24

Homework 4Due: 11:59pm on Sunday, March 27, 2011

Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy

[Switch to Standard Assignment View]

Induced EMF and Current in a Shrinking LoopShrinking Loop. A circular loop of flexible iron wire has an initial circumference of 164 , but itscircumference is decreasing at a constant rate of 15.0 due to a tangential pull on the wire. The loop is

in a constant uniform magnetic field of magnitude 0.600 , which is oriented perpendicular to the plane of the

loop. Assume that you are facing the loop and that the magnetic field points into the loop.

Part A

Find the magnitude of the emf induced in the loop after exactly time 7.00 has passed since the

circumference of the loop started to decrease.

Hint A.1 How to approach the problem

The induced emf in a loop is related to the rate of change of magnetic flux through the loop. (If you don'tknow the exact relation, look at Hint A.3.) Therefore, to find the induced emf, you first need to find themagnetic flux through the loop as a function of time. The magnetic flux through the loop is proportional tothe area of the loop, so a good starting point is to write the area of the loop as a function of time in termsof the given parameters. The area of the loop is related to its radius, which in turn can be related to itscircumference.

Hint A.2 An expression for the circumference of the loop as a function of time

Let be the initial circumference of the coil. At time , the circumference starts decreasing at the

constant rate . Then the circumference of the coil as a function of time is given by the relation

.

Hint A.3 An expression for the flux through the loop as a function of its circumference

The equation for the magnetic flux through the loop is

,

where is the magnetic field through the loop (which is a constant in this problem), is the area

vector associated with the loop, and is the angle between the magnetic field vector and the area

vector.In this problem, is given as (the area vector is parallel to the magnetic field vector). Therefore,

,

where and is the radius of the loop as a function of time.

Finally, the radius of the loop is related to its circumference by . Substituting this

MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme...

1 of 21 5/12/2011 8:03 PM

relation into the equation for gives

.

Hint A.4 A formula for the induced emf in the loop (Faraday's law)

The emf induced in the loop (Faraday's law) is

,

where is the magnetic flux through the loop.

Hint A.5 An expression for

The chain rule of calculus allows us to express , where is a function of , as follows:

.

Express your answer numerically in volts to three significant figures.

ANSWER: = 8.45×10−3

Correct V

Part B

Find the direction of the induced current in the loop as viewed looking along the direction of the magneticfield.

ANSWER: clockwise

counterclockwise

Correct

The induced current flows in the direction that tends to prevent the flux through the coil fromdecreasing. That is, it adds to the magnetic field through the coil as the coil's area is decreasing. Thismeans that the current has to flow clockwise, so that the magnetic field produced by it (right-hand rule)points away from you (you were asked to look at the loop along the direction of the original magneticfield). Alternatively, you could look at how each part of the wire moves toward the center of the loop asit gets smaller. As a result, we can use the standard equation for force on a particle and

the right-hand rule to determine the direction of the current.

± Magnetic Flux and Induced EMF in a Coil


2 of 21 5/12/2011 8:03 PM

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 10.6 is rotated during the

time interval 4.50×10−2 from a position in which its plane is perpendicular to Earth's magnetic field to one inwhich its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is 5.40×10−5

.

Part A

What is the total magnitude of the magnetic flux ( ) through the coil before it is rotated?

Hint A.1 Formula for the magnetic flux through a wire loop

Hint not displayed

Hint A.2 The initial angle between the magnetic field and the area vector

Hint not displayed

Hint A.3 Definition of the weber

Hint not displayed

Express your answer numerically, in webers, to at least three significant figures.

ANSWER: = 1.14×10−5

Correct Wb

Part B

What is the magnitude of the total magnetic flux through the coil after it is rotated?

Hint B.1 The angle between the magnetic field and the area vector

Hint not displayed

Express your answer numerically, in webers, to at least three significant figures.

ANSWER: = 0Correct Wb

Part C

What is the magnitude of the average emf induced in the coil?

Hint C.1 Formula for the average emf induced in a coil (Faraday's law)

Hint not displayed

Express your answer numerically (in volts) to at least three significant figures.

ANSWER: average induced emf = 2.54×10−4

Correct V

Electric Field Due to Increasing Flux

Learning Goal: To work through a straightforward application of Faraday's law to find the EMF and theelectric field surrounding a region of increasing flux

Faraday's law describes how electric fields and electromotive forces are generated from changing magneticfields. This problem is a prototypical example in which an increasing magnetic flux generates a finite lineintegral of the electric field around a closed loop that surrounds the changing magnetic flux through a surfacebounded by that loop. A cylindrical iron rod with cross-sectional area is oriented with its symmetry axis

coincident with the z axis of a cylindrical coordinate system as shown. It has a uniform magnetic field insidethat varies according to . In other words, the magentic field is always in the positive z

direction, and it has no other components.For your convenience, we restate Faraday's law here:

, where

is the line integral of the electric

field, and the magnetic flux is given by

, where is

the angle between the magnetic field and the localnormal to the surface bounded by the closed loop.Direction: The line integral and surface integral reversetheir signs if the reference direction of or is

reversed. The right-hand rule applies here: If thethumb of your right hand is taken along , then the

fingers point along . You are free to take the loop anywhere you choose, although usually it makes sense

to choose it to lie along the path of the circuit you are considering.

Part A

Find , the electromotive force (EMF) around a loop that is at distance from the z axis, where is

restricted to the region outside the iron rod as shown. Take the direction shown in the figure as positive.

Hint A.1 Selecting the loop

Hint not displayed

Hint A.2 Find the magnetic flux

Hint not displayed

Express in terms of , , , , and any needed constants such as , , and .

ANSWER: =

Correct

Part B


3 of 21 5/12/2011 8:03 PM

Due to the cylindrical symmetry of this problem, the induced electric field can depend only on the

distance from the z axis, where is restricted to the region outside the iron rod. Find this field.

Hint B.1 Calculate the line integral

Hint not displayed

Hint B.2 The z and r components of the electric field

Hint not displayed

Express in terms of quantities given in the introduction (and constants), using the unit

vectors in the cylindrical coordinate system, , , and .

ANSWER: =

Correct

A Magnet and a CoilWhen a magnet is plunged into a coil at speed , as shown in the figure, a voltage is induced in the coil and acurrent flows in the circuit.

Part A

If the speed of the magnet is doubled, the induced voltage is ________ .


Hint not displayed

ANSWER:

Correct


4 of 21 5/12/2011 8:03 PM

Part B

The same magnet is plunged into a coil that has twice the number of turns as before, as shown in the figure.If the speed of the magnet is again , the inducedcurrent in the coil is _______ .

Hint B.1 How to approach the problem

Hint not displayed

Hint B.2 Find the induced emf in the coil

Hint not displayed

Hint B.3 Find the resistance of the coil

Hint not displayed

Hint B.4 Induced current

Hint not displayed

ANSWER:

Correct

By increasing the number of turns in the coil, the induced emf increases, but so does the resistance ofthe coil. Since those two quantities increase by the same factor, their ratio remains constant, and theinduced current in the circuit is unchanged.

Mutual Inductance of a Double Solenoid

Learning Goal: To learn about mutual inductance from an example of a long solenoid with two windings.To illustrate the calculation of mutual inductance it is helpful to consider the specific example of two solenoidsthat are wound on a common cylinder. We will take the cylinder to have radius and length . Assume that

the solenoid is much longer than its radius, so that its field can be determined from Ampère's law throughout

its entire length: .

We will consider the field that arises from solenoid 1,


5 of 21 5/12/2011 8:03 PM

which has turns per unit length. The magnetic fielddue to solenoid 1 passes (entirely, in this case)through solenoid 2, which has turns per unit length.Any change in magnetic flux from the field generatedby solenoid 1 induces an EMF in solenoid 2 through

Faraday's law of induction, .

Part A

Consider first the generation of the magnetic field by the current in solenoid 1. Within the solenoid

(sufficiently far from its ends), what is the magnitude of the magnetic field due to this current?

Express in terms of , variables given in the introduction, and relevant constants.

ANSWER: =

Correct

Note that this field is independent of the radial position (the distance from the symmetry axis) for pointsinside the solenoid.

Part B

What is the flux generated by solenoid 1's magnetic field through a single turn of solenoid 2?

Hint B.1 The definition of flux

Hint not displayed

Express in terms of , quantities given in the introduction, and any needed constants.

ANSWER: =

Correct

Part C

Now find the electromotive force induced across the entirety of solenoid 2 by the change in current in

solenoid 1.

Hint C.1 Find the flux from

Hint not displayed


6 of 21 5/12/2011 8:03 PM

Hint C.2 The EMF for the entire solenoid

Hint not displayed

Hint C.3 Putting it together

Hint not displayed

Express your answer in terms of , , , other parameters given in the introduction, and

any relevant constants.

ANSWER: =

Correct

Part D

This overall interaction is summarized using the symbol to indicate the mutual inductance between the

two windings. Based on your previous two answers, which of the following formulas do you think is thecorrect one?

ANSWER:

Correct

Mutual inductance indicates that a change in the current in solenoid 1 induces an electromotive force(EMF) in solenoid 2. When the double solenoid is thought of as a circuit element, this electromotiveforce is added into Kirchhoff's loop law. The constant of proportionality is the mutual inductance,

denoted by . The negative sign in the equation comes from the negative sign

in Faraday's law, and reflects Lenz's rule: The changing magnetic field due to solenoid 1 will induce acurrent in solenoid 2; this induced current will itself generate a magnetic field within solenoid 2, suchthat changes in the induced magnetic field oppose the changes in the magnetic field from solenoid 1.

Part E


7 of 21 5/12/2011 8:03 PM

Using the formula for the mutual inductance, , find .

Express the mutual inductance in terms of , , quantities given in the introduction, and

relevant physical constants.

ANSWER: =

Correct

Part F

Not surprisingly, if a current is sent through solenoid 2, it induces a voltage in solenoid 1. The mutualinductance in this case is denoted by , the mutual inductance for voltage induced in solenoid 1 from

current in solenoid 2. What is ?

Hint F.1 A new symmetry

Hint not displayed

Express the mutual inductance in terms of , , quantities given in the introduction, and relevantphysical constants.

ANSWER: =

Correct

This result that is equal to reflects the interchangeability of the two coils and applies even if

the coils are only partially coupled (for example, if one coil is wound on a much larger cylinder or if onlya fraction of the larger coil's flux is intercepted by the smaller coil). Because of this fact, the subscriptsare generally omitted: There is only one mutual inductance between two coils, denoted by : An EMF

is generated in one coil by a change in current in the other coil.

Current Through LR Circuits Ranking TaskThe figures below show six circuits which consist of identical ideal batteries, resistors, and inductors. All ofthe switches are closed at the same time.

Part A

Rank the circuits based on the current through the battery immediately after the switch is closed.

Hint A.1 Ideal inductors in circuits

Inductors have time-dependent effects on the behavior of electric circuits. When a potential difference isfirst applied to an ideal inductor, the inductor generates a back emf equal in magnitude to the potentialdifference applied, but opposite in direction (this is what is meant by a back emf). After a long amount oftime, the emf generated by the inductor becomes zero, and an ideal inductor will act like a simpleresistance-free wire.


8 of 21 5/12/2011 8:03 PM

Hint A.2 Replacing inductors with "opens"

When the switch is first closed, the inductor generates a back emf equal in magnitude to the potentialdifference applied. This means that no net potential difference exists across the inductor, so no currentcan flow through the inductor. Thus, the inductor acts like an "open" in the circuit. Imagine simplyremoving the inductor from the circuit, leaving the circuit open at the location occupied by the inductor.Analyze the remaining circuit using ideas developed earlier.

Hint A.3 Replacement in a circuit

Examine the circuit shown in the figure.

Replace the inductor with an open switch at its location. This open will prevent any current from flowing tothe resistor that shares the inductor's branch. Thus, this circuit is reduced to a simple one-resistor circuit,with current .

Hint A.4 Replacement in a circuit


Replace the inductor with an open switch at its location. This circuit is reduced to a simple circuit with tworesistors in series and current equal to .

Rank from largest to smallest. To rank items as equivalent, overlap them.

ANSWER:

View


9 of 21 5/12/2011 8:03 PM

All attempts used; correct answer displayed

Part B

Rank the circuits based on the current through the battery a very long time after the switch is closed.

Hint B.1 Replacing inductors with "shorts"

Long after the switch is closed, the inductor generates no emf and acts like a wire with zero resistance.Thus, the inductor acts like a "short" in the circuit. Imagine simply replacing the inductor with a bare wire.Analyze the remaining circuit using ideas developed earlier in the course.

Hint B.2 Replacement in a circuit


Replace the inductor with a bare wire at its location. This circuit is reduced to a simple circuit with tworesistors in parallel and total current .

Hint B.3 Replacement in a circuit


Replace the inductor with a bare wire. This bare wire "shorts" the battery, resulting in a huge (infinite foran ideal battery) current. An infinite current is the largest possible current.

Rank from largest to smallest. To rank items as equivalent, overlap them.

ANSWER:


10 of 21 5/12/2011 8:03 PM

View All attempts used; correct answer displayed

± Mutual Inductance of a Tesla CoilA long solenoid (black coil) with cross-sectional area and length is wound with turns of wire. A

time-varying current flows through this wire. A

shorter coil (blue coil) with turns of wire surrounds

it. Use .

Part A

Find the value of the mutual inductance.

Note: The current in coil 1 is constantly changing. However, when using the hints it may help you to considerthe instant at which the current in coil 1 is .

Hint A.1 Mutual nature of mutual inductance

Hint not displayed

Hint A.2 Find the magnetic field of the solenoid

Hint not displayed

Hint A.3 Find the magnetic flux in coil 2

Hint not displayed

Hint A.4 Finding the mutual inductance

Hint not displayed


11 of 21 5/12/2011 8:03 PM

Express your answer numerically, in Henry.

ANSWER: =

Correct

As you can see, the more tightly wound each coil is (the bigger n is for a given length), the higher thevalue of M.

Determining Inductance from the Decay in an L-R CircuitIn this problem you will calculate the inductance of an inductor from a current measurement taken at aparticular time. Consider the L-R circuit shown in the figure. Initially, the switch connects a resistor ofresistance and an inductor to a battery, and a

current flows through the circuit. At time , the

switch is thrown open, removing the battery from thecircuit. Suppose you measure that the current decaysto at time .

Part A

Determine the time constant of the circuit.


Hint not displayed

Hint A.2 What is the definition of time constant?

Hint not displayed

Hint A.3 Match the condition at

Hint not displayed

Hint A.4 Solve for the time constant

Hint not displayed

Express your answer in terms of , , and . Recall that natural logarithms are entered as ln(x).


12 of 21 5/12/2011 8:03 PM

ANSWER:

=

Correct

Part B

What is the inductance of the inductor?

Hint B.1 What is the time constant of an L-R circuit?

Hint not displayed

Express your answer in terms of , , , and .

ANSWER:

=

Correct

Decay of Current in an L-R Circuit

Learning Goal: To understand the mathematics of current decay in an L-R circuitA DC voltage source is connected to a resistor ofresistance and an inductor with inductance ,

forming the circuit shown in the figure. For a long timebefore , the switch has been in the position

shown, so that a current has been built up in the

circuit by the voltage source. At the switch is

thrown to remove the voltage source from the circuit.This problem concerns the behavior of the current

through the inductor and the voltage across the

inductor at time after .

Part A

After , what happens to the voltage across the inductor and the current through the

inductor relative to their values prior to ?

Hint A.1 What is the relation between current and voltage for the inductor?

Hint not displayed


13 of 21 5/12/2011 8:03 PM

ANSWER: changes slowly and changes abruptly.

changes slowly and changes abruptly.

Both change slowly.

Both change abruptly.

Correct

After , the battery no longer provides a voltage that drives current around the circuit. If the circuit

did not contain an inductor, then the current would drop to zero immediately. However, inductors act tokeep the current flowing. If the current starts to change, this causes an electromotive force (EMF) toform across the inductor that (by Lenz's law) opposes the tendency for the current to change. Here,this causes the current through the inductor to persist for a while as it decays toward zero.

Part B

What is the differential equation satisfied by the current after time ?

Hint B.1 Kirchhoff's loop law

Hint not displayed

Express in terms of , , and .

ANSWER: =

Correct

The minus sign in this equation tells us that the current is decreasing with time. The current is decaying.This is the case because the DC voltage source no longer acts to sustain the current.

Part C

What is the expression for obtained by solving the differential equation that satisfies after ?

Hint C.1 Separation of variables

Hint not displayed

Hint C.2 Integrating

Hint not displayed

Express your answer in terms of the initial current , as well as , , and .


14 of 21 5/12/2011 8:03 PM

ANSWER: =

Correct

Part D

What is the time constant of this circuit?

Hint D.1 Definition of time constant

Hint not displayed

Hint D.2 The time constant for this circuit

Hint not displayed

Express your answer in terms of and ?

ANSWER: =

Correct

± Transformers

Learning Goal: To understand the concepts explaining the operation of transformers.One of the advantages of alternating current (ac) over direct current (dc) is the ease with which voltage levelscan be increased or decreased. Such a need is always present due to the practical requirements of energydistribution. On the one hand, the voltage supplied to the end users must be reasonably low for safetyreasons (depending on the country, that voltage may be 110 volts, 220 volts, or some other value of thatorder). On the other hand, the voltage used in transmitting electric energy must be as high as possible tominimize losses in the transmission lines. A device that uses the principle of electromagnetic induction to

increase or decrease the voltage by a certain factor is called a transformer.The main components of a transformer are two coils (windings) that are electrically insulated from each other.The coils are wrapped around the same core, which is typically made of a material with a very large relativepermeability to ensure maximum mutual inductance. One coil, called the primary coil, is connected to avoltage source; the other, the secondary coil, delivers the power. The alternating current in the primary coilinduces the changing magnetic flux in the core that creates the emf in the secondary coil. The magnitude ofthe emf induced in the secondary coil can be controlled by the design of the transformer. The key factor is thenumber of turns in each coil.Consider an ideal transformer, that is, one in which the coils have no ohmic resistance and the magnetic flux

is the same for each turn of both the primary and secondary coils. If the number of turns in the primary

coil is and that in the secondary coil is , then the emfs induced in the coils can be written as

,

and therefore,

.

Since both emfs oscillate with the same frequency as the ac source, the formula above can be applied to the


15 of 21 5/12/2011 8:03 PM

instantaneous amplitude or the rms values of the emfs. Moreover, if the coils have zero resistance (as weassumed), then for each coil the terminal voltage will be equal to the induced emf. Therefore, we can write

.

Note that if , then . This is a case of a step-up transformer. Conversely, if , then

. This is a case of a step-down transformer. Without energy losses, the power in the primary and

secondary coils is the same:.

If the secondary circuit is completed by a resistance , then . Combining this with the two equations

above gives

.

Dividing the first and last expressions by and then inverting gives

.

In other words, the current in the primary coil is the same as if it were connected directly to a resistance equal

to . In a way, transformers "transform" resistances as well as voltages and currents. In reality, no

transformer is ideal. There are always some energy losses. However, modern transformers have very highefficiencies, usually well exceeding 90%.

In answering the questions below, consider the transformer ideal unless otherwise noted.

Part A

The primary coil of a transformer contains 100 turns; the secondary has 200 turns. The primary coil isconnected to a size AA battery that supplies a constant voltage of 1.5 volts. What voltage would bemeasured across the secondary coil?

ANSWER: zero


16 of 21 5/12/2011 8:03 PM

Correct

In order for an emf to be induced in the secondary coil, the flux through it must be changing; therefore,the current in the primary coil must also be changing. If a constant voltage is supplied to the primarycoil, no emf would be induced in the secondary, and therefore, the secondary voltage would be zero.

Part B

A transformer is intended to decrease the rms value of the alternating voltage from 500 volts to 25 volts.The primary coil contains 200 turns. Find the necessary number of turns in the secondary coil.

ANSWER: = 10Correct

This is a step-down transformer: The voltage decreases.

Part C

A transformer is intended to decrease the rms value of the alternating current from 500 amperes to 25amperes. The primary coil contains 200 turns. Find the necessary number of turns in the secondary coil.

Hint C.1 How to approach this problem

Hint not displayed

ANSWER: = 4000Correct

This is a step-up transformer: The voltage increases by the same factor by which the currentdecreases.

Part D

In a transformer, the primary coil contains 400 turns, and the secondary coil contains 80 turns. If theprimary current is 2.5 amperes, what is the secondary current ?

Express your answer numerically in amperes.

ANSWER: = 12.5Correct


17 of 21 5/12/2011 8:03 PM

Part E

The primary coil of a transformer has 200 turns and the secondary coil has 800 turns. The power suppliedto the primary coil is 400 watts. What is the power generated in the secondary coil if it is terminated by a20-ohm resistor?

Hint E.1 In the ideal world...

Hint not displayed

ANSWER:

Correct

In case of an ideal transformer, the power in the primary circuit is the same as that in the secondarycircuit.

Part F

The primary coil of a transformer has 200 turns, and the secondary coil has 800 turns. The transformer isconnected to a 120-volt (rms) ac source. What is the (rms) current in the primary coil if the secondary

coil is terminated by a 20-ohm resistor?

Hint F.1 How to approach the problem

Recall that transformers "transform" resistances as well as voltages and currents.

Express your answer numerically in amperes.

ANSWER: = 96Correct

Part G

A transformer supplies 60 watts of power to a device that is rated at 20 volts (rms). The primary coil isconnected to a 120-volt (rms) ac source. What is the current in the primary coil?

Hint G.1 How to approach the problem


18 of 21 5/12/2011 8:03 PM

Hint not displayed

Express your answer in amperes.

ANSWER: = 0.5Correct

Part H

The voltage and the current in the primary coil of a nonideal transformer are 120 volts and 2.0 amperes.The voltage and the current in the secondary coil are 19.4 volts and 11.8 amperes. What is the efficiency of the transformer? The efficiency of a transformer is defined as the ratio of the output power to the input

power, expressed as a percentage: .

Express your answer as a percentage.

ANSWER: = 95.4

Correct %

Determining Inductance from Voltage and CurrentAn inductor is hooked up to an AC voltage source. The voltage source has EMF and frequency . The

current amplitude in the inductor is .

Part A

What is the reactance of the inductor?

Hint A.1 Definition of reactance

Hint not displayed

Express your answer in terms of and .

ANSWER: =

Correct

Part B

What is the inductance of the inductor?

Hint B.1 Reactance in terms of and

Hint not displayed


19 of 21 5/12/2011 8:03 PM

Express your answer in terms of , , and .

ANSWER: =

Correct

Part C

What would happen to the amplitude of the current in the inductor if the inductance were doubled?

Hint C.1 How to approach the problem

Hint not displayed

ANSWER: There would be no change in the amplitude of the current.

The amplitude of the current would be doubled.

The amplitude of the current would be halved.

The amplitude of the current would be quadrupled.

Correct

Inductive Reactance

Learning Goal: To understand the concept of reactance (of an inductor) and its frequency dependence.When an inductor is connected to a voltage source that varies sinusoidally, a sinusoidal current will flowthrough the inductor, its magnitude depending on the frequency. This is the essence of AC (alternatingcurrent) circuits used in radio, TV, and stereos. Circuit elements like inductors, capacitors, and resistors arelinear devices, so the amplitude of the current will be proportional to the amplitude of the voltage.

However, the current and voltage may not be in phase with each other. This new relationship between voltageand current is summarized by the reactance, the ratio of voltage and current amplitudes, , and :

, where the subscript L indicates that this formula applies to an inductor.

Part A

To find the reactance of an inductor, imagine that a current , is flowing through the

inductor. What is the voltage across this inductor?

Hint A.1 Voltage and current for an inductor

Hint not displayed

Express your answer in terms of , , and the inductance .


20 of 21 5/12/2011 8:03 PM

ANSWER: =

Correct

Part B

What is the reactance of an inductor?

Hint B.1 The definition of reactance

Hint not displayed

Express your answer in terms of and the inductance .

ANSWER: =

Correct

Part C

In thinking of an inductor as a circuit element, it is helpful to consider its limiting behavior at high and lowfrequencies. At one extreme, the inductor might behave like a short circuit, that is, like a resistor with almostno resistance (an ideal wire) having essentially no voltage drop across it no matter what the current.Alternatively, the inductor might behave like an open circuit, that is, like a resistor with large resistance sothat essentially no current will flow no matter what the applied voltage. Based on the formula you obtainedfor the reactance, how does an inductor behave at high and low frequencies?

ANSWER: like a short circuit at both high frequencies and low frequencies

like an open circuit at both high frequencies and low frequencies

like an open circuit at high frequencies and a short circuit at low frequencies

like an open circuit at low frequencies and a short circuit at high frequencies

Correct

Score Summary:Your score on this assignment is 93.1%.You received 93.1 out of a possible total of 100 points.


21 of 21 5/12/2011 8:03 PM

24

Documents

closed loop

magnetic field vector

increasing magnetic

magnetic field points

original magnetic field

changing magnetic flux

magnetic flux ot

loop faradays law