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MasteringPhysics: Assignment Print View

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http://session.masteringphysics.com/myct/assignmentPrintView?assignme...

Test 3 Due: 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 Speed A conducting rod with length

, mass

, and resistance

connected with eachother. A uniform magnetic field from rest and is acted on by a constant force

moves without friction on metal rails. The rails are

is directed into the plane of the figure. The rod starts

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 of the given quantities. ANSWER: = Correct

Problem 29.51 As a new electrical engineer for the local power company, you are assigned the project of deg a generator 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 of 10.4

over a square area with a length

on a side when the magnets are separated by a distance of 11.3

. The basic design should

consist of a square coil turning in the uniform magnetic field. To have an acceptable coil resistance, the coil can have at most 400 loops.

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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 25.58 A plastic tube 25.0 0.100

long and 4.00

in diameter is dipped into a silver solution, depositing a layer of silver

thick uniformly over the outer surface of the tube.

Part A If this coated tube is then connected across a 12.0-

ANSWER:

battery, what will be the current?

= 411 Correct

Test Your Understanding 25.1: Electric Current and Current Density Two 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 if the diameter of wire #2 is if the diameter of wire #2 is if the diameter of wire #2 is if the diameter of wire #2 is if the diameter of wire #2 is

the diameter of wire #1 the diameter of wire #1 the diameter of wire #1 times the diameter of wire #1 times the diameter of wire #1 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

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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 #2, it must be that

are the same for both wires. Since

is twice as great in wire #1 as in wire

is twice as great in wire #2 as in wire #1. The cross-sectional area

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

is

times the diameter

of wire #1.

Test Your Understanding 25.4: Electromotive Force and Circuits A simple circuit consists of a resistor connected to a battery. The battery has emf and terminal voltage

, and the resistor has resistance

, internal 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)

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(6) For the five individual circuits, we find

Exercise 25.11 A 1.60

cylindrical rod of diameter 0.500

potential difference of 12.0

is connected to a power supply that maintains a constant

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:

.

−6 = 7.87×10 Correct

Part B Find the temperature coefficient of resistivity at 20

ANSWER:

for the material of the rod.

−3 = 1.12×10 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 of aluminum wire with diameter 3.40 ?

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ANSWER:


= 2.69 All attempts used; correct answer displayed

Exercise 25.19 You 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 25.51 A 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 not available to the bulb? ANSWER:

= 12.5 Correct

Exercise 25.54 A typical small flashlight contains two batteries, each having an emf of 1.50 having a resistance of 19

connected in series with a bulb

.

Part A If the internal resistance of the batteries is negligible, what power is delivered to the bulb? Express your answer using two significant figures. ANSWER:

= 0.47 Correct

Part B

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If the batteries last for a time of 4.5


, what is the total energy delivered to the bulb?

Express your answer using two significant figures. ANSWER:

= 7700 Correct

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 half its initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current through the filament changes, because this changes the temperature of the filament and hence the resistivity of the filament wire.) Express your answer using two significant figures. ANSWER:

= 7.9 Correct

Problem 25.59 On your first day at work as an electrical technician, you are asked to determine the resistance per meter of a long piece of wire. The company you work for is poorly equipped. You find a battery, a voltmeter, and an ammeter, but no meter for directly measuring resistance (an ohmmeter). You put the leads from the voltmeter across 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 ammeter reads 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 the voltmeter has very large resistance. Part A What is the resistance of 1 meter of wire? ANSWER:

−2 = 5.42×10 Correct

Problem 25.70 A person with body resistance between his hands of 10

accidentally grasps the terminals of a 16-

power supply. Part A

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If the internal resistance of the power supply is 1800

, what is the current through the person's body?

Express your answer using two significant figures. ANSWER:

= 1.4 Correct

Part B What is the power dissipated in his body? Express your answer using two significant figures. ANSWER:

4 = 1.8×10 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 internal resistance be for the maximum current in the above situation to be or less? Express your answer using two significant figures. ANSWER:

7 = 1.6×10 Correct

Problem 25.77 According to the U.S. National Electrical Code, copper wire used for interior wiring of houses, hotels, office buildings, and industrial plants is permitted to carry no more than a specified maximum amount of current. The table 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 the diameter of the wire, the smaller the wire gauge. ) Wire gauge Diameter( 14 12 10 8 6 5 4

0.163 0.205 0.259 0.326 0.412 0.462 0.519

18 25 30 40 60 65 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:

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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 what

rate is energy dissipated in the wires? ANSWER:

= 111 Correct

Part D The house is built in a community where the consumer cost of electric energy is $0.11 per kilowatt-hour. If the house were built with wire of the next larger diameter than that found in part (b), what would be the savings in electricity costs in one year? Assume that the appliances are kept on for an average of 12 hours a day. Express your answer using two significant figures. ANSWER:

saving in electricity costs =

20 Correct

per year

Exercise 26.1 A 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 ).

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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 magnitude of current in the upper branch.

ANSWER:

= 0.800 All attempts used; correct answer displayed

Part B Find the magnitude of current in the middle branch. ANSWER:

= 0.200 Correct

Part C Find the magnitude of current in the lower branch. ANSWER:

= 0.600 Correct

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Part D What is the potential difference

ANSWER:

of point

relative to point ?

= -3.20 Correct

Problem 26.60 For 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

ANSWER:

) is this circuit melting the ice? (The latent heat of fusion for ice is

.)

−3 = 6.19×10 Correct

Problem 26.71 A resistor

consumes electrical power

the same emf, it consumes electrical power

when connected to an emf

. When resistor

is connected to

.

Part A In of

and

, what is the total electrical power consumed when they are both connected to this

emf source in parallel? ANSWER:

= Correct

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Part B In 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 Parallel A 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

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In the fifth arrangement, two resistors are in series (with equivalent resistance combination is in parallel with a single resistor

), and this

. The equivalent resistance is given by

so

Test Your Understanding 26.3: Electrical Measuring Instruments You 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 combination should then be connected in parallel with the 5-

resistor

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

; the

resistor

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

; the

; the

resistor

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

resistor

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

; the

resistor

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

; the

resistor

in series with a second resistor with resistance much less than 5 combination should then be connected in series with the 5-

; the

resistor

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

; the

; the

resistor

Correct

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

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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 of the idealized ammeter if the battery has an internal resistance of 3.56 .

ANSWER:

= 0.762 Correct

Problem 26.62 Part A What must the emf current through the

in the figure be in order for the resistor to be 1.76

?

Each emf source has negligible internal resistance.

ANSWER:

= 8.05 Correct

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Problem 26.65 Part A Find the potential of point

with respect to point

in the figure .

Express your answer using two significant figures.

ANSWER:

= 0.22 Correct

Part B If points

and

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

battery. Express your answer using two significant figures. ANSWER:

= 0.46 Correct

Exercise 31.1 The plate on the back of a certain computer scanner says that the unit draws 0.34 , 60

of current from a 120

line.

Part A Find the root-mean-square current. ANSWER:

= 0.340 Correct

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Part B Find the current amplitude. ANSWER:

= 0.481 Correct

Part C Find the average current. ANSWER:

= 0 Correct

Part D Find the average square of the current. ANSWER:

= 0.116 Correct

Exercise 31.25 The 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. ANSWER:

= 0.167 Correct

Part C Find the resistance of this player.

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ANSWER:


= 720 Correct

Problem 31.43 A sinusoidal current is given by

. The full-wave rectified current is shown in the figure 31.3b in the

textbook. Part A Let

and

of

be the two smallest positive times at which the rectified current is zero. Express

and

in

.

Express your answers in of the variable

and appropriate constants. Enter your answers

separated by a comma. ANSWER: = Correct

Part B Find the area under the rectified Since

versus

curve between

and

, this area equals the charge that flows during the

Express your answer in of the variables

and

by computing the integral to

.

time interval.

.

ANSWER: = Correct

Part C Set the result in part (b) equal to

and calculate

Express your answer in of the variable

in of the current amplitude .

and appropriate constants.

ANSWER: = Correct

Score Summary:

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

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