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physics
electricity and magnetism

Conceptual Physics 11th edition Paul G. Hewitt - Solutions

Assume that a uniform magnetic field exists perpendicular to the plane of this page (into it) and has a strength of 0.150 T. Assume further that this field ends sharply at the paper’s edges. A single circular loop of wire is also in the plane of the paper and moves across it from left to right at
A uniform magnetic field is at right angles to the plane of a wire loop. If the field decreases by 0.20 T in 1.0 x 10-3s and the magnitude of the average emf induced in the loop is 80 V, (a) What is the area of the loop? (b) What would be the value of the average induced emf if the field change
(a) A square loop of wire with sides of length 40 cm is in a uniform magnetic field perpendicular to its area. If the field’s strength is initially 100 mT and it decays to zero in 0.010 s, what is the magnitude of the average emf induced in the loop? (b) What would be the average emf if the
The magnetic flux through one loop of wire is reduced from 0.35Wb to 0.15Wb in 0.20 s. The average induced current in the coil is 10 A. (a) Can you determine the area of the loop from the data given? Explain. (b) Find the resistance of the wire.
When the magnetic flux through a single loop of wire increases by 30 T ∙ m2, an average current of 40 A is induced in the wire. Assuming that the wire has a resistance of 2.5 Ω, (a) Over what period of time did the flux increase? (b) If the current had been only 20 A, how long would the flux
The average current in a resistor in an ac circuit is zero. Explain why the average power delivered to a resistor isn’t zero.
An inductor is connected by itself to a 60-Hz ac voltage source. To ensure it has the same inductive reactance when it is connected to a 240-Hz source, would you decrease or increase its inductance value? By what factor should it change? Explain your reasoning.
An RLC circuit consists of a resistor, a 1.00-μF capacitor, and a 250-mH inductor. If it is driven by an ac voltage source whose frequency is 60 Hz, (a) What is the impedance of an RLC circuit at resonance? (b) How does its impedance compare to that in part (a) if the source frequency is
For each of the following cases for an RLC circuit, does the resonance frequency increase, decrease, or stay the same? If it changes tell by what factor. (a) Only the capacitance is changed—it is quadrupled. (b) Only the inductance is changed—it is increased by nine times. (c) Only the
If a driven RLC circuit has an inductive reactance of 250 Ω and a capacitive reactance of 150 Ω, is the driving frequency exactly at, above, or below the circuit’s resonant frequency? Explain how you can tell.
A 25-Ω resistor is wired directly across a 120-V ac source. What happens to the time-average power, rms voltage, and rms current when the resistor’s value changes to 50 Ω?
A 25-Ω resistor is wired directly across a 120-V ac source. What happens to the time-average power, rms voltage, and rms current when the ac source is changed to 240 V?
Explain why, under very low frequency ac conditions, a capacitor acts almost as an open circuit while an inductor acts almost as a short circuit.
Can an inductor oppose dc current? What about a capacitor? Explain each and why they are different.
If the current on a 10-μF capacitor is described by I = (120 A) sin (120πt + π/2), explain why the instantaneous voltage across it at t = 0 is zero whereas the cur-rent at that time is not.
What are the peak and rms voltages of a 120-V ac line and a 240-V ac line?
What are the resistance, peak current, and power level of a computer monitor that draws an rms current of 0.833 A when connected to a 120-V outlet?
Find the rms and peak currents in a 40-W, 120-V lightbulb. What is its resistance?
A50-kW electric heater is designed to run using a 240-V ac source. Find its (a) Peak current and (b) Peak voltage. (c) How much energy will you be billed for in a 30-day month if it operates 2.0 h per day?
The current in a resistor is given by I = (8.0 A) sin (40πt) when a voltage given by V = (60 V) sin (40πt) is applied to it. (a) What is the resistance value? (b) What are the frequency and period of the voltage source? (c) What is the average power delivered to the resistor?
The current and voltage outputs of an operating ac generator have peak values of 2.5 A and 16 V, respectively. (a) What is the average power output of the generator? (b) What is the effective resistance of the circuit it is in?
The current in a resistor is given by I = (2.0 A) sin (380t). (a) What is the frequency of the current? (b) What is the rms current? (c) How much aver-age power is delivered to the resistor? (d) Write an equation for the voltage across the resistor as a function of time. (e) Write an equation
At what frequency does a 25-μF capacitor have a reactance of 25-Ω?
A single 2.0-μF capacitor is connected across the terminals of a 60-Hz voltage source, and a current of 2.0 mA is measured on an ac ammeter. What is the capacitive reactance of the capacitor?
What capacitance value would give a reactance of 100-Ω in a 60-Hz ac circuit?
How much current is in a circuit containing only a 50-μF capacitor connected to an ac generator with an output of 120 V and 60 Hz?
An ac circuit has an rms current of 5.0 A. What is the peak current? What is the average current?
A single 50-mH inductor forms a complete circuit when connected to an ac voltage source at 120 V and 60 Hz. (a) What is the inductive reactance of the circuit? (b) How much current is in the circuit? (c) What is the phase angle between the current and the applied voltage? (Assume negligible
A variable capacitor in a circuit with a 120-V, 60-Hz source initially has a capacitance of 0.25 μf. The capacitance is then increased to 0.40 μF. (a) What is the percentage change in the capacitive reactance? (b) What is the percentage change in the current in the circuit?
(a) An inductor has a reactance of 90-Ω in a 60-Hz ac circuit. What is its inductance? (b) What frequency would be required to double its reactance?
(a) Find the frequency at which a 250-mH inductor has a reactance of 400-Ω. (b) At what frequency would a 0.40μF capacitor have the same reactance?
A capacitor is connected to a variable-frequency ac voltage source. (a) If the frequency increases by a factor of 3, the capacitive reactance will be (1) 3, (2) 1/3, (3) 9, (4) 1/9 times the original reactance. Why? (b) If the capacitive reactance of a capacitor at 120 Hz is 100-Ω, what is its
With a single 150-mH inductor in a circuit with a 60-Hz voltage source, a current of 1.6 A is measured on an ac ammeter. (a) What is the rms voltage of the source? (b) What is the phase angle between the current and that voltage?
(a) What inductance has the same reactance in a 120-V, 60-Hz circuit as a capacitance of 10 μF? (b) What would be the ratio of inductive reactance to capacitive reactance if the frequency were changed to 120 Hz?
A circuit with a single capacitor is connected to a 120-V, 60-Hz source. (a) What is its capacitance if there is a current of 0.20 A in the circuit? (b) What would be the current if the source frequency were halved?
An inductor is connected to a variable-frequency ac voltage source. (a) If the frequency decreases by a factor of 2, the rms current will be (1) 2, (2) 1/2, (3) 4, (4) 1/4times the original rms current. Why? (b) If the rms cur-rent in an inductor at 40 Hz is 9.0 A, what is its rms cur-rent if the
A coil in a 60-Hz circuit has a resistance of and an inductance of 0.45 H. Calculate (a) The coil’s reactance and (b) The circuit’s impedance.
How much ac rms current must be in a 10-Ω resistor to produce an average power of 15 W?
A series RC circuit has a resistance of 200-Ω and a capacitance of 25μF and is driven by a 120-V, 60-Hz source. (a) Find the capacitive reactance and impedance of the circuit. (b) How much current is drawn from the source?
A series RL circuit has a resistance of 100-Ω and an inductance of 100 mH and is driven by a 120-V, 60-Hz source. (a) Find the inductive reactance and the impedance of the circuit. (b) How much current is drawn from the source?
A series RC circuit has a resistance of a250-Ω and a capacitance of 6.0 μF. If the circuit is driven by a 60-Hz source, find (a) The capacitive reactance and (b) The impedance of the circuit.
A series RC circuit has a resistance of 100-Ω and a capacitive reactance of 50-Ω. (a) Will the phase angle be (1) positive, (2) zero, or (3) negative? Why? (b) What is the phase angle of this circuit?
A series RLC circuit has a resistance of 25-Ω, an inductance of 0.30 H, and a capacitance of 8.0μF. (a) At what frequency should the circuit be driven for the maximum power to be transferred from the driving source? (b) What is the impedance at that frequency?
In a series RLC circuit, R = XC = CL = 40-Ω for a particular driving frequency. (a) This circuit is (1) inductive, (2) capacitive, (3) in resonance. Explain your reasoning. (b) If the driving frequency is doubled, what will be the impedance of the circuit?
(a) An RLC series circuit is in resonance. Which one of the following can you change without upsetting the resonance: (1) resistance, (2) capacitance, (3) inductance, or (4) frequency? (b) A resistor, an inductor, and a capacitor have values of 500-Ω, 500 mH, and 3.5μF, respectively. They are
(a) How much power is dissipated in the circuit described in Exercise 36b using the initial values of resistance, inductance, and capacitance? In exercise A resistor, an inductor, and a capacitor have values of 500-Ω, 500 mH, and 3.5μF, respectively. They are connected in series to a power
(a) What is the resonance frequency of an RLC circuit with a resistance of 100-Ω, an inductance of 100 mH, and a capacitance of 5.00μF? (b) What is the resonance frequency if all the values in part (a) are doubled?
A tuning circuit in a radio receiver has a fixed inductance of 0.50 mH and a variable capacitor. (a) If the circuit is tuned to a radio station broadcasting at 980 kHz on the AM dial, what is the capacitance of the capacitor? (b) What value of capacitance is required to tune into a station
An ac circuit contains a resistor with a resistance of 5.0-Ω. The resistor has an rms current of 0.75 A. (a) Find its rms voltage and peak voltage. (b) Find the average power delivered to the resistor.
A coil with a resistance of and an inductance of 0.15 H is connected to a 120-V, 60-Hz source. (a) Is the phase angle of this circuit (1) positive, (2) zero, or (3) negative? Why? (b) What is the phase angle of the circuit? (c) How much rms current is in the circuit? (d) What is the average
A small welding machine uses a voltage source of 120 V at 60 Hz. When the source is operating, it requires 1200 W of power, and the power factor is 0.75. (a) What is the machine’s impedance? (b) Find the rms current in the machine while operating.
A series circuit is connected to a 220-V, 60-Hz power sup-ply. The circuit has the following components: a resistor, a coil with an inductive reactance of 120-Ω, and a capacitor with a reactance of 120-Ω. Compute the rms voltage across (a) The resistor, (b) The inductor, and (c) The
A series RLC circuit has a resistance of 25-Ω, a capacitance of 0.80μF, and an inductance of 250 mH. The circuit is connected to a variable-frequency source with a fixed rms voltage output of 12 V. If the frequency that is supplied is set at the circuit’s resonance frequency, what is the rms
(a) In Exercises 42 and 43, determine the numerical (scalar) sum of the rms voltages across the three circuit elements and explain why it is much larger than the source voltage. (b) Determine the sum of these voltages using the proper phasor techniques and show that your result is equal to the
(a) If the circuit in Fig. 21.17 is in resonance, the impedance of the circuit is (1) greater than 25-„¦,(2) Equal to 25-„¦, (3) less than 25-„¦. Why? (b) If the driving frequency is 60 Hz, what is the circuit€™s impedance?
A series RLC circuit with a resistance of 400-Ω has capacitive and inductive reactances of 300-Ω and 500-Ω, respectively. (a) What is the power factor of the circuit? (b) If the circuit operates at 60 Hz, what additional capacitance should be connected to the original capacitance to give a
A series RLC circuit has components with R = 50-Ω, L = 0.15H, and C = 20μF. The circuit is driven by a 120-V, 60-Hz source. (a) What is the current in the circuit, expressed as a percentage of the maximum possible cur-rent? (b) What is the power delivered to the circuit, expressed as a
A series RLC radio receiver circuit with an inductance of is tuned to an FM station at 98.9 MHz by adjusting a variable capacitor. When the circuit is tuned to this station, (a) What is its inductive reactance? (b) What is its capacitive reactance? (c) What is its capacitance?
A circuit connected to a 110-V, 60-Hz source contains a resistor and a coil with an inductance of 100 mH. Find (a) The reactance of the coil, (b) The impedance of the circuit, (c) The current in the circuit, and (d) The power dissipated by the coil, (e) Calculate the phase angle between the
A hair dryer is rated at 1200 W when plugged into a 120-V outlet. Find (a) Its rms current, (b) Its peak current, and (c) Its resistance.
A 1.0μF capacitor is connected to a 120-V, 60-Hz source. (a) What is the capacitive reactance of the circuit? (b) How much current is in the circuit? (c) What is the phase angle between the current and the applied voltage? (d) What is the maximum energy stored in the capacitor? (e) What is
(a) If an RLC circuit with a resistance of 450 is in resonance, the phase angle of the circuit is (1) positive, (2) zero, (3) negative. (b) A circuit has an inductive reactance of at 60 Hz. What value of capacitance would set this circuit into resonance? (c) What is the inductance value? (d) If
The circuit in Fig. 21.18a is called a low-pass filter because a large current and voltage (and thus a lot of power) are delivered to the load resistor (RL) only by a low-frequency source. The circuit in Fig. 21.18b is called a high-pass filter because a large current and voltage (and thus a lot of
An ideal transformer is plugged into a 12-V, 60-Hz ac outlet in a motor home, thus enabling the owners to use a 1500-W, 120-V hair dryer. (Ignore any inductance or capacitance associated with the hair dryer.) (a) What type of transformer should be used and what should its turn ratio be? When the
(a) Determine the resonance frequency for the circuit in Fig. 21.17.(b) If the signal generator was capable of a peak voltage output of 24 V, what is the maximum power out-put of the resistor? (c) Determine the resonance frequency and maximum power output if another identical resistor is wired in
(a) For the circuit in Fig. 21.17, what would be the effect on the resonance frequency if one of the capacitors had a capacitance value smaller than that shown: (1) it would decrease, (2) it would increase, or (3) it would remain the same? Explain your reasoning.(b) Determine the new resonance
The voltage across a 10-Ω resistor varies as V = (170 V) sin (100 πt). (a) Is the current in the resistor (1) in phase with the voltage, (2) ahead of the voltage by 90o, or (3) lagging behind the voltage by 90o? (b) Write the expression for the current in the resistor as a function of time and
An ac voltage is applied to a 25-0-Ω resistor so that it dissipates 500 W of power. Find the resistor’s (a) rms and peak currents and (b) rms and peak voltages.
An ac voltage source has a peak voltage of 85 V and a frequency of 60 Hz. The voltage at t = 0 is zero. (a) If a student measures the voltage at t = 1/240s, how many possible results are there: (1) one, (2) two, or (3) three? Why? (b) Determine all possible voltages the student might measure.
An ac voltage source has an rms voltage of 120 V. Its voltage goes from zero to its maximum positive value in 4.20 ms. Write an expression for the voltage as a function of time.
The three pairs of metal same-size spheres have different charges on their surfaces, as indicated. Each pair is brought together, allowed to touch, and then separated. Rank from greatest to least the total amount of charge on the pairs of spheres after separation.
Shown are three separate pairs of point charges. Assume the pairs interact only with each other. Rank the magnitudes of the force between the pairs from largest to smallest.
Why are the tires for trucks carrying gasoline and other flammable fluids manufactured to be electrically conducting?
An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin leaves of metal foil protected from air disturbances in a jar, as shown. When the ball is touched by a charged body, the leaves that normally hang straight down spread apart. Why?
The leaves of a charged electroscope collapse in time. At higher altitudes, they collapse more rapidly. Why is this true?
Is it necessary for a charged body actually to touch the ball of the electroscope for the leaves to diverge? Defend your answer.
Strictly speaking, when an object acquires a positive charge by the transfer of electrons, what happens to its mass? What happens to its mass when it acquires a negative charge?
Strictly speaking, will a penny be slightly more massive if it has a negative charge or a positive charge? Explain.
A crystal of salt consists of electrons and positive ions. How does the net charge of the electrons compare with the net charge of the ions? Explain.
How can you charge an object negatively with only the help of a positively charged object?
It is relatively easy to strip the outer electrons from a heavy atom like that of uranium (which then becomes a uranium ion), but it is very difficult to remove the inner electrons. Why do you suppose this is so?
How does the magnitude of electric force compare between a pair of charged particles when they are brought to half their original distance of separation? To one-quarter their original distance? To 4 times their original distance? (What law guides your answers?)
The proportionality constant k in Coulomb's law is huge in ordinary units, whereas the proportionality constant G in Newton's law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?
If you are caught outdoors in a thunderstorm, why should you not stand under a tree? Can you think of a reason why you should not stand with your legs far apart? Or why lying down can be dangerous?
If a large enough electric field is applied, even an insulator will conduct an electric current, as is evident in lightning discharges through the air. Explain how this happens, taking into account the opposite charges in an atom and how ionization occurs.
If you rub an inflated balloon against your hair and place it against a door, by what mechanism does it stick? Explain.
Why do clothes often cling together after tumbling in a clothes dryer?
How can a charged atom (an ion) attract a neutral atom?
How will the accelerations of the proton and electron in the previous problem compare?
Two pieces of plastic, a full ring and a half ring, have the same radius and charge density. Which electric field at the center has the greater magnitude? Defend your answer.
Imagine a proton at rest a certain distance from a negatively charged plate. It is released and collides with the plate. Then imagine the similar case of an electron at rest the same distance away from a positively charged plate. In which case will the moving particle have the greater speed when
A gravitational field vector points toward Earth; an electric field vector points toward an electron. Why do electric field vectors point away from protons?
By what specific means do the bits of fine threads align in the electric fields shown in Figure 22.19?
You are not harmed by contact with a charged metal ball, even though its voltage may be very high. Is the reason similar to why you are not harmed by the greater-than-1000°C sparks from a Fourth-of-July sparkler? Defend your answer in terms of the energies that are involved.
Why is it safe to remain inside a car during a lightning storm?
In order to store more energy in a parallel-plate capacitor whose plates differ by a fixed voltage, what change would you make in the plates?
Would you feel any electrical effects if you were inside the charged sphere of a Van de Graaff generator? Why or why not?
In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops were observed with a magnifying eyepiece,
Suppose that the charges attracting each other in the preceding problem have equal magnitude. Rearrange Coulomb's law and show that the magnitude of each charge is 2.8 × 10-6 C (2.8 micro coulombs).
Two pellets, each with a charge of 1 micro coulomb (10-6 C), are located 3 cm (0.03 m) apart. Show that the electric force between them is 10N. What would be the mass of an object that would experience this same force in Earth's gravitational field?

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