221

Test 3Due: 11:59pm on Thursday, March 10, 2011

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

[Switch to Standard Assignment View]

Problem 29.55: Terminal SpeedA conducting rod with length , mass , and resistance moves without friction on metal rails. The rails are

connected with eachother. A uniform magnetic field is directed into the plane of the figure. The rod starts

from rest and is acted on by a constant force directed to the right. The rails are infinitely long and have

negligible resistance.

Part A

Graph the speed of the rod as a function of time.

ANSWER:

View All attempts used; correct answer displayed

Part B

Find an expression for the terminal speed (the speed when the acceleration of the rod is zero).

Express your answer in terms of the given quantities.

ANSWER:

=Correct

Problem 29.51As a new electrical engineer for the local power company, you are assigned the project of designing agenerator of sinusoidal ac voltage with a maximum voltage of 120 . Besides plenty of wire, you have two

strong magnets that can produce a constant uniform magnetic field of 1.6 over a square area with a length

of 10.4 on a side when the magnets are separated by a distance of 11.3 . The basic design shouldconsist of a square coil turning in the uniform magnetic field. To have an acceptable coil resistance, the coilcan have at most 400 loops.

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

1 of 17 5/12/2011 8:08 PM

Part A

What is the minimum rotation rate of the coil so it will produce the required voltage?

Express your answer using two significant figures.

ANSWER: = 170

All attempts used; correct answer displayed

Problem 25.58A plastic tube 25.0 long and 4.00 in diameter is dipped into a silver solution, depositing a layer of silver0.100 thick uniformly over the outer surface of the tube.

Part A

If this coated tube is then connected across a 12.0- battery, what will be the current?

ANSWER: = 411Correct

Test Your Understanding 25.1: Electric Current and Current DensityTwo wires both carry the same current . The moving charged particles in both wires are electrons, but the

concentration of moving electrons in wire #1 is double the concentration of moving electrons in wire #2.

Part A

Under what circumstances will the drift speed of electrons be the same in both wires?

ANSWER: if the diameter of wire #2 is the diameter of wire #1

if the diameter of wire #2 is the diameter of wire #1

if the diameter of wire #2 is the diameter of wire #1

if the diameter of wire #2 is times the diameter of wire #1



Correct

The current density is related to the current and the cross-sectional area of the wire by the

relationship


2 of 17 5/12/2011 8:08 PM

The current density is also related to the concentration , charge , and drift speed of the

moving particles by the relationship

Combining these relationships, we find

The values of , , and are the same for both wires. Since is twice as great in wire #1 as in wire

#2, it must be that is twice as great in wire #2 as in wire #1. The cross-sectional area is

proportional to the square of the diameter, so the diameter of wire #2 must be times the diameter

of wire #1.

Test Your Understanding 25.4: Electromotive Force and CircuitsA simple circuit consists of a resistor connected to a battery. The battery has emf , internal resistance ,

and terminal voltage , and the resistor has resistance .

Part A

Rank the following circuits in order of current, from highest to lowest values.

ANSWER:

View All attempts used; correct answer displayed

The sum of potential changes around each circuit is zero. This statement can be written as (1)

The quantity is the terminal voltage across the battery of emf :

(2)

Combining (1) and (2), we have (3)

We can solve each of (1), (2), and (3) for , giving us three different expressions for the current in the

circuit:

(4)

(5)


3 of 17 5/12/2011 8:08 PM

(6)

For the five individual circuits, we find

Exercise 25.11A 1.60 cylindrical rod of diameter 0.500 is connected to a power supply that maintains a constantpotential difference of 12.0 across its ends, while an ammeter measures the current through it. You

observe that at room temperature (20.0 ) the ammeter reads 18.7 , while at 92.0 it reads 17.3 .

You can ignore any thermal expansion of the rod.

Part A

Find the resistivity and for the material of the rod at 20 .

ANSWER: = 7.87×10−6

Correct

Part B

Find the temperature coefficient of resistivity at 20 for the material of the rod.

ANSWER: = 1.12×10−3

Correct

Exercise 25.18

Part A

What diameter must a copper wire have if its resistance is to be the same as that of an equal length ofaluminum wire with diameter 3.40 ?


4 of 17 5/12/2011 8:08 PM

ANSWER: = 2.69All attempts used; correct answer displayed

Exercise 25.19You need to produce a set of cylindrical copper wires 4.00 long that will have a resistance of 0.140

each.

Part A

What will be the mass of each of these wires?

ANSWER: = 17.5

Correct

Exercise 25.51A 21.0 bulb is connected across the terminals of a 12.0- battery having 3.00 of internal resistance.

Part A

What percentage of the power of the battery is dissipated across the internal resistance and hence is notavailable to the bulb?

ANSWER: = 12.5

Correct

Exercise 25.54A typical small flashlight contains two batteries, each having an emf of 1.50 connected in series with a bulb

having a resistance of 19 .

Part A

If the internal resistance of the batteries is negligible, what power is delivered to the bulb?


ANSWER: = 0.47Correct

Part B


5 of 17 5/12/2011 8:08 PM

If the batteries last for a time of 4.5 , what is the total energy delivered to the bulb?



Part C

The resistance of real batteries increases as they run down. If the initial internal resistance is negligible,what is the combined internal resistance of both batteries when the power to the bulb has decreased to halfits initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat whenthe current through the filament changes, because this changes the temperature of the filament and hencethe resistivity of the filament wire.)


ANSWER: = 7.9

Correct

Problem 25.59On your first day at work as an electrical technician, you are asked to determine the resistance per meter ofa long piece of wire. The company you work for is poorly equipped. You find a battery, a voltmeter, and anammeter, but no meter for directly measuring resistance (an ohmmeter). You put the leads from the voltmeteracross the terminals of the battery, and the meter reads 12.2 . You cut off a 20.0- length of wire and

connect it to the battery, with an ammeter in series with it to measure the current in the wire. The ammeterreads 6.70 . You then cut off a 40.0- length of wire and connect it to the battery, again with the ammeter

in series to measure the current. The ammeter reads 4.20 . Even though the equipment you have available

to you is limited, your boss assures you of its high quality: The ammeter has very small resistance, and thevoltmeter has very large resistance.

Part A

What is the resistance of 1 meter of wire?

ANSWER: = 5.42×10−2

Correct

Problem 25.70A person with body resistance between his hands of 10 accidentally grasps the terminals of a 16-

power supply.

Part A


6 of 17 5/12/2011 8:08 PM

If the internal resistance of the power supply is 1800 , what is the current through the person's body?



Part B

What is the power dissipated in his body?


ANSWER: = 1.8×104

All attempts used; correct answer displayed

Part C

If the power supply is to be made safe by increasing its internal resistance, what should the internalresistance be for the maximum current in the above situation to be or less?


ANSWER: = 1.6×107

Correct

Problem 25.77According to the U.S. National Electrical Code, copper wire used for interior wiring of houses, hotels, officebuildings, and industrial plants is permitted to carry no more than a specified maximum amount of current. Thetable below shows the maximum current for several common sizes of wire with varnished cambric

insulation. The "wire gauge" is a standard used to describe the diameter of wires. Note that the larger thediameter of the wire, the smaller the wire gauge.Wire gaugeDiameter( )

14 0.163 1812 0.205 2510 0.259 308 0.326 406 0.412 605 0.462 654 0.519 85

Part A

What considerations determine the maximum current-carrying capacity of household wiring?

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

ANSWER: My Answer:


7 of 17 5/12/2011 8:08 PM

Part B

A total of 4200 of power is to be supplied through the wires of a house to the household electrical

appliances. If the potential difference across the group of appliances is 120 , determine the gauge of the

thinnest permissible wire that can be used.

ANSWER: wire gauge = 8

Correct

Part C

Suppose the wire used in this house is of the gauge found in part (b) and has total length 44.0 . At whatrate is energy dissipated in the wires?


Part D

The house is built in a community where the consumer cost of electric energy is $0.11 per kilowatt-hour. Ifthe house were built with wire of the next larger diameter than that found in part (b), what would be thesavings in electricity costs in one year? Assume that the appliances are kept on for an average of 12 hoursa day.


ANSWER: saving in electricity costs = 20

Correct per year

Exercise 26.1A uniform wire of resistance is cut into three equal lengths. One of these is formed into a circle and

connected between the other two (the figure ).


8 of 17 5/12/2011 8:08 PM

Part A

What is the resistance between the opposite ends and ?

ANSWER: =

Correct

Exercise 26.24

Part A

In the circuit shown in the figure , find the magnitudeof current in the upper branch.

ANSWER: = 0.800All attempts used; correct answer displayed

Part B

Find the magnitude of current in the middle branch.


Part C

Find the magnitude of current in the lower branch.



9 of 17 5/12/2011 8:08 PM

Part D

What is the potential difference of point relative to point ?

ANSWER: = -3.20Correct

Problem 26.60For the circuit shown in the figure a 20.0- resistor is

embedded in a large block of ice at 0.00 , and the

battery has negligible internal resistance.

Part A

At what rate (in ) is this circuit melting the ice? (The latent heat of fusion for ice is .)

ANSWER: = 6.19×10−3

Correct

Problem 26.71A resistor consumes electrical power when connected to an emf . When resistor is connected to

the same emf, it consumes electrical power .

Part A

In terms of and , what is the total electrical power consumed when they are both connected to this

emf source in parallel?

ANSWER: =

Correct


10 of 17 5/12/2011 8:08 PM

Part B

In terms of and , what is the total electrical power consumed when they are both connected to this

emf source in series?

ANSWER: =

Correct

Test Your Understanding 26.1: Resistors in Series and ParallelA simple circuit consists of a resistor or set of resistors connected to a battery. The battery has emf ,

internal resistance , and terminal voltage , and each resistor has resistance .

Part A

Rank the following arrangements in order of their equivalent resistance, from highest to lowest.Each individual resistor has the same resistance .

ANSWER:

View Correct

The equivalent resistance of the first arrangement (which includes a single resistor ) is .

In the second arrangement, the two resistors are in parallel. The equivalent resistance is given by

so

In the third arrangement, the three resistors are in parallel. The equivalent resistance is given by

so

In the fourth arrangement, a single resistor is in series with a parallel combination of two resistors

(which by itself has equivalent resistance , as in the second arrangement). The equivalent

resistance is given by


11 of 17 5/12/2011 8:08 PM

In the fifth arrangement, two resistors are in series (with equivalent resistance ), and this

combination is in parallel with a single resistor . The equivalent resistance is given by

so

Test Your Understanding 26.3: Electrical Measuring InstrumentsYou wish to use a d'Arsonval galvanometer to measure the voltage across a 5- resistor.

Part A

How should the meter be connected?

ANSWER: in parallel with a second resistor with resistance much greater than 5 ; the

combination should then be connected in parallel with the 5- resistor

in series with a second resistor with resistance much greater than 5 ; the

combination should then be connected in series with the 5- resistor

in parallel with a second resistor with resistance much less than 5 ; the


in parallel with a second resistor with resistance much greater than 5 ; thecombination should then be connected in series with the 5- resistor

in parallel with a second resistor with resistance much less than 5 ; thecombination should then be connected in parallel with the 5- resistor

in series with a second resistor with resistance much less than 5 ; the


in series with a second resistor with resistance much less than 5 ; the


in series with a second resistor with resistance much greater than 5 ; the


Correct

A voltmeter is always connected in parallel with the circuit element that is being measured. An idealvoltmeter would have infinite resistance so as not to draw off any of the current passing through thecircuit element being measured. This is an idealization, but the best results are obtained by making theresistance of the voltmeter as large as possible. This is done by placing a high-resistance resistor in


12 of 17 5/12/2011 8:08 PM

series with the meter, then connecting the combination in parallel with the circuit element under study.

Exercise 26.7

Part A

For the circuit shown in the figure find the reading ofthe idealized ammeter if the battery has an internalresistance of 3.56 .


Problem 26.62

Part A

What must the emf in the figure be in order for the

current through the resistor to be 1.76 ?

Each emf source has negligible internal resistance.



13 of 17 5/12/2011 8:08 PM

Problem 26.65

Part A

Find the potential of point with respect to point in the figure .

Express your answer using two significantfigures.


Part B

If points and are connected by a wire with negligible resistance, find the current in the 12.0

battery.



Exercise 31.1The plate on the back of a certain computer scanner says that the unit draws 0.34 of current from a 120

, 60 line.

Part A

Find the root-mean-square current.



14 of 17 5/12/2011 8:08 PM

Part B

Find the current amplitude.


Part C

Find the average current.

ANSWER: = 0Correct

Part D

Find the average square of the current.


Exercise 31.25The power of a certain CD player operating at 120 rms is 20.0 . Assume that the CD player behaves

like a pure resistance.

Part A

Find the maximum instantaneous power.

ANSWER: = 40.0

Correct

Part B

Find the rms current.


Part C

Find the resistance of this player.


15 of 17 5/12/2011 8:08 PM


Problem 31.43A sinusoidal current is given by . The full-wave rectified current is shown in the figure 31.3b in the

textbook.

Part A

Let and be the two smallest positive times at which the rectified current is zero. Express and interms of .

Express your answers in terms of the variable and appropriate constants. Enter your answersseparated by a comma.

ANSWER: =

Correct

Part B

Find the area under the rectified versus curve between and by computing the integral .

Since , this area equals the charge that flows during the to time interval.

Express your answer in terms of the variables and .

ANSWER: =

Correct

Part C

Set the result in part (b) equal to and calculate in terms of the current amplitude .

Express your answer in terms of the variable and appropriate constants.

ANSWER: =

Correct

Score Summary:


16 of 17 5/12/2011 8:08 PM

Your score on this assignment is 79.2%.You received 79.15 out of a possible total of 100 points.


17 of 17 5/12/2011 8:08 PM

221

Documents

Transcript of 221