Preface

xvii

Preface

This book is an outgrowth of forty years of teaching introductory physics courses.

The original manuscript has been used in the classroom for several of them.

Because the book is written for students, it contains a great many of the

intermediate steps that are often left out of the derivations and illustrative problem

solutions in many traditional textbooks. Students new to physics often find it

difficult to follow derivations when the intermediate steps are left out. In addition,

the units of measurement are carried along, step by step, in the equations to make

it easier for students to understand.

This text gives a good, fairly rigorous, traditional physics coverage for

students of science and engineering. There is more material here than most

instructors can cover in a two or three semester course. Therefore instructors are

expected to choose those topics they deem most important for their particular

course. Students can read on their own the detailed descriptions found in those

chapters, or parts of chapters, omitted from the course. Unfortunately, many

interesting and important topics in modern physics are never covered in physics

courses because of lack of time. These chapters, especially, are written in even more

detail to enable students to read them on their own.

The organization of the text follows the traditional sequence of mechanics,

wave motion, heat, electricity and magnetism, optics, and modern physics. The

emphasis throughout the book is on clarity. The book starts out at a very simple

level, and advances as students’ understanding and ability with the calculus grows.

There are a large number of diagrams and illustrative problems in the text to

help students visualize physical ideas. Important equations are highlighted to help

students find and recognize them. A summary of these important equations is given

at the end of each chapter.

Many students, taking physics for the first time, sometimes find the

mathematics frightening. In order to help these students, I have computerized

every illustrative example in the textbook using computer spreadsheets. These

computerized Interactive Examples will allow the student to solve the example

problem in the textbook, with all the in-between steps, many times over but with

different numbers placed in the problem. The Interactive Examples are available on

a computer disk for both the instructor and the student. More details on these

Interactive Examples can be found in the section “Computer Aided Instruction” at

the end of the Preface. These Interactive Examples make the book the first truly

interactive physics textbook for students of science and engineering.

Students sometimes have difficulty remembering the meanings of all the

vocabulary associated with new physical ideas. Therefore, a section called The

Language of Physics, found at the end of each chapter, contains the most important

ideas and definitions discussed in that chapter.

To comprehend the physical ideas expressed in the theory class, students

need to be able to solve physics problems for themselves. Problem sets at the end of

each chapter are grouped according to the section where the topic is covered.

Preface

xviii

Problems that are a mix of different sections are found in the Additional Problems

section. If you have difficulty with a problem, refer to that section of the chapter for

help. The problems begin with simple, plug-in problems to develop students’

confidence and to give them a feel for the numerical magnitudes of some physical

quantities. The problems then become progressively more difficult and end with

some that are very challenging. The more difficult problems are indicated by a star

(*). The starred problems are either conceptually more difficult or very long. Many

problems at the end of the chapter are very similar to the illustrative problems

worked out in the text. When solving these problems, students can use the

illustrative problems as a guide, and use the Interactive Examples as a check on

their work. To facilitate setting up a problem, the Hints for Problem Solving section,

which is found before the problem set in chapter 2, should be studied carefully.

A section called Interactive Tutorials, which also uses computer spreadsheets

to solve physics problems, can be found at the end of the problems section in each

chapter. These Interactive Tutorials are a series of physics problems, very much

like the interactive examples, but are more detailed and more general. They are

also available on a computer disk for both the instructor and the student. More

details on these Interactive Tutorials can be found in the section “Computer Aided

Instruction” at the end of the Preface.

A series of questions relating to the topics discussed in the chapter is also

included at the end of each chapter. Students should try to answer these questions

to see if they fully understand the ramifications of the theory discussed in the

chapter. Just as with the problem sets, some of these questions are either

conceptually more difficult or will entail some outside reading. These more difficult

questions are also indicated by a star (*).

A word about units. Some forty years ago when I started teaching physics I

said to my class, “We use the British Engineering System of Units in our daily lives

in the United States, but we are in the process of changing over to the metric

system of units (Now called the International System of Units or SI units). In a few

years the British Engineering System of Units will be obsolete and the entire world

will use the metric system.” Over forty years later I find myself giving that same

lecture at the beginning of the course. Something is very wrong! Except for the

United States and one or two small islands in the south pacific, the entire world

uses the International System of Units. Even the British do not use the British

Engineering System of Units. (I have even asked many of my colleagues

individually how far away from the campus do they live. Each gave an answer in

the British Engineering System of Units. If all the physics faculty still think in

terms of the British Engineering System, what can we expect of our students and

the rest of our society. Try asking your colleagues how far away from the campus do

they live and see what they reply.) It is time for the United States to get in step

with the rest of the world. To do that we must teach a new generation of physics

students SI units almost exclusively so that they will think and work in SI units.

Therefore in this book only SI units will be used in the description of physics.

However, to help the student in this transition, the first chapter will show how to

Preface

xix

convert from the British Engineering System to SI units and vice versa if it is ever

necessary. If a student is told that a car is traveling at 55 mph, the student will

convert that to 88.6 km/hr and then solve the entire problem in SI units. An

interactive computer tutorial will be found at the end of chapter 1 that will help the

student to make any of these conversions. After that, the rest of the book will be in

SI units almost exclusively. Occasionally, a few problems throughout the book will

still have some numbers in the British Engineering System of Units. When this

occurs the student should convert these numbers into SI units, and proceed in

solving the problem in the International System of Units.

Scattered throughout the text, at the ends of chapters, are sections entitled

“Have you ever wondered … ?” These are a series of essays on the application of

physics to areas such as meteorology, astronomy, aviation, space travel, the health

sciences, the environment, philosophy, traffic congestion, sports, and the like. Many

students are unaware that physics has such far-reaching applications. These

sections are intended to engage students’ varied interests but can be omitted, if

desired, without loss of continuity in the physics course. The “Have you ever

wondered … ?” section on the application of physics to traffic congestion is the only

major item still expressed in British Engineering Systems of Units in this book.

The relation between theory and experiment is carried throughout the book,

emphasizing that our models of nature are good only if they can be verified by

experiment. Concepts presented in the lecture and text can be well demonstrated in

a laboratory setting. To this end, Experiments In Physics, second edition by Peter J.

Nolan and Raymond E. Bigliani is available from Whittier Publishing Co.

Experiments in Physics contains some 55 experiments covering all the traditional

topics in a physics laboratory. The second edition of Experiments in Physics also

contains a complete computer analysis of the data for every experiment.

A Bibliography, given at the end of the book, lists some of the large number

of books that are accessible to students taking physics. These books cover such

topics in modern physics as relativity, quantum mechanics, and elementary

particles. Although many of these books are of a popular nature, they do require

some physics background. After finishing this book, students should be able to read

any of them for pleasure without difficulty.

Finally, we should note that we are living in a rapidly changing world. Many

of the changes in our world are sparked by advances in physics, engineering, and

the high-technology industries. Since engineering and technology are the

application of physics to the solution of practical problems, it behooves every

individual to get as much background in physics as possible. You can depend on the

fact that there will be change in our society. You can be either the architect of that

change or its victim, but there will be change.

Preface

xx

A Special Note to the Student

“One thing I have learned in a long life: that all our science

measured against reality, is primitive and childlike--and yet it is

the most precious thing we have.”

Albert Einstein

as quoted by Banesh Hoffmann in

Albert Einstein, Creator and Rebel

The language of physics is mathematics, so it is necessary to use mathematics in

our study of nature. However, just as sometimes “you cannot see the forest for the

trees,” you must be careful or “you will not see the physics for the mathematics.”

Remember, mathematics is only a tool used to help describe the physical world. You

must be careful to avoid getting lost in the mathematics and thereby losing sight of

the physics. When solving problems, a sketch or diagram that represents the

physics of the problem should be drawn first, then the mathematics should be

added.

Physics is such a logical subject that when a student sees an illustrative

problem worked out, either in the textbook or on the blackboard, it usually seems

very simple. Unfortunately, for most students, it is simple only until they sit down

and try to do a problem on their own. Then they often find themselves confused and

frustrated because they do not know how to get started.

If this happens to you, do not feel discouraged. It is a normal phenomenon

that happens to many students. The usual approach to overcoming this difficulty is

going back to the illustrative problem in the text. When you do so, however, do not

look at the solution of the problem first. Read the problem carefully, and then try to

solve the problem on your own. At any point in the solution, when you cannot

proceed to the next step on your own, peek at that step and only that step in the

illustrative problem. The illustrative problem shows you what to do at that step.

Then continue to solve the problem on your own. Every time you get stuck, look

again at the appropriate solution step in the illustrative problem until you can

finish the entire problem. The reason you had difficulty at a particular place in the

problem is usually that you did not understand the physics at that point as well as

you thought you did. It will help to reread the appropriate theory section. Getting

stuck on a problem is not a bad thing, because each time you do, you have the

opportunity to learn something. Getting stuck is the first step on the road to

knowledge. I hope you will feel comforted to know that most of the students who

have gone before you also had these difficulties. You are not alone. Just keep trying.

Eventually, you will find that solving physics problems is not as difficult as you first

thought; in fact, with time, you will find that they can even be fun to solve. The

more problems that you solve, the easier they become, and the greater will be your

enjoyment of the course.

Preface

xxi

Computer Assisted Instruction

Interactive Examples

Many students, taking physics for the first time, sometimes find the

mathematics frightening. In order to help these students, I have computerized

every illustrative example in the textbook. These computerized Interactive

Examples will allow the student to solve the example problem in the textbook, with

all the in-between steps, many times over but with different numbers placed in the

problem.

Figure 1 shows an example from Chapter 2 of the textbook for solving a

problem in Kinematics. It is a problem in kinematics in which a car, initially

traveling at 30.0 km/hr, accelerates at the constant rate of 1.50 m/s2. The student is

then asked how far will the car travel in 15.0 s? The example in the textbook shows

all the steps and reasoning done in the solution of the problem.

Example 2.6

Using the kinematic equation for the displacement as a function of time. A car,

initially traveling at 30.0 km/hr, accelerates at the constant rate of 1.50 m/s2. How

far will the car travel in 15.0 s?

To express the result in the proper units, km/hr is converted to m/s as

0

km 1 hr 1000 m30.0 8.33 m/s

hr 3600 s 1 kmv

The displacement of the car, found from equation 2.14, is

x = v0t + 1 at2

2

2

2

m 1 m8.33 15.0 s 1.50 15.0 s

s 2 s

= 125 m + 169 m

= 294 m

The first term in the answer, 125 m, represents the distance that the car

would travel if there were no acceleration and the car continued to move at the

velocity 8.33 m/s for 15.0 s. But there is an acceleration, and the second term shows

how much farther the car moves because of that acceleration, namely 169 m. The

Solution

Preface

xxii

total displacement of 294 m is the total distance that the car travels because of the

two effects.

To go to this interactive example click on this sentence.

Figure 1 Example 2.6 in the textbook.

The last sentence in blue type in the example (To go to this

interactive example click on this sentence.) allows the student to access the

interactive example for this same problem. Clicking on the blue sentence,

the spreadsheet shown in figure 2 opens. Notice that the problem is stated in

Figure 2 Interactive Example 2.6 in Microsoft Excel Spreadsheet.

Example 3.6 Using the kinematic equation for the displacement as a function of time. A car,

initially traveling at 30.0 km/hr, accelerates at the constant rate of 1.50 m/s2. How far

will the car travel in 15.0 s?

Initial Conditions

Initial velocity vo = 30 km/hr

acceleration a = 1.5 m/s2

time t = 15 s

Solution.

To express the result in the proper units, km/hr is converted to m/s as

vo = ( 30 km/hr) x [ 1 hr / ( 3600 s) ] x ( 1000 m/km)

vo = ( 8.33333 m/s

The displacement of the car, found from equation 3.14, is

x = vo t + 1/2 a t2

x = [( 8.3333 m/s) x ( 15 s)]

+ 1/2 [( 1.5 m/s2) x ( 15 s)

2]

x = [( 125 m)] + [( 168.75 m)]

x = 293.75 m

The first term in the answer, 125 m, represents the distance that the car would

travel if there were no acceleration and the car continued to move at the velocity

8.3333 m/s for 15 s. But there is an acceleration, and the second term

shows how much farther the car moves because of that acceleration, namely

168.75 m. The total displacement of 293.75 m is the total distance that the car

travels because of the two effects.

Preface

xxiii

the identical manner as in the textbook. Directly below the stated problem is a

group of yellow-colored cells labeled Initial Conditions. Into these yellow cells are

placed the numerical values associated with the particular problem. For this

problem the initial conditions consist of the initial velocity v0 of the car, the

acceleration a of the car, and the time t that the car is moving, as shown in figure 2.

The problem is now solved in the identical way it is solved in the textbook. Words

are used to describe the physical principles and then the equations are written

down. Then the in-between steps of the calculation are shown in light green-colored

cells, and the final result of the calculation is shown in a light blue-colored cell. The

entire problem is solved in this manner, as shown in figure 2. If the student wishes

to change the problem by using a different initial velocity or a different time or

acceleration, he or she then changes these values in the yellow-colored cells of the

initial conditions. When the initial conditions are changed the computer

spreadsheet recalculates all the new in-between steps in the problem and all the

new final answers to the problem. In this way the problem is completely interactive.

It changes for every new set of initial conditions. The Interactive Examples make the

book a living book. The examples can be changed many times over to solve for all

kinds of special cases. When the student is finished with the interactive

example, and is accessing it from a CD, he or she just clicks on the X in the

extreme upper right-hand corner of the spreadsheet screen, returning him

or her to the original example in the textbook chapter. If the student is

accessing the interactive example from a web page, then he or she presses

the go Back button on the top of the browser page. When Excel closes, you

will be returned to the first page of the present chapter. You can then go to

wherever page you want in that chapter by sliding the Scroll Bar box on the

right-hand side of the screen.

These Interactive Examples are a very helpful tool to aid in the learning of

physics if they are used properly. The student should try to solve the particular

problem in the traditional way using paper and an electronic calculator. Then the

student should open the spreadsheet, insert the appropriate data into the Initial

Conditions cells and see how the computer solves the problem. Go through each step

on the computer and compare it to the steps you made on paper. Does your answer

agree? If not, check through all the in-between steps on the computer and your

paper and find where your made a mistake. Do not feel bad if you make a mistake.

There is nothing wrong in making a mistake, what is wrong is not learning from

your mistake. Now that you understand your mistake, repeat the problem using

different Initial Conditions on the computer and your paper. Again check your

answers and all the in-between steps. Once you are sure that you know how to solve

the problem, try some special cases. What would happen if you changed an angle?, a

weight?, a force? etc. In this way you can get a great deal of insight into the physics

of the problem and also learn a great deal of physics in the process.

You must be very careful not to just plug numbers into the Initial Conditions

and look at the answers without understanding the in-between steps and the actual

Preface

xxiv

physics of the problem. You will only be deceiving yourself. Be careful, these

spreadsheets can be extremely helpful if they are used properly.

We should point out two differences in a text example and in a spreadsheet

example. Powers of ten that are used in scientific notation in the text are written

with the capital letter E in the spreadsheet. Hence, the number 5280, written in

scientific notation as 5.280 103, will be written on the spreadsheet as 5.280E+3.

Also, the square root symbol, , in the textbook is written as sqrt[ ] in a

spreadsheet. Finally, we should note that the spreadsheets are “protected” by

allowing you to enter data only in the designated light yellow-colored cells of the

Initial Conditions area. Therefore, the student cannot damage the spreadsheets in

any way, and they can be used over and over again.

To access these Interactive Examples the student must have

Microsoft’s Excel computer spreadsheet installed on his computer.

Computer Assisted Instruction

Interactive Tutorials

Besides the Interactive Examples in this text, I have also introduced a

section called Interactive Tutorials at the end of the problem section in each

chapter. These Interactive Tutorials are a series of physics problems, very much

like the interactive examples, but are more detailed and more general. The

Interactive Tutorials are available on the Internet, but the student must have

Microsoft’s Excel computer spreadsheet on his or her computer.

To access the Interactive Tutorial on the Internet, the student will

click on the sentence in blue type at the end of the Interactive Tutorials

section (To go to this interactive tutorial click on this sentence.) Clicking

on the blue sentence, opens the appropriate spreadsheet.

Figure 3 show a typical Interactive Tutorial for a problem in chapter 4 on

Kinematics In Two Dimensions. When the student opens this particular

spreadsheet, he or she sees the problem stated in the usual manor. That is, this

problem is an example of a projectile fired at a initial velocity vo = 53.0 m/s at an

angle = 50.00, and it is desired to find the maximum height of the projectile, the

total time the projectile is in the air, and the range of the projectile. Directly below

the stated problem is a group of yellow-colored cells labeled Initial Conditions.

Into these yellow cells are placed the numerical values associated with the

particular problem. For this problem the initial conditions consist of the initial

velocity vo, the initial angle , and the acceleration due to gravity g as shown in

figure 3. The problem is now solved in the traditional way of a worked out example

in the book. Words are used to describe the physical principles and then the

equations are written down. Then the in-between steps of the calculation are shown

in light green-colored cells, and the final result of the calculation is shown in a light

blue-green-colored cell. The entire problem is solved in this manor as shown in

figure 3. If the student wishes to change the problem by using a different initial

Preface

xxv

Chapter 3 Kinematics

Computer Assisted Instruction

Interactive Tutorial

72. A golf ball is hit with an initial velocity vo = 53.0 m/s at an angle = 50.00 above the

horizontal. (a) How high will the ball go? (b) What is the total time the ball is in the air? (c) How far will the ball travel horizontally before it hits the ground?

Initial Conditions The magnitude of the initial velocity vo = 53 m/s

The angle = 50 degrees

The acceleration of gravity g = 9.8 m/s2

The x-component of the initial velocity is found as vox = vo cos

vox = ( 53 m/s) x cos( 50 )

vox = 34.07 m/s

The y-component of the initial velocity is found as voy = vo sin

voy = ( 53 m/s) x sin( 50 )

voy = 40.6 m/s

(a) The maximum height ymax of the golf ball above the launch point is found from the kinematic equation vy

2 = voy

2 - 2 g y

When y = ymax, vy = 0. Therefore 0 = voy

2 - 2 g ymax

Solving for the maximum height ymax above the launch point, we get ymax = (voy

2) / 2 g

ymax = ( 40.6 m/s)2 / 2 ( 9.8 m/s

2)

ymax = 84.1 m

(b) The total time tt the ball is in the air is found from the kinematic equation y = voy t - (1/2) g t

2

When t is equal to the total time tt, the projectile is on the ground and y = 0, therefore 0 = voy tt - (1/2) g tt

2

or dividing each term by tt we get 0 = voy - (1/2) g tt

upon solving for the total time tt we get tt = 2 voy / g

tt = 2 x ( 40.6 m/s) / ( 9.8 m/s2)

tt = 8.29 s

(c) The maximum distance the ball travels in the x-direction before it hits the ground, is found from the kinematic equation for the displacement of the ball in

the x-direction x = vox t

The maximum distance xmax occurs for t = tt. Therefore xmax = vox tt

xmax = ( 34.07 m/s) x ( 8.29 s)

xmax = 282.28 m

Figure 3. A typical Interactive Tutorial.

velocity or a different launch angle, he or she then changes these values in the

yellowed-colored cells of the initial conditions. When the initial conditions are

Preface

xxvi

changed the computer spreadsheet recalculates all the new in-between steps in the

problem and all the new final answers to the problem. In this way the problem is

completely interactive. It changes for every new set of initial conditions. The

tutorials can be changed many times over to solve for all kinds of special cases.

Another example of an Interactive Tutorial is shown in figure 4. It is an

interactive tutorial for a problem on an RLC series AC circuit from chapter 28. The

initial conditions in the yellow-colored cells set the values of the resistance R, the

inductance L, the capacitance C, the frequency f, and the applied voltage V. The

spreadsheet then completely solves the problem for these initial values. The student

can follow through all the in-between steps of the problem in the light green-colored

cells of the spreadsheet, and all the answers in the light blue-green-colored cells.

The spreadsheet then draws a graph showing the phase relations for the voltage

across the resistor, VR, the voltage across the inductance VL, the voltage across the

capacitance, VC, and the resultant voltage V in the circuit depending upon the

initial values in the yellow cells. As special cases the student can then let L = 0 in

the yellow cell area, and observe the characteristics of an RC series circuit; then

replace a value of L in the initial conditions and then let C = 0 and observe the

characteristics of an RL series circuit. Finally inserting values for L and C and

letting R = 0 the student can observe the characteristics of an LC series circuit. In

all the cases the spreadsheet calculates all the quantities with all the in-between

steps, and shows the phase relations of the voltages.

Chapter 24 Alternating Current Circuits

Computer Assisted Instruction

Interactive Tutorial

56. RLC series circuit. An RLC series circuit has a resistance R = 800 , Inductance L = 2.00 H, capacitance C = 5.55 x 10

-6 F, and they are connected to an applied voltage V= 110 V, operating at a

frequency f = 60 Hz. Find (a) the inductive reactance XL, (b) the capacitive reactance, XC, (c) the impedance Z of the circuit, (d) the current i in the circuit, (e) the voltage drop VR across the resistor, (f) the voltage drop VL across the inductor, (g) the voltage drop VC across the capacitor, (h) the total voltage

drop across RLC, (i) the phase angle , and (j) the resonant frequency fo. (k) Plot the curves of the voltage across R, L, and C individually and the voltage across the combination. Show the phase relations for all these voltages.

Initial Conditions

R = 800 f = 60 Hz

L = 2.00E+00 H V = 110 V

C = 5.55E-06 F

(a) The inductive reactance XL is found from equation 24.15 as XL = 2 f L

XL = ( 2 ) x ( 3.14 ) x ( 60 Hz) x ( 2 XL = 7.54E+02

(b) The capacitive reactance XC is found from equation 24.17 as XC = 1 / [2 f C]

XC = ( 1 ) / ( 6.28 ) x ( 60 Hz) x ( 5.55E-06 XC = 4.78E+02

(c) The impedance Z of the circuit is found from equation 24.18 as Z = Sqrt[R

2 + (XL - XC)

2]

Z = Sqrt[( 800 )2 + (( 753.98 ) - ( 477.94 ))

2

Z = 8.46E+02

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xxvii

(d) The effective current in the circuit is found from Ohm’s law, equation 24.19, as i = V / Z

i = ( 110 V) / ( 8.46E+02 )

i = 1.30E-01 A

(e) The voltage drop VR across the resistor is found from equation 24.13, as VR = i R

VR = ( 1.30E-01 A) x ( 8.00E+02 )

VR = 1.04E+02 V

(f) The voltage drop VL across the inductor is found from equation 24.14, as VL = i XL

VL = ( 1.30E-01 A) x ( 7.54E+02 )

VL = 9.80E+01 V

(g) The voltage drop VC across the capacitor is found from equation 24.16, as VC = i XC

VC = ( 1.30E-01 A) x ( 4.78E+02 )

VC = 6.21E+01 V

(h) The total voltage across R, L, C in series is found from equation 24.11 as V = Sqrt[VR

2 + (VL - VC)

2]

V = Sqrt[( 103.98 )2 + (( 98 ) - ( 62.12 ))

2

V = 1.10E+02 V

which is equal to the applied voltage as expected.

(i) The phase angle is found from equation 24.12 as

= tan-1

[(VL - VC) / VR ]

= tan-1

[(( 98 V) - ( 62.12 V)) / ( 103.98 V) ]

= 19.04 degrees

(j) The resonant frequency fo is found from equation 24.21 as fo = 1 / [2 sqrt(L C)]

fo = ( 1 ) / ( 6.28 ) x sqrt( 2 H) x ( 5.55E-06 fo = 4.78E+01 Hz

The angular frequency of the alternating current is related to the frequency of the current by = 2 f

= ( 2 ) x ( 3.14 ) x ( 160 Hz)

= 3.77E+02 rad/s

The maximum value of the current, imax, is found from rearranging equation 24.5 as imax = ieff / 0.707

imax = ( 0.13 A) / ( 0.71 )

imax = 0.18 A

The equation for the alternating current is given by i = imax sin[ t]

i = ( 0.18 A) x sin[( 3.77E+02 rad/s) t]

The data to plot the current as a function of time is calculated from this equation and the results are shown in the graph below. The data to plot the voltage drop across the resistor as a function of time is calculated from the equation VR = i R

VR = imax R sin[ t]

and the results are shown in the graph below. The data to plot the voltage drop across the inductor as a function of time is calculated from the equation VL = i XL

VL = imax XL sin[ t + / 2]

The term + / 2 in the sine term is to show that VL leads VR by 900. The results are shown in the graph

below. The data to plot the voltage drop across the capacitor as a function of time is calculated from the equation VC = i XC

VC = imax XC sin[ t - / 2]

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xxviii

The term - / 2 in the sine term is to show that VC lags VR by 900. The results are shown in the graph

below. V is the sum of the voltages across R, L, and C in series and is given by V = VR + VL + VC

and is shown in the graph below.

0 100 200 300 400

-200

-100

0

100

200

degrees

vo

lts

Angle

Pote

ntia

l

V

VR

VL

VC

Phase relations in an RLC series circuit

Since VR is in phase with the current i in the circuit, we can compare the phase relationship between the voltage V and the current i, by comparing the voltage V and the voltage VR. The phase angle can best be determined from this diagram by observing where the V curve intersects the horizontal axis, and where the VR curve intersects the horizontal axis. The difference between these two values represents the

phase angle which was already calculated in part (i).

Special Cases

1) An RC series circuit. Let L = 0. 2) An RL series circuit. Let C = 0. 3) An LC series circuit. Let R = 0.

Figure 4. An Interactive Tutorial for Chapter 28 Alternating Current Circuits

These Interactive Tutorials are a very helpful tool to aid in the learning of

physics if they are used properly. The student should try to solve the particular

problem in the traditional way using paper and an electronic calculator. Then the

student should open the spreadsheet, insert the appropriate data into the Initial

Conditions cells and see how the computer solves the problem. Go through each step

on the computer and compare it to the steps you made on paper. Does your answer

agree? If not, check through all the in-between steps on the computer and your

paper and find where you made a mistake. Repeat the problem using different

Initial Conditions on the computer and your paper. Again check your answers and

all the in-between steps. Once you are sure that you know how to solve the problem,

try some special cases. What would happen if you changed an angle?, a weight?, a

Preface

xxix

force? etc. In this way you can get a great deal of insight into the physics of the

problem and also learn a great deal of physics in the process.

You must be very careful not to just plug numbers into the Initial Conditions

and look at the answers without understanding the in-between steps and the actual

physics of the problem. You will only be deceiving yourself. Be careful, these

spreadsheets can be extremely helpful if they are used properly.

When the student is finished with the interactive tutorial, and is

accessing it from a CD, he or she just clicks on the X in the extreme upper

right-hand corner of the spreadsheet screen, returning him or her to the

original tutorials in the textbook chapter. If the student is accessing the

interactive tutorial from a web page, then he or she presses the go Back

button on the top of the browser page. When Excel closes, you will be

returned to the first page of the present chapter. You can then go to

wherever page you want in that chapter by sliding the Scroll Bar box on the

right-hand side of the screen.

Click on this sentence to go to the “Brief Table of Contents” which will

allow you to go to any chapter in this book.