A diathermy machine, used in physiotherapy, generates

An rms voltage of 100 V is applied to a purely resistive load of 5.00 . Find (a) the maximum voltage applied, (b) the rms current supplied, (c) the maximum current supplied, and (d) the power dissipated.

(a) What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60-Hz power source with an peak voltage of 170 V? (b) What is the resistance of a 100-W bulb?

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 innite 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.

An audio amplier, 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 15.0V (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?

An AC voltage source has an output voltage given by v  (150 V) sin 377t. Find (a) the rms voltage output, (b) the frequency of the source, and (c) the voltage at t  1/120 s. (d) Find the maximum current in the circuit when the voltage source is connected to a 50.0- resistor.

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 F 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 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?

What maximum current is delivered by an AC generator with a maximum voltage of Vmax  48.0V and a frequency f  90.0Hz when it is connected across a 3.70 F capacitor?

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?

The generator in a purely capacitive AC circuit has an angular frequency of 120  rad/s. If Vmax  140 V and C  6.00  F, what is the rms current in the circuit?

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

The generator in a purely inductive AC circuit has an angular frequency of 120  rad/s. If Vmax  140 V and L  0.100 H, what is the rms current in the circuit?

An inductor has a 54.0- reactance at 60.0 Hz. What will be the maximum current if this inductor is connected to a 50.0-Hz source that produces a 100-V rms voltage?

An inductor is connected to a 20.0-Hz power supply that produces a 50.0-V rms voltage. What inductance is needed to keep the maximum current in the circuit below 80.0 mA?

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

An inductor (L  400 mH), a capacitor (C  4.43  F), 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 40.0 F 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.

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

A resistor (R  900 ), a capacitor (C  0.25  F), and an inductor (L  2.5 H) are connected in series across a 240-Hz AC source for which Vmax  140 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?

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

A 60.0- resistor, a 3.00 F 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 that 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.)

A coil of resistance 35.0 and inductance 20.5 H is in series with a capacitor and a 200-V (rms), 100-Hz source. The rms current in the circuit is 4.00 A. (a) Calculate the capacitance in the circuit. (b) What is Vrms across the coil?

An AC source with a maximum voltage of 150 V and f  50.0 Hz is connected between points a and d in Figure P21.27. Calculate the rms voltages between points (a) a and b, (b) b and c, (c) c and d, and (d) b and d.

A 50.0- resistor is connected to a 30.0 F capacitor and to a 60.0-Hz, 100-V (rms) source. (a) Find the power factor and the average power delivered to the circuit. (b) Repeat part (a) when the capacitor is replaced with a 0.300-H inductor.

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 with an amplitude of 100 V is applied to a series combination of a 200 F capacitor, a 100-mH inductor, and a 20.0- resistor. Calculate the power dissipation and the power factor for frequencies of (a) 60.0 Hz and (b) 50.0 Hz.

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  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.

An RLC circuit is used to tune a radio to an FM station broadcasting at 88.9 MHz. The resistance in the circuit is 12.0 and the capacitance is 1.40 pF. What inductance should be present in the circuit?

Consider a series RLC circuit with R  15 , L  200 mH, C  75  F, 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 greatestat resonance, at ten percent below the resonant frequency, or at ten percent above the resonant frequency? (d) What is the rms current in the circuit at a frequency of 60 Hz?

The AM band extends from approximately 500 kHz to 1 600 kHz. If a 2.0 H inductor is used in a tuning circuit for a radio, what are the extremes that a capacitor must reach in order to cover the complete band of frequencies?

A series circuit contains a 3.00-H inductor, a 3.00 F 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?

A 10.0- resistor, a 10.0-mH inductor, and a 100 F 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.

An AC adapter for a telephone-answering unit uses a transformer to reduce the line voltage of 120 V (rms) to a voltage of 9.0 V. The rms current delivered to the answering system is 400 mA. (a) If the primary (input) coil in the transformer in the adapter has 240 turns, how many turns are there on the secondary (output) coil? (b) What is the rms power delivered to the transformer? Assume an ideal transformer.

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 long-distance 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% efciency. 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  104 /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 difculties 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?

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 , where the constants  0  4   107 Ns2/C2 and  0  8.854  1012 C2/Nm2. What value (to four signicant 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, while 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 nger 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 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 which gives the decrease in intensity I in terms of the distance L the light has traveled through a uid with a concentration C of the light-absorbing molecule. The quantity  is called the extinction coefcient, and its value depends on the frequency of the light. (It has units of m2/mol.) Assume that the extinction coefcient for 660-nm light passing through a solution of oxygenated hemoglobin is identical to the coefcient for 940-nm light passing through deoxygenated hemoglobin. Assume also that 940-nm light has zero absorption (   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, determine the fraction of hemoglobin that is oxygenated.

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 reected 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 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 that 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 Sun delivers an average power of 1 340 W/m2 to the top of Earths atmosphere. Find the magnitudes of and for the electromagnetic waves at the top of the atmosphere.

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 (88108 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 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 C"O 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 that 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  1026 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 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 that, for speeds less than 0.03c, Equation 21.32 will lead to a value for the change of frequency accurate to approximately two signicant digits.)

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

The intensity of solar radiation at the top of Earths atmosphere is 1 340 W/m3. Assuming that 60% of the incoming solar energy reaches Earths surface, and assuming that 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.

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

A series RLC circuit has a resonance frequency of 2 000/  Hz. When it is operating at a frequency of  0, XL  12 and XC  8.0 . Calculate the values of L and C for the circuit.

Two connections allow contact with two circuit elements in series inside a box, but it is not known whether the circuit elements are R, L, or C. In an attempt to nd what is inside the box, you make some measurements, with the following results: when a 3.0-V DC power supply is connected across the terminals, a maximum direct current of 300 mA is measured in the circuit after a suitably long time. When a 60-Hz source with maximum voltage of 3.0 V is connected instead, the maximum current is measured as 200 mA. (a) What are the two elements in the box? (b) What are their values of R, L, or C?

(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 P21.63. The radio signal is a continuous sinusoidal wave with amplitude Emax  0.20  V/m. Assume that the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic 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 12V and a frequency of 60Hz, 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 ight is to place a perfectly reecting 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 for 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 reected wave is given by 2(average power per unit area)/c.]

Suppose you wish to use a transformer as an impedancematching device between an audio amplier that has an output impedance of 8.0 k and a speaker that has an input impedance of 8.0 . What should be the ratio of primary to secondary turns on the transformer?

Compute the average energy content of a liter of sunlight as it reaches the top of Earths atmosphere, where its intensity is 1 340 W/m2.

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

For this observation, you will need some items that can be found at many electronics stores. You will need a bicolored light-emitting diode (LED), a resistor of about 100 , 2 m of exible wire, and a step-down transformer with an output of 3 to 6 V. Use the wire to connect the LED and the resistor in series with the transformer. A bicolored LED is designed such that it emits a red color when the current in the LED is in one direction and green when the current reverses. When connected to an AC source, the LED is yellow. Why? Hold the wires and whirl the LED in a circular path. In a darkened room, you will see red and green bars at equally spaced intervals along the path of the LED. Why? As you continue to whirl the LED in a circular path, have your partner count the number of green bars in the circle, then measure the time it takes for the LED to travel ten times around the circular path. Based on this information, determine the time it takes for the color of the LED to change from green to red to green. You should obtain an answer of (1/60) s. Why?

Rotate a portable radio (with a telescoping antenna) about a horizontal axis while it is tuned to a weak station. Such an antenna detects the varying electric eld produced by the station. What can you determine about the direction of the electric eld produced by the transmitter? Now turn on your radio to a nearby station and experiment with shielding the radio from incoming waves. Is the reception affected by surrounding the radio by aluminum foil? By plastic wrap? Use any other material you have available. What kinds of material block the signal? Why?