Solved: Show that the SI unit of capacitive reactance Xc

A sinusoidally varying voltage has a maximum value of 170 V. What is its rms value? (a) 240 V (b) 170 V (c) 120 V (d) 0 (e) 120 V

When a particular inductor is connected to a source of sinusoidally varying voltage with constant amplitude and a frequency of 60.0 Hz, the rms current is 3.0 A. What is the rms current if the source frequency is doubled? (a) 12 A (b) 6.0 A (c) 4.2 A (d) 3.0 A (e) 1.5 A

What is the rms voltage across a capacitor with capacitance (1.00/2p) mF carrying 1.00-mA rms AC current at 60.0 Hz? (a) 16.7 V (b) 13.2 V (c) 32.2 V (d) 0.560 V (e) 4.43 V

Find the voltage across a (1.0/2p)-H inductor when it carries 2.0 A of rms current at 60.0 Hz. (a) 160 V (b) 140 V (c) 120 V (d) 95 V (e) 85 V

A series RLC circuit contains a resistor of 20 _, a capacitor of 0.75 mF, and an inductor of 120 mH. If a sinusoidally varying rms voltage of 120 V is applied across this combination of elements, what is the rms current in the circuit when operating at its resonance frequency? (a) 2.4 A (b) 6.0 A (c) 10 A (d) 17 A (e) 8.2 A

A 6.0-V battery is connected across the primary coil of a transformer having 50 turns. If the secondary coil of the transformer has 100 turns, what voltage appears across the secondary? (a) 24 V (b) 12 V (c) 6.0 V (d) 3.0 V (e) none of these

An electromagnetic wave with a peak magnetic fi eld component of magnitude 1.5 _ 107 T has an associated peak electric fi eld component of what value? (a) 0.50 _ 1015 N/C (b) 2.0 _ 105 N/C (c) 2.2 _ 104 N/C (d) 45 N/C (e) 22 N/C

An inductor and a resistor are connected in series across an AC generator, as shown in Figure MCQ21.8. Immediately after the switch is closed, which of the following statements is true? (a) The current is _V/R. (b) The voltage across the inductor is zero. (c) The current in the circuit is zero. (d) The voltage across the resistor is _V. (e) The voltage across the inductor is half its maximum value.

A capacitor and a resistor are connected in series across an AC generator, as shown in Figure MCQ21.9. After the switch is closed, which of the following statements is true? (a) The voltage across the capacitor lags the current by 90. (b) The voltage across the resistor is out of phase with the current. (c) The voltage across the capacitor leads the current by 90. (d) The current decreases as the frequency of the generator is increased, but its peak voltage remains the same. (e) none of these

A resistor, capacitor, and inductor are connected in series across an AC generator. Which of the following statements is false? (a) The instantaneous voltage across the capacitor lags the current by 90. (b) The instantaneous voltage across the inductor leads the current by 90. (c) The instantaneous voltage across the resistor is in phase with the current. (d) The voltages across the resistor, capacitor, and inductor are not in phase. (e) The rms voltage across the combination of the three elements equals the algebraic sum of the rms voltages across each element separately.

A resistor, capacitor, and inductor are connected in series across an AC generator. Which of the following statements is true? (a) All the power is lost in the inductor. (b) All the power is lost in the capacitor. (c) All the power is lost in the resistor. (d) Power is lost in all three elements. (e) The power delivered by the generator does not depend on the phase difference between the generator voltage and current.

If the voltage across a circuit element has its maximum value when the current in the circuit is zero, does it follow that (a) the circuit element is a resistor, (b) the circuit element is a capacitor, (c) the circuit element is an inductor, (d) the current and voltage are 90 out of phase, or (e) the current and voltage are 180 out of phase?

What is the phase angle in a series RLC circuit at resonance? (a) 180 (b) 90 (c) 0 (d) 90 (e) 45

A series RLC circuit contains a 20.0-_ resistor, a 0.75-mF capacitor, and a 120-mH inductor. If a sinusoidally varying rms voltage of 120 V at f _ 5.0 _ 102 Hz is applied across this combination of elements, what is the rms current in the circuit? (a) 2.3 A (b) 6.0 A (c) 10 A (d) 17 A (e) 4.8 A

Before the advent of cable television and satellite dishes, homeowners either mounted a television antenna on the roof or used rabbit ears atop their sets. (See Fig. CQ21.1.) Certain orientations of the receiving antenna on a television set gave better reception than others. Furthermore, the best orientation varied from station to station. Explain. FIGURE CQ21.1 Cengage Learning/George Semple

What is the impedance of an RLC circuit at the resonance frequency?

Receiving radio antennas can be in the form of conducting lines or loops. What should the orientation of each of these antennas be relative to a broadcasting antenna that is vertical?

If the fundamental source of a sound wave is a vibrating object, what is the fundamental source of an electromagnetic wave?

In radio transmission a radio wave serves as a carrier wave, and the sound signal is superimposed on the carrier wave. In amplitude modulation (AM) radio, the amplitude of the carrier wave varies according to the sound wave. The U.S. Navy sometimes uses fl ashing lights to send Morse code between neighboring ships, a process that has similarities to radio broadcasting. Is this process AM or FM? What is the carrier frequency? What is the signal frequency? What is the broadcasting antenna? What is the receiving antenna?

When light (or other electromagnetic radiation) travels across a given region, what is it that oscillates? What is it that is transported?

In space sailing, which is a proposed alternative for transport to the planets, a spacecraft carries a very large sail. Sunlight striking the sail exerts a force, accelerating the spacecraft. Should the sail be absorptive or refl ective to be most effective?

How can the average value of an alternating current be zero, yet the square root of the average squared value not be zero?

Suppose a creature from another planet had eyes that were sensitive to infrared radiation. Describe what it would see if it looked around the room that you are now in. That is, what would be bright and what would be dim?

Why should an infrared photograph of a person look different from a photograph taken using visible light?

Does a wire connected to a battery emit an electromagnetic wave?

If a high-frequency current is passed through a solenoid containing a metallic core, the core becomes warm due to induction. Explain why the temperature of the material rises in this situation.

If the resistance in an RLC circuit remains the same, but the capacitance and inductance are each doubled, how will the resonance frequency change?

Why is the sum of the maximum voltages across each of the elements in a series RLC circuit usually greater than the maximum applied voltage? Doesnt this violate Kirchhoffs loop rule?

What is the advantage of transmitting power at high voltages?

When an AC generator is connected across a 12.0-_ resistor, the rms current in the resistor is 8.00 A. Find (a) the rms voltage across the resistor, (b) the peak voltage of the generator, (c) the maximum current in the resistor, and (d) the average power delivered to the resistor.

A certain lightbulb is rated at 60.0 W when operating at an rms voltage of 1.20 _ 102 V. (a) What is the peak voltage applied across the bulb? (b) What is the resistance of the bulb? (c) Does a 1.00 _ 102 W bulb have greater or less resistance than a 60.0-W bulb? Explain.

An AC power supply that produces a maximum voltage of _Vmax _ 100 V is connected to a 24.0-_ resistor. The current and the resistor voltage are respectively measured with an ideal AC ammeter and an ideal AC voltmeter, as shown in Figure P21.3. What does each meter read? Note that an ideal ammeter has zero resistance and an ideal voltmeter has infi nite resistance.

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. Find the rms current and the resistance of each bulb. FIGURE P21.4 120 V 1 2 3

An audio amplifi er, represented by the AC source and the resistor R in Figure P21.5, delivers alternating voltages at audio frequencies to the speaker. If the source puts out an alternating voltage of 15.0 V (rms), the resistance R is 8.20 _, and the speaker is equivalent to a resistance of 10.4 _, what is the time-averaged power delivered to the speaker? FIGURE P21.5 Speaker R

The output voltage of an AC generator is given by _v _ (170 V) sin (60pt). The generator is connected across a 20.0-_ resistor. 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, and (f) power delivered to the resistor. (g) Should the argument of the sine function be in degrees or radians? Compute the current when t _ 0.005 0 s.

Show that the SI unit of capacitive reactance Xc is the ohm.

What is the maximum current delivered to a circuit containing a 2.20-mF capacitor when it is connected across (a) a North American outlet having _Vrms _ 120 V and f _ 60.0 Hz and (b) a European outlet having _Vrms _ 240 V and f _ 50.0 Hz?

When a 4.0-mF 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?

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-mF 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.

What must be the capacitance of a capacitor inserted in a 60-Hz circuit in series with a generator of 170-V maximum output voltage to produce an rms current output of 0.75 A?

A generator delivers an AC voltage of the form _v _ (98.0 V) sin (80pt) 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.

Show that the inductive reactance XL has SI units of ohms.

An AC generator has an output rms voltage of 78.0 V at a frequency of 80.0 Hz. If the generator is connected across a 25.0-mH inductor, fi nd the (a) inductive reactance, (b) rms current, and (c) maximum current in the circuit.

An inductor is connected to an AC power supply having a maximum output voltage of 4.00 V at a frequency of 300.0 Hz. What inductance is needed to keep the rms current less than 2.00 mA?

The output voltage of an AC generator is given by _v _ (1.20 _ 102 V) sin (30pt). 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 _ 0 does the instantaneous current fi rst reach 1.00 A? (Use the inverse sine function.)

Determine the maximum magnetic fl ux through an inductor connected to a standard outlet (_Vrms _ 120 V, f _ 60.0 Hz). RLC

A sinusoidal voltage _v _ (80.0 V) sin (150t) is applied to a series RLC circuit with L _ 80.0 mH, C _ 125.0 mF, and R _ 40.0 _. (a) What is the impedance of the circuit? (b) What is the maximum current in the circuit?

A 40.0-mF capacitor is connected to a 50.0-_ resistor and a generator whose rms output is 30.0 V at 60.0 Hz. Find (a) the rms current in the circuit, (b) the rms voltage drop across the resistor, (c) the rms voltage drop across the capacitor, and (d) the phase angle for the circuit.

An inductor (L _ 400 mH), a capacitor (C _ 4.43 mF), and a resistor (R _ 500 _) 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 _Vmax. (b) Determine the phase angle by which the current leads or lags the applied voltage.

A resistor (R _ 9.00 _ 102 _), a capacitor (C _ 0.250 mF), and an inductor (L _ 2.50 H) are connected in series across a 2.40 _ 102-Hz AC source for which _Vmax _ 1.40 _ 102 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?

A 50.0-_ resistor, a 0.100-H inductor, and a 10.0-mF 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.

A 60.0-_ resistor, a 3.00-mF capacitor, and a 0.400-H inductor are connected in series to a 90.0-V (rms), 60.0-Hz source. Find (a) the voltage drop across the LC combination and (b) the voltage drop across the RC combination.

An AC source operating at 60 Hz with a maximum voltage of 170 V is connected in series with a resistor (R _ 1.2 k_) and an inductor (L _ 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?

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 Cs, 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 Rb _ 50.0 k_, determine the rms voltage across the body. Hint: Redraw the circuit with the secondary of the transformer as a simple AC source. (d) Does the voltage lead or lag the current? How will putting an inductor in series with the existing capacitor and resistor affect the current? Explain.

A series RLC circuit contains the following components: R _ 1.50 _ 102 _, L _ 2.50 _ 102 mH, C _ 2.00 mF, and a generator with _Vmax _ 2.10 _ 102 V operating at 50.0 Hz. Calculate the (a) inductive reactance, (b) capacitive reactance, (c) impedance, (d) maximum current, and (e) phase angle between the current and generator voltage. (f) Calculate the individual maximum voltages across the resistor, inductor, and capacitor.

Consider the RLC circuit in Problem 21.27. When the voltage across the resistor is a maximum, what are the individual voltages across the capacitor and inductor? Explain.

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. FIGURE P21.25 Rb Cs 5 000 V Transformer

A 60.0-_ resistor is connected in series with a 30.0-mF capacitor and a generator having a maximum voltage of 1.20 _ 102 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. FIGURE P21.29 a b c d 40.0 _ 185 mH 65.0 F

An AC source operating at 60 Hz with a maximum voltage of 170 V is connected in series with a resistor (R _ 1.2 k_) and a capacitor (C _ 2.5 mF). (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?

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.

An AC voltage of the form _v _ (90.0 V) sin (350t) is applied to a series RLC circuit. If R _ 50.0 _, C _ 25.0 mF, and L _ 0.200 H, fi nd the (a) impedance of the circuit, (b) rms current in the circuit, and (c) average power delivered to the circuit.

Calculate the average power delivered to the circuit described in Problem 21.

A series RLC circuit has a resistance of 22.0 _ and an impedance of 80.0 _. If the rms voltage applied to the circuit is 160 V, what average power is delivered to the circuit?

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.

Consider a series RLC circuit with R _ 25 _, L _ 6.0 mH, and C _ 25 mF. 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. RLC

A resonant circuit in a radio receiver is tuned to a certain station when the inductor has a value of 3.00 mH and the capacitor has a value of 2.50 pF. The resistance of the circuit is 12 _. (a) Find the frequency of the radio station. (b) Is there any information given in the problem that is not needed to solve it? Explain.

The LC circuit of a radar transmitter oscillates at 9.00 GHz. (a) What inductance will resonate with a 2.00-pF capacitor at this frequency? (b) What is the inductive reactance of the circuit at this frequency?

The AM band extends from approximately 500 kHz to 1 600 kHz. If a 2.0-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?

Consider a series RLC circuit with R _ 15 _, L _ 200 mH, C _ 75 mF, and a maximum voltage of 150 V. (a) What is the impedance of the circuit at resonance? (b) What is the resonance frequency of the circuit? (c) When will the current be greatest: at resonance, at 10% below the resonant frequency, or at 10% above the resonant frequency? (d) What is the rms current in the circuit at a frequency of 60 Hz?

A 10.0-_ resistor, a 10.0-mH inductor, and a 100-mF capacitor are connected in series to a 50.0-V (rms) source having variable frequency. Find the energy delivered to the circuit during one period if the operating frequency is twice the resonance frequency.

A series circuit contains a 3.00-H inductor, a 3.00-mF capacitor, and a 30.0-_ 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?

The primary coil of a transformer has N1 _ 250 turns, and its secondary coil has N2 _ 1 500 turns. If the input voltage across the primary coil is _v _ (170 V) sin vt, what rms voltage is developed across the secondary coil?

A step-down transformer is used for recharging the batteries of portable devices. The turns ratio N2/N1 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.

An AC power generator produces 50 A (rms) at 3 600 V. The voltage is stepped up to 100 000 V by an ideal transformer, and the energy is transmitted through a longdistance power line that has a resistance of 100 _. What percentage of the power delivered by the generator is dissipated as heat in the power line?

A transformer is to be used to provide power for a computer disk drive that needs 6.0 V (rms) instead of the 120 V (rms) from the wall outlet. The number of turns in the primary is 400, and it delivers 500 mA (the secondary current) at an output voltage of 6.0 V (rms). (a) Should the transformer have more turns in the secondary compared with the primary, or fewer turns? (b) Find the current in the primary. (c) Find the number of turns in the secondary.

A transformer on a pole near a factory steps the voltage down from 3 600 V (rms) to 120 V (rms). The transformer is to deliver 1 000 kW to the factory at 90% effi ciency. Find (a) the power delivered to the primary, (b) the current in the primary, and (c) the current in the secondary.

A transmission line that has a resistance per unit length of 4.50 _ 104 _/m is to be used to transmit 5.00 MW over 400 miles (6.44 _ 105 m). 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 diffi culties would be encountered on attempting to transmit the 5.00 MW at the generator voltage of 4.50 kV (rms)?

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 quarterwavelength antenna for a transmitter generating ELF waves of frequency 75 Hz. How practical is this antenna?

(a) The distance to Polaris, the North Star, is approximately 6.44 _ 1018 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 _ 105 km.)

An electromagnetic wave in free space has an electric fi eld of amplitude 330 V/m. Find the amplitude of the corresponding magnetic fi eld.

Experimenters at the National Institute of Standards and Technology have made precise measurements of the speed of light using the fact that, in vacuum, the speed of electromagnetic waves is c 5 1/!m0P0, where the constants m0 _ 4p _ 107 N _ s2/C2 and P0 _ 8.854 _ 1012 C2/N _ m2. What value (to four signifi cant fi gures) does this formula give for the speed of light in vacuum?

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 persons fi nger and has two light- emitting diodesa red (660 nm) and an infrared (940 nm)and a photocell that detects the amount of light transmitted through the fi nger 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.

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 BeerLambert law I 5 I0102PCL or log10 a I I0 b 5 2PCL which gives the decrease in intensity I in terms of the distance L the light has traveled through a fl uid with a concentration C of the light-absorbing molecule. The quantity P is called the extinction coeffi cient, and its value depends on the frequency of the light. (It has units of m2/mol.) Assume the extinction coeffi cient for 660-nm light passing through a solution of oxygenated hemoglobin is identical to the coeffi cient for 940-nm light passing through deoxygenated hemoglobin. Also assume 940-nm light has zero absorption (P _ 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?

The Sun delivers an average power of 1 340 W/m2 to the top of Earths atmosphere. Find the magnitudes of E S max and B S max for the electromagnetic waves at the top of the atmosphere.

A laser beam is used to levitate a metal disk against the force of Earths 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 refl ecting and the beam is directed perpendicular to the disk. (b) If the disk has mass 5.00 g and radius 4.00 cm, fi nd the necessary light intensity. (c) Give two reasons why using light pressure as propulsion near Earths surface is impractical.

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 refl ected 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 fi xed 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.

Assume the solar radiation incident on Earth is 1 340 W/m2 (at the top of Earths atmosphere). Calculate the total power radiated by the Sun, taking the average separation between Earth and the Sun to be 1.49 _ 1011 m.

The eye is most sensitive to light of wavelength 5.50 _ 107 m, which is in the greenyellow region of the visible electromagnetic spectrum. What is the frequency of this light?

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?

What are the wavelength ranges in (a) the AM radio band (5401 600 kHz) and (b) the FM radio band (88 108 MHz)?

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 newsroom, 3.0 m from the newscaster. Who receives the news fi rst? Explain. Take the speed of sound in air to be 343 m/s.

Infrared spectra are used by chemists to help identify an unknown substance. Atoms in a molecule that are bound together by a particular bond vibrate at a predictable frequency, and light at that frequency is absorbed strongly by the atom. In the case of the CwO double bond, for example, the oxygen atom is bound to the carbon by a bond that has an effective spring constant of 2 800 N/m. If we assume the carbon atom remains stationary (it is attached to other atoms in the molecule), determine the resonant frequency of this bond and the wavelength of light that matches that frequency. Verify that this wavelength lies in the infrared region of the spectrum. (The mass of an oxygen atom is 2.66 _ 1026 kg.)

A spaceship is approaching a space station at a speed of 1.8 _ 105 m/s. The space station has a beacon that emits green light with a frequency of 6.0 _ 1014 Hz. What is the frequency of the beacon observed on the spaceship? What is the change in frequency? (Carry fi ve digits in these calculations.)

While driving at a constant speed of 80 km/h, you are passed by a car traveling at 120 km/h. If the frequency of light emitted by the taillights of the car that passes you is 4.3 _ 1014 Hz, what frequency will you observe? What is the change in frequency?

A speeder tries to explain to the police that the yellow warning lights 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 change of frequency accurate to approximately two signifi cant digits. ADDITIONAL PROBLEMS

A 50.0-_ resistor is connected in series with a 15.0-mF capacitor and a 60.0-Hz, 1.20 _ 102-V (rms) source. Find the (a) impedance of the circuit and (b) rms current in the circuit. (c) What is the value of the inductor that must be inserted in the circuit to reduce the current to onehalf that found in part (b)?

The intensity of solar radiation at the top of Earths atmosphere is 1 340 W/m3. Assuming 60% of the incoming solar energy reaches Earths surface and assuming you absorb 50% of the incident energy, make an order-ofmagnitude estimate of the amount of solar energy you absorb in a 60-minute sunbath.

A 200-_ resistor is connected in series with a 5.0-mF 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?

A series RLC circuit has a resonance frequency of 2 000/p Hz. When it is operating at a frequency of v _ v0, XL _ 12 _ and XC _ 8.0 _. Calculate the values of L and C for the circuit.

As a way of determining the inductance of a coil used in a research project, a student fi rst 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?

(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?

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 Emax _ 0.20 mV/m. Assume the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic fi eld in this wave? (b) What is the intensity of the radiation received by the antenna? (c) What is the power received by the antenna?

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?

One possible means of achieving space fl ight is to place a perfectly refl ecting aluminized sheet into Earths orbit and to use the light from the Sun to push this solar sail. Suppose such a sail, of area 6.00 _ 104 m2 and mass 6 000 kg, is placed in orbit facing the Sun. (a) What force is exerted on the sail? (b) What is the sails acceleration? (c) How long does it take this sail to reach the Moon, 3.84 _ 108 m away? Ignore all gravitational effects and assume a solar intensity of 1 340 W/m2. Hint: The radiation pressure by a refl ected wave is given by 2 (average power per unit area)/c.

The U.S. Food and Drug Administration limits the radiation leakage of microwave ovens to no more than 5.0 mW/cm2 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.