Deck 32: Alternating Current Circuits

Question 1

The law used to relate the voltage drops in a circuit containing a resistor, a capacitor, an inductor, and an AC source is

A) Norton's voltage law.
B) Kirchoff's voltage law.
C) Tesla's current law.
D) Ampere's current law.

Answer 1

Kirchoff's voltage law.

Question 2

An ideal resistor has no capacitance or inductance; therefore in an RLC series circuit, the current through the resistor

A) leads the voltage across the resistor.
B) lags the voltage across the resistor.
C) is in phase with the voltage across the resistor.
D) does none of the above.

Answer 2

is in phase with the voltage across the resistor.

Question 3

The time-averaged value of $\cos ^ { 2 } \omega t$ is

A) $\sqrt { 3 }$
B) $\sqrt { 2 }$
C) $1 / \sqrt { 2 }$
D) $1 / 2$

Answer 3

$1 / 2$

Question 4

To obtain the RMS (root-mean-square) voltage, we multiply the maximum voltage by

A) $\sqrt { 2 }$
B) 2.
C) 1/2.
D) 1/ $\sqrt { 2 }$

Question 5

The time-averaged power dissipated in a resistor is obtained by using

A) $V _ { \max } ^ { 2 } / R$
B) $V _ { m / s } ^ { 2 } / ( 2 R )$
C) $V _ { \max } ^ { 2 } / ( 3 R )$
D) $V _ { r m s } ^ { 2 } / R$

Question 6

A 45-VAC signal (rms) is present across a 5- $\Omega$ resistor. The time-averaged power dissipated in the resistor is

A) 400 W.
B) 800 W.
C) 200 W.
D) 100 W.

Question 7

Consider an ideal capacitor C connected directly to an AC voltage source V. Summing voltage drops around the loop yields

A) $C + V Q = 0$
B) $V - C Q = 0$
C) $V + C Q = 0$
D) $V C - Q = 0$

Question 8

The reactance of a 500- $\mu$ F capacitor connected to a 45 VAC signal (rms) that oscillates at $\omega = 500$ rad/s is

A) 1 $\Omega$
B) 2 $\Omega$
C) 3 $\Omega$
D) 4 $\Omega$

Question 9

In an ideal capacitor

A) the current leads the voltage by $\pi / 2$
B) the current lags the voltage by $\pi$
C) the current leads the voltage by $\pi$
D) the current lags the voltage by $\pi / 2$

Question 10

In an ideal inductor

A) the current leads the voltage by $\pi / 2$
B) the current lags the voltage by $\pi$
C) the current leads the voltage by $\pi$
D) the current lags the voltage by $\pi / 2$

Question 11

The maximum (instantaneous) emf across a capacitor is 160 V and the reactance of the capacitor is 12 $\Omega$ . The maximum current through the capacitor is

A) 22 A.
B) 77 mA.
C) 13 A.
D) 5.2 A.

Question 12

Consider an ideal inductor L connected directly to an AC voltage source V, with I being the current in the loop. Summing voltage drops around the loop yields

A) $d I / d t = V / L$
B) $d V / d t = I / L$
C) $d V / d t = L / I$
D) $d I / d t = L / V$

Question 13

The reactance of a 50-mH inductor connected to a 45-VAC signal (rms) that oscillates at $\omega = 500$ rad/s is

A) 0.04 $\Omega$
B) 25 $\Omega$
C) 12 $\Omega$
D) 7.5 $\Omega$

Question 14

The rms emf across an inductor is 5.2 V, and the reactance of the inductor is 0.77 $\Omega$ . The current (rms) through the inductor is

A) 1.5 A.
B) 6.8 A.
C) 510 mA.
D) 150 mA.

Question 15

A charged 200- $\mu$ F capacitor is connected to a 100-mH inductor to form an LC oscillator. The voltage across the inductor oscillates at

A) 210 Hz.
B) 120 Hz.
C) 36 Hz.
D) 82 Hz.

Question 16

The resonant frequency of a 1-H inductor and 1-F capacitor (forming an LC circuit) is

A) 0.16 Hz.
B) 1 Hz.
C) 1.2 Hz.
D) 1.4 Hz.

Question 17

The quality factor, Q, of an ideal LC circuit oscillating at $\omega _ { 0 } = 100$ rad/s with an inductor (L) of 120 mH is

A) 120.
B)6/5.
C) 100
D)infinite.

Question 18

Consider an RL circuit connected to a 20-VAC source that oscillates at 780 rad/s. The maximum voltage across the inductor is 18 V, and the maximum voltage across the resistor is 12 V. The phase angle (between the circuit impedance and the resistance) is

A) 34º.
B) 82º.
C) 22º.
D) 56º.

Question 19

Consider an RLC circuit connected to a 20-VAC source that oscillates at 780 rad/s. The maximum voltage across the inductor is 18 V, the maximum voltage across the capacitor is 6 V, and the maximum voltage across the resistor is 12 V. The phase angle (between the circuit impedance and the resistance) is

A) 45º.
B) 90º.
C) 0º.
D) 135º.

Question 20

An RLC circuit has a 12- $\Omega$ resistor connected to an inductor with 44 $\Omega$ reactance and a capacitor with 21 $\Omega$ reactance. The effective resistance as seen by the source (impedance) is

A) 26 $\Omega$
B) 12 $\Omega$
C) 23 $\Omega$
D) 21 $\Omega$

Question 21

The impedance (Z) of an RLC circuit with 15 $\Omega$ resistor, 7 $\Omega$ capacitive reactance, and 12 $\Omega$ inductive reactance is

A) 16 $\Omega$
B) 12 $\Omega$
C) 18 $\Omega$
D) 20 $\Omega$

Question 22

A transformer has 90 turns on the primary coil and 175 turns on the secondary coil. If the input voltage is 120 VAC, the output voltage is

A) 62 VAC.
B) 92 VAC.
C) 230 VAC.
D) 180 VAC.

Question 23

A transformer has 90 turns on the primary coil and 175 turns on the secondary coil. If the AC input current is 5 A, the output current is

A) 2.6 A.
B) 9.7 A.
C) 3.5 A.
D) 7.8 A.

Question 24

In an ideal transformer, the physical quantity that is conserved from the input to the output is

A) voltage.
B) power.
C) current.
D) resistance.

Question 25

In the transfer of electrical energy over power lines, it is desirable to minimize Joule heating. Therefore it is desirable to reduce the

A) resistance.
B) voltage.
C) current.
D) both (a) and (c).

Question 26

In the transfer of electrical energy over power lines, it is desirable to minimize Joule heating by increasing the operating voltage. What prevents the energy company from stepping up the voltage to an extremely high level?

A) Corona discharge
B) Joule heating
C) Melting point of conductor
D) Latent heat of fusion of conductor

Question 27

A particular transformer has a greater number of turns on the secondary winding than on the primary winding. This transformer is called

A) a step-up transformer.
B) a step-down transformer.
C) an ideal transformer.
D) a nonideal transformer.

Question 28

If the current is stepped up in a transformer, the

A) power is stepped down.
B) voltage is stepped up.
C) power is stepped up.
D) power remains constant.

Question 29

As the impedance in a simple series AC circuit gets larger, all of the following statements are valid except

A) for a given AC current, the AC voltage increases.
B) for a given AC power, the AC current decreases.
C) for a given AC voltage, the AC current decreases.
D) for a given AC voltage, the AC power increases.

Question 30

At high frequencies, the reactances of an inductor and capacitor are

A) both large.
B) large and small, respectively.
C) small and large, respectively.
D) both small.

Question 31

In a simple series RC circuit with a sinusoidal driving voltage, the phase relationship for a capacitor is that the

A) current leads the voltage by 90°.
B) voltage leads the current by 90°.
C) Either response might be correct, depending on further details.
D) The voltage and current are in phase.

Question 32

In a simple series AC circuit, an explanation for the phase relationship between current and voltage for a capacitor is that the voltage across a capacitor is proportional to

A) the current.
B) the time integral of the current.
C) the time derivative of the current.
D) none of the above.

Question 33

For ideal elements, energy can be dissipated in

A) a capacitor.
B) an inductor.
C) a resistor.
D) any of the above.

Question 34

The natural frequency for an LC circuit is

A) (LC) $1 / 2$
B) (L/C) $1 / 2$
C) (C/L) $1 / 2$
D) (1/LC) $1 / 2$

Question 35

We can check the answer to the previous question by remembering that the LC system is analogous to a mass-spring system whose natural frequency is (k/m) $1 / 2$ . The correct analogy is

A) C $\propto$ k and L $\propto$ m.
B) C $\propto$ 1/k and L $\propto$ m.
C) C $\propto$ m and L $\propto$ 1/k.
D) C $\propto$ 1/m and L $\propto$ 1/k.

Question 36

A possible clue to question 35 is that the electrical element that exhibits "inertia to the change of the current" is the

A) inductor.
B) capacitor.
C) Either of the previous responses is valid.
D) None of the previous responses is valid.

Question 37

The term in an RLC circuit that has the units of time (seconds) is

A) L/R.
B) RC.
C) R/L.
D) L/C.

Question 38

If the resistance for a simple series RLC circuit is increased, the resonant frequency of that circuit (provided it still readily oscillates)

A) is increased.
B) is decreased.
C) remains unchanged.
D) Insufficient information is given for a response.

Question 39

The quality factor ("Q") of a simple series RLC circuit is increased when each of the following elements is independently decreased except

A) capacitance.
B) inductance.
C) resistance.
D) There are no exceptions.

Question 40

A large quality factor ("Q") for an RLC circuit means that

A) its components have very precise values.
B) its resonant curve has a steep slope.
C) it is well shielded from stray electromagnetic fields.
D) its components are very durable.

Question 41

The instantaneous power loss in a circuit containing only a resistor through which DC current flows is given by the formula P = I² R. To retain the form of this equation for the case of AC current, it is enough to

A) interpret P as average power.
B) interpret I as rms current.
C) The first two answers are valid and sufficient.
D) Both of the first two answers are necessary, but they are not sufficient.

Question 42

The instantaneous power loss in a circuit containing a resistor and an inductor through which DC current flows is given by the formula P = I² Z. To retain the form of this equation for the case of AC current, it is enough to

A) interpret P as average power.
B) interpret I as rms current.
C) Both of the first two answers are necessary and sufficient.
D) Both of the first two answers are necessary, but they are not sufficient.

Question 43

RMS voltage is related to peak voltage by the equation

A) V_rms = V_peak.
B) V_rms = V_peak/ $\sqrt { 2 }$ .
C) V_rms = V_peak/2.
D) V_rms = V_peak/4.

Question 44

All of the following have the same dimensions except

A) second/farad.
B) henry/second.
C) volt/amp.
D) There are no exceptions.

Question 45

The appropriate phasor diagrams for the elements of a simple series RLC circuit and a simple parallel RLC circuit represent, respectively,

A) current and current.
B) current and voltage.
C) voltage and current.
D) voltage and voltage.

Question 46

A way to check your response to the previous question is to remember that for elements in series

A) currents add, and for elements in parallel currents add.
B) currents add, and for elements in parallel voltages add.
C) voltages add, and for elements in parallel currents add.
D) voltages add, and for elements in parallel voltages add.

Question 47

In an ideal transformer, the output

A) voltage cannot exceed the input voltage.
B) current cannot exceed the input current.
C) power cannot exceed the input power.
D) Each of the previous responses is valid.

Question 48

The power factor for an RLC circuit is

A) sin $\theta$ .
B) cos $\theta$
C) tan $\theta$
D) cot $\theta$

Question 49

The angle $\theta$ is the phase angle between

A) the voltage and current in the capacitor.
B) the voltage and current in the inductor.
C) the voltage and current in the resistor.
D) All of the previous responses are valid.

Question 50

Given the fact that a real inductor is composed of real wire, we can predict that the phase angle between the voltage across it and the current through it will be

A) greater than 90°.
B) exactly 90°.
C) less than 90°.
D) exactly 0°.