Deck 11: Alternating-Current Circuits

Question 1

Inductive reactance XL is given by:

A)L $\omega$
B)L/ $\omega$
C)1/L $\omega$
D)( $\omega$ /L)
E)( $\omega$ 2L)

Answer 1

L $\omega$

Question 2

Determine the impedance for the circuit.

A)600 $\Omega$
B)1200 $\Omega$
C)1800 $\Omega$
D)2300 $\Omega$
E)1100 $\Omega$

Answer 2

1800 $\Omega$

Question 3

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

Answer 3

4.40 pF

Question 4

An ac generator with peak voltage 100 volts is placed across a 10- $\Omega$ resistor.What is the average power dissipated?

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

Question 5

The total impedance Z of an RLC circuit driven by an ac voltage source at angular frequency $\omega$ is:

A)
B)
C)
D)
E)

Question 6

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 7

Determine the rms current for the circuit.

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

Question 8

The voltage 8.00 sin (400t) is applied to a series RLC circuit, with R = 200 $\Omega$ , L = 0.100 H, and C = 1.00 $\mu$ F.What are the impedance Z and the phase angle $\theta$ ?

A)200 $\Omega$ , -37.0 $\degree$
B)566 $\Omega$ , +87.0 $\degree$
C)2 470 $\Omega$ , -85.4 $\degree$
D)2 540 $\Omega$ , -88.8 $\degree$
E)393 $\Omega$ , -63.0 $\degree$

Question 9

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 $\Omega$ /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 10

Determine the resonant frequency of the circuit.

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

Question 11

At what frequency will a 50.0-mH inductor have a reactance XL = 700 $\Omega$ ?

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

Question 12

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

A)2.0 mF
B)1.0 $\mu$ F
C)0.020 $\mu$ F
D)1.0 pF
E)40 pF

Question 13

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 14

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 15

If the input to an RLC series circuit is V = Vm cos $\omega$ t, then the current in the circuit is:

A)cos $\omega$ t
B)
C)
D)
E)

Question 16

A 10.0- $\mu$ F 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 17

If an R = 1.0-k $\Omega$ resistor, a C = 1.0- $\mu$ F 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 18

At what frequency will a 12- $\mu$ F capacitor have a reactance XC = 300 $\Omega$ ?

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

Question 19

Capacitive reactance XC is given by:

A)1/ $\omega$ C
B)( $\omega$ C)
C)( $\omega$ /C)
D)C/ $\omega$
E)1/ $\omega$ 2C

Question 20

An electric heater designed for export to the US market draws an average power of 1100 Watts when plugged into a typical US 110 V-rms outlet.Calculate the resistance of the heater and the rms current.

A)11 $\Omega$ , 10 A (rms)
B)110 $\Omega$ , 10 A (rms)
C)10 $\Omega$ , 11 A (rms)
D)10 $\Omega$ , 110 A (rms)
E)0.09 $\Omega$ , 11 A (rms)

Question 21

A 10- $\mu$ F capacitor in an LC circuit made entirely of superconducting materials (R = 0 $\Omega$ ) is charged to 100 $\mu$ C.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 22

A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 $\Omega$ and C = 300 $\mu$ F.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 23

A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with R = 10.0 $\Omega$ and L = 10.0 mH.The impedance is:

A)3.77 $\Omega$ .
B)9.26 $\Omega$ .
C)10.0 $\Omega$ .
D)10.7 $\Omega$ .
E)13.8 $\Omega$ .

Question 24

A step-up transformer has an input voltage of 110 V (rms).There are 100 turns on the primary and 1 500 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 25

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 26

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 27

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 28

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

Question 29

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

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

Question 30

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 31

What is the average power dissipation in an RLC series circuit with R = 10 $\Omega$ , L = 0.1 H, C = 10 $\mu$ F 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 32

A 60.0-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with R = 10.0 $\Omega$ and C = 300 $\mu$ F.The power factor, cos $\phi$ , is:

A)(-1.00.)
B)(-0.749.)
C)+0.749.
D)+0.834.
E)+1.00.

Question 33

All three circuits shown below have R = 100 $\Omega$ , L = 0.1 H and emf $\varepsilon$ = (5.0 V) sin (377 t).Which statement regarding the angular resonance frequencies $\omega$ A, $\omega$ B and $\omega$ C is correct?

A) $\omega$ C > $\omega$ A = $\omega$ B)
B)( $\omega$ C < $\omega$ A = $\omega$ B)
C)( $\omega$ A = $\omega$ B = $\omega$ C)
D)( $\omega$ B < $\omega$ A = $\omega$ C)
E)( $\omega$ B > $\omega$ A = $\omega$ C)

Question 34

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

Question 35

The impedance of the parallel RLC circuit shown is given by:

A)
B)
C)
D)
E)

Question 36

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 37

The phase angle between V and I is:

A)
B)
C)
D)
E)

Question 38

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 39

For driving voltage V = Vm sin $\omega$ t, the current through the resistor is:

A)Vm sin ( $\omega$ t + $\phi$ )
B)Vm cos ( $\omega$ t + $\phi$ )
C)sin ( $\omega$ t + $\phi$ )
D)sin ( $\omega$ t + $\phi$ )
E)sin $\omega$ t

Question 40

Calculate Vout/Vin for the circuit if R = 2.0 k $\Omega$ , C = 0.020 $\mu$ F and V = 140V sin(50 000t).

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

Question 41

The graphs below represent current and voltage phasors at one instant of time.The solid arrows represent the voltage phasors, $\Delta$ Vmax, and the dashed arrows represent the current phasors, Imax.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

The graphs below show the phasors $\Delta$ Vmax and Imax for five RLC series circuits.The solid arrows represent the voltage phasors, $\Delta$ V, and the dashed arrows represent the current phasors, Imax.The graph which represents a circuit where the inductive reactance is greater than the capacitive reactance is:

A)
B)
C)
D)
E)

Question 43

In a parallel RLC circuit, where IR = IR, max sin( $\omega$ t), the current through the capacitor, IC, is:

A)IC = -IC, max sin( $\omega$ t).
B)IC = IC, max sin( $\omega$ t).
C)IC = -IC, max cos( $\omega$ t).
D)IC = IC, max cos( $\omega$ t).
E)IC = IC, max tan( $\omega$ t).

Question 44

An ac power generator produces 50 A (rms) at 3600 V.The voltage is stepped up to 100 000 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 45

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

Question 46

A 10.0- $\Omega$ resistor, 10.0-mH inductor, and 10.0- $\mu$ F 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 47

Which of the following is true about a diode?

A)A diode causes the voltage to shift in phase by 90 $\degree$ , 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 48

In a parallel RLC circuit, where IR = IR, max sin( $\omega$ t), the current through the inductor, IL, is:

A)IL = -IL, max sin( $\omega$ t).
B)IL = IL, max sin( $\omega$ t).
C)IL = -IL, max cos( $\omega$ t).
D)IL = IL, max cos( $\omega$ t).
E)IL = IL, max tan( $\omega$ t).

Question 49

The graphs below show the phasors $\Delta$ Vmax and Imax for five RLC series circuits.The solid arrows represent the voltage phasors, $\Delta$ V, and the dashed arrows represent the current phasors, Imax.The graph which represents a circuit where the capacitive reactance is greater than the inductive reactance is:

A)
B)
C)
D)
E)

Question 50

The graphs below represent current and voltage phasors at one instant of time.The solid arrows represent the voltage phasors, $\Delta$ V, and the dashed arrows represent the current phasors, Imax.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)