Deck 19: Dc Circuits

Question 1

Choose the one alternative that best completes the statement or answers the question.
A closed flat loop conductor with radius $2.0 \mathrm {~m}$ is located in a changing uniform magnetic field. If the emf induced in the loop is $2.0 \mathrm {~V}$ , what is the rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies?

A) $0.080 \mathrm {~T} / \mathrm { s }$
B) $2.0 \mathrm {~T} / \mathrm { s }$
C) $1.0 \mathrm {~T} / \mathrm { s }$
D) $0.16 \mathrm {~T} / \mathrm { s }$

Answer 1

D

Question 2

Choose the one alternative that best completes the statement or answers the question.
A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are
Perpendicular. A) $5.5 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $3.1 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $6.3 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Answer 2

D

Question 3

Choose the one alternative that best completes the statement or answers the question.
A flat coil is wrapped with 200 turns of very thin wire on a square frame with sides $18 \mathrm {~cm}$ long. A uniform magnetic field is applied perpendicular to the plane of the coil. If the field changes uniformly from $0.50 \mathrm {~T}$ to $0.00 \mathrm {~T}$ in $8.0 \mathrm {~s}$ , find the emf induced in the coil.

A) $2.1 \mathrm { mV }$
B) $4.1 \mathrm { mV }$
C) $0.41 \mathrm {~V}$
D) $0.21 \mathrm {~V}$

Answer 3

C

Question 4

Choose the one alternative that best completes the statement or answers the question.
A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $0.40 \mathrm {~T}$ , as shown in the figure. The length of the loop $L$ is $0.16 \mathrm {~m}$ and its width $w$ is $0.040 \mathrm {~m}$ . What is the magnetic flux through the loop when the plane of the loop is perpendicular to the magnetic field?

A) $13 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $2.6 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $2.6 \times 10 ^ { 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $0.80 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
E) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 5

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, a wire and a $10 - \Omega$ resistor are used to form a circuit in the shape of a square with dimensions $20 \mathrm {~cm}$ by $20 \mathrm {~cm}$ . A uniform but non-steady magnetic field is directed into the plane of the circuit. The magnitude of the magnetic field is steadily decreased from $2.70 \mathrm {~T}$ to $0.90 \mathrm {~T}$ in a time interval of $96 \mathrm {~ms}$ . What is the induced current in the circuit, and what is its direction through the resistor?

A) $75 \mathrm {~mA}$ , from $b$ to $a$
B) $45 \mathrm {~mA}$ , from $b$ to $a$
C) $45 \mathrm {~mA}$ , from $a$ to $b$
D) $110 \mathrm {~mA}$ , from $a$ to $b$
E) $75 \mathrm {~mA}$ , from $a$ to $b$

Question 6

Write the word or phrase that best completes each statement or answers the question.
A flat circular loop having one turn and radius 5.0 cm is positioned with its plane
perpendicular to a uniform 0.60-T magnetic field. The area of the loop is suddenly
reduced to essentially zero in 0.50 ms. What emf is induced in the loop?

Question 7

Choose the one alternative that best completes the statement or answers the question.
The magnetic flux through a coil changes steadily from $4.0 \times 10 - 5 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$ to $5.0 \times 10 - 5 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$ in $0.10 \mathrm {~s}$ . What emf is induced in this coil?

A) $1.0 \times 10 ^ { - 4 } \mathrm {~V}$
B) $5.0 \times 10 ^ { - 4 } \mathrm {~V}$
C) $4.0 \times 10^{ - 4} \mathrm {~V}$
D) None of the given answers are correct.

Question 8

Choose the one alternative that best completes the statement or answers the question.
A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are
Parallel. A) $3.1 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $5.5 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $6.3 \times 10 - 3 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 9

Choose the one alternative that best completes the statement or answers the question.
A circular conducting loop with a radius of $0.50 \mathrm {~m}$ and a small gap filled with a $10.0 - \Omega$ resistor is oriented in the $x y$ -plane. If a uniform magnetic field of $1.0 \mathrm {~T}$ , making an angle of $30 ^ { \circ }$ with the $z$ -axis, increases to $10.0 \mathrm {~T}$ , in $4.0 \mathrm {~s}$ , what is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance?

A) $0 \mathrm {~A}$
B) $0.01530393 \mathrm {~A}$
C) $0.15303932 \mathrm {~A}$
D) $0.08835729 \mathrm {~A}$

Question 10

Choose the one alternative that best completes the statement or answers the question.
A flat circular loop of radius $0.10 \mathrm {~m}$ is rotating in a uniform magnetic field of $0.20 \mathrm {~T}$ . Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are at an angle of $30 ^ { \circ }$ .

A) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $6.3 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $5.5 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $3.1 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 11

Choose the one alternative that best completes the statement or answers the question.
A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $0.40 \mathrm {~T}$ , as shown in the figure. The length of the loop $L$ is $0.16 \mathrm {~m}$ and its width $w$ is $0.040 \mathrm {~m}$ . What is the magnetic flux through the loop when the plane of the loop is parallel to the magnetic field?

A) $2.6 \times 10 ^ { 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $13 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $2.6 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
E) $0.80 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 12

Choose the one alternative that best completes the statement or answers the question.
A $2.00$ -m long metal wire is formed into a square and placed in the horizontal $x y$ -plane. A uniform magnetic field is oriented at $30 ^ { \circ }$ above the horizontal with a strength of $0.344 \mathrm {~T}$ . What is the magnetic flux through the square due to this field?

A) $0.0745 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $0.0430 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $0.172 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $0.298 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 13

Choose the one alternative that best completes the statement or answers the question.
A bar magnet is pushed through a coil of wire of cross-sectional area $0.020 \mathrm {~m} ^ { 2 }$ as shown in the figure. The coil has seven turns, and the rate of change of the strength of the magnetic field in it due to the motion of the bar magnet is $0.040 \mathrm {~T} / \mathrm { s }$ . What is the magnitude of the induced emf in that coil of wire?

A) $5.6 \times 10 ^ { - 4 } \mathrm {~V}$
B) $5.6 \times 10 ^ { - 2 } \mathrm {~V}$
C) $5.6 \times 10 ^ { - 3 } \mathrm {~V}$
D) $5.6 \times 10 ^ { - 5 } \mathrm {~V}$
E) $5.6 \times 10 ^ { - 1 } \mathrm {~V}$

Question 14

Choose the one alternative that best completes the statement or answers the question.
A flat square coil of wire with 15 turns and an area of $0.40 \mathrm {~m} ^ { 2 }$ is placed with the plane of its area parallel to a magnetic field of $0.75 \mathrm {~T}$ . The coil is flipped so its plane is perpendicular to the magnetic field in a time of $0.050 \mathrm {~s}$ . What is the magnitude of the average induced emf in the coil?

A) $90 \mathrm {~V}$
B) $6.0 \mathrm {~V}$
C) $45 \mathrm {~V}$
D) $36 \mathrm {~V}$

Question 15

Choose the one alternative that best completes the statement or answers the question.
A conductor is formed into a flat loop that encloses an area of $1.0 \mathrm {~m} ^ { 2 }$ . The plane of the loop is oriented at a $30.0 ^ { \circ }$ angle with the $x y$ -plane. A uniform time-varying magnetic field is oriented parallel to the $z$ -axis. If the emf induced in the loop is $25.0 \mathrm {~V}$ , what is the rate at which the magnetic field strength is changing?

A) $29 \mathrm {~T} / \mathrm { s }$
B) $22 \mathrm {~T} / \mathrm { s }$
C) $13 \mathrm {~T} / \mathrm { s }$
D) $50 \mathrm {~T} / \mathrm { s }$

Question 16

Write the word or phrase that best completes each statement or answers the question.
A flat circular coil having 16 turns, each of diameter 20 cm, is in a uniform and steady
0.13-T magnetic field.
(a) Find the total magnetic flux through the coil when the field is perpendicular to the
plane of the coil.
(b) If the coil is rotated in 10 ms so its plane is parallel to the field, find the average
induced emf in the coil.

Question 17

Choose the one alternative that best completes the statement or answers the question.
A flux of $4.0 \times 10 ^ { - 5 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$ is maintained through a coil of area $7.5 \mathrm {~cm} ^ { 2 }$ for $0.50 \mathrm {~s}$ . What emf is induced in this coil during this time by this flux?

A) $3.0 \times 10 ^ { - 5 } \mathrm {~V}$
B) $4.0 \times 10 ^ { - 5 } \mathrm {~V}$
C) $2.0 \times 10 ^ { - 5 } \mathrm {~V}$
D) $8.0 \times 10 ^ { - 5 } \mathrm {~V}$
E) No emf is induced in this coil.

Question 18

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, a uniform magnetic field $B$ is confined to a cylindrical volume of radius $0.050 \mathrm {~m}$ . This field is directed into the plane of the page and is increasing at a constant rate of $0.900 \mathrm {~T} / \mathrm { s }$ . Calculate the magnitude and direction (clockwise or counterclockwise) of the current induced in a circular wire ring of radius $0.16 \mathrm {~m}$ and resistance $7.1 \Omega$ that encircles the magnetic field region.

Question 19

Choose the one alternative that best completes the statement or answers the question.
A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $0.40 \mathrm {~T}$ , as shown in the figure. The length of the loop $L$ is $0.16 \mathrm {~m}$ and its width $w$ is $0.040 \mathrm {~m}$ . What is the magnetic flux through the loop when the plane of the loop makes an angle of $60 ^ { \circ }$ with the magnetic field?

A) $0.80 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
B) $2.6 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
C) $1.3 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
D) $2.2 \times 10 ^ { - 3 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$
E) $0 \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$

Question 20

Write the word or phrase that best completes each statement or answers the question.
A flat coil having 40 turns, each one of cross-sectional area 12.0 cm2, is oriented with its
plane perpendicular to a uniform magnetic field. The field varies steadily from 0.00 T to
1.20 T in 20.0 ms. What emf is induced in the coil during this time?

Question 21

Choose the one alternative that best completes the statement or answers the question.
A conducting rod of length $\ell = 25 \mathrm {~cm}$ is placed on a $U$ -shaped metal wire that is connected to a lightbulb having a resistance of $8.0 \Omega$ , as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $0.40 \mathrm {~T}$ is applied perpendicular to and into the paper. An applied external force pulls the rod to the right with a constant speed of $6.0 \mathrm {~m} / \mathrm { s }$ . What is the magnitude of the emf induced in the rod?

A) $0.40 \mathrm {~V}$
B) $0.20 \mathrm {~V}$
C) $0.50 \mathrm {~V}$
D) $0.60 \mathrm {~V}$
E) $0.30 \mathrm {~V}$

Question 22

Choose the one alternative that best completes the statement or answers the question.
A conducting rod whose length is $\ell = 25 \mathrm {~cm}$ is placed on a $U$ -shaped metal wire that is connected to a lightbulb having a resistance of $8.0 \Omega$ as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $0.40 \mathrm {~T}$ is applied perpendicular to and out of the paper. An external applied force moves the rod to the left with a constant speed of $12 \mathrm {~m} / \mathrm { s }$ . What are the magnitude and direction of the induced current in the circuit?

A) $150 \mathrm {~mA}$ clockwise
B) $100 \mathrm {~mA}$ clockwise
C) $34 \mathrm {~mA}$ clockwise
D) $34 \mathrm {~mA}$ counterclockwise
E) $150 \mathrm {~mA}$ counterclockwise

Question 23

Choose the one alternative that best completes the statement or answers the question.
A conducting rod whose length is $\ell = 1.60 \mathrm {~m}$ is placed on frictionless $\mathrm { U }$ -shaped metal rails that is connected to a lightbulb having a resistance of $4.00 \Omega$ as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength $2.20 \mathrm {~T}$ is applied perpendicular to and out of the paper. An external applied force moves the rod to the right with a constant speed of $6.00 \mathrm {~m} / \mathrm { s }$ . At what rate is energy dissipated in the lightbulb?

A) $21.2 \mathrm {~W}$
B) $112 \mathrm {~W}$
C) $11.5 \mathrm {~W}$
D) $60.0 \mathrm {~W}$
E) $121 \mathrm {~W}$

Question 24

Choose the one alternative that best completes the statement or answers the question.
An electromagnetic flowmeter is useful when it is desirable not to interrupt the system in which the fluid is flowing (such as the blood in an artery during heart surgery). Such a device is illustrated in the figure. The conducting fluid moves with speed $v$ in a tube of diameter $d$ . Perpendicular to this tube is a magnetic field B. A voltage $V$ is induced between opposite sides of the tube due to the motion of the conducting fluid in the magnetic field. For a certain case, $B =$ $0.120 \mathrm {~T} , d = 1.2 \mathrm {~cm}$ , and the measured voltage is $V = 2.88 \mathrm { mV }$ . Determine the speed of the fluid.

A) $11 \mathrm {~m} / \mathrm { s }$
B) $750 \mathrm {~m} / \mathrm { s }$
C) $0.075 \mathrm {~m} / \mathrm { s }$
D) $1.1 \mathrm {~m} / \mathrm { s }$
E) $2.0 \mathrm {~m} / \mathrm { s }$

Question 25

Choose the one alternative that best completes the statement or answers the question.
A round flat conducting loop is placed perpendicular to a uniform $0.50 \mathrm {~T}$ magnetic field. If the area of the loop increases at a rate of $3.0 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 } / \mathrm { s }$ , what is the induced emf in the loop?

A) $4.3 \mathrm { mV }$
B) $0 \mathrm { mV }$
C) $5.5 \mathrm { mV }$
D) $1.7 \mathrm { mV }$
E) $1.5 \mathrm { mV }$

Question 26

Choose the one alternative that best completes the statement or answers the question.
A single-turn loop of wire, having a resistance of $8.00 \Omega$ and a cross-sectional area $200 \mathrm {~cm} ^ { 2 }$ , is perpendicular to a uniform magnetic field that increases steadily from $0.200 \mathrm {~T}$ to $2.800 \mathrm {~T}$ in $2.20$ seconds. What is the magnitude of the induced current in the loop?

A) $0 \mathrm {~A}$
B) $2.95 \mathrm {~mA}$
C) $3.18 \mathrm {~mA}$
D) $2.95 \mathrm {~A}$
E) $3.18 \mathrm {~A}$

Question 27

Choose the one alternative that best completes the statement or answers the question.
You are designing an ac generator with a maximum emf of $8.0 \mathrm {~V}$ . If the generator coil has 200 turns, each with a cross-sectional area of $0.030 \mathrm {~m} ^ { 2 }$ , what should be the frequency of the generator in a magnetic field of $0.030 \mathrm {~T}$ ?

A) $44 \mathrm {~Hz}$
B) $8.0 \mathrm {~Hz}$
C) $7.1 \mathrm {~Hz}$
D) $7.5 \mathrm {~Hz}$

Question 28

Write the word or phrase that best completes each statement or answers the question.
An eagle, with a wingspread of $2.0 \mathrm {~m}$ , flies toward the north at $8.0 \mathrm {~m} / \mathrm { s }$ in a region where the vertical component of the earth's magnetic field is $0.20 \times 10 ^ { - 4 } \mathrm {~T}$ . What emf would be developed between the eagle's wing tips? (It has been speculated that this phenomenon could play a role in the navigation of birds, but the effect is too small, in all likelihood.)

Question 29

Write the word or phrase that best completes each statement or answers the question.
A airplane having a metal surface and a wingspan of $25.0 \mathrm {~m}$ flies horizontally at $200 \mathrm {~m} / \mathrm { s }$ where the earth's magnetic field is vertical with magnitude $45.0 \mu \mathrm { T }$ .
(a) What emf is induced across the wings?
(b) What wingspan would the plane need to produce $1.00 - \mathrm { V }$ emf across its wings?
(c) The plane now reverses direction. Does the polarity of the wingtip emf change? That is, if the left wing was positive before, does it now become negative?

Question 30

Choose the one alternative that best completes the statement or answers the question.
A conducting rod whose length is $\ell = 1.60 \mathrm {~m}$ is placed on frictionless $U$ -shaped metal rails that is connected to a lightbulb having a resistance of $4.00 \Omega$ as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength $2.20 \mathrm {~T}$ is applied perpendicular to and out of the paper. What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of $6.00 \mathrm {~m} / \mathrm { s }$ ?

A) $10.6 \mathrm {~N}$
B) $18.6 \mathrm {~N}$
C) $8.60 \mathrm {~N}$
D) $12.6 \mathrm {~N}$
E) $9.30 \mathrm {~N}$

Question 31

Choose the one alternative that best completes the statement or answers the question.
A constant uniform magnetic field of $0.50 \mathrm {~T}$ is applied at right angles to the plane of a flat rectangular loop of area $3.0 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 }$ . If the area of this loop changes steadily from its original value to a new value of $1.6 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 }$ in $1.6 \mathrm {~s}$ , what is the emf induced in the loop?

A) $0 \mathrm {~V}$
B) $7.5 \times 10 ^ { - 2 } \mathrm {~V}$
C) $4.4 \times 10 ^ { - 4 } \mathrm {~V}$
D) $1.6 \times 10 ^ { - 2 } \mathrm {~V}$
E) $9.0 \times 10 ^ { - 2 } \mathrm {~V}$

Question 32

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, a region of space contains a uniform magnetic field. The magnitude of this field is $2.8 \mathrm {~T}$ , and it is directed straight into the plane of the page in the region shown. Outside this region the magnetic field is zero. A rectangular loop measuring $0.20 \mathrm {~m}$ by $0.60 \mathrm {~m}$ and having a resistance of $2 \Omega$ is being pulled into the magnetic field by an external force, as shown.
(a) What is the direction (clockwise or counterclockwise) of the current induced in the loop?
(b) Calculate the magnitude of the external force $F _ { \text {ext } }$ that is required to move the loop at a constant speed of $3.9 \mathrm {~m} / \mathrm { s }$ .

Question 33

Choose the one alternative that best completes the statement or answers the question.
A long vertical wire carries a steady $70 \mathrm {~A}$ current. As shown in the figure, a pair of horizontal rails are $0.20 \mathrm {~m}$ apart. $\mathbf { A } 20 - \Omega$ resistor connects points $a$ and $b$ , at the end of the rails. $\mathbf { A }$ bar is in contact with the rails, and is moved by an external force with a constant horizontal velocity of $0.90 \mathrm {~m} / \mathrm { s }$ to the right, as shown. The bar and the rails have negligible resistance. At the instant that the bar is $0.20 \mathrm {~m}$ from the wire, what are the induced current in the resistor and its direction through the resistor? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A) $0.63 \mu \mathrm { A }$ , from $b$ to $a$
B) $0.32 \mu \mathrm { A }$ , from $b$ to $a$
C) $1.9 \mu \mathrm { A }$ , from $b$ to $a$
D) $0.32 \mu \mathrm { A }$ , from $a$ to $b$
E) $0.63 \mu \mathrm { A }$ , from $a$ to $b$

Question 34

Choose the one alternative that best completes the statement or answers the question.
The area of a rectangular loop of wire is $3.6 \times 10 ^ { - 3 } \mathrm {~m} ^ { 2 }$ . The loop is placed in a uniform magnetic field that changes steadily from $0.20 \mathrm {~T}$ to $1.4 \mathrm {~T}$ in $1.6 \mathrm {~s}$ . The plane of the loop is perpendicular to the direction of the magnetic field. What is the magnitude of the induced emf in that loop?

A) $3.0 \times 10 ^ { - 3 } \mathrm {~V}$
B) $0 \mathrm {~V}$
C) $1.8 \times 10 ^ { - 3 } \mathrm {~V}$
D) $2.8 \times 10 ^ { - 3 } \mathrm {~V}$
E) $2.7 \times 10 ^ { - 3 } \mathrm {~V}$

Question 35

Choose the one alternative that best completes the statement or answers the question.
A conducting rod whose length is $\ell = 27.0 \mathrm {~cm}$ is placed on frictionless $U$ -shaped metal rails that is connected to a lightbulb having a resistance of $5.00 \Omega$ as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength $1.20 \mathrm {~T}$ is applied perpendicular to and out of the paper. An external applied force moves the rod to the right with a constant speed. At what speed should the rod be pulled so that the lightbulb will consume energy at a rate of $1.10 \mathrm {~W}$ ?

A) $4.26 \mathrm {~m} / \mathrm { s }$
B) $3.50 \mathrm {~m} / \mathrm { s }$
C) $7.24 \mathrm {~m} / \mathrm { s }$
D) $6.00 \mathrm {~m} / \mathrm { s }$
E) $2.00 \mathrm {~m} / \mathrm { s }$

Question 36

Write the word or phrase that best completes each statement or answers the question.
You wish to construct a simple ac generator with a maximum output of $12 \mathrm {~V}$ when rotated at $60 \mathrm {~Hz}$ . A magnetic field of $0.050 \mathrm {~T}$ is available. If the area of the rotating coil is $100 \mathrm {~cm} ^ { 2 }$ , how many turns are needed?

Question 37

Choose the one alternative that best completes the statement or answers the question.
A flat rectangular coil with dimensions of $8.0 \mathrm {~cm} \times 10 \mathrm {~cm}$ is dropped from a zero magnetic field position into a 1.4-T magnetic field in $0.10 \mathrm {~s}$ . The coil has 60 turns and is perpendicular to the magnetic field. What is the average induced emf in the coil as a result of this action?

A) $3.6 \mathrm {~V}$
B) $6.7 \mathrm {~V}$
C) $2.4 \mathrm {~V}$
D) $0 \mathrm {~V}$
E) $8.6 \mathrm {~V}$

Question 38

Choose the one alternative that best completes the statement or answers the question.
It is known that birds can detect the earth's magnetic field, but the mechanism of how they do this is not known. It has been suggested that perhaps they detect a motional emf as they fly north to south, but it turns out that the induced voltages are small compared to the voltages normally encountered in cells, so this is probably not the mechanism involved. To check this out, calculate the induced voltage across the wingtips of a wild goose with a wingspan of $1.2$ mif it is flying directly south at $13 \mathrm {~m} / \mathrm { s }$ at a point where the earth's magnetic field is $5.0 \times 10 ^ { - 5 } \mathrm {~T}$ directed downward from the horizontal by $40 ^ { \circ }$ .

A) $0.060 \mathrm { mV }$
B) $0.78 \mathrm { mV }$
C) $0.50 \mathrm { mV }$
D) $0.25 \mathrm { mV }$
E) $0.60 \mathrm { mV }$

Question 39

Choose the one alternative that best completes the statement or answers the question.
A conducting rod with a length $\ell = 25 \mathrm {~cm}$ is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of $8.0 \Omega$ as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $0.40 \mathrm {~T}$ is applied perpendicular to and into the paper. An external applied force moves the rod to the right with a constant speed of $6.0 \mathrm {~m} / \mathrm { s }$ . What are the magnitude and direction of the induced current in the circuit?

A) $75 \mathrm {~mA}$ counterclockwise
B) $75 \mathrm {~mA}$ clockwise
C) $17 \mathrm {~mA}$ counterclockwise
D) $17 \mathrm {~mA}$ clockwise
E) $52 \mathrm {~mA}$ clockwise

Question 40

Choose the one alternative that best completes the statement or answers the question.
A round flat metal coil has 180 turns and negligible resistance. It is connected in a series circuit with a 17- $\Omega$ resistor, with nothing else in the circuit. You measure that a $6.0 - \mathrm { A }$ current flows through the resistor when a magnetic field through the coil, perpendicular to its area, is changing at $3.0 \mathrm {~T} / \mathrm { s }$ . What is the radius of the coil?

A) $0.25 \mathrm {~m}$
B) $0.014 \mathrm {~m}$
C) $0.043 \mathrm {~m}$
D) $0.54 \mathrm {~m}$

Question 41

Write the word or phrase that best completes each statement or answers the question.
The mutual inductance between two coils is 10 mH. The current in the first coil changes
uniformly from 2.7 A to 5.0 A in 160 ms. If the second coil has a resistance of 0.60 Ω, what
is the magnitude of the induced current in the second coil?

Question 42

Choose the one alternative that best completes the statement or answers the question.
You need an inductor that will store $20 \mathrm {~J}$ of energy when a $3.0$ -A current flows through it. What should be its self-inductance?

A) $90 \mathrm { H }$
B) $60 \mathrm { H }$
C) $4.4 \mathrm { H }$
D) $3.7 \mathrm { H }$

Question 43

Choose the one alternative that best completes the statement or answers the question.
An ideal solenoid with 3000 turns is $70.0 \mathrm {~cm}$ long. If its self-inductance is $25.0 \mathrm { mH }$ , what is its radius? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A) $0.00199 \mathrm {~m}$
B) $52.0 \mathrm {~m}$
C) $327 \mathrm {~m}$
D) $0.0222 \mathrm {~m}$

Question 44

Choose the one alternative that best completes the statement or answers the question.
The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is $120 \mathrm {~V}$ , what voltage is present in its secondary coil?

A) $400 \mathrm {~V}$
B) $30 \mathrm {~V}$
C) $100 \mathrm {~V}$
D) $480 \mathrm {~V}$
E) $70 \mathrm {~V}$

Question 45

Choose the one alternative that best completes the statement or answers the question.
The inductance of a solenoid that is $16.0 \mathrm {~cm}$ long and has a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ is $1.00 \mathrm { mH }$ . How many turns of wire does this solenoid have? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A) 159,000
B) 318,000
C) 282
D) 1130
E) 150

Question 46

Choose the one alternative that best completes the statement or answers the question.
What is the self-inductance of an ideal solenoid that is $300 \mathrm {~cm}$ long with a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ and has 1000 turns of wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A) $41.9 \mathrm { nH }$
B) $4.19 \mathrm { pH }$
C) $41.9 \mu \mathrm { H }$
D) $4.19 \mu \mathrm { H }$
E) $4.19 \mathrm { nH }$

Question 47

Choose the one alternative that best completes the statement or answers the question.
The coil of an ac generator has 50 loops and a cross-sectional area of $0.25 \mathrm {~m} 2$ . What is the maximum emf that can be generated by this generator if it is spinning with an angular speed of $4.0 \mathrm { rad } / \mathrm { s }$ in a $2.0$ - T magnetic field?

A) $100 \mathrm {~V}$
B) $400 \mathrm {~V}$
C) $200 \mathrm {~V}$
D) $50 \mathrm {~V}$

Question 48

Write the word or phrase that best completes each statement or answers the question.
The figure shows a solenoid having no appreciable resistance. When the current in this solenoid is decreasing at a rate of $5.5 \mathrm {~A} / \mathrm { s }$ , the self-induced emf in the solenoid is measured to be $9.5 \mathrm {~V}$ .
((a) What is the self-inductance of this solenoid?
(b) If the current is in the direction from $b$ to $a$ in the figure, which point, $a$ or $b$ , is at higher potential?

Question 49

Choose the one alternative that best completes the statement or answers the question.
An ac generator with a total resistance of $12 \Omega$ contains 100 flat loops of wire, each with an area of $0.090 \mathrm {~m} ^ { 2 }$ . The loops rotate at $60 \mathrm { rev } / \mathrm { s }$ in a magnetic field of magnitude $0.50 \mathrm {~T}$ . What is the maximum possible induced current?

A) $0.28 \mathrm { kA }$
B) $23 \mathrm {~A}$
C) $0.14 \mathrm { kA }$
D) $46 \mathrm {~A}$

Question 50

Write the word or phrase that best completes each statement or answers the question.
An ideal transformer with 120 turns in its secondary supplies 12 V at 220 mA to a toy
train. The primary is connected across a 120-V wall outlet.
(a) How many turns are in the primary?
(b) What is the primary current?
(c) What power is delivered by the wall outlet?

Question 51

Choose the one alternative that best completes the statement or answers the question.
An ac generator contains 80 flat rectangular loops of wire, each of which is $12 \mathrm {~cm}$ long and $8 \mathrm {~cm}$ wide. The loops rotate at $1200 \mathrm { rpm }$ about an axis through the center and parallel to the long side. If the magnetic field in which the loop rotates is uniform, has magnitude $0.30 \mathrm {~T}$ , and is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator?

A) $20 \mathrm {~V}$
B) $27 \mathrm {~V}$
C) $35 \mathrm {~V}$
D) $29 \mathrm {~V}$

Question 52

Write the word or phrase that best completes each statement or answers the question.
You need an ideal transformer to reduce a voltage of 150 V in the primary circuit to 25 V
in the secondary circuit. The primary circuit has 130 windings and the secondary circuit is
completed through a 55- resistor. How many windings should the secondary circuit
contain?

Question 53

Choose the one alternative that best completes the statement or answers the question.
A 73-mH solenoid inductor is wound on a form that is $0.80 \mathrm {~m}$ long and $0.10 \mathrm {~m}$ in diameter. A coil having a resistance of $7.7 \Omega$ is tightly wound around the solenoid at its center. The mutual inductance of the coil and solenoid is $19 \mu \mathrm { H }$ . At a given instant, the current in the solenoid is $820 \mathrm {~mA}$ and is decreasing at the rate of $2.5 \mathrm {~A} / \mathrm { s }$ . At the given instant, what is the induced current in the coil?

A) $8.6 \mu \mathrm { A }$
B) $9.9 \mu \mathrm { A }$
C) $4.9 \mu \mathrm { A }$
D) $6.2 \mu \mathrm { A }$
E) $7.4 \mu \mathrm { A }$

Question 54

Write the word or phrase that best completes each statement or answers the question.
An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If
120 V at 2.0 A is applied to the primary, what voltage and current are present in the
secondary?

Question 55

Write the word or phrase that best completes each statement or answers the question.
An ideal transformer steps down 120 V to 12. V and the 2630.-turn secondary supplies 12.
A.
(a) Determine the current in the primary.
(b) Determine the turns ratio.
(c) What is the ratio of output power to input power?

Question 56

Choose the one alternative that best completes the statement or answers the question.
An ac generator consists of 100 loops of wire, each of area $0.090 \mathrm {~m} ^ { 2 }$ , and has a total resistance $12 \Omega$ The loops rotate about a diameter in a magnetic field of $0.50 \mathrm {~T}$ at a constant angular speed of 60 revolutions per second. Find the maximum induced emf in the generator.

A) $0.54 \mathrm { kV }$
B) $1.7 \mathrm { kV }$
C) $0.27 \mathrm { kV }$
D) $3.4 \mathrm { kV }$

Question 57

Write the word or phrase that best completes each statement or answers the question.
An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If $120 \mathrm {~V}$ at $2.0 \mathrm {~A}$ is applied to the primary,
(a) what voltage is present in the secondary?
(b) what current is present in the secondary?

Question 58

Choose the one alternative that best completes the statement or answers the question.
A rectangular coil of $N$ turns, length $L = 25 \mathrm {~cm}$ , and width $w = 15 \mathrm {~cm}$ , as shown in the figure, is rotating in a magnetic field of $1.6 \mathrm {~T}$ with a frequency of $75 \mathrm {~Hz}$ . If the coil develops a maximum emf $56.9 \mathrm {~V}$ , what is the value of $N$ ?

A) 4
B) 6
C) 10
D) 2
E) 8

Question 59

Write the word or phrase that best completes each statement or answers the question.
An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V.
What must be the ratio of the number of turns in the secondary to the number of turns in
the primary?

Question 60

Choose the one alternative that best completes the statement or answers the question.
The current flowing through a circuit is changing at a rate of $6.0 \mathrm {~A} / \mathrm { s }$ . If the circuit contains a $190 - \mathrm { H }$ inductor, what is the emf across the inductor?

A) $32 \mathrm { mV }$
B) $11 \mathrm { mV }$
C) $32 \mathrm {~V}$
D) $1100 \mathrm {~V}$

Question 61

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, a circuit consists of a resistor $R = 22 \Omega$ in series with an ideal inductor $L = 31 \mathrm { H }$ having no resistance. At time $t = 0 \mathrm {~s}$ , there is a 12-A current in the circuit. At time $t = 5.0 \mathrm {~s}$ , what is the emf across the inductor?

A) $7.0 \mathrm {~V}$
B) $7.6 \mathrm {~V}$
C) $6.3 \mathrm {~V}$
D) $8.2 \mathrm {~V}$
E) $8.9 \mathrm {~V}$

Question 62

Choose the one alternative that best completes the statement or answers the question.
A series circuit consists of an open switch, an ideal emf source $\varepsilon _ { 0 }$ , a $5.0 - \mathrm { k } \Omega$ resistor, and a 4.0-H inductor. If the potential across the resistor is $65.0 \mathrm {~V}$ at $2.0 \mathrm {~ms}$ after the switch is closed, find the source emf, $\varepsilon _ { 0 }$ .

A) $56 \mathrm {~V}$
B) $36 \mathrm {~V}$
C) $76 \mathrm {~V}$
D) $71 \mathrm {~V}$

Question 63

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, a circuit consists of a resistor $R = 17 \Omega$ in series with an ideal inductor $L = 49 \mathrm { H }$ having no resistance. At time $t = 0 \mathrm {~s}$ , there is a 12-A current in the circuit. At that instant, what is the rate of change of the current?

A) $- 19 \mathrm {~A} / \mathrm { s }$
B) $- 35 \mathrm {~A} / \mathrm { s }$
C) $- 4.2 \mathrm {~A} / \mathrm { s }$
D) $- 27 \mathrm {~A} / \mathrm { s }$
E) $- 12 \mathrm {~A} / \mathrm { s }$

Question 64

Choose the one alternative that best completes the statement or answers the question.
A series circuit contains a $1.0 - \mathrm { k } \Omega$ resistor, a $5.0 - \mathrm { mH }$ inductor, and an ideal $25 - \mathrm { V }$ power supply. What is the time constant for the circuit?

A) $5.0 \mathrm {~s}$
B) $1.6 \mathrm {~s}$
C) $5.0 \mu \mathrm { s }$
D) $1.6 \mu \mathrm { s }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
The series circuit shown in the figure contains an ideal battery with a constant terminal voltage $V _ { \mathrm { B } } = 60 \mathrm {~V}$ , an ideal inductor $L = 42 \mathrm { H }$ , a resistor $R = 24$ ohm resistor, and a switch S.Initially, the switch is open, and there is no current in the inductor. At time $t = 0 \mathrm {~s}$ , the switch is suddenly closed. What is the current in the circuit when the voltage across the resistor is equal to the voltage across the inductor?

A) $0.75 \mathrm {~A}$
B) $1.0 \mathrm {~A}$
C) $0.50 \mathrm {~A}$
D) $1.3 \mathrm {~A}$
E) $1.5 \mathrm {~A}$

Question 66

Choose the one alternative that best completes the statement or answers the question.
A simple series circuit contains a $6.0 - \Omega$ resistor, an ideal $15 - \mathrm { V } D C$ power supply, and an $18 - \mathrm { H }$ inductor. What the time constant of this circuit?

A) $0.33 \mathrm {~s}$
B) $110 \mathrm {~s}$
C) $3.0 \mathrm {~s}$
D) None of the given answers are correct.

Question 67

Choose the one alternative that best completes the statement or answers the question.
A $25 - \mathrm { mH }$ inductor is connected in series with a $20 - \Omega$ resistor through an ideal $15 - \mathrm { V }$ dc power supply and a switch. If the switch is closed at time $t = 0 \mathrm {~s}$ , what is the current when $t = 2.0 \mathrm {~ms}$ ?

A) $0.80 \mathrm {~A}$
B) $0.60 \mathrm {~A}$
C) $0.40 \mathrm {~A}$
D) $0.50 \mathrm {~A}$
E) $0.70 \mathrm {~A}$

Question 68

Choose the one alternative that best completes the statement or answers the question.
A $4.0 - \mathrm { mH }$ coil carries a current of $5.0 \mathrm {~A}$ . How much energy is stored in its magnetic field?

A) $20 \mathrm {~mJ}$
B) $2.0 \mathrm {~mJ}$
C) $10 \mathrm {~mJ}$
D) none of the given answers

Question 69

Write the word or phrase that best completes each statement or answers the question.
The figure shows a circuit. The ideal battery has a constant terminal voltage of $\varepsilon = 27 \mathrm {~V}$ , the inductance is $L = 0.40 \mathrm { H }$ , and the resistances are $R _ { 1 } = 12 \Omega$ and $R _ { 2 } = 9.0 \Omega$ . Initially the switch $\mathrm { S }$ is open with no currents flowing. Then the switch is suddenly closed.
(a) What is the current in the resistor $R _ { 1 }$ the instant after the switch is closed?
(b) After leaving the switch has been closed for a very long time, it is opened again. Just after it is opened, what is the current in $R _ { 1 }$ ?

Question 70

Choose the one alternative that best completes the statement or answers the question.
A large electromagnet has a $22 \mathrm {~T}$ magnetic field between its poles. What is the magnetic energy density in that region of space? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

A) $88 \mathrm {~J} / \mathrm { cm } ^ { 3 }$
B) $190 \mathrm {~J} / \mathrm { cm } ^ { 3 }$
C) $240 \mathrm {~J} / \mathrm { cm } ^ { 3 }$
D) $30,000 \mathrm {~J} / \mathrm { cm } ^ { 3 }$

Question 71

Choose the one alternative that best completes the statement or answers the question.
A $1.5 - \mathrm { H }$ inductor is connected in series with a $200 - \Omega$ resistor through an ideal $15 - \mathrm { V }$ dc power supply and an open switch. After closing the, what is the maximum energy that will be contained in the inductor?

A) $3.2 \mathrm {~mJ}$
B) $2.2 \mathrm {~mJ}$
C) $1.2 \mathrm {~mJ}$
D) $4.2 \mathrm {~mJ}$
E) $5.2 \mathrm {~mJ}$

Question 72

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, a circuit consists of a resistor $R = 18 \Omega$ in series with an ideal inductor $L = 33 \mathrm { H }$ having no resistance. At time $t = 0 \mathrm {~s}$ , there is a 12-A current in the circuit. When the magnetic energy of the inductor is $1600 \mathrm {~J}$ , what is the rate of dissipation of energy in the resistor?

A) $1700 \mathrm {~W}$
B) $2200 \mathrm {~W}$
C) $870 \mathrm {~W}$
D) $1300 \mathrm {~W}$
E) $440 \mathrm {~W}$

Question 73

Choose the one alternative that best completes the statement or answers the question.
A 45- $\mathrm { mH }$ inductor is connected in series with a $60 - \Omega$ resistor through an ideal $15 - \mathrm { V }$ dc power supply and an open switch. What is the current $7.0 \mathrm {~ms}$ after closing the switch?

A) $550 \mathrm {~mA}$
B) $850 \mathrm {~mA}$
C) $280 \mathrm {~mA}$
D) $650 \mathrm {~mA}$
E) $250 \mathrm {~mA}$

Question 74

Write the word or phrase that best completes each statement or answers the question.
A 100-W light bulb is powered by 120 V ac 60.0-Hz household connection. Determine the
rms current and the current amplitude.

Question 75

Choose the one alternative that best completes the statement or answers the question.
The series circuit shown in the figure contains an ideal battery with a constant terminal voltage $V _ { \mathrm { B } } = 60 \mathrm {~V}$ , an ideal inductor $L = 50 \mathrm { H }$ , a resistor $R = 11 \mathrm { ohm }$ resistor, and a switch $\mathrm { S }$ . Initially, the switch is open, and there is no current in the inductor. At time $t = 0 \mathrm {~s}$ , the switch is suddenly closed. What is the current in the circuit $4.09 \mathrm {~s}$ after closing the switch?

A) $2.7 \mathrm {~A}$
B) $2.2 \mathrm {~A}$
C) $4.3 \mathrm {~A}$
D) $5.5 \mathrm {~A}$
E) $3.2 \mathrm {~A}$

Question 76

Choose the one alternative that best completes the statement or answers the question.
What resistance should be added in series with a $6.0 \mathrm { H }$ inductor to give a circuit with a time constant of $3.0 \mathrm {~ms}$ ?

A) $2.0 \Omega$
B) $2.9 \Omega$
C) $2.0 \mathrm { k } \Omega$
D) $18 \Omega$

Question 77

Choose the one alternative that best completes the statement or answers the question.
A $1.50 - \mathrm { H }$ inductor is connected in series with a $200 - \Omega$ resistor through an ideal $15.0$ - $\mathrm { V }$ dc power supply and an open switch. How much energy is contained in the inductor $20.0 \mathrm {~ms}$ after closing the switch?

A) $3.65 \mathrm {~mJ}$
B) $0.910 \mathrm {~mJ}$
C) $1.83 \mathrm {~mJ}$
D) $5.48 \mathrm {~mJ}$
E) $7.31 \mathrm {~mJ}$

Question 78

Write the word or phrase that best completes each statement or answers the question.
The peak current and voltage outputs of a generator are 20 A and 240 V, respectively.
What average power is provided by the generator?

Question 79

Write the word or phrase that best completes each statement or answers the question.
American power plants usually supply $120 \mathrm {~V}$ ac.
(a) At what frequency is this voltage supplied?
(b) What is the maximum voltage?

Question 80

Write the word or phrase that best completes each statement or answers the question.
The potential applied to a $20 - \Omega$ resistor is $v = ( 60 \mathrm {~V} ) \cos ( 33 t )$ . What is the rms current through this resistor?