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electricity and magnetism

Fundamentals of Ethics for Scientists and Engineers 1st Edition Edmund G. Seebauer, Robert L. Barry - Solutions

Figure 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 eachbulb.
An audio amplifier, represented by the AC source and the resistor R in figure, 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
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- Ω 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-µF 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- ΩF 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 = 48.0 V and a frequency f = 90.0 Hz when it is connected across a 3.70-µF 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 120π rad/s. If ∆Vmax = 140 V and C = 6.00 µF, 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 120π 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-Ω 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 flux 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 µF), and a resistor (R = 500 Ω) 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
A 40.0-µF capacitor is connected to a 50.0-Ω 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- Ω resistor, a 0.100-H inductor, and a 10.0-µF 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
A resistor (R = 900 Ω), a capacitor (C = 0.25 µF), 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
An AC source operating at 60 Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and a capacitor (C = 2.5 µF). (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
A 60.0-Ω resistor, a 3.00-µF 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 kΩ) 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
A person is working near the secondary of a transformer, as shown in figure. 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 =
A coil of resistance 35.0 Ω 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. Calculate the rms voltages between points(a) A and b,(b) B and c,(c) C and d, and(d) B andd.
A 50.0- Ω resistor is connected to a 30.0-µF 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-µF capacitor, a 100-mH inductor, and a 20.0-Ω 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 Ω, L = 6.0 mH, and C = 25 µF. 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
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 Ω and the capacitance is 1.40 pF. What inductance should be present in the circuit?
Consider a series RLC circuit with R = 15 Ω , L = 200 mH, C = 75 µF, 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 ten percent below the resonant
The AM band extends from approximately 500 kHz to 1600 kHz. If a 2.0-µH 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-µF capacitor, and a 30.0-Ω 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)
A 10.0-Ω resistor, a 10.0-mH inductor, and a 100-µF 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
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 Ω. What percentage of the power delivered by the generator is dissipated as heat in
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
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% efficiency. 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 x 10–4 Ω/m is to be used to transmit 5.00 MW over 400 miles (6.44 x 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
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
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 ℓ = 1√µ0ε0, where the constants µ0 = 4π x 10–7 N ∙ s2/C2 and ε0 = 8.854 x 10–12 C2/N ∙ m2.
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
The transmission of light energy as it passes through a solution of light-absorbing molecules is described by the Beer??Lambert lawwhich 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
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
Assume that the solar radiation incident on Earth is 1,340 W/m2 (at the top of Earth’s atmosphere). Calculate the total power radiated by the Sun, taking the average separation between Earth and the Sun to be 1.49 x 1011 m.
The Sun delivers an average power of 1,340 W/m2 to the top of Earth’s atmosphere. Find the magnitudes of Emax and Bmax 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 (540–1,600 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 first? 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
A spaceship is approaching a space station at a speed of 1.8 x 105 m/s. The space station has a beacon that emits green light with a frequency of 6.0 x 1014 Hz. What is the frequency of the beacon observed on the spaceship? What is the change in frequency? (Carry five 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 x 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
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
The intensity of solar radiation at the top of Earth’s atmosphere is 1,340 W/m3. Assuming that 60% of the incoming solar energy reaches Earth’s 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
A 200-Ω resistor is connected in series with a 5.0-µF 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/π Hz. When it is operating at a frequency of w > w0, XL = 12 Ω and XC = 8.0 Ω. 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 find 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
(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
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. 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
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)
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 x 104 m2 and mass 6 000 kg, is placed in orbit facing the Sun. (a) What force is exerted
Suppose you wish to use a transformer as an impedance matching device between an audio amplifier that has an output impedance of 8.0 kΩ and a speaker that has an input impedance of 8.0 Ω. 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 Earth’s atmosphere, where its intensity is 1 340 W/m2.
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 capacitor is reduced to one-half of its original value, the current in the circuit doubles. Find the
1. Why are the primary and secondary coils of a transformer wrapped on an iron core that passes through both coils?2. Why should an infrared photograph of a person look different from a photograph taken using visible light?
If the fundamental source of a sound wave is a vibrating object, what is the fundamental source of an electromagnetic wave?
When light (or other electromagnetic radiation) travels across a given region, what is it that oscillates? What is it that is transported?
How can the average value of an alternating current be zero, yet the square root of the average squared value not be zero?
Would an inductor and a capacitor used together in an AC circuit dissipate any energy?
1. 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.2. What is the impedance of an RLC circuit at the resonance frequency?
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? Doesn’t this violate Kirchhoff’s loop rule?
What determines the maximum voltage that can be used on a transmission line?
A parallel-plate capacitor in air has circular plates of radius 2.3 cm separated by 1.1 mm. Charge is flowing onto the upper plate and off the lower plate at a rate of 5 A.(a) Find the time rate of change of the electric field between the plates.(b) Compute the displacement current between the
In a region of space, the electric field varies according to E = (0.05 N / C) sin 2000 t0, where t is in seconds. Find the maximum displacement current through a 1-m2 area perpendicular to E.
For Problem 1, show that at a distance r from the axis of the plates the magnetic field between the plates is given by B = (1.89 × 10–3 T/m)r if r is less than the radius of the plates.
(a) Show that for a parallel-plate capacitor the displacement current is given by Id = C dV/dt, where C is the capacitance and V the voltage across the capacitor.(b) A parallel plate capacitor C = 5 nF is connected to an emf ← = ←0 cos ωt, where ←0 = 3 V and ω = 500π. Find the displacement
Current of 10 A flows into a capacitor having plates with areas of 0.5 m2.(a) What is the displacement current between the plates?(b) What is dE/dt between the plates for this current?(c) What is the line integral of B · dℓ around a circle of radius 10 cm that lies within and parallel to
A parallel-plate capacitor with circular plates is given a charge Q0. Between the plates is a leaky dielectric having a dielectric constant of κ and a resistivity ρ.(a) Find the conduction current between the plates as a function of time.(b) Find the displacement current between the plates as a
The leaky capacitor of Problem 6 is charged such that the voltage across the capacitor is given by V(t) = (0.01 V/s)t.(a) Find the conduction current as a function of time.(b) Find the displacement current.(c) Find the time for which the displacement current is equal to the conduction current.
The space between the plates of a capacitor is filled with a material of resistivity ρ = 104 Ω · m and dielectric constant κ = 2.5. The parallel plates are circular with a radius of 20 cm and are separated by 1 mm. The voltage across the plates is given by V0 cos ωt, with V0 = 40 V and
In this problem, you are to show that the generalized form of Ampère’s law (Equation 32-4) and the Biot– Savart law give the same result in a situation in which they both can be used. Figure shows two charges +Q and –Q on the x axis at x = –a and x = +a, with a current I = – dQ/dt along
Theorists have speculated on the possible existence of magnetic monopoles, and there have been several, as yet unsuccessful, experimental searches for such monopoles. Suppose magnetic monopoles were found and that the magnetic field at a distance r from a monopole of strength qm is given by B =
Show that the normal component of the magnetic field B is continuous across a surface. Do this by applying Gauss's law for B (∫Bn dA = 0) to a pillbox Gaussian surface that has a face on each side of the surface.
Find the wavelength for(a) A typical AM radio wave with a frequency of 1000 kHz and(b) A typical FM radio wave of 100 MHz.
What is the frequency of an X ray with a wavelength of 0.1 nm?
The intensity of radiation from an electric dipole is proportional to (sin2 θ)/r2, where θ is the angle between the electric dipole moment and the position vector r. A radiating electric dipole lies along the z axis (its dipole moment is in the z direction). Let I1 be the intensity
(a) For the situation described in Problem 20, at what angle is the intensity at r = 5 m equal to I1?(b) At what distance is the intensity equal to I1 at θ = 45º?
The transmitting antenna of a station is a dipole located atop a mountain 2000 m above sea level. The intensity of the signal on a nearby mountain 4 km distant and also 2000 m above sea level is 4 × 10–12 W/m2. What is the intensity of the signal at sea level and 1.5 km from the
A radio station that uses a vertical dipole antenna broadcasts at a frequency of 1.20 MHz with total power output of 500 kW. The radiation pattern is as shown in Figure, i.e., the intensity of the signal varies as sin2 θ, where θ is the angle between the direction of propagation and the vertical,
At a distance of 30 km from a radio station broadcasting at a frequency of 0.8 MHz, the intensity of the electromagnetic wave is 2 × 10–13 W/m2. The transmitting antenna is a vertical dipole. What is the total power radiated by the station?
A small private plane approaching an airport is flying at an altitude of 2500 m above ground. The airport's flight control system transmits 100 W at 24 MHz, using a vertical dipole antenna. What is the intensity of the signal at the plane's receiving antenna when the plane's position on a map is 4
An electromagnetic wave has an intensity of 100 W/m2. Find(a) The radiation pressure Pr,(b) Erms, and(c) Brms.
The amplitude of an electromagnetic wave is E0 = 400 V/m. Find(a) Erms,(b) Brms,(c) The intensity I, and(d) The radiation pressure Pr.
The rms value of the electric field in an electromagnetic wave is Erms = 400 V/m.(a) Find Brms,(b) The average energy density, and(c) The intensity.
(a) An electromagnetic wave of intensity 200 W/m2 is incident normally on a rectangular black card with sides of 20 cm and 30 cm that absorbs all the radiation. Find the force exerted on the card by the radiation.(b) Find the force exerted by the same wave if the card reflects all the radiation
An AM radio station radiates an isotropic sinusoidal wave with an average power of 50 kW. What are the amplitudes of Emax and Bmax at a distance of(a) 500 m,(b) 5 km, and(c) 50 km?
The intensity of sunlight striking the earth's upper atmosphere (called the solar constant) is 1.35 kW/m2.(a) Find Erms and Brms due to the sun at the upper atmosphere of the earth.(b) Find the average power output of the sun.(c) Find the intensity and the radiation pressure at the surface of the
A demonstration laser has an average output power of 0.9 mW and a beam dia meter of 1.2 mm. What is the force exerted by the laser beam on(a) A 100% absorbing black surface?(b) A 100% reflecting surface?
A laser beam has a diameter of 1.0 mm and average power of 1.5 mW. Find(a) The intensity of the beam,(b) Erms,(c) Brms, and(d) The radiation pressure.

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