Deck 20: Induced Voltages and Inductance

Question 1

A 38-turn square coil of area 0.100 m² and a 152-turn circular coil are both placed perpendicular to the same changing magnetic field.The voltage induced in each of the coils is the same.What is the area of the circular coil?

A) 0.400 m²
B) 0.0063 m²
C) 0.025 m²
D) 0.100 m²
E) ​1.600 m²

Answer 1

0.025 m²

Question 2

A flat coil of wire consisting of 15 turns,each with an area of 90 cm²,is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 3.5 T to 5.9 T in 2.0 s.If the coil has a total resistance of 0.20 Ω,what is the magnitude of the induced current?

A) 1990 mA
B) 81 mA
C) 810 mA
D) 130 mA
E) ​320 mA

Answer 2

810 mA

Question 3

A planar loop consisting of four turns of wire,each of which encloses 350 cm²,is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 19 mT to 35 mT in a time of 6.0 ms.What is the resulting induced current in the coil if the resistance of the coil is 6.0 Ω?

A) 16 mA
B) 1560 mA
C) 140 mA
D) 62 mA
E) ​560 mA

Answer 3

62 mA

Question 4

The operation of a tape player to play music depends on which of the following?

A) the Doppler effect
B) the photoelectric effect
C) the force acting on a current-carrying wire in a magnetic field
D) induced current from the motion of a magnet past a wire

Question 5

A bar magnet is falling through a loop of wire with constant velocity.The south pole enters first.As the magnet leaves the wire,the induced current (as viewed from above):

A) is clockwise.
B) is counterclockwise.
C) is zero.
D) is along the length of the magnet.

Question 6

A sensitive ammeter is connected to a wire loop and placed within the magnetic field of a strong horseshoe magnet.The ammeter shows a deflection when:

A) the wire is moved parallel to the field.
B) the wire is moved perpendicularly to the field.
C) neither wire nor magnet is moving.
D) the wire's axis is parallel to the field.

Question 7

According to Lenz's law the direction of an induced current in a conductor will be that which tends to produce which of the following effects?

A) enhance the effect which produces it
B) produce a greater heating effect
C) produce the greatest voltage
D) oppose the effect which produces it

Question 8

A uniform 1.1-T magnetic field passes perpendicularly through the plane of a wire loop 0.40 m² in area.What flux passes through the loop?

A) 4.4 T⋅m²
B) 0.44 T⋅m²
C) 3 T⋅m²
D) 0.18 T⋅m²
E) ​1.3 T·m²

Question 9

A coil in a magnetic field encloses a flux of 0.196 T·m² when the angle between the normal to the coil and the direction of the magnetic field is 42.0°.What flux would go through the coil if the angle were changed to 29.0°?

A) 0.167 T·m²
B) 0.135 T·m²
C) 0.27 T·m²
D) 0.231 T·m²
E) ​0.142 T·m²

Question 10

A uniform 1.0-T magnetic field passes through the plane of a wire loop 0.30 m² in area.What flux passes through the loop when the direction of the 1.0-T field is at a 10° angle to the normal of the loop plane?

A) 3.3 T⋅m²
B) 0.29 T⋅m²
C) 0.30 T⋅m²
D) 0.05 T⋅m²
E) ​0.30 T⋅m²

Question 11

A coil is placed in a magnetic field and has a flux Φ_B through it.The coil is stressed so that its area reduces to 75% of its original value.If the plane of the coil stays the same and the flux through it remains the same,how must the magnetic field change?

A) It must increase by 25%.
B) It must increase by 33%.
C) It must increase by 125%.
D) It must decrease by 25%.

Question 12

Two loops of wire are arranged so that a changing current in one will induce a current in the other.If the current in the first is increasing clockwise by 1.0 A every second,the induced current in the second loop will:

A) be increasing counterclockwise.
B) stay constant.
C) increase clockwise also.
D) stay zero.

Question 13

The units T·m²/s are equivalent to:

A) W.
B) V.
C) N/m.
D) webers.

Question 14

"GFI" stands for:

A) grand flux indicator.
B) ground forcing indicator.
C) ground fault interrupter.
D) gauss-free invention.

Question 15

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.The induced current will be greatest in magnitude when the magnet is located so that:

A) the loop is near either the north or the south pole.
B) the loop is near the north pole only.
C) the loop is near the middle of the magnet.
D) with no acceleration,the induced current is zero.

Question 16

A bar magnet is falling through a loop of wire with constant velocity.The north pole enters first.As the south pole leaves the loop of wire,the induced current (as viewed from above)will be:

A) clockwise.
B) counterclockwise.
C) zero.
D) along the length of the magnet.

Question 17

The principle or law that says "an induced emf in a circuit loop produces a current whose magnetic field opposes further change of magnetic flux" is credited to:

A) Faraday.
B) Lenz.
C) Ampere.
D) Volta.

Question 18

A square coil,enclosing an area with sides 3.0 cm long,is wrapped with 2500 turns of wire.A uniform magnetic field perpendicular to its plane is turned on and increases to 0.15 T during an interval of 1.9 s.What average voltage is induced in the coil?

A) 0.18 V
B) 0.34 V
C) 0.7 V
D) 0.06 V
E) ​0.9 V

Question 19

A loop of area 0.120 m² is in a uniform 0.0500-T magnetic field.If the flux through the loop is 4.09 × 10^-3 T·m²,what angle does the normal to the plane of the loop make with the direction of the magnetic field?

A) 47.0°
B) 83.5°
C) 43.0°
D) 79.1º
E) ​This is not possible.

Question 20

A coil is placed in a changing magnetic field and an emf is induced.What happens to the induced emf if the rate of change of magnetic field quadruples?

A) There is no change.
B) The emf doubles.
C) The emf quadruples.
D) The emf increases by a factor of 16.

Question 21

A straight wire of length l is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.If the resistance of the rod is R,what is the current through the rod?

A) R/Blv
B) Blv/R
C) B²l²v²/R²
D) not given

Question 22

A 600-turn circular coil with an area of 0.0700 m² is mounted on a rotating frame that turns at a rate of 20.0 rad/s in the presence of a 0.0300-T uniform magnetic field that is perpendicular to the axis of rotation.What is the instantaneous emf in the coil at the moment that the normal to its plane is at a 35.0° angle to the field?

A) zero
B) 14.5 V
C) 25.2 V
D) 289 V
E) ​15.4 V

Question 23

A straight wire of length
Is oriented east-west and is in a magnetic field B pointing north.The wire is moving downward at a constant speed v.Which end of the rod is positively charged?

A) neither
B) the east end
C) the west end
D) both ends

Question 24

A motor with a coil resistance of 12 Ω is attached to a voltage supply of 75 V.What is the current in the motor when it is running at its maximum speed with a back emf of 25 V?

A) zero
B) 4.2 A
C) 8.3 A
D) 6.3 A
E) ​600 A

Question 25

A metal rod is falling toward the surface of the Earth near the equator.As it falls,one end of the rod becomes positively charged due to the motional emf of the rod through the Earth's magnetic field.The rod is oriented so that:

A) the rod is vertical with the positive end higher.
B) the rod is horizontal with the positive end toward the north.
C) the rod is horizontal with the positive end toward the east.
D) the rod is horizontal with the positive end toward the west.

Question 26

A large jetliner with a wingspan of 37 m flies horizontally and due north at a speed of 190 m/s in a region where the magnetic field of the earth is 56 µT directed 55° below the horizontal.What is the magnitude of the induced emf between the ends of the wing?

A) 230 mV
B) 390 mV
C) 320 mV
D) 22 mV
E) ​9 mV

Question 27

A bar magnet is held above the center of a conducting ring in the horizontal plane.The magnet is dropped so it falls lengthwise toward the center of the ring.Will the falling magnet be attracted toward the ring or be repelled by the ring due to the magnetic interaction of the magnet and the ring?

A) It will be attracted.
B) It will be repelled.
C) It will be attracted only if the north end of the magnet is the leading end as it falls toward the ring.
D) It will be attracted only if the south end of the magnet is the leading end as it falls toward the ring.

Question 28

The magnet moving past an object will produce eddy currents in the object if the object:

A) is magnetic material only.
B) is a conductor.
C) is an insulator.
D) is a liquid.

Question 29

A 500-turn circular coil with an area of 0.0650 m² is mounted on a rotating frame,which turns at a rate of 18.0 rad/s in the presence of a 0.0350-T uniform magnetic field that is perpendicular to the axis of rotation.What is the instantaneous emf in the coil at the moment that the normal to its plane is perpendicular to the field?

A) 20.5 V
B) zero
C) 0.063 V
D) 369 V
E) ​1.14 V

Question 30

An airplane with a wingspan of 68.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.380 × l0−⁴ T.If the induced potential between wingtips is 0.600 V,what is the plane's speed?

A) 33.5 m/s
B) 15.5 m/s
C) 232 m/s
D) 15,800 m/s
E) ​88 m/s

Question 31

A 600-turn circular coil with an area of 0.0350 m² is mounted on a rotating frame,which turns at a rate of 21.0 rad/s in the presence of a 0.0650-T uniform magnetic field that is perpendicular to the axis of rotation.What is the instantaneous emf in the coil at the moment that the normal to its plane is at a 75.0° angle to the field?

A) zero
B) 28.7 V
C) 37.5 V
D) 27.7 V
E) ​0.065 V

Question 32

If a bar magnet is falling through a loop of wire,the induced current in the loop of wire sets up a field which exerts a force on the magnet.This force between the magnet and the loop will be attractive when:

A) the magnet enters the loop.
B) the magnet is halfway through.
C) the magnet is leaving the loop.
D) never.

Question 33

The back emf in an electric motor is its maximum value under which condition?

A) motor speed is zero
B) current is a maximum
C) voltage is a maximum
D) motor speed is a maximum

Question 34

The function of the electric motor is which one of the following conversion processes?

A) mechanical energy to electrical
B) electrical energy to mechanical
C) low voltage to high or vice versa
D) alternating current to direct

Question 35

The operation of an electric motor depends on which of the following effects?

A) the Doppler effect
B) the photoelectric effect
C) the force acting on a current-carrying wire in a magnetic field
D) current from the motion of a wire in a magnetic field

Question 36

If the induced current in a wire loop were such that the flux it produces were in the same direction as the change in external flux causing the current,which of the following conservation laws would end up being violated?

A) momentum
B) charge
C) energy
D) angular momentum

Question 37

A straight wire lies along the y-axis initially carrying a current of 10 A in the positive y-direction.The current decreases and reverses to 10 A in the negative y-direction,the change in current happening at a uniform rate.In the 1st quadrant a square conducting coil has 2 sides parallel to the y-axis and the other 2 sides parallel to the x-axis.The side of the coil nearest and parallel to the straight wire is at a distance equal to the length of one of the sides of the square.As the current is going from 10 A in one direction to 10 A in the other,in which direction is the induced current in this side of the square coil nearest to the straight wire?

A) It is in the positive y-direction.
B) It is in the negative y-direction.
C) At first it is in the positive y-direction,but after the current passes through zero,it is in the negative y-direction.
D) At first it is in the negative y-direction but after the current passes through zero,it is in the positive y-direction.

Question 38

The basic function of the electric generator is which of the following conversion processes?

A) mechanical energy to electrical
B) electrical energy to mechanical
C) low voltage to high or vice versa
D) alternating current to direct

Question 39

The wiring in a motor has resistance of 4.0 Ω and produces a back emf of 1.1 V when connected to a 15.0-V battery of negligible resistance.Find the current flow through the motor.

A) 4.0 A
B) 3.8 A
C) 0.28 A
D) 3.5 A
E) ​2.7 A

Question 40

A 0.200-m wire is moved parallel to a 0.500-T magnetic field at a speed of 1.50 m/s.What emf is induced across the ends of the wire?

A) 2.25 V
B) 1.00 V
C) 0.600 V
D) zero

Question 41

The "back emf" of a motor refers to a source of voltage that:

A) occurs when the motor runs backwards.
B) occurs when the motor is used as a generator.
C) is biggest when the current through the motor is biggest.
D) is biggest when the motor turns fastest.

Question 42

By what factor is the self-inductance of an air solenoid changed if only its cross-sectional area,A,multiplied by six?

A) 1/6
B) 6
C) 12
D) 36
E) ​1/36

Question 43

A rectangular loop (area = 0.30 m²)turns in a uniform magnetic field with B = 0.50 T.At an instant when the angle between the magnetic field and the normal to the plane of the loop is π/2 rads and increasing at the rate of 0.52 rad/s,what is the magnitude of the emf induced in the loop?

A) 150 mV
B) zero
C) 78 mV
D) 290 mV
E) ​41 mV

Question 44

By what factor is the self-inductance of an air solenoid changed if only its number of coil turns,N,is tripled?

A) 1/3
B) 3
C) 6
D) 9
E) ​1/9

Question 45

When a voltage is generated by rotating a coil in a magnetic field at a constant rate,the period of the voltage equals the time that it takes for the coil to rotate through ________ radians.

A) 1
B) π/2
C) π
D) 2π

Question 46

In the United States,the value of ω for commercially generated power is ________ in SI units.

A) 50
B) 60
C) 120
D) 377

Question 47

What is the minimum frequency with which a 200-turn,flat coil of cross sectional area 380 cm² can be rotated in a uniform 32-mT magnetic field if the maximum value of the induced emf is to equal 7.9 V?

A) 0.19 Hz
B) 2.3 Hz
C) 5.2 Hz
D) 32 Hz
E) ​0.032 Hz

Question 48

In a circuit made up of inductor L,resistance R,ammeter,battery and switch in series,the current is greatest at which of the following times,as measured after the switch is closed?

A) zero
B) one time constant
C) at a time t = L/R
D) ten time constants

Question 49

A circular loop (area = 0.20 m²)turns in a uniform magnetic field with B = 0.13 T.At an instant when the angle between the magnetic field and the normal to the plane of the loop is π rads and is decreasing at the rate of 0.50 rad/s,what is the magnitude of the emf induced in the loop?

A) zero
B) 13 mV
C) 26 mV
D) 20 mV

Question 50

What is the self-inductance in a coil that experiences a 4.7-V induced emf when the current is changing at a rate of 200 A/s?

A) 43 mH
B) 110 mH
C) 200 mH
D) 24 mH
E) ​94 mH

Question 51

By what factor is the self-inductance of an air solenoid changed if its length and number of coil turns both multiplied by eight?

A) 1/8
B) 8
C) 1
D) 64
E) ​1/64

Question 52

Two loops of wire are arranged so that a changing current in one,the primary,will induce a current in the other,the secondary.The secondary loop has twice as many turns as the primary loop.As long as the current in the primary is steady at 3 A,the current in the secondary will be:

A) 3 A.
B) 6 A.
C) 1.5 A.
D) zero.

Question 53

A motor has an internal resistance of 13 Ω.When running,the motor has a back emf of 35 V and draws a current of 3.9 A.What is the supply voltage in this case?

A) 35 V
B) 51 V
C) 86 V
D) 16 V
E) ​38 V

Question 54

An electric motor draws a current of 2.30 A from a 13.0-V battery when it runs at normal speed.If the motor's armature is "jammed" so that it cannot rotate,the current suddenly rises to 11.7 A.What is the back emf of the motor when running at normal speed?

A) 2.56 V
B) 11.7 V
C) 15.6 V
D) 10.4 V
E) ​122 V

Question 55

Electricity may be generated by rotating a loop of wire between the poles of a magnet.The induced current is greatest when:

A) the plane of the loop is parallel to the magnetic field.
B) the plane of the loop is perpendicular to the magnetic field.
C) the magnetic flux through the loop is a maximum.
D) the plane of the loop makes an angle of 45° with the magnetic field.

Question 56

A coil with a self-inductance of 0.80 mH experiences a constant current buildup from zero to 16 A in 0.50 s.What is the induced emf during this interval?

A) 0.0064 V
B) 0.026 V
C) 6.4 V
D) 0.040 V
E) ​0.032 V

Question 57

A coil is rotated in a magnetic field generating an emf given by emf = NBAω sin θ,where θ = ωt.At which angle θ is the emf one sixth of its maximum value?

A) 0°
B) 10°
C) 1.6°
D) 80°
E) ​30º

Question 58

Two loops of wire are arranged so that a changing current in one,the primary,will induce a current in the other,the secondary.The secondary loop has twice as many turns as the primary loop.The current in the primary at this moment is 3 A and increasing.The current in the secondary must be:

A) 3 A.
B) 6 A.
C) zero.
D) There is insufficient information to work this problem.

Question 59

The current in a coil with a self-inductance of 2.3 mH increases from 0 to 1.9 A in a tenth of a second.What is the induced emf in the coil?

A) 44 mV
B) 4.4 mV
C) 830 mV
D) 0.012 V
E) ​87 mV

Question 60

The self-inductance of a solenoid increases under which of the following conditions?

A) Only the solenoid length is increased.
B) Only the cross sectional area is decreased.
C) Only the number of coils per unit length is decreased.
D) Only the number of coils is increased.

Question 61

A circular loop of wire has its radius reduced in half in time Ät.A uniform magnetic field is at an angle of 60^° to the plane of the coil,and the magnetic field doubles its intensity in the same time interval Ät.During this interval,what happens to the flux through the coil?

A) It increases.
B) It decreases.
C) It remains the same.
D) More information is needed to make this conclusion.

Question 62

The unit of inductance,the henry,is equivalent to:

A) V·s/A.
B) V/m.
C) J/C.
D) none of the units given.

Question 63

A circuit consists of a 9.2-mH coil,a 17-Ω resistor,a 6.0-Ω resistor,a 9-V battery and a switch,all in series.What is the time constant of this circuit?

A) 2.5E-3 s
B) 3.6E-3 s
C) 2.1E-3 s
D) 4.0E-4 s
E) ​0.39 s

Question 64

What is the stored energy in a 0.30-mH coil carrying a current of 6.0 A?

A) 1.1E-2 J
B) 5.4E-3 J
C) 1.8E-3 J
D) 2.2E-2 J
E) ​2.0E-2 J

Question 65

How is the energy stored in a current-carrying inductor related to its self-inductance,L?

A) directly proportional to L²
B) directly proportional to L^1/2
C) directly proportional to L
D) inversely proportional to L

Question 66

In a circuit made up of inductor,resistance,ammeter,battery and switch in series,at which of the following times after the switch is closed is the rate of current increase greatest?

A) zero
B) one time constant
C) reciprocal of one time constant
D) ten time constants

Question 67

An emf of 0.52 V is induced in a 0.62-H inductor.What is the rate of change of current through the inductor?

A) 0.84 A/s
B) 1.2 A/s
C) 0.32 A/s
D) 1.14 A/s
E) ​0.62 A/s

Question 68

How is the energy stored in a current-carrying inductor related to the current value,I?

A) directly proportional to I ²
B) directly proportional to I ^1/2
C) directly proportional to I
D) inversely proportional to I

Question 69

An RL series circuit has: 5.3-mH coil,2.2-Ω resistor,15-V battery,ammeter and switch.After the switch is closed for a long time,find the final value of the current.

A) 1300 A
B) 6.8 A
C) 0.8 mA
D) 33 A
E) ​0.17 A

Question 70

A series circuit contains a 14-V battery,a 3.3-Ω resistor,and a 3.8-mH inductor.If the switch to the battery is closed at t = 0,find the time required for the current in the circuit to reach 63% of its final value.

A) 1.2 ms
B) 13 ms
C) 0.87 ms
D) 16 ms
E) ​0.08 ms

Question 71

An RL circuit has L = 0.45 H and R = 5.5 Ω.It is connected to a battery with ε = 19 V at time t = 0.Find the energy stored in the inductor when the current in the circuit is 0.40 A.

A) 36 mJ
B) 72 J
C) 180 J
D) 5.4 J
E) ​620 J

Question 72

A circuit consists of a 11.5-mH coil,a 9.0-V battery,a parallel combination of a 10-Ω resistor and a 6.0-Ω resistor,and a switch,all in series.What is the time constant of this circuit?

A) 7.2E-4 s
B) 3.1E-3 s
C) 1.2E-3 s
D) ​2.8E-2 s
E) ​This circuit has 2 time constants.

Question 73

A 9.6-V battery is connected in series with a switch,6.0-Ω resistor and coil.What energy is stored in the coil when the current is 1.6 A? The time constant is 4.3 × 10−⁴ s.

A) 3.3E-3 J
B) 6.6E-3 J
C) 4.1E-3 J
D) 1.1E-3 J
E) ​1.3E-3 J

Question 74

An air-core inductor has 2000 turns/m and an internal volume of 1.3 cm³.What is its inductance?

A) 6.5 μH
B) 2.6 mH
C) 0.33 H
D) 65 μH
E) ​Insufficient information is given.

Question 75

An RL series circuit has the following components: 4.8-mH coil,1.6-Ω resistor,13-V battery,ammeter and switch.What is the time constant of this circuit?

A) 3.3E+2 s
B) 3.0E-3 s
C) 1.7E-3 s
D) 5.9E-4 s
E) ​3.9E-2 s

Question 76

The magnetic field going through a stationary circular loop increases from zero to 5 T in a certain time t.The induced current in the loop will depend on the radius of the loop,r,the resistance of the loop,R,and the time,t.If two of these stay constant,the induced current can be directly proportional to:

A) t.
B) r.
C) R.
D) none of these

Question 77

Superconductors have been discussed as a means for electrical energy storage.Because they are resistanceless,a current once started in a loop would continue without loss.If a current of 1.0 × 10⁴ A were started in a huge toroidal coil of radius 1.0 km and inductance 50 H,how much electrical energy (in kWh)could be stored?

A) 300 kWh
B) 480 kWh
C) 690 kWh
D) 840 kWh

Question 78

A double loop of wire (making 2 turns)is in the x-y plane centered at the origin.A uniform magnetic field is increasing at a constant rate in the positive z-direction.Viewed from the positive z-axis,in which direction is the induced magnetic field in the loop?

A) in the positive z-direction
B) in the negative z-direction
C) There is no induced field because of the double loop.
D) There is no induced field because the rate of change of the magnetic field is constant.

Question 79

A 16-V battery is connected in series with a switch,resistor and coil.If the circuit's time constant is 4.2 × 10−⁴ s and the final steady current after the switch is closed becomes 2.9 A,what is the value of the inductance?

A) 19 mH
B) 2.3 mH
C) 0.76 mH
D) 1.1 mH
E) ​7.6 mH

Question 80

An inductor,battery,resistance,and ammeter and switch are connected in series.If the switch,initially open,is now closed,what is the current's final value?

A) zero
B) battery voltage divided by inductance
C) battery voltage times inductance
D) battery voltage divided by resistance