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College Physics 2017

Raymond A. Serway, Chris Vuille, John hughes

Chapter 21

Alternating- Current Circuits and Electromagnetic Waves

Educators


Problem 1

(a) What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60.0 - Hz power source having a maximum voltage of 170. V? (b) What is the resistance of a 100. - W lightbulb?

Salamat A.
Numerade Educator

Problem 2

A certain lightbulb is rated at 60.0 W when operating at an rms voltage of 120. V. (a) What is the peak voltage applied across the bulb? (b) What is the resistance of the bulb? (c) Does a 100. - W bulb have greater or less resistance than a 60.0 - W bulb? Explain.

Averell H.
Carnegie Mellon University

Problem 3

A 1.5 $-k \Omega$ resistor is connected to an AC voltage source with an rms voltage of 120 V. (a) What is the maximum voltage across the resistor? (b) What is the maximum current through the resistor? (c) What is the rms current through the resistor? (d) What is the average power dissipated by the resistor?

Salamat A.
Numerade Educator

Problem 4

Figure P21.4 shows three lamps connected to a 120. - V AC (rms) household supply voltage. Lamps 1 and 2 have 150 - W bulbs; lamp 3 has a 100. - W bulb. For each bulb, find (a) the rms current and (b) the resistance.

Averell H.
Carnegie Mellon University

Problem 5

A $24.0-k \Omega$ resistor connected to an AC voltage source dissipates an average power of 0.600 W. (a) Calculate the rms current in the resistor. (b) Calculate the rms voltage of the AC source.

Salamat A.
Numerade Educator

Problem 6

The output voltage of an AC generator is given by $\Delta v=$ $(170 \mathrm{V}) \sin (60 \pi t) .$ The generator is connected across a $20.0=\Omega$ By inspection, what are the (a) maximum voltage and (b) frequency? Find the (c) rms voltage across the resistor, (d) rms current in the resistor, (e) maximum current in the resistor, (f) power delivered to the resistor, and (g) current when t 5 0.005 0 s. (h) Should the argument of the sine function be in degrees or radians?

Averell H.
Carnegie Mellon University

Problem 7

(a) For what frequencies does a 22.0 - mF capacitor have a reactance below 175$\Omega ?$ (b) What is the reactance of a 44.0 -$\mu \mathrm{F}$capacitor over this same frequency range?

Salamat A.
Numerade Educator

Problem 8

North American outlets supply AC electricity with a frequency of f 5 60.0 Hz while the European standard is f 5 50.0 Hz. What value of capacitance provides a capacitive reactance of 1.00 $\mathrm{k\Omega}$ (a) in North America and (b) in Europe?

Averell H.
Carnegie Mellon University

Problem 9

When a $4.0-\mu \mathrm{F}$ capacitor is connected to a generator whose rms output is 30. V, the current in the circuit is observed to be 0.30 A. What is the frequency of the source?

Salamat A.
Numerade Educator

Problem 10

An AC generator with an output rms voltage of 36.0 V at a frequency of 60.0 Hz is connected across a $12.0-\mu \mathrm{F}$ capacitor. Find the (a) capacitive reactance, (b) rms current, and (c) maximum current in the circuit. (d) Does the capacitor have its maximum charge when the current takes its maximum value? Explain.

Averell H.
Carnegie Mellon University

Problem 11

What maximum current is delivered by an AC source with $\Delta V_{\max }=48.0 \mathrm{V}$ and $f=90.0 \mathrm{Hz}$ when connected across a $3.70-\mu \mathrm{F}$ capacitor?

Salamat A.
Numerade Educator

Problem 12

A generator delivers an AC voltage of the form $\Delta v=(98.0 \mathrm{V})$ sin $(80 \pi t)$ to a capacitor. The maximum current in the circuit is 0.500 A. Find the (a) rms voltage of the generator, (b) frequency of the generator, (c) rms current, (d) reactance, and (e) value of the capacitance.

Averell H.
Carnegie Mellon University

Problem 13

An inductor has a $54.0-\Omega$ reactance when connected to a 60.0 -Hz source. The inductor is removed and then connected to a 50.0 - Hz source that produces a 100. - V rms voltage. What is the maximum current in the inductor?

Salamat A.
Numerade Educator

Problem 14

An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 47 - H inductor, determine (a) the inductive reactance and (b) the rms current through the inductor.

Averell H.
Carnegie Mellon University

Problem 15

In a purely inductive AC circuit as shown in Figure $\mathrm{P} 21.15, \Delta V_{\max }=100 . \mathrm{V}$ (a) The maximum current is 7.50 A at 50.0 Hz. Calculate the inductance L. (b) At what angular frequency v is the maximum current 2.50 A?

Salamat A.
Numerade Educator

Problem 16

The output voltage of an AC generator is given by $\Delta v=$ $(1.20 \times 10^{2} \mathrm{V}) \sin (30 \pi t)$ The generator is connected across a 0.500 - H inductor. Find the (a) frequency of the generator, (b) rms voltage across the inductor, (c) inductive reactance, (d) rms current in the inductor, (e) maximum current in the inductor, and (f) average power delivered to the inductor. (g) Find an expression for the instantaneous current. (h) At what time after t 5 0 does the instantaneous current first reach 1.00 A? (Use the inverse sine function.)

Averell H.
Carnegie Mellon University

Problem 17

Determine the maximum magnetic flux through an inductor connected to a standard outlet $\left(\Delta V_{\mathrm{rms}}=120 . \mathrm{V}, f=60.0 \mathrm{Hz}\right)$

Salamat A.
Numerade Educator

Problem 18

A sinusoidal voltage $\Delta v=(80.0 \mathrm{V})$ sin $(150 t)$ is applied to a series RLC circuit with $L=80.0 \mathrm{mH}, C=125.0 \mu \mathrm{F},$ and $R=$ 40.0$\Omega$ . (a) What is the impedance of the circuit? (b) What is the maximum current in the circuit?

Averell H.
Carnegie Mellon University

Problem 19

A series $R L C$ circuit has resistance $R=50.0 \Omega$ and inductance L 5 0.500 H. (a) Find the circuit’s capacitance C if the voltage source operates at a frequency of f 5 60.0 Hz and the impedance is Z 5 $R=50.0 \Omega$ (b) What is the phase angle between the current and the voltage?

Salamat A.
Numerade Educator

Problem 20

An inductor $(L=400 . \mathrm{mH}),$ a capacitor $(C=4.43 \mu \mathrm{F})$ and a resistor $(R=500 . \Omega)$ are connected in series. A 50.0 - Hz AC generator connected in series to these elements produces a maximum current of 250 mA in the circuit. (a) Calculate the required maximum voltage $\Delta V_{\max }$ (b) Determine the phase angle by which the current leads or lags the applied
voltage.

Averell H.
Carnegie Mellon University

Problem 21

A resistor $\left(R=9.00 \times 10^{2} \Omega\right),$ a capacitor $(C=0.250 \mu \mathrm{F})$ and an inductor (L 5 2.50 H) are connected in series across a $2.40 \times 10^{2}-\mathrm{Hz}$ AC source for which $\Delta V_{\mathrm{max}}=1.40 \times 10^{2} \mathrm{V}$ Calculate (a) the impedance of the circuit, (b) the maximum current delivered by the source, and (c) the phase angle between the current and voltage. (d) Is the current leading or lagging the voltage?

Salamat A.
Numerade Educator

Problem 22

A $50.0-\Omega$ resistor, a $0.100-\mathrm{H}$ inductor, and a $10.0-\mu \mathrm{F}$ capacitor are connected in series to a 60.0 - Hz source. The rms current in the circuit is 2.75 A. Find the rms voltages across (a) the resistor, (b) the inductor, (c) the capacitor, and (d) the RLC combination. (e) Sketch the phasor diagram for this circuit.

Averell H.
Carnegie Mellon University

Problem 23

A series $R L C$ circuit has resistance $R=12.0 \Omega,$ inductive reactance $X_{L}=30.0 \Omega,$ and capacitive reactance $X_{C}=20.0 \Omega$ . If the maximum voltage across the resistor is $\Delta V_{R}=145 \mathrm{V}$ , find the maximum voltage across (a) the inductor and (b) the capacitor. (c) What is the maximum current in the circuit? (d) What is the circuit’s impedance?

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Problem 24

An AC source operating at $60 . \mathrm{Hz}$ with a maximum voltage of 170 $\mathrm{V}$ is connected in series with a resistor $(R=1.2 \mathrm{k} \Omega)$ and an inductor (L 5 2.8 H). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potential difference across the resistor and the inductor? (c) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the inductor, and the AC source? (d) When the current is zero, what are the magnitudes of the potential difference across the resistor, the inductor, and the AC source?

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Problem 25

A person is working near the secondary of a transformer, as shown in Figure P21.25. The primary voltage is 120. V (rms) at 60.0 Hz. The capacitance $C_{s}$ which is the stray capacitance between the hand and the secondary winding, is 20.0 pF. Assuming the person has a body resistance to ground of $R_{b}=50.0 \mathrm{k} \Omega$ determine the rms voltage across the body. Hint: Redraw the circuit with the secondary of the transformer as a simple AC source.

Salamat A.
Numerade Educator

Problem 26

A 60.0 - $\Omega$ resistor is connected in series with a $30.0-\mu \mathrm{F}$ capacitor and a generator having a maximum voltage of $1.20 \times 10^{2} \mathrm{V}$ and operating at 60.0 Hz. Find the (a) capacitive reactance of the circuit, (b) impedance of the circuit, and (c) maximum current in the circuit. (d) Does the voltage lead or lag the current? (e) How will putting an inductor in series with the existing capacitor and resistor affect the current? Explain.

Averell H.
Carnegie Mellon University

Problem 27

A series AC circuit contains a resistor, an inductor of 150. mH, a capacitor of $5.00 \mu \mathrm{F},$ and a generator with $\Delta V_{\max }=$ 240. V operating at 50.0 Hz. The maximum current in the cir-
cuit is 100. mA. Calculate (a) the inductive reactance, (b) the capacitive reactance, (c) the impedance, (d) the resistance in the circuit, and (e) the phase angle between the current and the generator voltage.

Salamat A.
Numerade Educator

Problem 28

At what frequency does the inductive reactance of a $57.0-\mu \mathrm{H}$ inductor equal the capacitive reactance of a $57.0-\mu \mathrm{F}$ capacitor?

Averell H.
Carnegie Mellon University

Problem 29

An AC source with a maximum voltage of 150. V and f = 50.0 Hz is connected between points a and d in Figure P21.29. Calculate the rms voltages between points (a) a and b, (b) b and c, (c) c and d, and (d) b and d.

Salamat A.
Numerade Educator

Problem 30

An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor $(R=1.2 \mathrm{k} \Omega)$ and a capacitor $(C=2.5 \mu \mathrm{F})$ (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potential difference across the resistor and the capacitor? (c) When the current is zero, what are the magnitudes of the potential difference across the resistor, the capacitor, and the AC source? How much charge is on the capacitor at
this instant? (d) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the capacitor, and the AC source? How much charge is on the capacitor at this instant?

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Problem 31

A multimeter in an RL circuit records an rms current of 0.500 A and a 60.0 - Hz rms generator voltage of 104 V. A wattmeter shows that the average power delivered to the resistor is 10.0 W. Determine (a) the impedance in the circuit, (b) the resistance R , and (c) the inductance L.

Salamat A.
Numerade Educator

Problem 32

An AC voltage of the form $\Delta v=(90.0 \mathrm{V})$ sin $(350 t)$ is applied to a series $R L C$ circuit. If $R=50.0 \Omega, C=25.0 \mu \mathrm{F}$ and $L=0.200 \mathrm{H}$ , find the (a) impedance of the circuit, (b) rms current in the circuit, and (c) average power delivered to the circuit.

Averell H.
Carnegie Mellon University

Problem 33

An $R L C$ circuit has resistance $R=225 \Omega$ and inductive reactance $X_{L}=175$ \Omega. (a) Calculate the circuit's capacitive reactance $X_{C}$ if its power factor is $\cos \phi=0.707 .$ Repeat the
calculation for $(b) \cos \phi=1.00$ and $(c) \cos \phi=1.00 \times 10^{-2}$

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Problem 34

A series $R L C$ circuit has a resistance of 22.0$\Omega$ and an impedance of 80.0$\Omega$ . If the rms voltage applied to the circuit is $160 . \mathrm{V},$ what average power is delivered to the circuit?

Averell H.
Carnegie Mellon University

Problem 35

An inductor and a resistor are connected in series. When connected to a 60. - Hz, 90. - V (rms) source, the voltage drop across the resistor is found to be 50. V (rms) and the power delivered to the circuit is 14 W. Find (a) the value of the resistance and (b) the value of the inductance.

Salamat A.
Numerade Educator

Problem 36

Consider a series RLC circuit with $R=25 \Omega, L=6.0 \mathrm{mH}$ and $C=25 \mu \mathrm{F}$ The circuit is connected to a 10. - V (rms), 600. - Hz AC source. (a) Is the sum of the voltage drops across R , L, and C equal to 10. V (rms)? (b) Which is greatest, the power delivered to the resistor, to the capacitor, or to the inductor? (c) Find the average power delivered to the circuit.

Averell H.
Carnegie Mellon University

Problem 37

An RLC circuit is used in a radio to tune into an FM station broadcasting at f 5 99.7 MHz. The resistance in the circuit is $R=12.0 \Omega,$ and the inductance is $L=1.40 \mu \mathrm{H}$ . What capacitance should be used?

Salamat A.
Numerade Educator

Problem 38

The resonant frequency of a certain series $R L C$ circuit is 2.84 $\mathrm{kHz}$ , and the value of its capacitance is 6.50$\mu \mathrm{F}$ . What is the value of the resonant frequency when the capacitance of the circuit is 9.80$\mu \mathrm{F}^{2}$

Averell H.
Carnegie Mellon University

Problem 39

The AM band extends from approximately 500. kHz to $1600, \mathrm{kHz}$ . If a $2.0-\mu \mathrm{H}$ mH inductor is used in a tuning circuit for a radio, what are the extremes that a capacitor must reach to cover the complete band of frequencies?

Salamat A.
Numerade Educator

Problem 40

Electrosurgical units (ESUs) supply high - frequency electricity from resonant RLC circuits to cut, coagulate, or otherwise modify biological tissue. (a) Find the resonant frequency of an $\mathrm{ESU}$ with an inductance of $L=1.25 \mu \mathrm{H}$ and a capacitance of 47.0 nF. (b) Calculate the capacitance required for a resonant frequency of 1.33 MHz.

Averell H.
Carnegie Mellon University

Problem 41

Two electrical oscillators are used in a heterodyne metal detector to detect buried metal objects (see
Fig. P21.41). The detector uses two identical electrical oscillators in the form of LC circuits having resonant frequencies of 725 kHz. When the signals from the two oscillating circuits are combined, the beat frequency is zero because each has the same resonant frequency. However, when the coil of
one circuit encounters a buried metal object, the inductance of this circuit increases by 1.000%, while that of the second is unchanged. Determine the beat frequency that would be detected in this situation.

Salamat A.
Numerade Educator

Problem 42

A series circuit contains a 3.00 - H inductor, a 3.00 - mF capacitor, and a 30.0 - V resistor connected to a 120. - V (rms) source of variable frequency. Find the power delivered to the circuit when the frequency of the source is (a) the resonance frequency, (b) one - half the resonance frequency, (c) one - fourth
the resonance frequency, (d) two times the resonance frequency, and (e) four times the resonance frequency. From your calculations, can you draw a conclusion about the frequency at which the maximum power is delivered to the circuit?

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Problem 43

The primary coil of a transformer has $N_{1}=250 .$ turns, and its secondary coil has $N_{2}=1500$ . turns. If the input voltage across the primary coil is $\Delta v=(170 . \mathrm{V})$ sin $\omega t,$ what rms voltage is developed across the secondary coil?

Salamat A.
Numerade Educator

Problem 44

A step - down transformer is used for recharging the batteries of portable devices. The turns ratio $N_{2} / N_{1}$ for a particular transformer used in a CD player is 1:13. When used with 120. - V (rms) household service, the transformer draws an rms current of 250. mA. Find the (a) rms output voltage of the transformer and (b) power delivered to the CD player.

Averell H.
Carnegie Mellon University

Problem 45

An AC power generator produces 50. A (rms) at 3 600 V. The voltage is stepped up to $1.0 \times 10^{5} \mathrm{V}$ by an ideal transformer, and the energy is transmitted through a long - distance power
line that has a resistance of $100 . \Omega$ What percentage of the power delivered by the generator is dissipated as heat in the power line?

Salamat A.
Numerade Educator

Problem 46

An ideal neon sign transformer provides 9 250 V at 30.0 mA with an input voltage of 115 V. Calculate the transformer’s input (a) power and (b) current.

Averell H.
Carnegie Mellon University

Problem 47

A transformer on a pole near a factory steps the voltage down from 3600 V (rms) to 120 V (rms). The transformer is to deliver $1.0 \times 10^{3} \mathrm{kW}$ to the factory at 90% efficiency. Find
(a) the power delivered to the primary, (b) the current in the primary, and (c) the current in the secondary.

Salamat A.
Numerade Educator

Problem 48

A transmission line that has a resistance per unit length of $4.50 \times 10^{-1} \Omega / \mathrm{m}$ is to be used to transmit 5.00 MW over 400 miles $\left(6.44 \times 10^{5} \mathrm{m}\right)$ The output voltage of the generator is 4.50 kV (rms). (a) What is the line loss if a transformer is used to step up the voltage to 500. kV (rms)? (b) What fraction of the input power is lost to the line under these circumstances? (c) What difficulties would be encountered on attempting to transmit the 5.00 MW at the generator voltage of 4.50 kV (rms)?

Averell H.
Carnegie Mellon University

Problem 49

The U.S. Navy has long proposed the construction of extremely low frequency (ELF waves) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter - wavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this antenna?

Salamat A.
Numerade Educator

Problem 50

(a) The distance to Polaris, the North Star, is approximately $6.44 \times 10^{18} \mathrm{m}$ . If Polaris were to burn out today, how many years would it take to see it disappear? (b) How long does
it take sunlight to reach Earth? (c) How long does it take a microwave signal to travel from Earth to the Moon and back? (The distance from Earth to the Moon is $3.84 \times 10^{5} \mathrm{km} . )$

Averell H.
Carnegie Mellon University

Problem 51

The Earth reflects approximately 38.0% of the incident sunlight from its clouds and surface. (a) Given that the intensity of solar radiation at the top of the atmosphere is 1 370 W/m2 , find the radiation pressure on the Earth, in pascals, at the location where the Sun is straight overhead. (b) State how this quantity compares with normal atmospheric pressure at the Earth’s surface, which is 101 kPa.

Salamat A.
Numerade Educator

Problem 52

The speed of light in vacuum is defined to be $c=299792458 \mathrm{m} / \mathrm{s}=1 / \sqrt{\mu_{0} \epsilon_{0}}$ . The permeability constant of vacuum is defined to be $\mu_{0}=4 \pi \times 10^{-7} \mathrm{N} \cdot \mathrm{s}^{2} / \mathrm{C}^{2}$ . Use these definitions to calculate the value of $\epsilon_{0},$ the permittivity of free space, to eight significant figures.

Averell H.
Carnegie Mellon University

Problem 53

Oxygenated hemoglobin absorbs weakly in the red (hence its red color) and strongly in the near infrared, whereas deoxygenated hemoglobin has the opposite absorption. This fact is used in a “pulse oximeter” to measure oxygen saturation in arterial blood. The device clips onto the end of a person’s finger and has two light - emitting diodes—a red (660. nm) and an infrared (940. nm)—and a photocell that detects the amount of light transmitted through the finger at each wavelength. (a) Determine the frequency of each of these light sources. (b) If 67% of the energy of the red source is absorbed in the blood, by what factor does the amplitude of the electromagnetic wave change? Hint: The intensity of the wave is equal to the average power per unit area as given by Equation 21.28.

Salamat A.
Numerade Educator

Problem 54

Operation of the pulse oximeter (see previous problem). The transmission of light energy as it passes through a solution of light - absorbing molecules is described by the Beer–Lambert law
$$I=I_{0} 10^{-e C L} \quad$ or $\quad \log _{10}\left(\frac{I}{I_{0}}\right)=-\epsilon C L$$
which gives the decrease in intensity I in terms of the distance L the light has traveled through a fluid with a concentration C of the light - absorbing molecule. The quantity $\epsilon$ is called the
extinction coefficient, and its value depends on the frequency of the light. (It has units of $\mathrm{m}^{2} / \mathrm{mol} . )$ Assume the extinction coefficient for 660 - nm light passing through a solution of oxygenated hemoglobin is identical to the coefficient for 940 - nm light passing through deoxygenated hemoglobin. Also assume 940 - nm light has zero absorption $(\epsilon=0)$ in oxygenated hemoglobin and 660 - nm light has zero absorption in deoxygenated hemoglobin. If 33% of the energy of the red source and 76% of the infrared energy is transmitted
through the blood, what is the fraction of hemoglobin that is oxygenated?

Averell H.
Carnegie Mellon University

Problem 55

The Sun delivers an average power of $1370 . \mathrm{W} / \mathrm{m}^{2}$ to the top of Earth's atmosphere. Find the magnitudes of $\overrightarrow{\mathrm{E}}_{\max }$ and $\overrightarrow{\mathrm{B}}_{\max }$ for the electromagnetic waves at the top of the atmosphere.

Salamat A.
Numerade Educator

Problem 56

A laser beam is used to levitate a metal disk against the force of Earth’s gravity. (a) Derive an equation giving the required intensity of light, I, in terms of the mass m of the disk, the gravitational acceleration g , the speed of light c, and the cross - sectional area of the disk A. Assume the disk is perfectly reflecting and the beam is directed perpendicular to the disk. (b) If the disk has mass 5.00 g and radius 4.00 cm, find the necessary light intensity. (c) Give two reasons why using light pressure as propulsion near Earth’s surface is impractical.

Averell H.
Carnegie Mellon University

Problem 57

A microwave oven is powered by an electron tube called a magnetron that generates electromagnetic waves of frequency 2.45 GHz. The microwaves enter the oven and are reflected
by the walls. The standing - wave pattern produced in the oven can cook food unevenly, with hot spots in the food at antinodes and cool spots at nodes, so a turntable is often used to rotate the food and distribute the energy. If a microwave oven is used with a cooking dish in a fixed position, the antinodes can appear as burn marks on foods such as carrot strips or cheese. The separation distance between the burns is measured to be 6.00 cm. Calculate the speed of the microwaves from these data.

Salamat A.
Numerade Educator

Problem 58

Consider a bright star in our night sky. Assume its distance from the Earth is 20.0 light - years (ly) and its power output is $4.00 \times 10^{28}$W, about 100 times that of the Sun. (a) Find the intensity of the starlight at the Earth. (b) Find the power of the starlight the Earth intercepts. One light - year is the distance traveled by light through a vacuum in one year.

Averell H.
Carnegie Mellon University

Problem 59

What are the wavelengths of clectromagnetic waves in free space that have frequencies of (a) $5.00 \times 10^{19} \mathrm{Hz}$ and (b) $4.00 \times 10^{9} \mathrm{Hz}$ ?

Salamat A.
Numerade Educator

Problem 60

A diathermy machine, used in physiotherapy, generates electromagnetic radiation that gives the effect of “deep heat” when absorbed in tissue. One assigned frequency for diathermy is 27.33 MHz. What is the wavelength of this radiation?

Averell H.
Carnegie Mellon University

Problem 61

What are the wavelength ranges in (a) the AM radio band (540–1 600 kHz) and (b) the FM radio band (88–108 MHz)?

Salamat A.
Numerade Educator

Problem 62

An important news announcement is transmitted by radio waves to people who are 100. km away, sitting next to their radios, and by sound waves to people sitting across the news- room, 3.0 m from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s.

Averell H.
Carnegie Mellon University

Problem 63

The rainbow of visible colors in the electromagnetic spectrum varies continuously from the longest wavelengths (the reddest colors) to the shortest wavelengths (the deepest violet colors) our eyes can detect. Wavelengths near 655 nm are perceived as red. Those near 515 nm are green and those near 475 nm are blue. Calculate the frequency of light with a wavelength of (a) 655 nm, (b) 515 nm, and (c) 475 nm.

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Problem 64

A spaceship is approaching a space station at a speed of $1.8 \times$ $10^{5} \mathrm{m} / \mathrm{s}$ . The space station has a beacon that emits green lightwith a frequency of $6.0 \times
10^{14} \mathrm{Hz}$ (a) What is the frequency of the beacon observed on the spaceship? (b) What is the change in frequency? (Carry five digits in these calculations.)

Averell H.
Carnegie Mellon University

Problem 65

Police radar guns measure the speed of moving vehicles by transmitting electromagnetic waves at a vehicle and detecting a Doppler shift in the reflected wave. Suppose police radar transmits at a frequency of 24.0 GHz and receives a wave reflected from a car moving toward the radar at 65.0 mph. Find the frequency shift $\Delta f=f_{O}-f_{S}$ between the observed (received) and source (transmitted) frequencies.

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Problem 66

A speeder tries to explain to the police that the yellow warning lights she was approaching on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength 580 nm had been shifted to green with a wavelength of 560 nm? Note: For
speeds less than 0.03c, Equation 21.32 will lead to a value for the observed frequency accurate to approximately two significant digits.

Averell H.
Carnegie Mellon University

Problem 67

A 25.0 - mW laser beam of diameter 2.00 mm is reflected at normal incidence by a perfectly reflecting mirror. Calculate the radiation pressure on the mirror.

Salamat A.
Numerade Educator

Problem 68

The intensity of solar radiation at the top of Earth's atmosphere is 1370 $\mathrm{W} / \mathrm{m}^{3}$ . Assuming 60$\%$ of the incoming solar energy reaches Earth’s surface and assuming you absorb 50% of the incident energy, make an order - of - magnitude estimate of the amount of solar energy you absorb in a 60 - minute sunbath.

Averell H.
Carnegie Mellon University

Problem 69

A $200 .$ -\Omega resistor is connected in series with a $5.0-\mu \mathrm{F}$ capacitor and a 60 - Hz, 120 - V rms line. If electrical energy costs $0.080/ kWh, how much does it cost to leave this circuit connected for 24 h?

Salamat A.
Numerade Educator

Problem 70

In an RLC series circuit that includes a source of alternating current operating at fixed frequency and voltage, the resistance R is equal to the inductive reactance. If the plate separation of the parallel - plate capacitor is reduced to one - half its original value, the current in the circuit doubles. Find the initial capacitive reactance in terms of R.

Averell H.
Carnegie Mellon University

Problem 71

As a way of determining the inductance of a coil used in a research project, a student first connects the coil to a 12.0 - V battery and measures a current of 0.630 A. The student then connects the coil to a 24.0 - V (rms), 60.0 - Hz generator and measures an rms current of 0.570 A. What is the inductance?

Salamat A.
Numerade Educator

Problem 72

(a) What capacitance will resonate with a one - turn loop of inductance 400. pH to give a radar wave of wavelength 3.0 cm? (b) If the capacitor has square parallel plates separated by 1.0 mm of air, what should the edge length of the plates be? (c) What is the common reactance of the loop and capacitor at resonance?

Averell H.
Carnegie Mellon University

Problem 73

A dish antenna with a diameter of 20.0 m receives (at normal incidence) a radio signal from a distant
source, as shown in Figure P21.73. The radio signal is a continuous sinusoidal wave with amplitude $F_{\max }=$ 0.20$\quad \mu \mathrm{V} / \mathrm{m} .$ Assume the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic field in this wave? (b) What is the intensity of the radiation received by the antenna? (c) What is the power received by the antenna?

Salamat A.
Numerade Educator

Problem 74

A particular inductor has appreciable resistance. When the inductor is connected to a 12 - V battery, the current in the inductor is 3.0 A. When it is connected to an AC source with an rms output of 12 V and a frequency of 60. Hz, the current drops to 2.0 A. What are (a) the impedance at 60. Hz and (b) the inductance of the inductor?

Averell H.
Carnegie Mellon University

Problem 75

The U.S. Food and Drug Administration limits the radiation leakage of microwave ovens to no more than 5.0 $\mathrm{mW} / \mathrm{cm}^{2}$ at a distance of 2.0 in. A typical cell phone, which also transmits microwaves, has a peak output power of about 2.0 W. (a) Approximating the cell phone as a point source, calculate the radiation intensity of a cell phone at a distance of 2.0 in. How does the answer compare with the maximum allowable microwave oven leakage? (b) The distance from your ear to your brain is about 2 in. What would the radiation intensity in your brain be if you used a Bluetooth headset, keeping the phone in your pocket, 1.0 m away from your brain? Most headsets are so - called Class 2 devices with a maximum output power of 2.5 mW.

Salamat A.
Numerade Educator

Problem 76

One possible means of achieving space flight is to place a perfectly reflecting aluminized sheet into Earth’s orbit and to use the light from the Sun to push this solar sail. Suppose such a sail, of area $6.00 \times 10^{4} \mathrm{m}^{2}$ and mass $6.00 \times 10^{3} \mathrm{kg}$ is placed in orbit facing the Sun. (a) What force is exerted on the sail? (b) What is the sail’s acceleration? (c) How long does it take this sail to reach the Moon, $3.84 \times 10^{8} \mathrm{m}$ away? Ignore all gravitational effects and assume a solar intensity of 1340 $\mathrm{W} / \mathrm{m}^{2}$ Hint: The radiation pressure by a reflected wave is given by 2 (average power per unit area)/c.

Averell H.
Carnegie Mellon University