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electricity and magnetism

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

For the circuit shown in Fig. 18.31, find(a) The cur-rent in each resistor, (b) The voltage across each resistor, and (c) The total power delivered.
Suppose that the resistor arrangement in Fig. 18.28 is connected to a 12-V battery. What will be(a) The current in each resistor, (b) The voltage drop across each resistor, and (c) The total power delivered?
Suppose, in Exercise 14, that another 2.0-Ω resistor is in series with one in the lower branch. (a) Redraw the circuit and predict how the currents in the three different arms will change (increase, decrease, or stay the same) compared to those in the original circuit. (b) Calculate the new
The terminals of a 6.0-V battery are connected to points A and B in Fig. 18.29.(a) How much current is in each resistor? (b) How much power is delivered to each? (c) Compare the sum of the individual powers with the power delivered to the equivalent resistance for the circuit.
Lightbulbs with the power ratings (expressed in watts) given in Fig. 18.32 are connected in a circuit as shown.(a) What current does the voltage source deliver to the circuit? (b) Find the power delivered to each bulb. (Take the bulbs€™ resistances to be the same as at their nor-mal
Two resistors R1 and R2 are in series with a 7.0-V battery. If R1 has a resistance of 2.0-Ω and R2 receives energy at the rate of 6.0 W, what is (are) the value(s) for the circuit’s current(s)? (There may be more than one answer.)
For the circuit in Fig. 18.33, find(a) The current in each resistor, (b) The voltage across each resistor, (c) The power delivered to each resistor, and (d) The total power delivered by the battery.
Two identical resistors (each with resistance R) are connected together in series and then this combination is wired in parallel to a 20-Ω resistor. If the total equivalent resistance is 10-Ω, what is the value of R?
(a) Determine the equivalent resistance of the circuit in Fig. 18.34 Find(b) The current in each resistor,(c) The voltage across each resistor, and(d) The total power delivered to the circuit.
(a) For the circuit show in Fig. 18.10, traverse loop 3 opposite to the direction shown, and demonstrate that the resulting equation is the same as that obtained if you had followed the direction of the arrows.(b) Repeat the procedure in part (a) by traversing loops 1 and 2 in the direction
Use Kirchhoff€™s loop theorem to find the current in each resistor in Fig. 18.30.
Apply Kirchhoff€™s rules to the circuit in Fig. 18.31 to find the current in each resistor.
Two batteries with terminal voltages of 10 V and 4 V are connected with their positive terminals together. A 12-Ω resistor is wired between their negative terminals. (a) The current in the resistor is (1) 0 A, (2) between 0 A and 1.0 A, (3) greater than 1.0 A. Explain your choice. (b) Use
Using Kirchhoff€™s rules, find the current in each resistor in Fig. 18.35.
Apply Kirchhoff€™s rules to the circuit in Fig. 18.36, and find(a) The current in each resistor and (b) The rate at which energy is being delivered to the 8.0-„¦ resistor 8.0.
Find the current in each resistor in the circuit shown in Fig. 18.37.
Find the currents in the circuit branches in Fig 18.38.
For the multiloop circuit shown in Fig. 18.39, what is the current in each branch?
Two identical resistors (R) are connected in parallel and then wired in series to a 40-Ω resistor. If the total equivalent resistance is 55-Ω, what is the value of R?
A capacitor in a single-loop RC circuit is charged to of its final voltage in 1.5 s. Find (a) The time constant for the circuit and (b) The percentage of the circuit’s final voltage after 3.5 s.
In Fig. 18.11b, the switch is closed at t = 0, and the capacitor begins to charge. What is the voltage across the resistor and across the capacitor, expressed as fractions of Vo (to two significant figures), (a) Just after the switch is closed, (b) After two time constants have elapsed, and (c)
In a flashing neon sign display, a certain time constant is desired. (a) To increase this time constant, you should (1) increase the resistance, (2) decrease the resistance, (3) eliminate the resistor. Why? (b) If a 2.0 s time constant is to be tripled and you have a 1.0-μF capacitor, by how
How many time constants will it take for a charged capacitor to be discharged to one-fourth of its initial stored energy?
A 1.00-μF capacitor, initially charged to 12 V, discharges when it is connected in series with a resistor. (a) What resistance is necessary to cause the capacitor to have only of its initial charge 1.50 s after starting? (b) What is the voltage across the capacitor at if the capacitor is instead
A 3.00-μF capacitor, initially charged to 24 V, discharges when it is connected in series with a resistor. (a) How much energy does this capacitor store when fully charged? (b) What is the capacitor’s voltage when it has only half of its maximum energy? Is it 12 V? Why or why not? (c) What
A series RC circuit with C = 40-μF and R = 6.0Ω has a 24-V source in it. With the capacitor initially uncharged, an open switch in the circuit is closed. (a) What is the volt-age across the resistor immediately afterward? (b) What is the voltage across the capacitor at that time? (c) What is
(a) For the circuit in Exercise 36, after the switch has been closed for t = rτ, what is the charge on the capacitor? (b) After a long time has passed, what are the volt-ages across the capacitor and the resistor?
A series RC circuit consisting of a 5.0-MΩ resistor and a 0.40-μF capacitor is connected to a 12-V battery. If the capacitor is initially uncharged, (a) What is the change in voltage across it between and t = 2τ and t = 4τ? (b) By how much does the capacitor’s stored energy change in the
A 3.0-MΩ resistor is connected in series with an initially uncharged 0.28-μF capacitor. This arrangement is then connected across four 1.5-V batteries (also in series). (a) What is the maximum current in the circuit and when does it occur? (b) What percentage of the maximum cur-rent is in the
(a) In how many different ways can three 4.0-Ω resistors, be wired: (1) three, (2) five, or (3) seven? (b) Sketch the different ways you found in part (a) and determine the equivalent resistance for each.
A galvanometer with a full-scale sensitivity of 2000 μA has a coil resistance of 100-Ω. It is to be used in an ammeter with a full-scale reading of 30 A. (a) Should you use (1) a shunt resistor, (2) a zero resistor, or (3) a multiplier resistor? Why? (b) What is the necessary resistance for
The galvanometer in Exercise 40 is to be used in a voltmeter with a full-scale reading of 15 V. (a) Should you use (1) a shunt resistor, (2) a zero resistor, or (3) a multiplier resistor? Why? (b) What is the required resistance for your answer choice in part (a)?
A galvanometer with a full-scale sensitivity of 600 μA and a coil resistance of 50-Ω is to be used to build an ammeter designed to read 5.0 A at full scale. What is the required shunt resistance?
A galvanometer has a coil resistance of 20-Ω. A current of 200μA deflects the needle through ten divisions at full scale. What resistance is needed to convert the galvanometer to a full-scale 10-V voltmeter?
An ammeter has a resistance of 1.0mΩ. Sketch the circuit diagram and find (a) The current in the ammeter and (b) The voltage drop across a 10-Ω resistor that is in series with a 6.0-V ideal battery when the ammeter is properly connected to that resistor. (Express your answer to five
A voltmeter has a resistance of 30-kΩ. (a) Sketch the circuit diagram and find the current in a 10-Ω resistor that is in series with a 6.0 V ideal battery when the volt-meter is properly connected across that 10-Ω resistor. (b) Find the voltage across the resistor under the same conditions.
In principle, when used together, an ammeter and voltmeter allow for the measurement of the resistance of any circuit element. Let’s assume that that element is a simple ohmic resistor. Suppose that the ammeter is connected in series with the resistor (which is connected to an ideal power source
In Exercise 46, suppose instead that the ammeter is connected in series with the resistor and that the volt-meter is placed across both the ammeter and the resistor. (a) Sketch this circuit (with instruments connected) and use it to explain why the correct resistance is not given by R = V/I, where
Suppose you are using a drill that is incorrectly wired as in Fig. 18.22a, and you make electrical contact with an ungrounded metal case. (a) Explain why this is a dangerous situation for you. (b) Estimate the current in you, assuming an overall body resistance of 300-Ω between your hand and
(a) In Exercise 48, suppose instead the case had been properly wired and grounded as shown in Figure 18.23. If the grounding wire had a total resistance of 0.10-Ω, what is the ratio of the current in you to the current in the ground wire, assuming that the fuse/ circuit breaker does not
Three resistors with values of 5.0-Ω, 10-Ω, and 15-Ω are connected in series in a circuit with a 9.0-V battery. (a) What is the total equivalent resistance? (b) What is the current in each resistor? (c) At what rate is energy delivered to the 15-Ω resistor?
One day your electric stove does not turn on. You decide to check the 240-V outlet to see if it is the problem. You use two voltmeter probes inserted into the out-let slots, but because of cramped conditions, you accidentally touch the metal part of both probes, one with each hand. (a) How much
Find the(a) Current in,(b) Voltage across, and(c) Power generated for each resistor shown in the circuit in Fig. 18.40.
Four resistors are connected in a circuit with a 110-V source, as shown in Fig. 18.41.(a) What is the current in each resistor?(b) How much power is delivered to each resistor?
Nine resistors, each of value R, are connected in a €œladder€ fashion, as shown in Fig. 18.42.(a) What is the effective resistance of this network between points A and B? (b) If R = 10 „¦ and a 12.0-V battery is connected from point A to point B, how much current
Fig. 18.43 shows a schematic circuit of an instrument called a potentiometer, which is a device for determining very accurate emf values of power supplies. It consists of three batteries, an ammeter, several resistors, and a uniform wire that can be €œtapped€ for a specific
A battery has three cells connected in series, each with an internal resistance of 0.020-Ω and an emf of 1.50 V. This battery is connected to a 10.0-Ω resistor. (a) Determine the voltage across the resistor. (b) How much current is in each cell? (c) What is the rate at which heat is
A 10.0-μF capacitor in a heart defibrillator unit is charged fully by a 10 000-V power supply. Each capacitor plate is connected to the chest of a patient by wires and flat “paddles,” one on either side of the heart. The energy stored in the capacitor is delivered through an RC circuit, where
During an operation, one of the electrical instruments in use has its metal case shorted to the 120-V “hot” wire that powers it. The attending physician, who is isolated from ground because of rubber-soled shoes, inadvertently touches the case with his elbow, while simultaneously touching the
An air-filled parallel plate capacitor is being used in an electrical circuits laboratory. The plates are separated by 1.50 mm and each has a diameter of 15.0 cm. (a) What is the capacitance of this plate arrangement? (b) The capacitor is then connected in series to a 100-Ω resistor and a 100-V
An air-filled parallel plate capacitor consists of square plates 10.0 cm on a side separated by 2.25 mm. (a) What is the capacitance of this arrangement? (b) The capacitor is then connected in series to a 500-Ω resistor and a 25-V DC power supply. What is the time constant of this circuit? (c)
Three resistors with values 1.0-Ω, 2.0-Ω, and 4.0-Ω are connected in parallel in a circuit with a 6.0-V battery. What are (a) The total equivalent resistance, (b) The volt-age across each resistor, and (c) The power delivered to the 4.0-Ω resistor?
A length of wire with a resistance R is cut into two equal-length segments. These segments are then twisted together to form a conductor half as long as the original wire. (a) The resistance of the shortened conductor is (1) R/4, (2) R/2, (3) R. Explain your reasoning. (b) If the resistance of
You are given four resistors. (a) Show how to connect all the resistors so as to produce an effective total resistance of . (b) If this network were then connected to a 12-V battery, determine the current in and voltage across each resistor.
Two resistors are connected in parallel, as are two 4.0-Ω resistors. These two combinations are then connected in series in a circuit with a 12-V battery. What is the current in each resistor and the voltage across each resistor?
Along wire is placed 2.0 cm directly below a rigidly mounted second wire (Fig. 19.42).(a) Use the right-hand source and force rules to determine whether the currents in the wires should be in (1) the same or (2) the opposite direction so that the lower wire is in equilibrium. (It
A beam of protons is accelerated easterly from rest through a potential difference of 3.0 kV. It enters a region where there exists an upward pointing uniform electric field. This field is created by two parallel plates separated by 10 cm with a potential difference of 250 V across them. (a) What
A cylindrical solenoid 10 cm long has 3000 turns of wire and carries a current of 5.0 A. A second solenoid, consisting of 2000 turns of wire and the same length as the first solenoid, surrounds it and is concentric (shares a common central axis) with it. The outer coil carries a current of 10 A in
A charge of 0.250 C moves vertically in a field of 0.500 T that is oriented some angle from the vertical. If the charge’s speed is 2.0 x 102 m/s, what field angle(s) will ensure that the force acting on the charge is 5.0 N?
A proton enters a uniform magnetic field that is at a right angle to its velocity. The field strength is 0.80 T and the proton follows a circular path with a radius of 4.6 cm. What are (a) The magnitude of its linear momentum and (b) Its kinetic energy? (c) If its speed were doubled, what would
Exiting a linear accelerator, a narrow horizontal beam of protons travels due north. If 1.75 x 1013 protons pass a given point per second, (a) Determine the magnetic field direction and strength at a location of 2.40 m east of the beam. (b) Does it seem likely this would demagnetize the encoded
A 200-turn circular coil of wire has a radius of 10.0 cm and a total resistance of . At its center the magnetic field strength is 7.45 mT. (a) Determine the voltage of the power supply creating the current in the coil. (b) What would be the field strength at a point 4.5 cm directly above or below
A 100-turn circular coil of wire has a radius of 20.0 cm and carries a current of 0.400 A. The normal to the coil area points due east. A compass, when placed at the center of the coil, does not point east, but instead makes an angle of 60o north of east. Using this data, determine (a) The
A circular coil of current-carrying wire has the normal to its area pointing upward. A second smaller concentric circular coil carries a current in the opposite direction. (a) Where, in the plane of these coils, could the magnetic field be zero: (1) only inside the smaller one, (2) only between
Consider the following arrangement (called Helmholtz coils) of two identical current-carrying coils. They are €œstacked€ vertically with their centers on a common vertical axis and their areas arranged horizontally, as shown in Fig. 19.43. Assume each has 100 loops of wire,
Abeam of protons is accelerated to a speed of 5.0 x 106 m/s in a particle accelerator and emerges horizontally from the accelerator into a uniform magnetic field. What magnetic field (give its direction and magnitude) oriented perpendicularly to the velocity of the proton would cancel the force of
An electron travels in the +x-direction in a magnetic field and is acted on by a magnetic force in the – y-direction. (a) In which of the following directions could the magnetic field be oriented: (1) – x, (2) +y, (3) + z, or (4) – z? Explain. (b) If the electron speed is 3.0 x 106 m/s and
An electron travels at a speed of 2.0 x 104 m/s through a uniform magnetic field whose magnitude is 1.2 x 10-3 T. What is the magnitude of the magnetic force on the electron if its velocity and the magnetic field (a) Are perpendicular, (b) Make an angle of 45o, (c) Are parallel, and (d) Are
Given two identical iron bars, one of which is a permanent magnet and the other unmagnetized, how could you tell which is which by using only the two bars?
The enlarged circular inset in Fig. 19.11 shows how the positive sodium ions in seawater are accelerated out the rear of the submarine to provide a propulsive force. But what about the negative chlorine ions in the seawater? Because they have charge of the opposite sign, aren’t they accelerated
(a) Redraw the charged particle path in the apparatus diagrammed in Fig. 19.9 if the electric field of the velocity selector were reduced in magnitude. (b) Redraw the charged particle path in the apparatus diagrammed in Fig. 19.9 if the magnetic field of the velocity selector were reduced in
(a) How would you orient a square current loop in a uniform magnetic field so that there is no torque on the loop? (b) How would the orientation change to maximize the torque on the loop? (c) In each case, is there a net magnetic force on this loop? Explain.
Explain the operation of the doorbell and door chimes illustrated in Fig. 19.35.
In a long, straight, current- carrying wire, the electrons are moving to the west. If the wire is in a uniform magnetic field pointing upward, what is the direction of the force on the wire? Answer this from two different view-points: that of the force on the electrons, and then that of the force
(a) Show that the SI unit for magnetic moment multiplied by the SI unit for magnetic field yields the SI unit for torque. (b) If you are looking down onto the area of a current- carrying loop of wire and the current is counter-clockwise, what is the direction of the loop’s magnetic moment?
The direction of any magnetic field is taken to be in the direction that a compass points. Explain why this means that magnetic field lines must leave from the north pole of a permanent bar magnet and enter its south pole.
Suppose a long, straight, current- carrying wire had a current from west to east. If it were immersed in a vertically upward magnetic field that was stronger on its west side than on its east side, what would be the initial motion of the wire if released from rest? Explain.
Given two solenoids, one with 100 turns and the other with 200 turns. If both carry the same current, will the one with more turns necessarily produce a stronger magnetic field at its center? Explain.
To minimize the effects of the magnetic field when needed, the wires carrying current to equipment or appliances are placed close together. Explain how this works to reduce the magnetic field created by the cur-rent in the wire.
Two circular wire loops are coplanar (that is, their areas are in the same plane) and have a common center. The outer loop carries a current of 10 A in the clockwise direction. To create a zero magnetic field at the center of the loops, what should be the direction of the current in the inner loop?
Discuss several ways that the magnetic field of a permanent magnet can be destroyed or reversed.
(a) As you start in the very middle of Fig. 19.3b and move horizontally to the right, what happens to the magnetic field spacing as indicated by the iron filing pat-tern? What does this imply in terms of the magnetic field strength? (b) What is the direction of the magnetic field in this region of
Determine the direction of the force due to the Earth’s magnetic field on an electron near the equator when the electron’s velocity is directed (a) Due south, (b) North-west, and (c) Upward.
A proton and an electron are moving at the same velocity perpendicularly to a constant magnetic field. (a) How do the magnitudes and directions of the magnetic forces on them compare? (b) What about the magnitudes of their accelerations?
If a charged particle moves in a straight line and there are no other forces on it except possibly from a magnetic field, can you say with certainty that no magnetic field is present? Explain.
Three particles enter the same uniform magnetic field as shown in Fig. 19.33a. Particles 1 and 3 have equal speeds and charges of the same magnitude. What can you say about(a) The charges of the particles and(b) Their masses?
You want to deflect a positively charged particle in an S- shaped path, as shown in Fig. 19.33b, using only magnetic fields. (a) Explain how this could be done by using magnetic fields perpendicular to the plane of the page. (b) How does the emerging particle’s kinetic energy compare with the
A magnetic field can be used to determine the sign of charge carriers in a current- carrying wire. Consider a wide conducting strip in a magnetic field oriented as shown in Fig. 19.34. The charge carriers are deflected by the magnetic force and accumulate on one side of the strip, giving rise to a
A permanent bar magnet (# 1) is vertically oriented so that its north end is below its south end. The north end of this magnet feels an upward magnetic force of 1.5 mN from an identical vertically oriented magnet (# 2) that has one end located 2.5 cm directly below the north end of # 1. (a) Make a
(a) What angle(s) does a particle’s velocity have to make with the magnetic field direction for the particle to be subjected to half the maximum possible magnetic force, Fmax? (b) Express the magnetic force on a charged particle in terms of Fmax if the angle between its velocity and the magnetic
A beam of protons exits from a particle accelerator due east at a speed of 3.0 x 105 m/s. The protons then enter a uniform magnetic field of magnitude 0.50 T that is oriented at above 37o the horizontal relative to the beam direction. (a) What is the initial acceleration of a proton as it enters
An ionized deuteron (a bound proton–neutron system with a net +e charge) passes through a velocity selector whose perpendicular magnetic and electric fields have magnitudes of 40 mT and 8.0 kV/m, respectively. Find the speed of the ion.
In a velocity selector, the uniform magnetic field of 1.5 T is produced by a large magnet. Two parallel plates with a separation of 1.5 cm produce the perpendicular electric field. What voltage should be applied across the plates so that (a) A singly charged ion traveling at 8.0 x 104 m/s will
A charged particle travels undeflected through per-pendicular electric and magnetic fields whose magnitudes are 3000 N/C and 30mT, respectively. Find the speed of the particle if it is (a) A proton and (b) An alpha particle. (An alpha particle is a helium nucleus—a positive ion with a double
In an experimental technique for treating deep tumors, unstable positively charged pions (π+, elementary particles with a mass of 2.25 x 10-28 kg) penetrate the flesh and disintegrate at the tumor site, releasing energy to kill cancer cells. If pions with a kinetic energy of 10 keV are required
In a mass spectrometer, a singly charged ion having a particular velocity is selected by using a magnetic field of 0.10 T perpendicular to an electric field of 1.0 x 103 v/m. A magnetic field of this same magnitude is then used to deflect the ion, which moves in a circular path with a radius of 1.2
In a mass spectrometer, a doubly charged ion having a particular velocity is selected by using a magnetic field of 100 mT perpendicular to an electric field of 1.0 kV/m. This same magnetic field is then used to deflect the ion in a circular path with a radius of 15 mm. Find (a) The mass of the ion
In a mass spectrometer, a beam of protons enters a magnetic field. Some protons make exactly a one-quarter circular arc of radius 0.50 m. If the field is always perpendicular to the proton’s velocity, (a) What is the field’s magnitude if exiting protons have a kinetic energy of 10 keV? (b)
(a) Use a right-hand force rule to find the direction of the current in the wires shown in Fig. 19.36. In each case, the magnetic force direction is shown.(b) If in each case the wire is a straight segment 15 cm long carrying a current of 5.5 A, and is in a B-field whose strength is 1.0mT,
Two identical bar magnets of negligible width are located in the x-y plane. Magnet # 1 lies on the x-axis and its north end is at while its south end is at Magnet # 2 lies on the y-axis and its north end is at y = + 1.0cm, while its south end is at y = + 5.0 cm. (a) In what direction would a

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