11th Edition Exam Prep Ch.30 Induction And Inductance - Physics Extended 11e | Test Bank by Halliday by David Halliday. DOCX document preview.
Chapter: Chapter 30
Learning Objectives
LO 30.1.0 Solve problems related to Faraday's Law and Lenz's Law.
LO 30.1.1 Identify that the amount of magnetic field piercing a surface (not skimming along the surface) is the magnetic flux Φ through the surface.
LO 30.1.2 Identify that an area vector for a flat surface is a vector that is perpendicular to the surface and that has a magnitude equal to the area of the surface.
LO 30.1.3 Identity that any surface can be divided into area elements (patch elements) that are each small enough and flat enough for an area vector to be assigned to it, with the vector perpendicular to the element and having a magnitude equal to the area of the element.
LO 30.1.4 Calculate the magnetic flux Φ through a surface by integrating the dot product of the magnetic field vector and the area vector (for patch elements) over the surface, in magnitude-angle notation and unit-vector notation.
LO 30.1.5 Identify that a current is induced in a conducting loop while the number of magnetic field lines intercepted by the loop is changing.
LO 30.1.6 Identify that an induced current in a conducting loop is driven by an induced emf.
LO 30.1.7 Apply Faraday’s law, which is the relationship between an induced emf in a conducting loop and the rate at which magnetic flux through the loop changes.
LO 30.1.8 Extend Faraday’s law from a loop to a coil with multiple loops
LO 30.1.9 Identify the three general ways in which the magnetic flux through a coil can change.
LO 30.1.10 Use a right-hand rule for Lenz’s law to determine the direction of induced emf and induced current in a conducting loop.
LO 30.1.11 Identify that when a magnetic flux through a loop changes, the induced current in the loop sets up a magnetic field to oppose that change.
LO 30.1.12 If an emf is induced in a conducting loop containing a battery, determine the net emf and calculate the corresponding current in the loop.
LO 30.2.0 Solve problems related to induction and energy transfers.
LO 30.2.1 For a conducting loop pulled into or out of a magnetic field, calculate the rate at which energy is transferred to thermal energy.
LO 30.2.2 Apply the relationship between an induced current and the rate at which it produces thermal energy.
LO 30.2.3 Describe eddy currents.
LO 30.3.0 Solve problems related to induced electric fields.
LO 30.3.1 Identify that a changing magnetic field induces an electric field, regardless of whether there is a conducting loop.
LO 30.3.2 Apply Faraday’s law to relate the electric field induced along a closed path (whether it has conducting material or not) to the rate of change dΦ/dt of the magnetic flux encircled by the path.
LO 30.3.3 Identify that an electric potential cannot be associated with an induced electric field.
LO 30.4.0 Solve problems related to inductors and inductance.
LO 30.4.1 Identify an inductor.
LO 30.4.2 For an inductor, apply the relationship between inductance L, total flux NΦ, and current i.
LO 30.4.3 For a solenoid, apply the relationship between the inductance per unit length L/ℓ, the area A of each turn, and the number of turns per unit length n.
LO 30.5.0 Solve problems related to self-induction.
LO 30.5.1 Identify that an induced emf appears in a coil when the current through the coil is changing and that this emf is included in a loop equation for the circuit.
LO 30.5.2 Apply the relationship between the induced emf in a coil, the coil’s inductance L, and the rate di/dt at which the current is changing.
LO 30.5.3 When an emf is induced in a coil by a changing current, determine the direction of the
emf by using Lenz’s law to show that the emf always opposes the change in the current, attempting to maintain the initial current.
LO 30.6.0 Solve problems related to RL circuits.
LO 30.6.1 Sketch a schematic diagram of an RL circuit in which the current is rising.
LO 30.6.2 Write a loop equation (a differential equation) for an RL circuit in which the current is rising.
LO 30.6.3 For an RL circuit in which the current is rising, apply the equation i(t) for the current as a function of time.
LO 30.6.4 For an RL circuit in which the current is rising, find equations for the potential difference V across the resistor, the rate di/dt at which the current changes, and the emf of the inductor, as functions of time.
LO 30.6.5 Calculate an inductive time constant τL.
LO 30.6.6 Sketch a schematic diagram of an RL circuit in which the current is decaying.
LO 30.6.7 Write a loop equation (a differential equation) for an RL circuit in which the current is decaying.
LO 30.6.8 For an RL circuit in which the current is decaying, apply the equation i(t) for the current as a function of time.
LO 30.6.9 From an equation for decaying current in an RL circuit, find equations for the potential difference V across the resistor, the rate di/dt at which current is changing, and the emf of the inductor, as functions of time.
LO 30.6.10 For an RL circuit, identify the current through the inductor and the emf across it just as current in the circuit begins to change and a long time later when equilibrium is reached.
LO 30.7.0 Solve problems related to energy stored in a magnetic field.
LO 30.7.1 Describe the derivation of the equation for the magnetic field energy of an inductor in an RL circuit.
LO 30.7.2 For an inductor, apply the relationship between that magnetic field energy U, the inductance L, and the current i.
LO 30.8.0 Solve problems related to energy density of a magnetic field.
LO 30.8.1 Identify that energy is associated with any magnetic field.
LO 30.8.2 Apply the relationship between energy density u of a magnetic field and the magnetic field magnitude B.
LO 30.9.0 Solve problems related to mutual induction.
LO 30.9.1 Describe the mutual induction of two coils and sketch the arrangement.
LO 30.9.2 Calculate the mutual inductance of one coil with respect to a second coil (or some second current that is changing).
LO 30.9.3 Calculate the emf induced in one coil by a second coil in terms of the mutual inductance and the rate of change of the current in the second coil.
Multiple Choice
1. The emf that appears in Faraday's law is:
A) around a conducting circuit
B) around the boundary of the surface used to compute the magnetic flux
C) throughout the surface used to compute the magnetic flux
D) perpendicular to the surface used to compute the magnetic flux
E) none of the above
Difficulty: E
Section: 30-1
Learning Objective 30.1.0
2. 1 weber is the same as:
A) 1 V/s
B) 1 T/s
C) 1 T/m
D) 1 Tm2
E) 1 T/m2
Difficulty: E
Section: 30-1
Learning Objective 30.1.0
3. 1 weber is the same as:
A) 1 Vs
B) 1 Ts
C) 1 T/m
D) 1 V/s
E) 1 T/m2
Difficulty: E
Section: 30-1
Learning Objective 30.1.0
4. The units of motional emf are:
A) volt/second
B) voltmeter/second
C) volt/tesla
D) tesla/second
E) teslameter2/second
Difficulty: E
Section: 30-1
Learning Objective 30.1.0
5. The magnetic flux ΦB through a surface:
A) is the amount of magnetic field piercing the surface.
B) is the magnetic field multiplied by the area.
C) does not depend on the area involved.
D) is the line integral of the magnetic field around the edge of the surface.
E) is the amount of magnetic field skimming along the surface.
Difficulty: E
Section: 30-1
Learning Objective 30.1.1
6. The normal to a certain 1.0 m2 area makes an angle of 60 with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:
A) 0.50 m2
B) 0.87 m2
C) 1.0 m2
D) 1.2 m2
E) 2.0 m2
Difficulty: E
Section: 30-1
Learning Objective 30.1.4
7. Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30 around an edge the flux through it will be:
A) 2.5 Wb
B) 4.3 Wb
C) 5.0 Wb
D) 5.8 Wb
E) 10 Wb
Difficulty: E
Section: 30-1
Learning Objective 30.1.4
8. A 2.0 T uniform magnetic field makes an angle of 30 with the z axis. The magnetic flux through a 3.0 m2 portion of the xy plane is:
A) 2.0 Wb
B) 3.0 Wb
C) 5.2 Wb
D) 6.0 Wb
E) 12 Wb
Difficulty: E
Section: 30-1
Learning Objective 30.1.4
9. A uniform magnetic field makes an angle of 30 with the z axis. If the magnetic flux through a 1.0 m2 portion of the xy plane is 5.0 Wb then the magnetic flux through a 2.0 m2 portion of the same plane is:
A) 2.5 Wb
B) 4.3 Wb
C) 5.0 Wb
D) 5.8 Wb
E) 10 Wb
Difficulty: E
Section: 30-1
Learning Objective 30.1.4
10. In the experiment shown:
A) there is a steady reading in G as long as S is closed
B) a motional emf is generated when S is closed
C) the current in the battery goes through G
D) there is a current in G just after S is opened or closed
E) since the two loops are not connected, the current in G is always zero
Difficulty: E
Section: 30-1
Learning Objective 30.1.5
11. Faraday's law states that an induced emf is proportional to:
A) the rate of change of the magnetic field
B) the rate of change of the electric field
C) the rate of change of the magnetic flux
D) the rate of change of the electric flux
E) zero
Difficulty: E
Section: 30-1
Learning Objective 30.1.5
12. If the magnetic flux through a certain region is changing with time:
A) energy must be dissipated as heat
B) an electric field must not exist at the boundary
C) a current must flow around the boundary
D) an emf must exist around the boundary
E) a magnetic field must exist at the boundary
Difficulty: E
Section: 30-1
Learning Objective 30.1.5
13. The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:
A) magnetic field in X
B) rate of change of magnetic field in X
C) resistance of X
D) thickness of the wire in X
E) current in Y
Difficulty: E
Section: 30-1
Learning Objective 30.1.5
14. In the circuit shown, there will be a non-zero reading in galvanometer G:
A) only just after S is closed
B) only just after S is opened
C) only while S is kept closed
D) never
E) only just after S is opened or closed
Difficulty: E
Section: 30-1
Learning Objective 30.1.5
15. Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. Now that S is closed, to make the pointer of G deflect toward the right one could:
A) move the slide of the rheostat R quickly to the right
B) move coil P toward coil Q
C) move coil Q toward coil P
D) open S
E) do none of the above
Difficulty: E
Section: 30-1
Learning Objective 30.1.5
16. A rod lies across frictionless rails in a uniform magnetic field B, as shown. The rod moves to the right with speed v. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should:
A) not change
B) increase linearly with time
C) decrease linearly with time
D) increase quadratically with time
E) decrease quadratically with time
Difficulty: M
Section: 30-1
Learning Objective 30.1.5
17. A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 10–4 T. The emf induced between the left and right side, separated by 1.7 m, is:
A) 0 V
B) 1.8 mV
C) 3.6 mV
D) 6.4 mV
E) 23 mV
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
18. A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is:
A) BAf/2π
B) BAf
C) 2BAf
D) 2BAf
E) 4BAf
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
19. The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the plane of a conducting loop. Rank the four regions indicated on the graph according to the magnitude of the emf induced in the loop, from least to greatest.
A) 1, 2, 3, 4
B) 2, 4, 3, 1
C) 4, 3, 1, 2
D) 1, 3, 4, 2
E) 4, 3, 2, 1
Difficulty: E
Section: 30-1
Learning Objective 30.1.7
20. A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected as shown. V1 reads 1 mV across R. V2 reads the voltage across the other two resistors, which is:
A) 0 V
B) 1/3 mV
C) 1/2 mV
D) 1 mV
E) 2 mV
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
21. The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the same speed into a region of uniform magnetic field directed out of the page. Rank them according to the maximum magnitude of the induced emf, least to greatest.
A) 1 and 2 tie, then 3 and 4 tie
B) 3 and 4 tie, then 1 and 2 tie
C) 4, then 2 and 3 tie, then 1
D) 1, then 2 and 3 tie, then 4
E) 1, 2, 3, 4
Difficulty: E
Section: 30-1
Learning Objective 30.1.7
22. A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun around one of its sides at frequency f. The induced emf is a maximum when:
A) the flux is zero
B) the flux is a maximum
C) the flux is half its maximum value
D) the derivative of the flux with respect to time is zero
E) none of the above
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
23. A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines run along the north-south direction. The largest induced emf is produced when the hoop is:
A) rotated about a north-south axis
B) rotated about an east-west axis
C) moved rapidly, without rotation, toward the east
D) moved rapidly, without rotation, toward the south
E) moved rapidly, without rotation, toward the northwest
Difficulty: E
Section: 30-1
Learning Objective 30.1.7
24. A 10 turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a magnetic field of 0.50 T. The maximum emf generated is:
A) 0.014 V
B) 0.085 V
C) 0.53 V
D) 0.85 V
E) 5.3 V
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
25. The diagram shows a circular loop of wire that rotates at a steady rate about a diameter O that is perpendicular to a uniform magnetic field. The maximum induced emf occurs when the point X on the loop passes:
A) a
B) b
C) c
D) d
E) e
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
26. A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at:
A) 0 rad/s
B) 2.7 rad/s
C) 5.6 rad/s
D) 35 rad/s
E) 71 rad/s
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
27. A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 10–5 T. The emf around the rim is:
A) 0 V
B) 0.5 mV
C) 3.1 mV
D) 15 mV
E) 190 mV
Difficulty: M
Section: 30-1
Learning Objective 30.1.7
28. One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.100 m2. The circuit is completed by connecting the coil to a 10- resistor. As the magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other direction, the total charge that flows through the resistor is:
A) 0.01 C
B) 0.02 C
C) 0.2 C
D) 1 C
E) 2 C
Difficulty: M
Section: 30-1
Learning Objective 30.1.8
29. A magnet moves inside a coil. Consider the following factors:
I. | strength of the magnet | ||
II. | number of turns in the coil | ||
III. | speed at which the magnet moves |
Which can affect the emf induced in the coil?
A) I only
B) II only
C) III only
D) I and II only
E) I, II, III
Difficulty: E
Section: 30-1
Learning Objective 30.1.9
30. A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into the page. The induced current in the loop is:
A) counterclockwise
B) clockwise
C) zero
D) up the left edge and from right to left along the top edge
E) through the middle of the page
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
31. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries a constant current i, as shown. While the wire is being moved toward the loop, the current in the loop is:
A) zero
B) clockwise
C) counterclockwise
D) clockwise in the left side and counterclockwise in the right side
E) counterclockwise in the left side and clockwise in the right side
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
32. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries an increasing current in the direction shown. The current in the loop is:
A) zero
B) clockwise
C) counterclockwise
D) clockwise in the left side and counterclockwise in the right side
E) counterclockwise in the left side and clockwise in the right side
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
33. A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially carries a constant current i in the direction shown. While the current i is being shut off, the current in the loop is:
A) zero
B) clockwise
C) counterclockwise
D) clockwise in the left side and counterclockwise in the right side
E) counterclockwise in the left side and clockwise in the right side
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
34. A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i1 and i2 as indicated. If i1 is increasing and i2 is constant, then the induced current in the loop is:
A) zero
B) clockwise
C) counterclockwise
D) depends on i1 – i2
E) depends on i1 + i2
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
35. You push a permanent magnet with its north pole away from you toward a loop of conducting wire in front of you. Before the north pole enters the loop the current in the loop is:
A) zero
B) clockwise
C) counterclockwise
D) to your left
E) to your right
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
36. A vertical bar magnet is dropped through the center of a horizontal loop of wire, with its north pole leading. At the instant when the midpoint of the magnet is in the plane of the loop, the induced current in the loop, viewed from above, is:
A) maximum and clockwise
B) maximum and counterclockwise
C) not maximum but clockwise
D) not maximum but counterclockwise
E) essentially zero
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
37. A circular loop of wire rotates about a diameter in a magnetic field that is perpendicular to the axis of rotation. Looking in the direction of the field at the loop the induced current is:
A) always clockwise
B) always counterclockwise
C) clockwise in the lower half of the loop and counterclockwise in the upper half
D) clockwise in the upper half of the loop and counterclockwise in the lower half
E) sometimes clockwise and sometimes counterclockwise
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
38. A circular loop of wire is positioned half in and half out of a square region of constant uniform magnetic field directed into the page, as shown. To induce a clockwise current in this loop:
A) move it in +x direction
B) move it in +y direction
C) move it in –x direction
D) move it in –y direction
E) increase the strength of the magnetic field
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
39. The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field between the rails should be in what direction?
A) Right
B) Left
C) Into the page
D) Out of the page
E) Impossible, cannot be done with a constant magnetic field
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
40. A square loop of wire moves with a constant speed v from a field-free region into a region of uniform B field, as shown. Which of the five graphs correctly shows the induced current i in the loop as a function of time t?
A) I
B) II
C) III
D) IV
E) V
Difficulty: E
Section: 30-1
Learning Objective 30.1.10
41. As an externally generated magnetic field through a certain conducting loop increases in magnitude, the field produced at points inside the loop by the current induced in the loop must be:
A) increasing in magnitude
B) decreasing in magnitude
C) in the same direction as the applied field
D) directed opposite to the applied field
E) perpendicular to the applied field
Difficulty: E
Section: 30-1
Learning Objective 30.1.11
42. At a particular instant of time the total magnetic flux through a stationary conducting loop is less in magnitude than the flux associated with an externally applied field. This might occur because:
A) the applied field is normal to the loop and increasing in magnitude
B) the applied field is normal to the loop and decreasing in magnitude
C) the applied field is parallel to the plane of the loop and increasing in magnitude
D) the applied field is parallel to the plane of the loop and decreasing in magnitude
E) the applied field is tangent to the loop
Difficulty: E
Section: 30-1
Learning Objective 30.1.11
43. The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit is 0.20 A. At what rate is the magnitude of the magnetic field changing? Is it increasing or decreasing?
A) 0 T/s
B) 140 T/s, decreasing
C) 140 T/s, increasing
D) 420 T/s, decreasing
E) 420 T/s, increasing
Difficulty: M
Section: 30-1
Learning Objective 30.1.12
44. A copper penny slides on a horizontal frictionless table. There is a square region of constant uniform magnetic field perpendicular to the table, as shown. Which graph correctly shows the speed v of the penny as a function of time t?
A) I
B) II
C) III
D) IV
E) V
Difficulty: E
Section: 30-2
Learning Objective 30.2.0
45. A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed v is:
A) 0
B) BLv
C) BLv/R
D) B2L2v/R
E) B2Lxv/R
Difficulty: M
Section: 30-2
Learning Objective 30.2.1
46. A rod of length L and electrical resistance R moves through a constant uniform magnetic field ; both the magnetic field and the direction of motion are parallel to the rod. The force that must be applied by a person to keep the rod moving with constant velocity is:
A) 0
B) BLv
C) BLv/R
D) B2L2v/R
E) B2L2v2/R
Difficulty: M
Section: 30-2
Learning Objective 30.2.1
47. As a loop of wire with a resistance of 10 moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5.0 mJ/s. The induced current in the loop is:
A) 0 A
B) 2.0 mA
C) 2.8 mA
D) 22 mA
E) cannot be calculated from the given data
Difficulty: M
Section: 30-2
Learning Objective 30.2.2
48. As a loop of wire with a resistance of 10 moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop is:
A) 0 V
B) 0.22 V
C) 0.28 V
D) 2.0 V
E) cannot be calculated from the given data
Difficulty: M
Section: 30-2
Learning Objective 30.2.2
49. Which statement about eddy currents is false?
A) They can be prevented by cutting a slot in a solid conducting plate, to prevent electrons from being able to make a complete circuit.
B) The mechanical energy that is lost when eddy currents are created returns when the eddy currents cease.
C) They can be used as a passive braking system, as no external power source is needed if permanent magnets are used.
D) They are created in solid conducting plates as they move in and out of magnetic fields.
E) The faster the conductor moves, the larger the eddy currents will be.
Difficulty: M
Section: 30-2
Learning Objective 30.2.3
50. An electric field is associated with every:
A) magnetic field
B) time-dependent magnetic field
C) position-dependent magnetic field
D) object moving in a magnetic field
E) conductor moving in a magnetic field
Difficulty: E
Section: 30-3
Learning Objective 30.3.1
51. A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its axis. If the electric field induced at a point R/2 from the cylinder axis is 4.5 10-3 V/m the magnitude of the magnetic field must be changing at the rate of:
A) 0 T/s
B) 0.30 T/s
C) 0.60 T/s
D) 1.2 T/s
E) 2.4 T/s
Difficulty: M
Section: 30-3
Learning Objective 30.3.2
52. A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the electric field induced at a point 2R from the cylinder axis is:
A) 0
B) 2R dB/dt
C) R dB/dt
D) (R/2) dB/dt
E) (R/4) dB/dt
Difficulty: E
Section: 30-3
Learning Objective 30.3.2
53. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time. If r is the radial distance from the cylinder axis, the magnitude of the induced electric field inside the cylindrical region is proportional to:
A) R
B) r
C) r2
D) 1/r
E) 1/r2
Difficulty: E
Section: 30-3
Learning Objective 30.3.2
54. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time. If r is the radial distance from the cylinder axis, the magnitude of the induced electric field outside the cylinder is proportional to:
A) R
B) r
C) r2
D) 1/r
E) 1/r2
Difficulty: E
Section: 30-3
Learning Objective 30.3.2
55. The unit "henry" is equivalent to:
A) voltsecond/ampere
B) volt/second
C) ohm
D) amperevolt/second
E) amperesecond/volt
Difficulty: E
Section: 30-4
Learning Objective 30.4.0
56. A 10-turn ideal solenoid has an inductance of 3.5 mH. When the solenoid carries a current of 2.0 A the magnetic flux through each turn is:
A) 0 Wb
B) 3.5 10–4 Wb
C) 7.0 10–4 Wb
D) 7.0 10–3 Wb
E) 7.0 10–2 Wb
Difficulty: M
Section: 30-4
Learning Objective 30.4.2
57. A long narrow solenoid has length ℓ and a total of N turns, each of which has cross-sectional area A. Its inductance is:
A) µ0N2Aℓ
B) µ0N2A/ℓ
C) µ0NA/ℓ
D) µ0N2 ℓ/A
E) none of these
Difficulty: M
Section: 30-4
Learning Objective 30.4.3
58. A flat coil of wire, having 5 turns, has an inductance L. The inductance of a similar coil having 20 turns is:
A) 4L
B) L/4
C) 16L
D) L/16
E) L
Difficulty: M
Section: 30-4
Learning Objective 30.4.3
59. A 10-turn ideal solenoid has an inductance of 4.0 mH. To generate an emf of 2.0 V the current should change at a rate of:
A) 0 A/s
B) 0.5 A/s
C) 50 A/s
D) 250 A/s
E) 500 A/s
Difficulty: M
Section: 30-5
Learning Objective 30.5.2
60. A 3.5 mH inductor and a 4.5 mH inductor are connected in series. The equivalent inductance is:
A) 0.13 mH
B) 0.51 mH
C) 1.0 mH
D) 2.0 mH
E) 8.0 mH
Difficulty: M
Section: 30-5
Learning Objective 30.5.2
61. A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them. When the total emf of the combination is 16 V, the emf of the larger inductor is:
A) 2.3 V
B) 7.0 V
C) 9.0 V
D) 28 V
E) 36 V
Difficulty: M
Section: 30-5
Learning Objective 30.5.2
62. A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. The equivalent inductance is:
A) 0.13 mH
B) 0.51 mH
C) 1.0 mH
D) 2.0 mH
E) 8.0 mH
Difficulty: M
Section: 30-5
Learning Objective 30.5.2
63. A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:
A) 2.0 103 A/s
B) 3.6 103 A/s
C) 4.6 103 A/s
D) 7.0 103 A/s
E) 8.1 103 A/s
Difficulty: M
Section: 30-5
Learning Objective 30.5.2
64. An inductor with inductance L and an inductor with inductance 2L are connected in parallel. When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is:
A) 400 A/s
B) 1000 A/s
C) 1600 A/s
D) 2000 A/s
E) 4000 A/s
Difficulty: M
Section: 30-5
Learning Objective 30.5.2
65. The diagram shows an inductor that is part of a circuit. The direction of the emf induced in the inductor is indicated. Which of the following is possible?
A) The current is constant and rightward
B) The current is constant and leftward
C) The current is increasing and rightward
D) The current is increasing and leftward
E) None of the above
Difficulty: E
Section: 30-5
Learning Objective 30.5.3
66. An 8.0-mH inductor and a 2.0- resistor are wired in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The current reaches half its final value at a time of:
A) 2.8 ms
B) 4.0 ms
C) 3.0 s
D) 170 s
E) 250 s
Difficulty: M
Section: 30-6
Learning Objective 30.6.3
67. An inductance L, resistance R, and ideal battery of emf are wired in series. A switch in the circuit is closed at time t = 0, at which time the current is zero. At any later time t the current i is given by:
A) (/R)(1 – e–Lt/R)
B) (/R)e–Lt/R
C) (/R)(1 + e–Rt/L)
D) (/R)e–Rt/L
E) (/R)(1 – e–Rt/L)
Difficulty: M
Section: 30-6
Learning Objective 30.6.4
68. An inductance L, resistance R, and ideal battery of emf are wired in series. A switch in the circuit is closed at time t = 0, at which time the current is zero. At any later time t the potential difference across the resistor is given by:
A) (1 – e–Lt/R)
B) e–Lt/R
C) (1 + e–Rt/L)
D) e–Rt/L
E) (1 – e–Rt/L)
Difficulty: M
Section: 30-6
Learning Objective 30.6.4
69. If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:
A) twice the old
B) four times the old
C) half the old
D) one-fourth the old
E) unchanged
Difficulty: M
Section: 30-6
Learning Objective 30.6.5
70. When the switch S in the circuit shown is closed, the time constant for the growth of current in R2 is:
A) L/R1
B) L/R2
C) L/(R1 + R2)
D) L(R1 + R2)/(R1R2)
E) (L/R1 + L/R2)/2
Difficulty: M
Section: 30-6
Learning Objective 30.6.5
71. An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium. A switch in the circuit is opened at time t = 0, at which time the current is /R. At any later time t the current i is given by:
A) (/R)(1 – e–Lt/R)
B) (/R)e–Lt/R
C) (/R)(1 + e–Rt/L)
D) (/R)e–Rt/L
E) (/R)(1 – e–Rt/L)
Difficulty: M
Section: 30-6
Learning Objective 30.6.8
72. An inductance L, resistance R, and ideal battery of emf are wired in series and the circuit is allowed to come to equilibrium. A switch in the circuit is opened at time t = 0, at which time the current is /R. At any later time t the potential difference across the resistor is given by:
A) (1 – e–Lt/R)
B) e–Lt/R
C) (1 + e–Rt/L)
D) e–Rt/L
E) (1 – e–Rt/L)
Difficulty: M
Section: 30-6
Learning Objective 30.6.9
73. An inductance L, resistance R, and ideal battery of emf are wired in series. A switch in the circuit is closed at time t = 0, at which time the current is zero. At any later time t the emf of the inductor is given by:
A) (1 – e–Lt/R)
B) e–Lt/R
C) (1 + e–Rt/L)
D) e–Rt/L
E) (1 – e–Rt/L)
Difficulty: M
Section: 30-6
Learning Objective 30.6.10
74. An 8.0-mH inductor and a 2.0- resistor are wired in series to a 20-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. After a long time the current in the resistor and the current in the inductor are:
A) 0 A, 0 A
B) 10 A, 10 A
C) 2.5 A, 2.5 A
D) 10 A, 2.5 A
E) 10 A, 0 A
Difficulty: M
Section: 30-6
Learning Objective 30.6.10
75. An 8.0-mH inductor and a 2.0- resistor are wired in series to a 20-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. Immediately after the switch is thrown the potential differences across the inductor and resistor are:
A) 0 V, 20 V
B) 20 V, 0 V
C) 10 V, 10 V
D) 16 V, 4 V
E) unknown since the rate of change of the current is not given
Difficulty: M
Section: 30-6
Learning Objective 30.6.10
76. An inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf . A switch in the circuit is closed at time t = 0, at which time the current is zero. A long time after the switch is thrown the potential differences across the inductor and resistor are:
A) 0,
B) , 0
C) /2, /2
D) (L/R), (R/L)
E) unknown since the rate of change of the current is not given
Difficulty: M
Section: 30-6
Learning Objective 30.6.10
77. The diagrams show three circuits with identical batteries, identical inductors, and identical resistors. Rank them according to the current through the battery just after the switch is closed, from least to greatest.
A) 3, 2, 1
B) 2 and 3 tie, then 1
C) 1, 3, 2
D) 1, 2, 3
E) 2, 3, 1
Difficulty: M
Section: 30-6
Learning Objective 30.6.10
78. Immediately after switch S in the circuit shown is closed, the current through the battery is:
A) 0
B) V0/R1
C) V0/R2
D) V0/(R1 + R2)
E) V0(R1 + R2)/(R1R2)
Difficulty: M
Section: 30-6
Learning Objective 30.6.10
79. A 6.0 mH inductor is in a circuit. At the instant the current is 5.0 A and its rate of change is 200 A/s, the rate with which the energy stored in the inductor is increasing is:
A) 7.5 10–2 W
B) 3.0 W
C) 6.0 W
D) 120 W
E) 240 W
Difficulty: M
Section: 30-7
Learning Objective 30.7.0
80. An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The rate of increase of the energy stored in the inductor is a maximum:
A) just after the switch is closed
B) at the time t = L/R after the switch is closed
C) at the time t = 2L/R after the switch is closed
D) at the time t = (L/R)ln 2 after the switch is closed
E) a long time after the switch is closed
Difficulty: H
Section: 30-7
Learning Objective 30.7.0
81. The stored energy in an inductor:
A) depends, in sign, upon the direction of the current
B) depends on the rate of change of current
C) is proportional to the square of the inductance
D) has units J/H
E) is none of the above
Difficulty: E
Section: 30-7
Learning Objective 30.7.2
82. An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The energy stored in the inductor is a maximum:
A) just after the switch is closed
B) at the time t = L/R after the switch is closed
C) at the time t = L/R2 after the switch is closed
D) at the time t = 2L/R after the switch is closed
E) a long time after the switch is closed
Difficulty: M
Section: 30-7
Learning Objective 30.7.2
83. In each of the following operations, energy is expended. The LEAST percentage of returnable electrical energy will be yielded by:
A) charging a capacitor
B) charging a storage battery
C) sending current through a resistor
D) establishing a current through an inductor
E) moving a conducting rod through a magnetic field
Difficulty: E
Section: 30-7
Learning Objective 30.7.2
84. A current of 10 A in a certain inductor results in a stored energy of 40 J. When the current is changed to 5 A in the opposite direction, the stored energy changes by:
A) 20 J
B) 30 J
C) 40 J
D) 50 J
E) 60 J
Difficulty: M
Section: 30-7
Learning Objective 30.7.2
85. A 6.0 mH inductor is in a series circuit with a resistor and an ideal battery. At the instant the current in the circuit is 5.0 A the energy stored in the inductor is:
A) 0 J
B) 7.5 10–2 J
C) 15 10–2 J
D) 30 10–2 J
E) unknown since the rate of change of the current is not given
Difficulty: M
Section: 30-7
Learning Objective 30.7.2
86. A 6.0-mH inductor and a 3.0- resistor are wired in series to a 12-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. 2.0 ms later the energy stored in the inductor is:
A) 0 J
B) 9.6 10–3 J
C) 1.9 10–2 J
D) 2.5 10–2 J
E) 3.8 10–2 J
Difficulty: M
Section: 30-7
Learning Objective 30.7.2
87. The quantity (B2/o) has units of:
A) J
B) J/H
C) J/m
D) J/m3
E) H/m3
Difficulty: E
Section: 30-8
Learning Objective 30.8.0
88. A 0.20-cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the instant the magnetic field in the interior is 5.0 mT, the energy stored in the field is:
A) 0 J
B) 3.8 10–6 J
C) 7.5 10–6 J
D) 7.5 10–4 J
E) 9.9 J
Difficulty: M
Section: 30-8
Learning Objective 30.8.2
89. In the diagram, assume that all the magnetic field lines generated by coil 1 pass through coil 2. Coil 1 has 100 turns and coil 2 has 400 turns. Then:
A) the currents will be the same in the two coils
B) the emf around coil 1 will be 1/4 the emf around coil 2
C) the current in coil 1 will be 1/4 the current in coil 2
D) the emfs will be the same in the two coils
E) none of the above
Difficulty: E
Section: 30-9
Learning Objective 30.9.1
90. Two coils have a mutual inductance of 3.5 mH. If the current in one coil is changing at a rate of 4.8 A/s, what is the emf induced in the second coil?
A) 7.3 x 10-4 V
B) 0.017 V
C) 1400 V
D) cannot tell without knowing the inductance of the second coil
E) cannot tell without knowing the current in the second coil
Difficulty: M
Section: 30-9
Learning Objective 30.9.3