• Home
  • Textbooks
  • Essential University Physics Global Edition
  • Alternating-Current Circuits

Essential University Physics Global Edition

Richard Wolfson

Chapter 28

Alternating-Current Circuits - all with Video Answers

Educators

+ 2 more educators

Chapter Questions

01:57

Problem 1

What's meant by the statement, "A capacitor acts like a DC open circuit"?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:14

Problem 2

Why is an LC circuit dominated by inductors at high frequencies?

Vysakh M
Vysakh M
Numerade Educator
01:50

Problem 3

In an $\mathrm{AC}$ circuit, why is the resistor always in phase, while the capacitor and inductor are out of phase relative to the phase of the alternating current?

Vysakh M
Vysakh M
Numerade Educator
03:35

Problem 4

When a particular inductor and capacitor are connected across the same $\mathrm{AC}$ voltage, the current in the inductor is higher than in the capacitor. Is this true at all frequencies?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:35

Problem 5

An inductor and capacitor are connected in series across an AC generator, and the voltage across the inductor is higher than across the capacitor. Is the generator frequency above or below resonance?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:14

Problem 6

Why is Equation $28.5$ not a full description of the relation between voltage and current in a capacitor?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:59

Problem 7

The applied voltage in a series $R L C$ circuit lags the current. Is the frequency above or below resonance?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:18

Problem 8

The voltage across two components in series is zero. Is it possible that the voltages across the individual components aren't zero? Give an example.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:28

Problem 9

If you measure the rms voltages across the resistor, capacitor, and inductor in a series $R L C$ circuit, will they add to the rms generator voltage?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:01

Problem 10

A step-up transformer increases voltage, or energy per unit charge. Why doesn't this violate energy conservation?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:59

Problem 11

North America uses AC power at $120 \mathrm{~V} \mathrm{rms}$ and $60 \mathrm{~Hz}$. Express this $\mathrm{AC}$ voltage in the form of Equation $28.3$, taking $\phi_{V}=0$.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:06

Problem 12

An AC current is given by $I=693 \sin (7.54 t)$, with $I$ in mA and $t$ in ms. Find (a) the rms current and (b) the frequency in Hz.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:00

Problem 13

What are the phase constants for the signals in Fig. 28.24?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:31

Problem 14

Find the rms current in a $1.0-\mu \mathrm{F}$ capacitor connected across 230 -V rms, 50 -Hz AC power.

Vishal Gupta
Vishal Gupta
Numerade Educator
04:06

Problem 15

A $140-\Omega$ resistor, $47-\mu \mathrm{F}$ capacitor, and $220-\mathrm{mH}$ inductor are each connected across $6.3-\mathrm{V} \mathrm{rms}, 50-\mathrm{Hz} \mathrm{AC}$ power. Find the rms current in each.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:30

Problem 16

Find the reactance of a $6.8-\mu \mathrm{F}$ capacitor at (a) $50 \mathrm{~Hz}$, (b) $1.0 \mathrm{kHz}$, and (c) $20 \mathrm{kHz}$.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:43

Problem 17

A $33-\mu \mathrm{F}$ capacitor carries $2.2$ A rms. What's its minimum safe voltage rating if the frequency is (a) $50 \mathrm{~Hz}$ and (b) $1.0 \mathrm{kHz}$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:36

Problem 18

A capacitor and a $2.9-\mathrm{k} \Omega$ resistor pass the same current when connected across $50-\mathrm{Hz}$ power. Find the capacitance.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:45

Problem 19

A $50-\mathrm{mH}$ inductor is connected across a $10-\mathrm{V} \mathrm{rms} \mathrm{AC}$ generator, and a $2.0-\mathrm{mA}$ rms current flows. What's the generator frequency?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:30

Problem 20

Find the resonant frequency of an $L C$ circuit consisting of a $0.22-\mu \mathrm{F}$ capacitor and a $1.7-\mathrm{mH}$ inductor.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:26

Problem 21

You have a $68.0-\mu \mathrm{F}$ capacitor and you'd like to make an $L C$ circuit that oscillates at $256 \mathrm{~Hz}$. What inductance should you use?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:36

Problem 22

Your sister who's building the radio (Chapter 27 Exercise 18) wants to use a variable capacitor with her toilet-paper-tube inductor to span the AM radio band $(550-1600 \mathrm{kHz})$. What capacitance range do you suggest?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:28

Problem 23

An $L C$ circuit with a $20-\mu \mathrm{F}$ capacitor oscillates with period $5.0$ ms. The peak current is $25 \mathrm{~mA}$. Find (a) the inductance and (b) the peak voltage.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:42

Problem 24

A series $R L C$ circuit has $R=75 \mathrm{k} \Omega, L=18 \mathrm{mH}$, and resonates at $5.0 \mathrm{kHz}$. (a) What's the capacitance? (b) Find the circuit's impedance at resonance and (c) at $4.0 \mathrm{kHz}$.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:35

Problem 25

Find the impedance at $10 \mathrm{kHz}$ of a circuit consisting of a $1.5-\mathrm{k} \Omega$ resistor, 6.0- $\mu \mathrm{F}$ capacitor, and 55-mH inductor in series.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:40

Problem 26

A series $R L C$ circuit has $R=18 \mathrm{k} \Omega, C=14 \mu \mathrm{F}$, and $L=0.20 \mathrm{H}$. (a) At what frequency is its impedance lowest? (b) What's the impedance at this frequency?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:49

Problem 27

if the peak voltage applied to produce the curves in Fig. $28.17$ is $120 \mathrm{~V}$, and if $R=10 \mathrm{k} \Omega$, what are the peak currents at resonance for the three curves shown?

Dominador Tan
Dominador Tan
Numerade Educator
01:26

Problem 28

An electric saw draws $4.1 \mathrm{~A}$ rms at $230 \mathrm{~V}$ rms. If the current lags the voltage by $32^{\circ}$, what's the saw's power consumption?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:24

Problem 29

A $60-\mathrm{W}$ fluorescent lamp has power factor $0.79$ and operates from the $230-\mathrm{V} \mathrm{ms} \mathrm{AC}$ power line. How much current does it draw?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:36

Problem 30

An electric water heater draws $20 \mathrm{~A} \mathrm{rms}$ at $240 \mathrm{~V} \mathrm{rms}$ and is purely resistive. An AC motor has the same current and voltage, but its inductance causes the voltage to lead the current by $20^{\circ}$.
Find the power consumption in each device.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:29

Problem 31

For safety, medical equipment connected to patients is often
Bi0 powered by an isolation transformer, whose primary is connected to $230-\mathrm{V} \mathrm{AC}$ power and whose secondary delivers $230-\mathrm{V}$ power. What's the turns ratio of such a transformer?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:27

Problem 32

An exchange student from Canada will spend one semester in Germany, so she wants to purchase a transformer to step the $230-\mathrm{V}$ German power down to $120 \mathrm{~V}$ to power her hairdryer.
(a) If the transformer's primary has 460 turns, how many should the secondary have? (b) She can save money with a transformer whose maximum primary current is $6.0 \mathrm{~A}$. If her hairdryer draws $12.5 \mathrm{~A}$, will this transformer work?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:50

Problem 33

Example 28.2: In a North American application, a capacitor is connected across the $60-\mathrm{Hz}, 120-\mathrm{V} \mathrm{rms}$ power line, and an rms current of $295 \mathrm{~mA}$ flows. (a) Find the capacitance. (b) What inductance, connected across the same power line, would result in the same current?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:51

Problem 34

Example 28.2: A $0.470-\mu \mathrm{F}$ capacitor and a $144-\mu \mathrm{H}$ inductor are connected across identical AC voltage sources. (a) If the rms current in the capacitor is the same as in the inductor, what's the frequency of the sources?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:32

Problem 35

Example 28.2: A radio transmitter applies $480 \mathrm{~V}$ rms across a $6800-\mathrm{pF}$ capacitor and an inductor, connected in parallel to make a resonant circuit that determines the transmitter's frequency. The resulting current in each component is $22.0 \mathrm{~A} \mathrm{rms}$. Find (a) the transmitter frequency and (b) the inductance.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
04:31

Problem 36

Example 28.2: You're building a radio transmitter whose frequency is to be determined by an $L C$ circuit. The voltage across the $L C$ circuit will be $480 \mathrm{~V}$ rms, and the maximum allowable current in the $L C$ circuit is $500 \mathrm{~mA} \mathrm{rms}$. You have available capacitors in the standard values of $1.3 \mathrm{pF}$ and $2.2 \mathrm{pF}$, and inductors of $1.3 \mu \mathrm{H}$ and $2.4 \mu \mathrm{H}$. (a) Find a pair of values for $C$ and $L$ that will keep the current under the $500-\mathrm{mA}$ maximum and will give a frequency in the FM broadcast band, which covers 88 $\mathrm{MHz}$ to $108 \mathrm{MHz}$. (b) What are the values for the corresponding frequency and rms current?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:16

Problem 37

Example 28.4: A crossover network in a loudspeaker "steers" current to the midrange speaker through a $1.80-\mathrm{mH}$ inductor in series with a capacitor. (a) What should the capacitance be so that a given voltage produces the greatest current at $1.25 \mathrm{kHz}$ ? (b) If the same voltage produces half this current at $525 \mathrm{~Hz}$, what's the speaker's resistance?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:16

Problem 38

Example 28.4: The midrange speaker in a loudspeaker system has resistance $8.00 \Omega$. It's in series with a $2.70-\mathrm{mH}$ inductor in series with a $6.80-\mu \mathrm{F}$ capacitor that steer midrange frequencies to the speaker. (a) What's the frequency that results in maximum current to the speaker? (b) If the speaker can dissipate a maximum of $45.0 \mathrm{~W}$ rms without overheating, what's the maximum rms voltage that can be applied to the system at the frequency you found in (a)?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:03

Problem 39

Example 28.4: In Fig. 28.25, take $R=1.50 \mathrm{k} \Omega$ and $C=1.50 \mu \mathrm{F}$. A variable-frequency AC voltage source producing $18 \mathrm{~V} \mathrm{rms}$ is connected across the circuit, and an AC ammeter in series with the voltage source shows a minimum reading when the frequency of the applied voltage is $855 \mathrm{~Hz}$. Find (a) the inductance and (b) that minimum value of the ammeter reading.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
03:57

Problem 40

Example 28.4: (a) For the circuit of Fig. 28.25, use a phasor diagram to find an expression for the circuit's impedance $Z$ in terms of the resistance $R$ and the capacitive and inductive reactances $X_{C}$ and $X_{L}$. Your result should be analogous to the expression for $Z$ of the series $R L C$ circuit given after Equation $28.12$ on page 570 .
(b) Explain how your result implies the minimum current of the preceding problem at the appropriate frequency.

Sailesh Mohanty
Sailesh Mohanty
Numerade Educator
02:13

Problem 41

(a) A 1.7-H inductor is connected across 230-V rms, 50-Hz power. Find the rms inductor current. (b) Repeat if the same inductor is connected across the $120-\mathrm{V} \mathrm{ms}, 60-\mathrm{Hz}$ power commonly used in North America.

Vishal Gupta
Vishal Gupta
Numerade Educator
03:43

Problem 42

A $3.0-\mu \mathrm{F}$ capacitor has $1.0-\mathrm{k} \Omega$ reactance. (a) What's the frequency of the applied voltage? (b) What inductance would give the same reactance at this frequency? (c) How would the reactances compare if the frequency were doubled?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:32

Problem 43

Show that the unit of both capacitive and inductive reactance is the ohm.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:40

Problem 44

Electroencephalography (EEG) elucidates brain function by ana-
Bo lyzing brain waves, AC voltages resulting from electrical activity in the brain. Alpha waves are brain waves with frequencies from $7.5 \mathrm{~Hz}$ to $12.5 \mathrm{~Hz}$. A particular alpha wave has frequency $9.84 \mathrm{~Hz}$ and rms amplitude $31.8 \mu \mathrm{V}$. Express this voltage in the form of Equation $28.3$, assuming zero phase constant.

Morgan Cheatham
Morgan Cheatham
Numerade Educator
05:04

Problem 45

A 2.2-nF capacitor and one of unknown capacitance are in parallel across a $10-\mathrm{V}$ rms sine-wave generator. At $1.0 \mathrm{kHz}$, the generator supplies a total current of $3.4 \mathrm{~mA} \mathrm{rms}$. The generator frequency is then decreased until the rms current drops to $1.2 \mathrm{~mA}$. Find (a) the unknown capacitance and (b) the lower frequency.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:13

Problem 46

Connections to the body for electrocardiography $(\mathrm{ECG})$ and
B10 electroencephalography (EEG) are normally made with metal electrodes and conductive gels to ensure good electrical contact. An alternative is the capacitively coupled noncontact electrode, which uses a conductor near but not contacting the skin, to form a capacitor. Clothing can serve as the capacitor's insulation, eliminating skin contact. A particular EEG instrument calls for capacitive electrodes with maximum reactance $10 \mathrm{M} \Omega$ at a typical EEG beta-wave frequency of $25 \mathrm{~Hz}$. What's the minimum electrode capacitance?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:37

Problem 47

The FM radio band covers the frequency range $88-108 \mathrm{MHz}$ If the variable capacitor in an FM receiver ranges from $10.9 \mathrm{pF}$ to $16.4 \mathrm{pF}$, what inductor should be used to make an $L C$ circuit whose resonant frequency spans the FM band?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
04:43

Problem 48

An $L C$ circuit includes a $0.025-\mu \mathrm{F}$ capacitor and a $340-\mu \mathrm{H}$ inductor. (a) If the peak capacitor voltage is $190 \mathrm{~V}$, what's the peak inductor current? (b) How long after the voltage peak does the current peak occur?

Vishal Gupta
Vishal Gupta
Numerade Educator
01:29

Problem 49

At time $t=0$, the capacitor in an $L C$ circuit is fully charged, and there's no current in the circuit. Find expressions, in terms of $L$ and $C$, for the time at which (a) the capacitor voltage has half its initial value, (b) the energy stored in the capacitor has half its initial value, and (c) the current has its maximum value.

Dominador Tan
Dominador Tan
Numerade Educator
08:30

Problem 50

The $2420-\mu \mathrm{F}$ capacitor in Fig. $28.26$ is initially charged to $250 \mathrm{~V}$. (a) Describe how you would manipulate switches $A$ and $B$ to transfer all the energy from the $2420-\mu \mathrm{F}$ capacitor to the $605-\mu \mathrm{F}$ capacitor. Include the times you would throw the switches. (b) What will be the voltage across the $605-\mu \mathrm{F}$ capacitor once you've finished?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
01:31

Problem 51

A damped $L C$ circuit consists of a $0.14-\mu \mathrm{F}$ capacitor and a $20-\mathrm{mH}$ inductor with resistance $1.7 \Omega$. How many oscillation cycles will occur before the peak capacitor voltage drops to half its initial value?

Dominador Tan
Dominador Tan
Numerade Educator
01:17

Problem 52

A damped $R L C$ circuit includes a $5.0-\Omega$ resistor and a $100-\mathrm{mH}$ inductor. If half the initial energy is lost after 15 cycles, what's the capacitance?

Dominador Tan
Dominador Tan
Numerade Educator
View

Problem 53

An $R L C$ circuit includes a $1.7-\mathrm{H}$ inductor and a $270-\mu \mathrm{F}$ capacitor rated at $350 \mathrm{~V}$. The circuit is connected across a sine-wave generator with $V_{\mathrm{p}}=29 \mathrm{~V}$. What minimum resistance will ensure that the capacitor voltage does not exceed its rated value when the circuit is at resonance?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:10

Problem 54

The table below shows the ratio of peak voltage to peak curDATA rent-that is, the impedance Z-as a function of frequency for a series $R L C$ circuit. Plot the data and use your graph to estimate (a) the resonant frequency and (b) the resistance $R$.
\begin{tabular}{|l|}
\hline Frequency $(\mathrm{Hz})$ \\
\hline Impedance $(\Omega)$ \\
\hline
\end{tabular}

Dominador Tan
Dominador Tan
Numerade Educator
02:10

Problem 55

54. The table below shows the ratio of peak voltage to peak curDATA rent-that is, the impedance Z-as a function of frequency for a series $R L C$ circuit. Plot the data and use your graph to estimate (a) the resonant frequency and (b) the resistance $R$.
\begin{tabular}{|l|}
\hline Frequency $(\mathrm{Hz})$ \\
\hline Impedance $(\Omega)$ \\
\hline
\end{tabular}

Dominador Tan
Dominador Tan
Numerade Educator
06:40

Problem 56

An $\mathrm{AC}$ voltage of fixed amplitude is applied across a series $R L C$ circuit. The components are such that the current at half the resonant frequency is half the current at resonance. Show that the current at twice the resonant frequency is also half the current at resonance.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:25

Problem 57

A series $R L C$ circuit has resistance $150 \Omega$ and impedance $250 \Omega$. (a) What's the power factor? (b) If the rms current is $250 \mathrm{~mA}$, what's the power dissipation?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:00

Problem 58

A series $R L C$ circuit has power factor $0.764$ and impedance $182 \Omega$ at $442 \mathrm{~Hz}$. (a) What's the resistance? (b) If the inductance is $25.0 \mathrm{mH}$, what's the resonant frequency?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:37

Problem 59

You're the Chief Financial Officer for a power company, and you consult your engineering department in an effort to minimize power-line losses. Your power plant produces $50-\mathrm{Hz}$ power at $365 \mathrm{kV} \mathrm{rms}$ and $200 \mathrm{~A} \mathrm{rms}$ and delivers it via transmission lines with total resistance $95 \Omega$. You ask the engineers for the percentage of power that's lost. They reply that it depends on the power factor. What's the percentage loss for power factors of (a) $1.0$ and (b) $0.80$ ?

Morgan Cheatham
Morgan Cheatham
Numerade Educator
02:58

Problem 60

A sawmill uses a 10-hp electric motor operating at $480 \mathrm{~V} \mathrm{rms}$. Its power factor is $0.82$. When a power-factor-correcting capacitor is added to the system, the power factor increases to $0.95$. Find the rms current in the wires supplying the motor (a) before and (b) after the power factor increase.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:31

Problem 61

A power supply like that of Fig. $28.23$ is supposed to deliver $22-\mathrm{V}$ DC at a maximum current of $180 \mathrm{~mA}$. The transformer's peak output voltage can charge the capacitor to a full $22 \mathrm{~V}$, and the primary is supplied with $50-\mathrm{Hz} \mathrm{AC}$. What capacitance will ensure that the output voltage stays within $4 \%$ of the rated $22 \mathrm{~V}$ ?

Dominador Tan
Dominador Tan
Numerade Educator
View

Problem 62

An $R L C$ circuit includes a $3.3-\mu \mathrm{F}$ capacitor and a $27-\mathrm{mH}$ inductor. The capacitor is charged to $35 \mathrm{~V}$, and the circuit begins oscillating. Ten full cycles later the capacitor voltage peaks at $28 \mathrm{~V}$. Find the resistance.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
View

Problem 63

A series $R L C$ circuit with $R=1.1 \Omega, L=29 \mathrm{mH}$, and $\mathrm{C}=0.43 \mu \mathrm{F}$ is connected across a sine-wave generator. If the capacitor's peak voltage rating is $600 \mathrm{~V}$, what's the maximum safe value for the generator's peak output voltage when it's tuned to resonance?

Clayton Bennett
Clayton Bennett
Numerade Educator
03:26

Problem 64

Differentiate Equation $28.9$ to find the current in the $L C$ circuit, and use $q=C V$ to find the voltage. From these, obtain the electric energy in the capacitor and the magnetic energy in the inductor, and sum to show that the total energy remains constant. (Hint: You'll need Equation $28.10$ and a familiar trig identity.)

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
02:32

Problem 65

Find a second frequency where the current in the speaker of CH Example 28.4 has half its maximum value.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
06:00

Problem 66

Two capacitors are connected in parallel across a 24 -V rms, cH $7.5-\mathrm{kHz}$ sine-wave generator, and the generator supplies a total rms current of $56 \mathrm{~mA}$. With capacitors rewired in series, the rms current drops to $2.8 \mathrm{~mA}$. What are the two capacitances?

Vishal Gupta
Vishal Gupta
Numerade Educator
07:12

Problem 67

A sine-wave generator with $15.0-\mathrm{V}$ peak output is applied across cH a series $R L C$ circuit. At the circuit's resonant frequency of 775 $\mathrm{Hz}$ the peak current is $112 \mathrm{~mA}$; at $1.22 \mathrm{kHz}$ it's $44.8 \mathrm{~mA}$. Find $R, L$, and $C$.

Vishal Gupta
Vishal Gupta
Numerade Educator
06:00

Problem 68

For $R L C$ circuits in which the resistance isn't too high, the $Q$ cH factor may be defined as the ratio of the resonant frequency to the difference between the two frequencies where the power dissipated in the circuit is half the power dissipated at resonance. Using suitable approximations, show that this definition leads to $Q=\omega_{0} L R$, with $\omega_{0}$ the resonant frequency.

Narayan Hari
Narayan Hari
Numerade Educator
04:12

Problem 69

A triangle wave swings linearly between voltages $-V_{\mathrm{P}}$ and $+V_{\mathrm{P}}$.
CH Show that the rms voltage of a triangle wave is $V_{\mathrm{p}} / \sqrt{3}$.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:22

Problem 70

Substitute the expression for $q(t)$ in Equation $28.11$ into the difcH ferential equation for an $L C$ circuit with resistance, and find an expression for the angular frequency of the damped oscillations in terms of $R, L$, and $C$.

Raj Bala
Raj Bala
Numerade Educator
04:07

Problem 71

Although the maximum current flows in the speaker circuit of Example $28.4$ at the 1-kHz resonant frequency, the peak voltage across the capacitor is a maximum at a somewhat lower frequency. Find that frequency and the corresponding peak voltage.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:02

Problem 72

The circuit shown in Fig. $28.28$ is
a. a low-pass filter.
b. a high-pass filter.
c. a band-pass filter.
d. impossible to tell without knowing the component values.

Vishal Gupta
Vishal Gupta
Numerade Educator
02:23

Problem 73

When the angular frequency $\omega$ of the input voltage $V_{\text {in }}$ is such that the capacitor's reactance is equal to the resistance, the output voltage is
a. $V_{\text {in }} / 4$.
b. $V_{\mathrm{in}} / 2$.
c. $V_{\mathrm{in}} / \sqrt{2}$.
d. $2 V_{\mathrm{in}}$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:43

Problem 74

The circuit of Fig. $28.28$
a. exhibits resonance at frequency $\omega=1 / R C$.
b. exhibits resonance at frequency $\omega=1 / \sqrt{R C}$.
c. produces an output voltage whose frequency differs from that of the input.
d. produces an output voltage whose phase differs from that of the input.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:33

Problem 75

If you replace the capacitor in Fig. $28.28$ with an inductor, the circuit
a. continues to function as before.
b. becomes the opposite kind of filter.
c. produces zero output voltage because the inductor is a short circuit.
d. produces an output voltage that exceeds the input voltage.

Vishal Gupta
Vishal Gupta
Numerade Educator