)
C)
D)
E)

Question 56

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 57

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 58

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 59

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 60

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

A)
B)
C)
D)
E)

Question 61

A 10.0-Ω resistor,10.0-mH inductor,and 10.0-μF capacitor are connected in series with a 10.0-kHz voltage source.The rms current through the circuit is 0.200 A.Find the rms voltage drop across each of the 3 elements.

Question 62

In a parallel RLC circuit,where I_R = IR_,max sin(ωt),the current through the inductor,I_L,is

A)I_L = −IL_,max sin(ωt).
B)I_L = IL_,max sin(ωt).
C)I_L = −IL_,max cos(ωt).
D)I_L = IL_,max cos(ωt).
E)I_L = IL_,max tan(ωt).

Question 63

Which of the following is true about a diode?

A)A diode causes the voltage to shift in phase by 90°,i.e.,a right angle.
B)A diode has high resistance in one current direction and low resistance in the opposite current direction.
C)A diode can only be used with a transformer.
D)All filter circuits contain a diode.
E)All of the above.

Question 64

An ac power generator produces 50 A (rms)at 3600 V.The voltage is stepped up to 100000 V by an ideal transformer and the energy is transmitted through a long distance power line which has a resistance of 100 ohms.What percentage of the power delivered by the generator is dissipated as heat in the long-distance power line?

Question 65

Suppose the circuit parameters in a series RLC circuit are: L = 1.00 μH,C = 10.0 nF,R = 100 Ω,and the source voltage is 220 V.Determine the resonant frequency of the circuit and the amplitude of the current at resonance.