Physics

James S. Walker

Chapter 24

Alternating-Current Circuits - all with Video Answers

Educators

Chapter Questions

Problem 1

An ac generator produce a peak voltage of 55 V. What is the rms voltage of this generator?

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 2

European Electricity In many European homes the rms voltage available from a wall socket is 240 V . What is the maximum voltage in this case?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 3

- An rms voltage of $120 \mathrm{V}$ produces a maximum current of $2.1 \mathrm{A}$ in a certain resistor. Find the resistance of this resistor.

Vishal Gupta

Numerade Educator

Problem 4

The rms current in an ac circuit with a resistance of $150 \Omega$ is 0.85 A. What are (a) the average and (b) the maximum power consumed by this circuit?

Vishal Gupta

Numerade Educator

Problem 5

A 3.33-k $\Omega$ resistor is connected to a generator with a maximum voltage of $141 \mathrm{V}$. Find $(\mathrm{a})$ the average and
(b) the maximum power delivered to this circuit.

Vishal Gupta

Numerade Educator

Problem 6

$\mathrm{A}$ "75-watt" lightbulb uses an average power of $75 \mathrm{W}$ when connected to an rms voltage of $120 \mathrm{V}$. (a) What is the resistance of the lightbulb? (b) What is the maximum current in the bulb?
(c) What is the maximum power used by the bulb at any given instant of time?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 7

Square-Wave Voltage I The relationship $V_{\text {rms }}=V_{\max } / \sqrt{2}$ is valid only for voltages that vary sinusoidally. Find the relationship between $V_{\text {rms }}$ and $V_{\text {max }}$ for the "square-wave" voltage shown in Figure $24-26$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 8

The reactance of a capacitor is $65 \Omega$ at a frequency of $57 \mathrm{Hz}$. What is its capacitance?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 9

The capacitive reactance of a capacitor at $60.0 \mathrm{Hz}$ is $105 \mathrm{A}$. At what frequency is its capacitive reactance $72.5 \Omega ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 10

A $105-\mu F$ capacitor is connected to an ac generator with an rms voltage of $20.0 \mathrm{V}$ and a frequency of $100.0 \mathrm{Hz}$. What is the rms current in this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 11

$\cdot$ The rms voltage across a $0.010-\mu F$ capacitor is $1.8 \mathrm{V}$ at a frequency of $52 \mathrm{Hz}$. What are (a) the rms and
(b) the maximum current through the capacitor?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 12

-An ac generator with a frequency of $30.0 \mathrm{Hz}$ and an $\mathrm{rms}$ voltage of $12.0 \mathrm{V}$ is connected to a $45.5-\mu \mathrm{F}$ capacitor.
(a) What is the maximum current in this circuit?
(b) What is the current in the circuit when the voltage across the capacitor is $5.25 \mathrm{V}$ and increasing? (c) What is the current in the circuit when the voltage across the capacitor is $5.25 \mathrm{V}$ and decreasing?

Breanna Kloczkowski

Breanna Kloczkowski

Numerade Educator

Problem 13

The maximum current in a 22 - $\mu$ F capacitor connected to an ac generator with a frequency of $120 \mathrm{Hz}$ is $0.15 \mathrm{A}$.
(a) What is the maximum voltage of the generator?
(b) What is the voltage across the capacitor when the current in the circuit is $0.10 \mathrm{A}$ and increasing?
(c) What is the voltage across the capacitor when the current in the circuit is $0.10 \mathrm{A}$ and $\mathrm{decreasing} ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 14

IP An rms voltage of $20.5 \mathrm{V}$ with a frequency of $1.00 \mathrm{kHz}$ is applied to a $0.395-\mu \mathrm{F}$ capacitor. (a) What is the rms current in this circuit? (b) By what factor does the current change if the frequency of the voltage is doubled? $(c)$ Calculate the current for a frequency of $2.00 \mathrm{kHz}$

Ajay Singhal

Numerade Educator

Problem 15

A circuit consists of a $1.00-\mathrm{kHz}$ generator and a capacitor. When the rms voltage of the generator is $0.500 \mathrm{V}$, the rms current in the circuit is $0.430 \mathrm{mA}$.
(a) What is the reactance of the capacitor at $1.00 \mathrm{kHz}$ ? (b) What is the capacitance of the capacitor? (c) If the rms voltage is maintained at $0.500 \mathrm{V},$ what is the rms current at $2.00 \mathrm{kHz}$ ? At $10.0 \mathrm{kHz}$ ?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 16

IP A capacitor has an rms current of $21 \mathrm{mA}$ at a frequency of $60.0 \mathrm{Hz}$ when the rms voltage across it is $14 \mathrm{V}$. (a) What is the capacitance of this capacitor?
(b) If the frequency is increased, will the current in the capacitor increase, decrease, or stay the same? Explain. (c) Find the rms current in this capacitor at a frequency of $410 \mathrm{Hz}$

Willis James

Numerade Educator

Problem 17

A 0.22- $\mu F$ capacitor is connected to an ac generator with an rms voltage of $12 \mathrm{V}$. For what range of frequencies will the rms current in the circuit be less than $1.0 \mathrm{mA}$ ?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 18

- At what frequency will a generator with an rms voltage of $504 \mathrm{V}$ produce an rms current of $7.50 \mathrm{mA}$ in a $0.0150-\mu \mathrm{F}$ capacitor?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 19

Find the impedance of a $60.0-\mathrm{Hz}$ circuit with a $45.5-\Omega$ resistor connected in series with a $95.0-\mu \mathrm{F}$ capacitor.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 20

An ac generator with a frequency of $105 \mathrm{Hz}$ and an rms voltage of $22.5 \mathrm{V}$ is connected in series with a $10.0-\mathrm{k} \Omega$ resistor and a $0.250-\mu \mathrm{F}$ capacitor. What is the rms current in this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 21

The rms current in an $R C$ circuit is 0.72 A. The capacitor in this circuit has a capacitance of $13 \mu \mathrm{F}$ and the ac generator has a frequency of $150 \mathrm{Hz}$ and an rms voltage of $95 \mathrm{V}$. What is the resistance in this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 22

A 65.0-Hz generator with an rms voltage of $135 \mathrm{V}$ is connected in series to a $3.35-k \Omega$ resistor and a $1.50-\mu \mathrm{F}$ capacitor. Find (a) the rms current in the circuit and (b) the phase angle, $\phi$ between the current and the voltage.

Penny Riley

Numerade Educator

Problem 23

(a) At what frequency must the circuit in Problem 22 be operated for the current to lead the voltage by $23.0^{\circ} ?$
(b) Using the frequency found in part (a), find the average power consumed by this circuit.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 24

(a) Sketch the phasor diagram for an ac circuit with a $105-\Omega$ resistor in series with a $32.2-\mu \mathrm{F}$ capacitor. The frequency of the generator is $60.0 \mathrm{Hz}$. (b) If the rms voltage of the generator is $120 \mathrm{V},$ what is the average power consumed by the circuit?

Ankur S

Numerade Educator

Problem 24

Sketch the phasor diagram for an ac circuit with a $105-\Omega$ resistor in series with a $32.2-\mu \mathrm{F}$ capacitor. The frequency of the generator is $60.0 \mathrm{Hz}$.
(b) If the rms voltage of the generator is $120 \mathrm{V},$ what is the average power consumed by the circuit?

Ankur S

Numerade Educator

Problem 25

Find the power factor for an $R C$ circuit connected to a $70.0-\mathrm{Hz}$ generator with an rms voltage of 155 V. The values of $R$ and $C$ in this circuit are $105 \Omega$ and $82.4 \mu F,$ respectively.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 25

Find the power factor for an $R C$ circuit connected to a $70.0-1 \mathrm{Hz}$ generator with an rms voltage of 155 V. The values of $R$ and $C$. in this circuit are $105 \Omega$ and $82.4 \mu \mathrm{F}$, respectively.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 26

IP (a) Determine the power factor for an $R C$ circuit with $R=4.0 \mathrm{k} \Omega$ and $C=0.35 \mu \mathrm{F}$ that is connected to an ac generator with an rms voltage of $24 \mathrm{V}$ and a frequency of $150 \mathrm{Hz}$
(b) Will the power factor for this circuit increase, decrease, or stay the same if the frequency of the generator is increased? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 27

Square-Wave Voltage II The "square-wave" voltage shown in Figure $24-27$ is applied to an $R C$ circuit. Sketch the shape of the instantaneous voltage across the capacitor, assuming the time constant of the circuit is equal to the period of the applied voltage.

Carson Merrill

Numerade Educator

Problem 28

CE Predict/Explain When a long copper wire of finite resistance is connected to an ac generator, as shown in Figure $24-28$ (a). a certain amount of current flows through the wire. The wire is

Sunita Kumari

Numerade Educator

Problem 28

CE Predict/Explain When a long copper wire of finite resistance is connected to an ac generator, as shown in Figure $24-28$ (a). a certain amount of current flows through the wire. The wire is now wound into a coil of many loops and reconnected to the generator, as indicated in Figure $24-28$ (b). (a) Is the current supplied to the coil greater than, less than, or the same as the current supplied to the uncoiled wire? (b) Choose the best explanation from among the following:
I. More current flows in the circuit because the coiled wire is an inductor, and inductors tend to keep the current flowing in an ac circuit.
II. The current supplied to the circuit is the same because the wire is the same. Simply wrapping the wire in a coil changes nothing.
III. Less current is supplied to the circuit because the coiled wire acts as an inductor, which increases the impedance of the circuit.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 29

An inductor has a reactance of $56.5 \Omega$ at $75.0 \mathrm{Hz}$. What is its
reactance at $60.0 \mathrm{Hz}$ ?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 30

What is the rms current in a $77.5-\mathrm{mH}$ inductor when it is connected to a $60.0-\mathrm{Hz}$ generator with an rms voltage of $115 \mathrm{V} ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 31

What rms voltage is required to produce an rms current of $2.1 \mathrm{A}$ in a $66-\mathrm{mH}$ inductor at a frequency of $25 \mathrm{Hz} ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 32

$4.525-\Omega$ resistor and a $295-\mathrm{mH}$ inductor are connected in series with an ac generator with an rms voltage of $20.0 \mathrm{V}$ and a frequency of $60.0 \mathrm{Hz}$. What is the rms current in this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 33

The rms current in an $R L$ circuit is $0.26 \mathrm{A}$ when it is connected to an ac generator with a frequency of $60.0 \mathrm{Hz}$ and an
(a) Given that the inductor has an inducrms voltage of 25 V. tance of $145 \mathrm{mH},$ what is the resistance of the resistor?
(b) Find
the rms voltage across the resistor.
(c) Find the rms voltage across the inductor. (d) Use your results from parts (b) and (c) to show that $\sqrt{V_{\mathrm{rms}, R}^{2}+V_{\mathrm{rms}, l}^{2}}$ is equal to 25 V.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 34

An ac generator with a frequency of $1.34 \mathrm{kHz}$ and an rms voltage of $24.2 \mathrm{V}$ is connected in series with a $2.00-\mathrm{k} \Omega$ resistor and a $315-\mathrm{mH}$ inductor.
(a) What is the power factor for this circuit?
(b) What is the average power consumed by this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 35

IP An rms voltage of $22.2 \mathrm{V}$ with a frequency of $1.00 \mathrm{kHz}$ is applied to a $0.290-\mathrm{mH}$ inductor. (a) What is the rms current in this circuit? (b) By what factor does the current change if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of $2.00 \mathrm{kHz}$

Ajay Singhal

Numerade Educator

Problem 36

A $0.22-\mu \mathrm{H}$ inductor is connected to an ac generator with an rms voltage of 12 V. For what range of frequencies will the rms current in the circuit be less than $1.0 \mathrm{mA} ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 37

The phase angle in a certain $R L$ circuit is $76^{\circ}$ at a frequency of $60.0 \mathrm{Hz}$. If $\mathrm{R}=2.7 \mathrm{f}$ for this circuit, what is the value of the inductance, L?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 38

An $R L$ circuit consists of a resistor $R=68 \Omega$, an inductor, $L=31 \mathrm{mH},$ and an ac generator with an rms voltage of $120 \mathrm{V}$
(a) At what frequency will the rms current in this circuit be $1.5 \mathrm{A} ?$ For this frequency, what are (b) the rms voltage across the resistor, $V_{\mathrm{rms}, R},$ and $(c)$ the rms voltage across the inductor, $V_{\mathrm{rms}, l} ?$
(d) Show that $V_{\mathrm{rms}, k}+V_{\mathrm{rms}, L}>120 \mathrm{V},$ but that
$\sqrt{V_{\mathrm{rms}, R}^{2}+V_{\mathrm{rms}, L}^{2}}=120 \mathrm{V}$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 39

(a) Sketch the phasor diagram for an ac circuit with a $105-\Omega$ resistor in series with a $22.5-\mathrm{mH}$ inductor. The frequency of the generator is $60.0 \mathrm{Hz}$. (b) If the rms voltage of the generator is $120 \mathrm{V},$ what is the average power consumed by the circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 40

IP In Problem 37 , does the phase angle increase, decrease, or stay the same when the frequency is increased? Verify your answer by calculating the phase angle at $70.0 \mathrm{Hz}$.

Vishal Gupta

Numerade Educator

Problem 41

-A large air conditioner has a resistance of $7.0 \Omega$ and an inductive reactance of $15 \Omega$. If the air conditioner is powered by a $60.0-\mathrm{Hz}$ generator with an rms voltage of $240 \mathrm{V}$, find $(\mathrm{a})$ the impedance of the air conditioner, (b) its rms current, and (c) the average power consumed by the air conditioner.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 42

Square-Wave Voltage III The "square-wave" voltage shown in Figure $24-27$ is applied to an $R L$ circuit. Sketch the shape of the instantaneous voltage across the inductor, assuming the time constant of the circuit is much less than the period of the applied voltage.

Amit Srivastava

Amit Srivastava

Numerade Educator

Problem 43

CE An inductor and a capacitor are to be connected to a generator. Will the generator supply more current at high frequency if the inductor and capacitor are connected in series or in parallel? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 44

C E An inductor and a capacitor are to be connected to a generator. Will the generator supply more current at low frequency if the inductor and capacitor are connected in series or in parallel? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 45

- CE Predict/Explain (a) When the ac generator in Figure $24-29$ operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following:
I. The current is the same because at high frequency the inductor is like an open circuit, and at low frequency the capacitor is like an open circuit. In either case the resistance of the circuit is $R$.
II. Less current flows at high frequency because in that limit the inductor acts like an open circuit, allowing no current to flow.
III. More current flows at high frequency because in that limit the capacitor acts like an ideal wire of zero resistance.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 46

CE Predict/Explain (a) When the ac generator in Figure $24-30$ operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following:
I. The current at high frequency is greater because the higher the frequency the more charge that flows through a circuit.
II. Less current flows at high frequency because in that limit the inductor is like an open circuit and current has only one path to flow through.
III. The inductor has zero resistance, and therefore the resistance of the circuit is the same at all frequencies. As a result the current is the same at all frequencies.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 47

CE Predict/Explain (a) When the ac generator in Figure $24-31$ operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following:
I. The capacitor has no resistance, and therefore the resistance of the circuit is the same at all frequencies. As a result the current is the same at all frequencies.
II. Less current flows at high frequency because in that limit the capacitor is like an open circuit and current has only one path to flow through.
III. More current flows at high frequency because in that limit the capacitor is like a short circuit and current has two parallel paths to flow through.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 48

Find the rms voltage across each element in an $R L C$ circuit with $R=9.9 \mathrm{k} \Omega, C=0.15 \mu \mathrm{F},$ and $L=25 \mathrm{mH}$. The generator supplies an rms voltage of $115 \mathrm{V}$ at a frequency of $60.0 \mathrm{Hz}$.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 49

What is the impedance of a $1.50-k \Omega$ resistor, a $105-\mathrm{mH}$ inductor, and a $12.8-\mu \mathrm{F}$ capacitor connected in series with a $60.0-\mathrm{Hz}$ ac generator?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 50

Consider the circuit shown in Figure $24-30 .$ The ac generator in this circuit has an rms voltage of 65 V. Given that $R=15 \Omega$ and $L=0.22 \mathrm{mH},$ find the rms current in this circuit in the limit of (a) high frequency and
(b) low frequency.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 51

Consider the circuit shown in Figure $24-31$. The ac generator in this circuit has an rms voltage of $75 \mathrm{V}$. Given that $R=15 \Omega$ and $C=41 \mu F$, find the rms current in this circuit in the limit of
(a) high frequency and
(b) low frequency.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 52

What is the phase angle in an $R L C$ circuit with $R=9.9 \mathrm{k} \Omega$, $C=1.5 \mu F,$ and $L=250 \mathrm{mH} ?$ The generator supplies an $\mathrm{rms}$ voltage of $115 \mathrm{V}$ at a frequency of $60.0 \mathrm{Hz}$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 53

IP An RLC circuit has a resistance of $105 \Omega$, an inductance of $85.0 \mathrm{mH},$ and a capacitance of $13.2 \mu \mathrm{F} .$ (a) What is the power factor for this circuit when it is connected to a $125-\mathrm{Hz}$ ac generator? (b) Will the power factor increase, decrease, or stay the same if the resistance is increased? Explain. (c) Calculate the power factor for a resistance of $525 \Omega$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 54

An ac voltmeter, which displays the rms voltage between the two points touched by its leads, is used to measure voltages in the circuit shown in Figure $24-32$. In this circuit, the ac genera tor has an rms voltage of $6.00 \mathrm{V}$ and a frequency of $30.0 \mathrm{kHz}$. The inductance in the circuit is $0.300 \mathrm{mH},$ the capacitance is $0.100 \mu F,$ and the resistance is $2.50 \Omega .$ What is the reading on a voltmeter when it is connected to points (a) $A$ and $B,(b) B$ and $C,(c) A$ and $C,$ and
(d) $A$ and $D ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 55

IP Consider the ac circuit shown in Figure $24-32$, where we assume that the values of $R, L,$ and $C$ are the same as in the previous problem, and that the rms voltage of the generator is still $6.00 \mathrm{V} .$ The frequency of the generator, however, is doubled to $60.0 \mathrm{kHz}$. Calculate the rms voltage across (a) the resistor, $R$
(b) the inductor, $L,$ and $(c)$ the capacitor, $C$.
(d) Do you expect the sum of the rms voltages in parts (a), (b), and
(c) to be greater than, less than, or equal to $6.00 \mathrm{V}$ ? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 56

(a) Sketch the phasor diagram for an ac circuit with a $105-\Omega$ resistor in series with a $22.5-\mathrm{mH}$ inductor and a $32.2-\mu \mathrm{F}$ capacitor. The frequency of the generator is $60.0 \mathrm{Hz}$ (b) If the rms voltage of the generator is $120 \mathrm{V},$ what is the average power consumed by the circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 57

- A generator connected to an $R L C$ circuit has an rms voltage of $120 \mathrm{V}$ and an $\mathrm{rms}$ current of $34 \mathrm{mA}$. If the resistance in the cir-
cuit is $3.3 \mathrm{k} \Omega$ and the capacitive reactance is $6.6 \mathrm{k} \Omega,$ what is the inductive reactance of the circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 58

Manufacturing Plant Power A manufacturing plant uses $2.22 \mathrm{kW}$ of electric power provided by a $60.0-\mathrm{Hz}$ ac generator with an rms voltage of 485 V. The plant uses this power to run a number of high-inductance electric motors. The plant's total resistance is $R=25.0 \Omega$ and its inductive reactance is $X_{L}=45.0 \Omega .$ (a) What is the total impedance of the plant? (b) What is the plant's power factor?
(c) What is the rms current used by the plant?
(d) What capacitance, connected in series with the power line, will increase the plant's power factor to unity? (e) If the power factor is unity, how much current is needed to provide the $2.22 \mathrm{kW}$ of power needed by the plant? Compare your answer with the current found in part (c). (Because power-line losses are proportional to the square of the current, a utility company will charge an industrial user with a low power factor a higher rate per $\mathrm{kWh}$ than a company with a power factor close to unity.)

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 59

CE A capacitor and an inductor connected in series have a period of oscillation given by $T . A t$ the time $t=0$ the capacitor has its maximum charge. In terms of $T$, what is the first time after $t=0$ that $(a)$ the current in the circuit has its maximum value and
(b) the energy stored in the electric field is a maximum?

Shoukat Ali

Other Schools

Problem 60

CE Predict/Explain In an $R L C$ circuit a second capacitor is added in series to the capacitor already present. (a) Does the resonance frequency increase, decrease, or stay the same?
(b) Choose the best explanation from among the following:
I. The resonance frequency stays the same because it depends only on the resistance in the circuit.
II. Adding a capacitor in series increases the equivalent capacitance, and this decreases the resonance frequency.
III. Adding a capacitor in series decreases the equivalent capacitance, and this increases the resonance frequency.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 61

CE In an $R L C$ circuit a second capacitor is added in parallel to the capacitor already present. Does the resonance frequency increase, decrease, or stay the same? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 62

An $R L C$ circuit has a resonance frequency of $2.4 \mathrm{kHz}$. If the capacitance is $47 \mu \mathrm{F},$ what is the inductance?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 63

At resonance, the rms current in an $R L C$ circuit is $2.8 \mathrm{A}$. If the rms voltage of the generator is $120 \mathrm{V},$ what is the resistance, $R ?$

Keshav Singh

Numerade Educator

Problem 64

CE The resistance in an $R L C$ circuit is doubled. (a) Does the resonance frequency increase, decrease, or stay the same? Explain. (b) Does the maximum current in the circuit increase, decrease, or stay the same? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 65

CE The voltage in a sinusoidally driven $R L C$ circuit leads the current. (a) If we want to bring this circuit into resonance by changing the frequency of the generator, should the frequency be increased or decreased? Explain.
(b) If we want to bring this circuit into resonance by changing the inductance instead, should the inductance be increased or decreased? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 66

- $\mathrm{A} 115-\Omega$ resistor, a $67.6-\mathrm{mH}$ inductor, and a $189-\mu \mathrm{F}$ capacitor are connected in series to an ac generator. (a) At what frequency will the current in the circuit be a maximum?
(b) At what frequency will the impedance of the circuit be a minimum?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 67

- $A 115-\Omega$ resistor, a $67.6-\mathrm{mH}$ inductor, and a $189-\mu \mathrm{F}$ capacitor are connected in series to an ac generator. (a) At what frequency will the current in the circuit be a maximum?
(b) At what frequency will the impedance of the circuit be a minimum?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 68

(a) Find the frequency at which a $33-\mu F$ capacitor has the same reactance as a $33-\mathrm{mH}$ inductor.
(b) What is the resonance frequency of an $L C$ circuit made with this inductor and capacitor?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 69

consider an $R L C$ circuit with $R=105 \Omega, L=518 \mathrm{mH},$ and $C=0.200 \mu F .$ (a) At what frequency is this circuit in resonance?
(b) Find the impedance of this circuit if the frequency has the value found in part (a), but the capacitance is increased to $0.220 \mu \mathrm{F}$
(c) What is the power factor for the situation described in part (b)?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 70

IP An RLC circuit has a resonance frequency of $155 \mathrm{Hz}$ (a) If both $L$ and $C$ are doubled, does the resonance frequency increase, decrease, or stay the same? Explain.
(b) Find the resonance frequency when $L$ and $C$ are doubled.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 71

$\cdot$ An $R L C$ circuit has a capacitance of $0.29 \mu F$, (a) What inductance will produce a resonance frequency of $95 \mathrm{MHz} ?$ (b) It is desired that the impedance at resonance be one-fifth the impedance at $11 \mathrm{kHz}$. What value of $R$ should be used to obtain this result?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 72

CE BIO Persistence of Vision Although an incandescent lightbulb appears to shine with constant intensity, this is an artifact of the eye's persistence of vision. In fact, the intensity of a bulb's light rises and falls with time due to the alternating current used in household circuits. If you could perceive these oscillations, would you see the light attain maximum brightness 60 or 120 times per second? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 73

$\mathrm{CE}$ An inductor in an $L C$ circuit has a maximum current of $2.4 \mathrm{A}$ and a maximum energy of $36 \mathrm{mJ}$. When the current in the inductor is $1.2 \mathrm{A},$ what is the energy stored in the capacitor?

Abhishek Jana

Numerade Educator

Problem 74

CE An $R L C$ circuit is driven at its resonance frequency. Is its impedance greater than, less than, or equal to $R$ ? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 75

CE Predict/Explain Suppose the circuits shown in Figures $24-29$ and $24-31$ are connected to identical batteries, rather than to ac generators. (a) Assuming the value of $R$ is the same in the two circuits, is the current in Figure $24-29$ greater than, less

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 75

CE Predict/Explain Suppose the circuits shown in Figures $24-29$ and $24-31$ are connected to identical batteries, rather than to ac generators.
(a) Assuming the value of $R$ is the same in the two circuits, is the current in Figure $24-29$ greater than, less than, or the same as the current in Figure $24-31 ?$ (b) Choose the best explanation from among the following:
I. The circuits have the same current because the capacitor acts like an open circuit and the inductor acts like a short circuit.
II. The current in Figure $24-29$ is larger because it has more circuit elements, each of which can carry current.
III. The current in Figure $24-31$ is larger because it has fewer circuit elements, meaning less resistance to current flow.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 76

CE Suppose the circuits shown in Figures $24-30$ and $24-31$ are connected to identical batteries, rather than to ac generators. Assuming the value of $R$ is the same in the two circuits, is the current in Figure $24-30$ greater than, less than, or the same as the current in Figure $24-31$ ? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 77

CE Predict/Explain Consider a circuit consisting of a lightbulb and a capacitor, as shown in circuit 2 of Conceptual Checkpoint $24-2 .$ (a) If the frequency of the generator is increased, does the intensity of the lightbulb increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. As the frequency increases it becomes harder to force current through the capacitor, and therefore the intensity of the lightbulb decreases.
II. The intensity of the lightbulb increases because as the frequency becomes higher the capacitor acts more like a short circuit, allowing more current to flow.
III. The intensity of the lightbulb is independent of frequency because the circuit contains a capacitor but not an inductor.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 78

CE Consider a circuit consisting of a lightbulb and an inductor, as shown in Conceptual Checkpoint $24-3$. If the frequency of the generator is increased, does the intensity of the lightbulb increase, decrease, or stay the same? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 79

A $4.40-\mu \mathrm{F}$ and an $8.80-\mu \mathrm{F}$ capacitor are connected in parallel to
a $60.0-\mathrm{Hz}$ generator operating with an rms voltage of $115 \mathrm{V}$ What is the rms current supplied by the generator?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 80

$\bullet \mathrm{A} 4.40-\mu \mathrm{F}$ and an $8.80-\mu \mathrm{F}$ capacitor are connected in series to a $60.0-\mathrm{Hz}$ generator operating with an $\mathrm{rms}$ voltage of $115 \mathrm{V} .$ What is the rms current supplied by the generator?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 81

$\bullet \mathrm{A} 10.0-\mu \mathrm{F}$ capacitor and a $30.0-\mu \mathrm{F}$ capacitor are connected in parallel to an ac generator with a frequency of $60.0 \mathrm{Hz}$. What is the capacitive reactance of this pair of capacitors?

Kayla Gephart

Numerade Educator

Problem 82

$\bullet$ CE A generator drives an $R L C$ circuit with the voltage $V$ shown in Figure $24-33 .$ The corresponding current $I$ is also shown in the figure. (a) Is the inductive reactance of this circuit greater than, less than, or equal to its capacitive reactance? Explain.
(b) Is the frequency of this generator greater than, less than, or equal to the resonance frequency of the circuit? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 83

- - IP Consider the $R L C$ circuit shown in Example $24-6$, and the corresponding phasor diagram given in the Insight. (a) On the basis of the phasor diagram, can you conclude that the resonance frequency of this circuit is greater than, less than, or equal to $60.0 \mathrm{Hz}$ ? Explain. (b) Calculate the resonance frequency for this circuit. (c) The impedance of this circuit at $60.0 \mathrm{Hz}$ is $226 \Omega$. What is the impedance at resonance?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 84

P When a certain resistor is connected to an ac generator with a maximum voltage of $15 \mathrm{V},$ the average power dissipated in the resistor is 22 W. (a) What is the resistance of the resistor? (b) What is the rms current in the circuit? (c) We know that $P_{\mathrm{ar}}=I_{\mathrm{rms}}^{2} R,$ and hence it seems that reducing the resistance should reduce the average power. On the other hand, we also know that $P_{a v}=V_{\text {rms }}^{2} / R,$ which suggests that reducing $R$ increases $P_{a v}$. Which conclusion is correct? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 85

A 9.5-Hz generator is connected to a capacitor. If the current in the generator has its maximum value at $t=0,$ what is the earliest possible time that the voltage across the capacitor is a maximum?

Vishal Gupta

Numerade Educator

Problem 86

The voltage across an inductor reaches its maximum value $25 \mathrm{ms}$ before the current supplied by the generator reaches its maximum value. What is the lowest possible frequency at which the generator operates?

Sachin Rao

Numerade Educator

Problem 87

Find the average power consumed by an $R C$ circuit connected to a $60.0-\mathrm{Hz}$, generator with an rms voltage of $122 \mathrm{V}$. The values of $R$ and $C$ in this circuit are $3.30 \mathrm{k} \Omega$ and $2.75 \mu \mathrm{F},$ respectively.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 88

A $1.15-k \Omega$ resistor and a $505-\mathrm{mH}$ inductor are connected in series to a $1250-\mathrm{Hz}$ generator with an rms voltage of $14.2 \mathrm{V}$.
(a) What is the rms current in the circuit? (b) What capacitance must be inserted in series with the resistor and inductor to reduce the rms current to half the value found in part (a)?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 89

IP $R L C$ Phasor The phasor diagram for an $R L C$ circuit is shown in Figure $24-34 .$ (a) If the resistance in this circuit is $525 \Omega$, what is the impedance? (b) If the frequency in this circuit is increased, will the impedance increase, decrease, or stay the same? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 90

IP Figure $24-34$ shows the phasor diagram for an $R L C$ circuit in which the impedance is $337 \Omega .$ (a) What is the resistance, $R,$ in this circuit? (b) Is this circuit driven at a frequency that is greater than, less than, or equal to the resonance frequency of the circuit? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 91

IP An RLC circuit has a resistance $R=25 \mathrm{A}$ and an inductance $L=160 \mathrm{mH},$ and is connected to an ac generator with a frequency of $55 \mathrm{Hz}$. The phasor diagram for this circuit is shown in Figure $24-34 .$ Find $(a)$ the impedance, $Z,$ and $(b)$ the capacitance, $C$, for this circuit. (c) If the value of $C$ is decreased, will the impedance of the circuit increase, decrease, or stay the same? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 92

IP Black-Box Experiment You are given a sealed box with two electrical terminals. The box contains a $5.00-\Omega$ resistor in
series with either an inductor or a capacitor. When you attach an ac generator with an rms voltage of $0.750 \mathrm{V}$ to the terminals of the box, you find that the current increases with increasing frequency.
(a) Does the box contain an inductor or a capacitor?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 93

IP A circuit is constructed by connecting a $1.00-\mathrm{k} \Omega$ resistor, a $252-\mu \mathrm{F}$ capacitor, and a $515-\mathrm{mH}$ inductor in series.
(a) What is the highest frequency at which the impedance of this circuit is equal to $2.00 \mathrm{k} \Omega ?$
(b) To reduce the impedance of this circuit, should the frequency be increased or decreased from its value in part (a)? Explain.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 94

An $R L C$ circuit with $R=25.0 \Omega, L=325 \mathrm{mH},$ and $C=$ $45.2 \mu \mathrm{F}$ is connected to an ac generator with an $\mathrm{rms}$ voltage of 24 V. Determine the average power delivered to this circuit when the frequency of the generator is (a) equal to the resonance frequency, (b) twice the resonance frequency, and (c) half the resonance frequency.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 95

A Light-Dimmer Circuit The intensity of a lightbulb with a resistance of $120 \Omega$ is controlled by connecting it in series with an inductor whose inductance can be varied from $L=0$ to $L=L_{\text {max }}$. This "light dimmer" circuit is connected to an ac generator with a frequency of $60.0 \mathrm{Hz}$ and an rms voltage of $110 \mathrm{V}$.
(a) What is the average power dissipated in the lightbulb when $L=0 ?$ (b) The inductor is now adjusted so that $L=L_{\max } .$ In this case, the average power dissipated in the lightbulb is onefourth the value found in part (a). What is the value of $L_{\max } ?$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 96

An electric motor with a resistance of $15 \mathrm{A}$ and an inductance of $53 \mathrm{mH}$ is connected to a $60.0-\mathrm{Hz}$ ac generator. (a) What is the power factor for this circuit? (b) In order to increase the power factor of this circuit to $0.80,$ a capacitor is connected in series with the motor and inductor. Find the required value of the capacitance.

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 97

IP Tuning a Radio A radio tuning circuit contains an RLC circuit with $R=5.0 \Omega$ and $L=2.8 \mu \mathrm{H.}$ (a) What capacitance is needed to produce a resonance frequency of $85 \mathrm{MHz}$ ? (b) If the capacitance is increased above the value found in part (a), will the impedance increase, decrease, or stay the same? Explain. (c) Find the impedance of the circuit at reso-
nance.
(d) Find the impedance of the circuit when the capacitance is $1 \%$ higher than the value found in part (a).

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 98

If the maximum voltage in the square wave shown in Figure $24-27$ is $V_{\max },$ what are $(a)$ the average voltage, $V_{a v},$ and
(b) the rms voltage, $V_{\text {rms }}$ ?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 99

$\bullet$ An ac generator supplies an rms voltage of $5.00 \mathrm{V}$ to an $R C$ circuit. At a frequency of $20.0 \mathrm{kHz}$ the rms current in the circuit is $45.0 \mathrm{mA} ;$ at a frequency of $25.0 \mathrm{kHz}$ the rms current is $50.0 \mathrm{mA}$. What are the values of $R$ and $C$ in this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 100

An ac generator supplies an rms voltage of $5.00 \mathrm{V}$ to an $\mathrm{RL}$ circuit. At a frequency of $20.0 \mathrm{kHz}$ the rms current in the circuit is $45.0 \mathrm{mA} ;$ at a frequency of $25.0 \mathrm{kHz}$ the rms current is $40.0 \mathrm{mA}$. What are the values of $R$ and $L$ in this circuit?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 101

An $R C$ circuit consists of a resistor $R=32 \Omega$, a capacitor $C=25 \mu F,$ and an ac generator with an rms voltage of $120 \mathrm{V}$
(a) At what frequency will the rms current in this circuit be 2.9 A? For this frequency, what are (b) the rms voltage across the resistor, $V_{\text {rms. } R}$, and
(c) the rms voltage across the capacitor, $V_{\mathrm{rms}} c^{2}$ (d) Show that $V_{\mathrm{rms}, \mathrm{R}}+V_{\mathrm{rms}, \mathrm{C}}>120 \mathrm{V},$ but that
$\sqrt{V_{\mathrm{rms}, R}^{2}+V_{\mathrm{rms}, \mathcal{C}}^{2}}=120 \mathrm{V}$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 102

$\bullet$ Suppose a theremin uses an oscillator with a fixed frequency of
$90.1 \mathrm{MHz}$ and an $\mathrm{RLC}$ circuit with $R=1.5 \mathrm{\Omega}, L=2.08 \mu \mathrm{H},$ and
$C=1.50 \mathrm{pF.What}$ is the beat frequency of these two oscillators? (Audio frequencies range from about $20 \mathrm{Hz}$ to $20,000 \mathrm{Hz}$.)
A. $3740 \mathrm{Hz}$
B. $5100 \mathrm{Hz}$
C. $4760 \mathrm{Hz}$
D. $9000 \mathrm{Hz}$

Prem Bijarniya

Numerade Educator

Problem 103

If the thereminist moves one of her fingers and increases the capacitance of the system slightly, does the beat frequency increase, decrease, or stay the same?

Vysakh M

Numerade Educator

Problem 104

What is the rms current in the theremin's $R L C$ circuit (Problem 102 ) if it is attached to an ac generator with an rms voltage of $25.0 \mathrm{V}$ and a frequency of $90.0 \mathrm{MHz}$ ?
A. $2.14 \mathrm{m} \mathrm{A}$
B. $3.46 \mathrm{m} \mathrm{A}$
$\mathrm{C} .8 .06 \mathrm{A}$
D. $16.7 \mathrm{A}$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 105

What is the rms current in the theremin's $R L C$ circuit (Problem 102 ) if it is attached to an ac generator with an rms voltage of $25.0 \mathrm{V}$ and a frequency of $90.0 \mathrm{MHz}$ ?
A. $2.14 \mathrm{mA}$
B. $3.46 \mathrm{m} \mathrm{A}$
C. $8.06 \mathrm{A}$
D. $16.7 \mathrm{A}$

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 106

IP Referring to Example $24-6$ Suppose we would like to change the phase angle for this circuit to $\phi=-25.0^{\circ}$, and that we would like to accomplish this by changing the resistor to a value other than $175 \Omega$. The inductor is still $90.0 \mathrm{mH}$, the capacitor is $15.0 \mu \mathrm{F}$, the rms voltage is $120.0 \mathrm{V}$, and the ac frequency is $60.0 \mathrm{Hz}$. (a) Should the resistance be increased or decreased? Explain. (b) Find the resistance that gives the desired phase angle. (c) What is the rms current in the circuit with the resistance found in part (b)?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator

Problem 107

IP Referring to Example $24-6$ You plan to change the frequency of the generator in this circuit to produce a phase angle of smaller magnitude. The resistor is still $175 \Omega$, the inductor is $90.0 \mathrm{mH},$ the capacitor is $15.0 \mu \mathrm{F},$ and the rms voltage is $120.0 \mathrm{V}$
(a) Should you increase or decrease the frequency? Explain.
(b) Find the frequency that gives a phase angle of $-22.5^{\circ}$
(c) What is the rms current in the circuit at the frequency found in part (b)?

João Gabriel Alencar Caribé

João Gabriel Alencar Caribé

Numerade Educator