LABORATORY MANUAL PHYSICS 1402 - Al Akhawayn …Physics_Lab/labman/Phy_1402_Lab_Manual.pdf · 11 EXPERIMENT 01 THE FORMATION OF STANDING WAVES --MELDE’S EXPERIMENT INTRODUCTION:

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School of School of School of School of Science &Science &Science &Science & Engineering Engineering Engineering Engineering

LABORATORY MANUAL

PHYSICS 1402

Cours : Phy 1402

Semester : Fall 2008

By :

Dr.Khalid Loudyi

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Table of Content

Physics II Laboratories

INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES.. 3

PHYSICS LABORATORY RULES.......................................................................................... 4

LABORATORY SUPPLIES & EQUIPMENT.......................................................................... 5

GRADING POLICY IN THE PHYSICS LABORATORY....................................................... 6

THE PRESENTATION OF EXPERIMENTAL DATA............................................................ 8

ACURACY OF MEASURMENTS......................................................................................... 10

The experiment:

THE FORMATION OF STANDING WAVES --MELDE’S EXPERIMENT........................ 11

MILLIKAN OIL DROP EXPERIMENT ................................................................................. 17

ELCTRIC FIELDS AND LINES OF FORCE ......................................................................... 29

RESISTANCE AND POWER IN ELECTRICAL CIRCUITS................................................ 39

THE TEMPERATURE COEFFICIENT OF RESISTANCE WHEATSTONE BRIDGE

METHOD................................................................................................................................. 51

MEASUREMENT OF CAPACITANCE BY THE BRIDGE METHOD ............................... 58

INDUCTION AND LR CIRCUITS ......................................................................................... 65

RCL CIRCUITS ....................................................................................................................... 76

OBSERVATION OF SPECTRA ............................................................................................. 84

PRECISE MEASUREMENT OF THE INDEX OF REFRACTION ...................................... 92

THE SIMPLE LENS .............................................................................................................. 100

THE WAVELENGTH OF LIGHT; THE DIFFRACTION GRATING ................................ 107

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INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS

LABORATORIES

In science, no idea is accepted, no theory is believed, until they have been tested, then

tested again. Only then can the truth of the theory emerge. The ultimate test of any physical

theory is by experiment. This reliance on experiment differentiates science form other important

human activities. Unfortunately the beginning student often misses the importance of

experiment to physics. Years or centuries after the crucial experiments have been done, the

student finds scientific truth by studying a textbook. To show the student the importance of

experiment in establishing "truth", we provide the Physics Laboratory as part of your General

Physics Course. The physical laws make predictions. We do experiments to see if these

predictions hold true, and, if they do, then, and only then, can we have confidence in the truth of

the laws.

The goal of any science is to arrive at a simple and universal explanation of natural

events. These explanations start out as theories, and they become physical laws if they are

shown to be true by comparing their predictions with the results of many experiments. Your

experience in the physics laboratory will, in a way, be similar to that of scientists in research

laboratories around the world. However, our laboratory differs form the research laboratories of

professional scientists in that we already know what theory will be applied to explain the

experimental results. This means that you will probably not discover any new physical laws this

semester in the physics lab. However, you will learn some of the methods of experimental

physics used by scientists at the forefront of physics research.

While taking a physics laboratory; you will learn how to make scientific measurements

and how to present and understand these measurements by means of graphs and tables. You will

also learn the inherent limitations of measurements by discussing error analysis. These

techniques can be applied to problems in a large number of fields, other than physics such as the

social, behavioral, and life sciences.

Finally, we want you to enjoy yourself in the physics laboratory. Those of you who plan

to make a career of science will find it immensely satisfying to verify the predictions of a

scientific theory. We also hope that those of you who do not go on to become practicing

scientists take with you the excitement of "doing" physics.

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PHYSICS LABORATORY RULES

The following suggestions will help you do your work in the physics laboratory:

1. Report to the laboratory promptly, ready to work. Expect to remain for the full lab period.

2. Your laboratory station should have everything you need to complete the lab assignment. If

you encounter a shortage (or damaged equipment), notify your instructor immediately. Never

borrow any apparatus from another station even though it may not be in use. At the end of

the lab period, check your station and leave it in good order. Again, call attention of the

instructor to any equipment problems you may have encountered. Space at the lab station is

limited. You should have only the laboratory manual and one or two sheets of clean scratch

paper at your workstation. Books, coats, hats, large purses, etc. should be stored elsewhere.

3. No food, drink, or tobacco in any form is permitted in the laboratory.

4. Each student working on his own conducts laboratory work.

5. The laboratory is a working area. Feel free to get up and stretch or go out for a drink of

water. Talk with your fellow students or your instructor. Consult your instructor when you

have a question about your work.

6. Do not waist time. Report to your work area, review the previous week's work and return it

to the instructor (5 minutes), and then get involved in the experiment activity. Do not wait

for the instructor to tell you what to do.

7. Be prepared before you come to the lab. Read the experiment as well as any helpful

information provided in the introductory portion of the laboratory manual before you attend

lab. Failure to be prepared will cause delays and you may not be able to complete the

experiment in the allotted time.

8. Always keep your emphasis on quality of work and completeness of understanding. Do not

set a high priority on the amount of work accomplished in a laboratory period.

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LABORATORY SUPPLIES & EQUIPMENT

This laboratory manual contains write-ups of experiments to be performed during the

semester, as well as materials explaining laboratory policies and generally accepted laboratory

practices.

In addition to the laboratory manual, every student should bring the following supplies

to each lab session:

• One or two pencils (We prefer that you use pencil instead of pen in the laboratory.)

• A good eraser

• A combination straightedge and protractor.

• Bring your own calculator and DO NOT plan to borrow one from your laboratory partner

NOTE: We do not allow students to fail to buy these materials and then borrow

them from other students during the lab. There will be no need to carry your physics

textbook to the laboratory. The current experiment should be read before coming to each

lab period.

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GRADING POLICY IN THE PHYSICS LABORATORY

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THE PRESENTATION OF EXPERIMENTAL DATA

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ACURACY OF MEASURMENTS

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EXPERIMENT 01

THE FORMATION OF STANDING WAVES --MELDE’S EXPERIMENT

INTRODUCTION:

By sound we mean that phenomenon which is capable of stimulating the sensation of hearing.

Sound always originates in some type of motion. In many instances the source of sound is a standing

wave in some vibrating body, e.g. a drum-head, the vocal cords, a guitar string, or the air column in an

organ pipe. Our goal in this experiment is to learn both about the formation of standing waves in

strings and about the boundary conditions that determine the pitch (frequency) of the sound produced.

THEORY:

Imagine a long string attached to the wall at one end, we grasp the other end, place the string

under some tension T and vibrate this end up and down at some constant frequency f.

Successive crests and troughs are

produced by the motion of the hand and are seen to

move in succession down the string with constant

speed v. Such a wave is called a traveling wave.

The distance between any two successive points in

the wave train which have the same phase is called

the wavelength λ. Careful study shows that the wavelength λ, frequency f, and wave speed are related by the wave equation.

v f= λ (Eq1)

Experiments also show that the speed of the wave through the string is independent of the

frequency and amplitude of the wave. It depends only on the characteristics of the medium (the

string) through which the wave moves. This is a general property of many types of wave motion.

Specifically, the speed of the traveling wave in the string is related to the tension in the string T and

the linear density of the string µ (the mass per unit length of the string). The velocity is given by

v T= µ (Eq. 2)

In this experiment, we use an electrically

driven turning fork to generate the wave and we

are interested in the standing waves that are

produced in the string under certain circumstances.

Consider the following situation (see the diagram

to the right). A traveling wave produced by the

vibration of the fork. The wave moves to the right

where it encounters the wall. If the wall was not

present and the string was longer, the wave would

have continued beyond the wall as shown by the

dotted wave. However the wall is present and the

initial traveling wave (solid wave-form) is

reflected back into the string as a second traveling

wave (see second sketch).

The instantaneous shape of the string is found by adding together the displacements that would

be produced by the two waves acting independently.

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The series of sketches on the right show the

resulting wave form (shape of the string) at six

different times as the incident wave continues to

move to the right and the reflected wave continues

to move to the left. NOTE that there are points on

the string (called nodes, N) where the

instantaneous displacement of the string is also

zero. At intermediate points the wave amplitude

builds up to a positive maximum, dies out and then

builds to a negative maximum. Thus instead of

seeing waves move successively down the string,

one sees the string vibrating in a series of loops.

Each loop is one half wavelength in extent. This

type of wave is called a standing wave or a

stationary wave.

Standing waves will form in the string

only if certain boundary conditions are satisfied.

Specifically, the length of the string must be some

integral number of half-wavelengths for the initial

traveling wave. Since the wave frequency of is

fixed by the fork, this means that we can adjust the

string tension in and therefore the wave speed until

the wavelength satisfies this condition.

Under these circumstances, the string vibrates with the same frequency as the fork, i.e. the

system is said to be in resonance and energy flows from the fork into the vibrating string. The

amplitude of the string builds to quite large magnitudes at resonance.

THE EXPERIMENT:

1- Experimental Apparatus:

Your laboratory station should be equipped with the following items: electrical tuning fork,

string, power supply, weight hanger, slotted weights, meter stick, and electrical balance.

2- Experimental Procedure:

• Attach the string to the fork and pass it over the pulley to the weight hanger.

• Start the fork vibrating and adjust the hanging weight until the string vibrates in a series of

distinct loops.

• Adjust the weight carefully so as to arrive at the approximation of the resonant condition;

Examine the wave motion carefully. Are all the loops of the same size? Is the point where the

string is attached to the fork a nodal point?

• In Table 1 of your laboratory report record the number of vibrating segments of the string, n, the

tension in the string (Newtons), and the wavelength (meters). NOTE that the best value for the

wavelength is just twice the average length of a loop in the vibrating string.

• Repeat the above observations for at least five different values of n.

• Record the frequency of the fork

• Measure the mass of the string and its length, then calculate its linear density, that is mass per unit

length (use the electronic balance to determine the string’s mass).

ANALYSIS OF RESULTS:

• On a graph paper plot the wave velocity-versus-tension.

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• On the same graph paper plot the wave velocity squared-versus-tension. Watch your coordinates

labels, graph titles, etc.

• What conclusions can be drawn from each of the two graphs?

• Determine the slope of the wave velocity squared-versus-tension graph. Show your work and the

results directly on the graph paper.

• Calculate the linear density of the string from the slope just determined and compare it with the

value you found using the electronic balance. Show all work.

QUESTIONS:

1. Describe an experiment you might conduct to show that the speed of a transverse wave in a

string is inversely proportional to the square root of the linear density of the string. Be

specific as to the necessary experimental steps.

2. A lineman installing a power line strikes the line at point (a) with a heavy stick and

measures the time required for a wave pulse to reflect from point (b). What information does

this give him about the wire? Explain.

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AUI PHY 1402 LAB. REPORT

EXPERIMENT 01

NAME: . . DATE: . .

SECTION: . .

* * *

1. EXPERIMENTAL PURPOSE:

State the purpose of the experiment.( 5 points )

2. 2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points)

Briefly outline the apparatus

General procedures adopted

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3. DATA and ANALYSIS:

TABLE 1: (20 points)

n

T

λ

v

v²

Mass of String:

Linear Density Measurement: (10 points)

Summary of Graphs: (10 points)

Comparison between linear densities of string: (5 points)

CONCLUSION: (10 points)

QUESTIONS: (5 points)

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GRAPH: (30 points)

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EXPERIMENT 02

MILLIKAN OIL DROP EXPERIMENT

INTRODUCTION

Robert Andrews Millikan was an important person in the development of physics. Best

known for his oil drop experiment, Robert Millikan also verified experimentally the Einstein equation

for the photoelectric effect. For these two investigations, he was presented the Nobel Prize in 1923.

Millikan’s oil drop experiment is one of the classic experiments of this century. His

apparatus included a fine-mist atomizer (to create the tiny drops of oil needed), a three-windowed

metal box with two separate metal plates connected to a voltage supply, a microscope, and an electric

light. The diagram of the physical apparatus used:

Small drops of oil are injected into the area between the plates using an atomizer. Due to gravity they

begin to fall slowly downward. If the voltage supply is turned on, the drops may begin to move at a

different speed or even to move upward. The drops are usually electrically charged and the electric

field between the plates exerts a force on them. By controlling the voltage between the plates, the

experimenter can make the drops move up or down and control their speed. By studying the

relationships between the voltage and the velocities of various drops, much can be learned about the

nature of electrical charges. Using apparatus similar to this, Millikan demonstrated that charge comes

in finite units. He also was able to measure the smallest electrical charge- the charge on one electron.

Too often this fascinating experiment is passed over by high school, and college classes

because it is simply too difficult to do. Even if the students are lucky enough to get the atomizer

working properly, the entry tube clear, and the plates properly aligned, they still may spend the entire

lab period just trying to capture a drop in the field of view. Ultimately, it is a major frustration for

students at all levels using the relatively crude equipment available at many schools. This computer

program enables you to circumvent the frustrations normally associated with this experiment and still

collect analyzable data and get a feeling for the Millikan oil drop experiment.

This experiment is a simplified version of the Millikan oil drop experiment. You are

to use the computer simulation to determine as much as possible about the electrical charges

on oil drops. You will do this by balancing the force of gravity with the force on the drop due

to the electric field.

THEORY:

When an electrically charged object is placed in an electric field (E), an electrical force (Fe)

is exerted on it. This force is given by:

F qEe = (1)

Since the electric field strength is given by the voltage between the plates (V) divided by the

distance between the plates (d), we can also write:

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FqV

de = (2)

The oil drop is also in the earth’s gravitational field, so it also has a gravitational force (Fg)

acting on it.

One way of studying the charge on the oil drops is to adjust the voltage between the plates

until the electrical forces acting up on the drop exactly balance the pull of gravity down. In this case:

( )F F

mg Vd

q

qmgd

V

e g=

=

=

(3)

The charge on the drop is inversely proportional to the voltage required to balance the drop.

Also, if the mass of the drop and the distance between the plates are known, you can calculate the

actual charge on the drop.

Another way to study the charge on the oil drop is by considering the total force acting on the

drop. For small objects moving through air under the influence of a constant force (like this drops),

the drift velocity is proportional to the force. Therefore, by measuring the drift velocity, you can

indirectly get a measure of the force acting. With this simulation, you can easily measure drift

velocities; in fact, you can measure both the drift velocity of the drop under the influence of gravity

alone (Vg) and the drift velocity of the drop under the influence of both gravity and the electric field.

By vector subtraction, you can then determine the force due to the electric field alone (Ve). This

quantity is proportional to the charge on the drop.

THE EXPERIMENT:

1. STARTING THE PROGRAM:

This part an explanation of how to use the MILLIKAN OIL DROP PROGRAM, and

instructions on how to conduct the experiments. You should read this part and try out the

program following the instructions in the section entitled “A Little Practice” before you began

the experiment itself.

To start the MILLIKAN OIL DROP EXPERIMENT, make sure the directory

containing the program is selected, then type MILLIKAN and press <ENTER>. You will than

be presented with the title screen. Press <ENTER> to go to the main experimenting screen.

The screen should now look similar to this:

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Figure 1: The Main Experimenting Screen

Drops are injected from the nozzle at the right side of the screen. Only one drop will be

displayed at a time.

The two bars at the top and bottom are charged metal plates between which the drop

will be suspended. The pluses and minuses indicate the sign of the electrical charge on that

plate. It is important to understand that because of the magnification from the microscope, the

viewing area often represents only a small portion of the area between the plate. The actual

plates may be far above or below the edges of the screen. Wires connect the plates to the

power source.

The box on the left of the screen represents the high-voltage power supply. The

display at the top of the box shows the voltage across the two plates. A positive voltage

means that the top plate is positively charged and the bottom plate is negatively charged. A

negative voltage means that the top plate is negatively charged and the bottom plate is

positively charged. Whenever this display reads XXXXX, the power source is disconnected

from the plates and no electric field exists. A quick summary of all the commands used to

regulate the voltage to the plates appears in the power source box.

The horizontal dotted lines between the plates mark the divisions used to measure the

distance moved by a drop when measuring velocity.

The lower left-hand corner of the screen contains information that will be necessary to

complete the experiment. Plate separation is the distance in millimeters (mm) between the

plates. µm/div is the distance in micrometers (µm) between each division on the screen. A micrometer is 1x10

-6 meters. The radius display will show the current drop’s radius in µm.

The direction gauge and timer display are on the right side of the screen. Whenever a

drop is between the plates, this direction gauge will indicate what direction the drop is

moving. This is useful whenever the drop is moving so slowly that it appears to be still. It is

also useful if for some reason your drop has drifted above or below the edges of the screen

and you are trying to bring it back onto the screen. Whenever you have reached the voltage

that comes as close as possible to balancing the drop, the direction gauge will read “0”. The

interval timer display reads the number of seconds since the timer was started. It is blank until

you use the interval timer to measure the velocity of a drop. When you start the timer, it will

begin at 0 and count up to 10 seconds. This is described further in the next section.

2. THE CONTROLS

The controls used in this program are described below. In each case, both the lower

and upper case of the letter will work. This section can be used as a reference guide to the

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commands when practicing and when actually performing the experiment. Read through the

list once to get a feel for the available commands, then to the “A Little Practice” section.

The <↑↑↑↑> and <↓↓↓↓> keys: In creasing or decreasing the voltage The arrow keys allow you to adjust the voltage up or down in small steps. The <↑↑↑↑> key will increase the voltage, while the <↓↓↓↓> key will decrease it. The amount that the voltage changes at each keystroke depends upon what you have set using the <SPACE BAR>.

<SPACE BAR>: FINE/COARSE voltage adjustment

This key allows you to toggle between fine and coarse voltage adjustment. You can tell which

mode you are in by which word is boxed just below the voltage display. A FINE setting will

allow you to change the voltage (using the arrow keys) in 1-volt increments. The COARSE

setting jumps by 10-volt increments.

The number keys (<0> through <9>): Set 100’s voltage

Number keys are used to set the hundreds place of the voltage. They provide a quick way of

making large voltage changes. The tens place and the units place are set to “0”. The number

keys have no effect upon the thousands place of the voltage. Here are some examples:

VOLTAGE BEFORE KEY PRESSED VOLTAGE AFTER

0 volts <3> 300 volts





-1988 volts <7> -1700 volts

The function keys (<F1> through <F10>): Set 1000’s voltage

The function keys are used to set the thousands place of the voltage. They will not be used

very often. Whenever you press one of the function keys, the last three digits of voltage are

always set to 000. For example, in order to enter in a voltage of 5400 quickly and easily, you

need only type <F5> and <4>. Pressing <F10> sets the voltage to 0 volts. Here are some

examples:

VOLTAGE BEFORE KEY PRESSED VOLTAGE AFTER

0 volts <F3> 3000 volts

9873 volts <F10> 0 volts

-2000 volts <F> -1000 volts

<S>: Switch plate polarity

Pressing <S> switches the charge on the plates. To make the real-world analog, this is the

same as switching the leads on the power supply.

<D>: Disconnect/reconnect power source

Pressing <D> will disconnect the power source if it is currently connected, or reconnected it if

it has been disconnected. Whenever the power source is disconnected, the voltage display

will read XXXXX and there will be no electrical field between the plates.

<M>: Mark voltage

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This key is used to record a voltage so that it can be quickly restored at a later time. When

you mark a voltage, you may return to that voltage at any time by pressing <R>.

<R>: Return to voltage

When this key is pressed, you return to the voltage that you have previously marked using the

<M> key. This key is often used to return to a standard voltage quickly and easily.

<N>: New drop

When this key is pressed, any drop currently in use will be destroyed, and a new drop will

come out of the tube on the right side of the screen. In about a second, air friction will stop

the drop’s leftward movement and you will be ready to start the experiment.

<Z>: Zap drop

Pressing <Z> exposes the current drop to a dose of X rays that cause it to gain or lose

electrical charge.

<T>: Start timer

This command causes the interval timer to start. When you press <T> a small mark appears

immediately to the right of the current drop and the box labeled TIMER begins to count up

from 0. When the timer reaches 10 seconds, a second mark is placed next to the drop. This

allows you to estimate the distance the drop traveled in the 10 seconds and calculate the

drop’s velocity during this period. (The amount of time passed between markers will remain

in the timer box even after the timer has completed the timing).

<Tab> and <Shift> <Tab>: Control interval timer period

The interval timer normally counts for 10 seconds. In some situations, you may want to have

the timer count for a different time period. To increase the timer period press the <Tab> key.

When you do this you will see the new timer period flashed briefly just above the timer

display. The period will increase by one second each time you press the <Tab> keys. To

decrease the period of the timer press both the <Shift> and the <Tab> keys at the same time.

The interval timer may rage from 1 to 90 seconds.

<+>: Zoom in

This command changes the magnification of the viewing area. Each press will increase the

magnification. The maximum magnification is 100 times. Changing the magnification

changes the µm per division setting. Due to the limitations in graphics, the size of the drop on the computer screen will not change when you change the magnification.

< - >: Zoom out

This is opposite of the Zoom in command. It decreases the magnification of the viewing area.

The minimum magnification is 1x. Changing the magnification changes the µ m per division setting.

<B>: Control the beeping sound

The program normally makes a beeping sound once a second. This sound can be helpful in

determining the speed of drops. It can sometimes be irritating. Pressing the <B> key turns off

the sound if it is on or on if it is off.

<Q>: Quit the program

3. A LITTLE PRACTICE

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Now that you have had an introduction to the screen and the commands used to

perform the experiment, it is time to get a little practice. Follow the step-by-step instructions

below, taking as much time as necessary at each step. If you go through these practice steps,

you should have all the skills necessary to perform the MILLIKAN OIL DROP

EXPERIMENT.

• Getting a New Drop

1. Press <N> to get a new drop between the plates. Do this a few times to see how it works.

Each time you press <N>, the current drop will be destroyed, and a new drop will come

out of the tube on the right side of the screen.

• Adjusting the voltage

1. Press <SPACE BAR> to switch to FINE voltage adjustment and now experiment with the

arrow keys.

2. Notice that pressing <SPACE BAR> again will return you to COARSE voltage

adjustment. The space bar toggles between FINE and COARSE.

3. Adjust the voltage to 173 volts using the arrow keys and <SPACE BAR> for practice.

Pick some other values and try to reach them as quickly as you can.

• Switching Plate Polarity

1. Press the <S> key. Notice that the sign on the voltage changed, as did the signs on the

plates.

2. Experiment with the arrow keys after you have switched the polarity using the <S> key.

• Setting the Voltage with Number Keys and Function Keys

1. Experiment with the keys from <0> to <9> and get a feel for how they control the

voltage by 100-volt increments.

2. Switch the plate polarity so that you have a negative voltage. Notice that the voltage

remains negative when you press any of the number keys. To return to positive voltage,

you must switch the plate polarity with the <S> key.

3. Notice that after you have set the voltage above 999 volts (or below -999 volts), pressing a

number key only sets the hundreds place of the voltage. In order to quickly return to 0

volts, you can press the <F10> key.

4. Set the voltage to 344 as quickly as possible using both the number keys and the arrow

keys. Choose a few other values and practice with them until you get the hang of it.

• Disconnecting the Power Source

1. Press <D> a couple of times. Whenever the voltage display reads XXXXX, this means

the power source is disconnected and therefore the plates have no charge.

2. Notice that while the power source is disconnected, the computer reminds you with a beep

whenever you adjust the voltage.

• Balancing A Drop

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You should now be fairly comfortable with adjusting the voltage. To balance a drop

you must adjust the voltage until electrical force up on the drop just balances gravity pulling

down on the drop. When a drop is perfectly balanced, the direction gauge should read “0”.

Note that most drops are positively charged, but a few are negatively and a few have no

charge.

1. Set the voltage to 0.(Press <F10>).

2. Press <N> to get a new drop .

3. Increase the voltage rapidly using first the number keys, then the arrows, until the drop

slows down. If you lose the drop, try again with a new one.

4. Finally, adjust the voltage using the arrow keys, (remember that<SPACE BAR> toggles

between FINE and COARSE adjustment) until the drop comes to rest. The direction gage

should display “0”.

5. Repeat the whole process a number of times with new drops until you get good at it.

Notice that different drops take different voltages to balance. This is because they have

different electrical charges. You may notice that some drops do not respond, no matter

what voltage you use. These drops are electrically neutral, and therefore unaffected by

electric fields.

• Marking and Returning to a Balancing Voltage

1. If you have a drop balanced, press <M> to mark the balancing voltage. Now adjust the

voltage to a different setting using the arrow keys, number keys, or the function keys.

2. Press <R> and notice how the voltage returns to the marked voltage and the drop is

balanced again.

• Dragging a Drop

The term dragging a drop refers to moving a drop to a desired place on the screen. If

the drop is at the bottom of the screen and you want it at the top, you must drag it up the

screen. You do this by varying the voltage in the manner explained below:

1. First of all, get a new drop and balance it using the method detailed above.

2. Press<D> to disconnect the battery from the plates and let the drop begin to fall down the

screen.

3. Reconnect the power source (by pressing <D> again) when the drop is close to the bottom

of the screen. You are now ready to “drag” the drop up the screen.

4. Press <M> to mark the current balancing voltage.

5. Increase the voltage until the drop is slowly moving up the screen.

6. When the drop has reached the top of the screen, press <R> to return to the balancing

voltage (which you marked with the <M> key). The drop should now be stationary near

the top of the screen.

• Measuring the Velocity of a Drop

In all but the simplest of the experiments, it will be necessary to measure the velocity

of a drop as it moves up and down the screen. The example below shows how to measure the

velocity of a drop falling under gravity with no electric field present (Vg).

1. Balance a drop.

2. Mark the balancing voltage (by pressing <M>).

3. Drag the drop up to the top of the screen.

4. Turn off the voltage (using the <F10> or the <D> key).

5. Quickly press <T> to start the interval timer. A mark will appear to the right of the drop.

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6. After 10 seconds, another mark will appear and the timer will stop increasing.

7. Rebalance the drop using the <R> key.

8. You now have all the information you need to compute the velocity of the drop. To do

this, you must count the divisions between the starting mark and ending mark. This gives

you the distance traveled by the drop. The time it took the drop to fall that distance is

shown in the timer display. It is now a simple matter to compute the drop’s velocity using

the formula: velocity = distance traveled/time. If you use the distance measured in

divisions when you calculate velocity, the result will be in units of divisions/sec. This

may be adequate for some experiments. If necessary you can convert the velocity to µm /sec (micrometers/second) by multiplying the result by the µm/div value displayed in the box on the lower left side of the screen.

9. Practice taking the velocity for a few more drops. Pay particular attention to how the

interval timer works.

• Changing the Charge on a Drop

1. Balance a drop.

2. Press <Z> to simulate exposing the drop to X rays. This will usually but not always, cause

the charge of the drop to change.

3. The drop should start moving. If it doesn’t, try zapping it again. The reason it is no

longer balanced is that when the charge on the drop changed, the electrical force on the

drop also changed.

• “Zooming” In and Out

1. Balance a drop close to the center of the screen.

2. Increase magnification by pressing <+> several times.

3. Change the voltage and notice how the drop moves more quickly across the viewing area.

This is because you are now at a higher magnification, and are therefore examining a

smaller portion of the viewing area.

4. Allow the drop to drift towards the bottom or top of the screen. Now press <+>. The drop

should appear to move away from the center of the viewing area, or if it was close to the

top or the bottom of the screen it should disappear out of the viewing area altogether. This

is because the microscope in this simulation is fixed on the spot exactly in the middle

between the two plates, and if the drop isn’t close to this spot, you won’t be able to see it

through the microscope at high powers. Note: you will be able to see any drop that is

between the plates when the magnification is set to 1x.

5. By decreasing the magnification (using <-> key), you can bring a drop that is off the

screen (but still between the plates) back into the viewing area.

6. Changing the magnification is often useful because with higher magnifications the drop

drifts more quickly across the screen, so a more accurate reading of velocity is possible in

a shorter a mount of time. (Another way to get a more accurate reading of the velocity is

to use a low magnification and simply allow the drop to drift for a longer period of time.)

If you have worked your way through all of these procedures, you should now be ready

to begin the actual experimentation.

4. Procedure:

In this experiment, you will determine the voltage necessary to balance the oil drop in

20 to 40 different trials. Between each trial, change the charge of the drop. You can do this

25

by either using the <Z> key to simulate exposing the drop to X rays (which causes ionization

of the drop) or by getting a new drop (which will have a random charge).


In your lab. report record, in Table 1, a list of all of the balancing voltages in

numerical order. Now using MICROSOFT EXCEL; plot a histogram of the balancing

voltages and see if you can observe obvious groupings of the voltages. Have a print out of

your graph attached to your laboratory report. If you are not familiar with the use of MS

EXCEL than you should consult with your laboratory instructor for help.

In this simplified version of the experiment, the radius of the drop is displayed at the

bottom of the screen. The density of the drop is known (plastic density = 128 kg/m3). The

mass of the drop can therefore be calculated using the equation:

m r density= ×43

3π

Calculate the charge on the drop for each of the balance voltages measured above (use MS

EXCEL to accomplish this). Plot a new histogram of the calculated charges for each

balancing voltage. Have a print-out of your graph attached to your laboratory report.

Report the value of the smallest charge that you measured.

Questions:

1. Why are some of the drops not affected by electrical fields?

2. Why do some of the drops require a negative rather than a positive balancing voltage?

3. What is your best estimate of the minimum electrical charge?

26


EXPERIMENT 02

MILLIKAN OIL DROP EXPERIMENT

NAME: . . DATE: . .

SECTION: . .

* * *



2. EXPERIMENTAL PROCEDURES AND APPARATUS:

Briefly outline the apparatus used and the general procedures adopted. (5 points )

27

3. RESULTS AND ANALYSIS

Table 1: (20 points)

ATTACH MS EXCEL GRAPHS AND DATA: (45 points)

28

Smallest measured charge: (5 points)

CONCLUSIONS: (10 points)


29

EXPERIMENT 03

ELCTRIC FIELDS AND LINES OF FORCE

INTRODUCTION:

A fixed distribution of electric charge causes an electric force to act on every other

electric charge in the universe. Another very convenient way to look at it is to say that the

charge distribution sets up an electric field E at every point in space, and that it is the field that

causes and electric force on the other electric charges. This experiment will serve to examine

certain electric fields; and in particular to map the equipotential lines of an electric field and

hence determine the electric lines of force.

THEORY:

The first quantitative investigation of the law of force between electrically charged bodies

was carried out by C. A . Coulomb in 1784-1785. His measurements showed that the force of

attraction for unlike charges or repulsion for like charges followed an inverse square law of

distance of separation. It was later shown that for a given distance of separation r the force is

proportional to the product of the individual charges Q and Q’, and is a function of the nature

of the medium surrounding the charges. Expressed in symbols, Coulomb’s law is

F QQ Kr∝ ' 2 (1)

where the factor K, called the dielectric constant, is introduced to take care of the nature of the

medium. The factor K is arbitrarily assigned a value of 1 for empty space. Coulomb’s Law is

restricted to point charges, that is, the charged body must have dimensions which are small

compared to the separation distance.

Several systems of units, each with its particular advantages, are in use. The electrostatic

system will be emphasized in this experiment. In the electrostatic system forces are expressed

in dynes, distances in centimeters, and the unit of charge, called the statcoulomb, is chosen of

such magnitude that the proportionality constant in coulomb’s law is equal to unity. Thus

coulomb’s law may be expressed by,

F QQ Kr= ' 2

(2)

When all quantities in equation (2) are unity the definition of the electrostatic unit (esu) of

charge or statcoulomb is indicated -The statcoulomb is a charge of such magnitude that it is

repelled by a force of 1 dyne when placed 1 cm from an equal charge in vacuum. The charge

of one electron is a natural basic unit of quantity of electricity. Its charge is 4.80x10-19

statcoulomb. Thus 1 statcoulomb represents a charge of 2.09 x109 electrons or approximately

two billion electrons. For practical use, however, the statcoulomb is exceedingly small and a

charge known as the coulomb or ampere-second is used. The coulomb is approximately equal

to three billion statcoulombs.

The factor K in coulomb’s law, called the dielectric constant of the medium, is assigned a

value of 1 for vacuum. When the medium separating the charges is not empty space, the force

between the charged bodies is altered because charges are induced in the molecules of the

medium. Air at one atmosphere pressure has a dielectric constant of 1.00059. Thus as a

30

practical matter, equation 1 using K=1 is acceptable to one part in two thousand for

Coulomb’s law experiments in air.

The common dielectrics have “constants” K from 1 to 10 in value. The dielectric

constant of glass ranges from 5 to 10, mica from 3 to 6 and oil from 2 to 2.5. The specific

value of the “constant” for a given medium may vary with a change in temperature, pressure,

frequency of current, etc. It noted also that K is not a pure number but has dimensions

dependent on the system of units used.

An electric field, commonly called field of force, is a region in which forces act on

electric charges if present. If a force F acts on a charge q at a point in the field, the field

strength E, by definition the force per unit charge, is

E F q= (3)

that is the magnitude of electric field strength is the force per unit charge. Force is a vector

quantity having direction as well as magnitude. The direction of an electric field at any point

is the direction of the force on a positive test charge placed at the point in the field.

Faraday introduced the concept of lines of force to visualize the strength and direction of

an electric field. A line of force is the path which a free test charge would follow is traversing

the electric field. The path is everywhere tangent to the field direction at each point. As an

illustration, consider the isolated positive charge Q placed at A in Figure 1. A small positive

test charge q at any point in the field experiences a radial force of repulsion from A. The lines

of force are drawn with arrows to point this direction. When Q is a negative charge, that is an

excess of electrons, these lines would be directed towards A to

indicate an attraction of the positive test charge q.

The magnitude of the force per unit charge may also be

graphically shown by the artifice of lines of force. By convention,

the number of lines of forces drawn through a unit area placed

normal to the field at the point considered, is made numerically

equal to the field strength. For example, if the field strength at a

point is 5 dynes per statcoulomb, one visualizes 5 lines of force per

square centimeter at that position in the field. Figure 1: E around an isolated positive charge.

The diagram of Figure 2 shows a plane section near a pair of equal charges of opposite

sign. Each charge exerts a force on a unit test charge placed in the field. The resultant force

is the vector sum of these forces. Thus, at a point b, f1 is the repulsion force on the unit test

charge due to the positive charge on A, and f2 is the force of attraction to the negative charge

on B. The resultant R is tangent to the line of force at the point b.

Figure 2: Electric Field near Two Equal Charges of Opposite Sign.

31

It is evident that a uniform field is represented by a set of parallel lines of force. A

converging set of lines of force indicates a field of increasing strength; while a field of

decreasing strength would be represented by a diverging set of these lines.

Two points in an electric field have a difference of potential if

work is required to carry a charge from the one point to the other.

This work is independent of the path between the two points.

Consider the simple electric field illustrated in Figure 3. Since the

charge +Q produces an electric field, a test charge +q at any point

in the field will be acted upon by a force. Hence it will be

necessary to do work to move the test charge between any such

points as B and C at different distances from the charge Q. The

potential difference between two points in an electric field is

defined as the ratio of the work done in moving a small positive

charge between the points considered to the charge moved. In

symbols

V W q= (4)

where V is the potential difference, W is the work done and q is the charge moved. In the

electrostatic system V is expressed in statvolts when W is in ergs and q in statcoulombs. One

statvolts is approximately equal to 300 volts. If the work W is measured in joules and the

charge q in coulombs then the potential difference V is measured in volts.

The conservation of energy principle requires that the work done must be independent of

path over which the charge is transported. Otherwise energy could be created or destroyed by

moving a charge from one point such as B in Figure 3 to C by path a, involving a certain

energy, and returning by path b of different energy.

If point B in Figure 3 is taken very far from A, the force on the test charge q at this point

would be practically zero (see Equation 1). The potential difference between C and this point

at an infinitely large distance away is called the absolute potential of the point C. The

absolute potential of a point in an electric field may, therefore, be defined numerically as the

work per unit charge required to bring a small positive charge from a point outside the field to

the point considered.

Since both work and charge are scalar quantities, if follows that potential is a scalar

quantity. The potential near an isolated positive charge is positive, while that near an isolated

negative charge is negative.

It is possible to find a large number of points in an electric field, all of which have the

same potential. If a line or a surface is so drawn that it includes all such points, the line or

surface is known as an equipotential line or surface. A test charge may be moved along an

equipotential line or over an equipotential surface without doing any work.

Since no work is done in moving a charge over an

equipotential surface it follows that there can be no

component of the electric field along an equipotential

surface. Thus the electric field or lines of force must be

everywhere perpendicular to the equipotential surface.

Equipotential lines or surfaces in an electric field are more

readily located experimentally than lines of force, but if

either is known the other may be constructed as shown in

Figure 4. The two sets of lines must everywhere be

normal to one another. .

Figure 3: Potential difference.

Figure 4: Lines of Force and Equipotential

Lines Near Two Charges of Equal Magnitude

32

Electron in a conductor can move under the action of an electric field. Thus if an

electrical conductor is placed in an electric field, this electron flow, which constitutes an

electric current, will take place until all points in the conductor reach the same potential.

There will then be no net electric field inside the conductor whether solid or hollow provided

it contains no insulated charge. Thus, to screen a region of space from an electric field it need

only be enclosed within a conducting container. Since all parts of the conductor are at the

same potential, the electric lines of force always leave or enter the conductor at right angles to

its surface.

When charged bodies of different potentials are located in a medium in which some

flow of charge can occur, the field of force will cause these charges to be transported from one

body to the other. To maintain the difference of potential the bodies must then be connected

to a source of electromotive force. The flow lines of the charge follow the paths of the lines

of force, that is, they are also at all points perpendicular to the equipotential surfaces.

THE EXPERIMENT:

1. Apparatus

Your lab station should be equipped with the following: Field mapping board and U-

shaped probe, Figure 5. Eight similar resistors connected in series (A to I in Figure 5) and

mounted on this board. Field plates with conductive and corresponding template. Source of

potential. Sensitive galvanometer as a null-point detector.

Figure 5: Diagrammatic Representation of Electric Field Apparatus.

1.1 The Galvanometer:

The galvanometer is an instrument for measuring small electric currents. It consists

essentially of a coil of fine wire mounted so that it can rotate in the field of a permanent

magnet. When a current flows through the coil, it becomes an electromagnet. The field of the

permanent magnet exerts a torque on the coil and makes it rotate until equilibrium is

established between the torque due to the field and that exerted by the restoring spring or by

the suspension of the coil. The angle of rotation is directly proportional to the current flowing

through the coil, if the field of the permanent magnet is uniform in the region of the coil.

1.2 The DC Power Supply:

33

Figure 6: The Tektronix DC Power Supply Front Panel.

The Tektronix Laboratory DC Power Supply (Figure 6) is a multifunction bench or

portable instrument. This regulated power supply provides a fixed 5 V output, and two

variable outputs that you can vary from 0 to 30 V. The current varies from 0 to 2 A

A brief description of the front-panel controls, connectors; and indicators of this power

supply is given below:

1. LED Display. Lights when the instrument is turned on. The numbers indicate the voltage

or current produced by the left variable power supply.

2. AMPS/VOLTS Switch. This switch selects whether the LED display for the left variable

power supply shows the current or the voltage. If the switch is pushed to the left, the

display shows the current. If the switch is pushed to the right, the display shows the

voltage.

3. AMPS Indicator. Lights when AMPS is selected with the AMPS/VOLTS switch for the

left variable power supply.

4. VOLTS Indicator. Light when VOLTS is selected with the AMPS/VOLTS switch for the

left variable power supply.

5. AMPS Indicator. Lights when AMPS is selected with the AMPS/VOLTS switch for the

right variable power supply.

6. VOLTS Indicator. Light when VOLTS is selected with the AMPS/VOLTS switch for the

right variable power supply.

7. AMPS/VOLTS Switch. This switch selects whether the LED display for the right variable

power supply shows the current or the voltage. If the switch is pushed to the left, the

display shows the current. If the switch is pushed to the right, the display shows the

voltage.

8. LED Display. Lights when the instrument is turned on. The numbers indicate the voltage

or current produced by the right variable power supply.

9. POWER Button. Turns on the instrument when pressed. When pressed again, it turns off

the instrument.

10. CURRENT knob. Use this control to set the output current for the right, variable power

supply. If the instrument is in a tracking mode, the left power supply is the slave and the

CURRENT knob has no effect.

11. C.C. Indicator. If this is lighted, the left variable power supply is producing a constant

current.

12. C.V. Indicator. If this is lighted, the left variable power supply is producing a constant

voltage.

13. Output Terminals. These terminals for the left, variable power supply allow you plug in

the test leads as follows:

34

• The red terminal on the right is the positive polarity output terminal. It is indicated by

a + sign above it.

• The black terminal on the left is the negative polarity output terminal. It is indicated

by a - sign above it.

• The green terminal in the middle is the earth and chassis ground.

14. VOLTAGE Knob. Allows you to set the output voltage for the left variable power supply.

If the instrument is in a tracking mode, the left power supply is the slave and the

VOLTAGE knob has no effect.

15. TRACKING Buttons. These buttons select the test mode of the instrument. The

instrument has two tracking modes: series and parallel. If both push-button switches are

disengaged (out), the two variable power supplies operate independently. If the left switch

is pushed in, the instrument operates in series mode. If both switches are pushed in, the

instrument operates in parallel mode.

In series mode, the master power supply controls the voltage for both power supplies,

which can then range from 0 to 60 V.

In Parallel mode, the master power supply controls both the voltage and the current for

both power supplies. The current can then range from 0 to 4 A.

16. CURRENT Knob. Use this control to set the output current for the right, variable power

supply. If the instrument is in a tracking mode, the right power supply is the master and

the CURRENT knob affects both variable power supplies.

17. Output Terminals. These terminals for the right, variable power supply allow you plug in

the test leads as follows:

• The red terminal on the right is the positive polarity output terminal. It is indicated by

a + sign above it.

• The black terminal on the left is the negative polarity output terminal. It is indicated

by a - sign above it.

• The green terminal in the middle is the earth and chassis ground.

18. C.C. Indicator. If this is lighted, the power supply is producing a constant current.

19. C.V. Indicator. If this is lighted, the power supply is producing a constant voltage.

20. VOLTAGE Knob. Allows you to set the output voltage for the right variable power

supply. If the instrument is in a tracking mode, the right power supply is the master and

the VOLTAGE knob effects both variable power supplies.

21. Output Terminals. These terminals for the 5 V FIXED power supply allow you plug in the

test leads as follows:

• The red terminal on the right is the positive polarity output terminal.

• The black terminal on the left is the negative polarity output terminal.

The overload indicator lights when the current on the 5 V FIXED power supply becomes

too large.

2. PROCEDURE:

In order to begin using the power supply, you should set its current limit lower

than the maximum safe current for the device to be powered.

For this experiment you will use a current of 0.2 A and a voltage of 4 V. You will

have to follow these procedures in order to get these set.

1. Push both tracking buttons (No. 15 of Figure 6) outs, so that you in the independent mode.

2. With the test lead (cable) temporarily short the positive and the negative output terminals

of the left output terminals (no. 13 of Figure 6).

3. Rotate the VOLTAGE knob (knob 14 of Figure 6) away from zero sufficiently to light the

C.C. indicator.

35

4. Set the meter selection switch to AMPS (switch 2 of Figure 6) so that the LED display

show the current (no. 1 of Figure 6).

5. Adjust the CURRENT knob (knob 10 of Figure 6) for the desired current limit.

6. The value appearing in the LED display should be around 0.2 A, this is your preset

current.

7. Remove the short between the positive and negative output terminal. Notice: The LED

will display 0.00 A after you remove the cable, that is because you have an open circuit

you shouldn’t worry about this.

8. Turn the meter selection switch to VOLTS so that the LED display show the voltage.

9. Adjust the VOLTAGE knob for the desired 4 V value.

10. The value appearing in the LED display should be around 4 V, this is your preset voltage.

Now you should prepare the electric field mapping apparatus. Turn the field mapping

board over and notice the two metal bars. Each bar has two threaded holes. Two of these

holes hold plastic-headed thumb screws with knurled lock nuts. Remove these thumb screws.

Now center any one of the field plates in such a manner that the holes in the plate coincide

with holes in the metal bars. Insert a thumb screw into each hole and turn it until it touches

the board below. Turn the knurled lock nut to hold the field plate securely in place. Turn the

field mapping board right-side-up.

Binding posts marked “Bat.” and Osc.” are located on the upper side of the board.

Connect the DC power supply to the appropriate binding post (point X and Y in Figure 5).

When the voltage is applied to the terminals, charges flow between them across the field plate

following the lines of force of the electric field established. This same potential difference

will be equally divided between the end terminals of the series of similar resistors.

Fasten a sheet of graph paper to the upper side of the board. The paper is secured by

depressing the board on either side and slipping the paper under the four rubber bumpers.

Select the design template (plastic template) containing the field plate configuration you have

chosen. Place the design template on the two metal projections (template guides) above the

paper edge and let the two holes on top of the template slide over the projections. Trace the

design corresponding to the field plate pattern in place on the underside of the mapping board

and remove the template.

Carefully slide the U-shaped probe onto the mapping board with the ball end facing the

underside of the field mapping board. Connect one lead of the null-point detector

(galvanometer) to the U-shaped probe and one to one of the banana jacks, which are

numbered E1 through E7.

Notice the knurled knob on the top of the probe (adjacent to the spotting hold) and the

screw below the probe with one finger of one hand resting lightly on the knurled knob, and a

finger of the other hand lightly contacting the nut of the leg. The leg slides on the table top

and in so doing stabilizes the probe. Do not apply pressure to the probe, and avoid

squeezing its jaws.

Using the selected banana jack, move the U-shaped probe over the paper to a zero

reading of the galvanometer (Make sure that the galvanometer does not go off scale, that will

damage it). The circular hole in the top arm of the probe is directly above the contact point

which touches the graphite-coated paper. Record the location of the equipotential point

directly on the paper. Move the probe to another null-point position and record it. Continue

this procedure until you have generated a series of these points across the paper. All the

points corresponding to the same equipotential curve should be labeled with the number of the

corresponding resistor (i.e. E1 or E2...etc.). Connect the equipotential points with a smooth

curve to show the equipotential line of that banana jack. For example the series of points C’,

all of the same potential as C in Figure 5, define an equipotential line.

36

Connect the detector to a new banana jack and plot its equipotential line. Repeat until

equipotential lines are plotted for all banana jacks E1 through E7. Since the potential

difference is the same across each similar resistor, the equipotential lines obtained will be

spaced to show an equal potential drop between successive lines.

With the help of a voltmeter record the potential drop across each series resistors and

record in Table 1 of your lab report.

Upon completion, select a different field plate and repeat the above procedure until all

electric fields from all the provided plates are drawn.

3. ANALYSIS:

The flow lines or lines of force are everywhere perpendicular to the equipotential lines.

Draw in, by dash lines, the lines of force for the electric fields studied.

Draw the tangent to two adjacent equipotential curves and draw the perpendicular line

between these tangent lines. Find the distance ∆X, by measuring in cm using a ruler, between these tangent lines. Find the magnitude Ex on the worksheet and indicate the direction by a vector placed at X on the graph paper.

QUESTIONS:

1. Why are the equipotential lines near conductor surfaces parallel to the surface and why

perpendicular to the insulator surface mapped?

2. Under what conditions will the field between the plates of parallel plate capacitor be

uniform?

3. Sketch the field pattern of two positively charged small spheres placed a short distance

from each other.

37


EXPERIMENT 03

ELECTRIC FIELDS AND LINES OF FORCE

NAME: . . DATE: . .

SECTION: . .

* * *





38

3. RESULTS AND ANALYSIS:

Table 1: Potential Drop across the Resistors (15 points)

Resistor 1 2 3 4 5 6 7 8

VR

Attach the Graphs: (45 points)

Measurement of ∆X: (5 points)

Measurement of Ex and E field direction: (10 points)



39

EXPERIMENT 04

RESISTANCE AND POWER IN ELECTRICAL CIRCUITS

INTRODUCTION:

We will study electricity as a flow of electric charge, sometimes making analogies to

the flow of water through a pipe. In order for electric charge to flow a complete loop, called a

circuit, must be established. A simple electrical circuit consists of three elements:

1. a source of electromotive force, such as battery

2. a load with a resistance, such as a lamp, which operates when a current flows through it,

and

3. two or more conducting paths of negligible resistance (wires) which can be used to

connect the source and the load in a closed loop. See figure 1.

Figure 1: A Simple Electrical Circuit.

THEORY:

An electrical circuit transfers energy from one point to another, converging it from

electrical energy to heat, light or mechanical energy. Here are some of the terms used to

describe electric circuits.

A source of electromotive force (emf) is some device in the circuit that produces a

separation of (+) and (-) charges and in doing so provides the energy to move the charges

around the circuit. A typical example is a battery which uses chemical energy to produce an

emf. Sources of emf are rated by amount of energy they give to each coulomb of charge

passing through the source. The unit of emf is the volt (V); 1 V = 1 J/C ( joule per coulomb).

One word of caution: note that emf is not a “force” at all ; it is the amount of work done per

unit charge by the source to separate the charge. To use our analogy with water flow on a

pipe, emf can be loosely thought of as the electrical ‘ pressure’ causing the water (that is, the

electric charge) to flow.

Electric current is the flow of charged particles, usually expressed as the amount of

charge passing a given point per second. Usually these particles are negatively charged

electrons. The unit of current is the coulomb per second, called an ampere ( amp, symbolized

by A). The amp is a large unit of current; we will often work in milliamps.

Resistance is the opposition to the flow of current, and is measured in ohms (Ω), (1Ω = 1V/A). Resistance depends on several factors such as length, cross-sectional area,

temperature and the type of material through which the charge is flowing. Some electrical

devices (called resistors) are designed to have a large resistance.

As charge flows through a load (any part of the circuit that has a resistance is in

general called a load; most often our loads will be resistors) energy is dissipated from the

circuit, usually in the form of heat or light. The amount of energy dissipated by the load per

40

coulomb of charge is known as the potential difference across the load. Potential difference

has the same unit as emf, namely the volt, and gives a measure of energy dissipated in the load

per coulomb of charge passing through it.

Sketching a circuit as we did in Figure 1 is time consuming and sometimes ambiguous.

We will sketch circuits using a set of standard figures, a few of which are shown below.

Battery (DC source of emf) ↓ Resistor ↓

AC source of emf ↓ DC voltmeter ↓

V

DC ammeter ↓ Diode ↓

The battery is a source of DC (direct current) emf. The charge accumulates at the

‘poles’ of the battery, indicated by the long (positive charge) and the short (negative charge)

lines. In a DC circuit the current always flows in one direction, from the positive pole of the

battery to the negative pole through the circuit. In an AC (alternating current) source the

current reverses direction over intervals of time. For example, the wall outlets of your home

provide an AC current which switches direction 100 times each second.

The ammeter and voltmeter are instruments used to measure current and voltage

(either an emf or a potential difference) respectively. It is important that you become

proficient with the use of these two instruments, as you will be using them quite often.

The resistor is a component designed to provide a certain amount of resistance (to

within a certain tolerance). It converts electrical energy into heat energy, and in addition to

being rated by the amount of resistance it has is also rated by its ability to dissipate energy

over time (measured in watts).

There are two types of basic electric circuit, series and parallel.

A circuit with only one conducting path is a series circuit. It can contain any number

of loads and sources of emf. Figure 2 is a series circuit, shown schematically in Figure 2(b).

- + - +

2 Batteries in Series

2 Resistors in Series

a) Two Batteries and Two Resistors in Series b) Schematic Diagram of Part (a)

Figure 2: a) A Series circuit (2 Batteries and 2 Resistors), b) Schematic Diagram.

There are no junctions allowing the current to split in a series circuit; all the elements are

placed one after other. All the current must pass through the source and the resistor(s).

41

Consequently, the current through each resistor is the same. Again using our water flow

example, the resistors are like constrictions in a pipe. If a certain volume per second flows in

one end the same volume per second must flow out the other end.

For “n” resistors in series the current in every part of the circuit is the same, namely,

I I I In= = = =1 2 K (1)

and the voltage across the group of “n” resistors is equal to the sum of the voltages across the

individual resistors, namely,

V V V Vn= + + +1 2 L (2)

Using Ohm’s law, V = IR, we find that the total resistance of the series group is equal to the

sum of the individual resistance:

R R R Rn= + + +1 2 L (3)

A simple parallel circuit is shown in Figure 3. The opposite ends of each resistor have

a common connection to the source. In this circuit the potential difference of each resistor is

the same. Unlike the series circuit in a parallel circuit, there are one or more junctions which

allow the current to split. Therefore, the current through each resistor need not be the same.

If we think of the flow of water again, the point P in Figure 3 is like a “tee” allowing water to

go in two different directions. The amount of water flowing in each side of the tee is

determined by the “resistance”. Thus, a branch with high electrical resistance will have little

electrical current passing through it, branch with low resistance will have a high current

flowing through it.

P P

2 Resistors

in Parallel

2 Batteries in Parallel

(a) (b)

Figure 3: a) A Parallel Circuit (2 Batteries and 2 Resistors), b) Schematic Diagram.

For “n” resistors in parallel connection, the voltage across each resistor is the same as

that across any other resistor; this voltage is also the same as that across the entire group:

V V V Vn= = = =1 2 L (4)

and the total current is the sum of the separate currents, that is,

I I I I n= + + +1 2 L (5)

Using Ohm’s law we find that the reciprocal of the effective resistance of the group is

equal to the sum of the reciprocal of the separate resistance:

1 1 1 1

1 2R R R Rn

= + + +L (6)

42

The power dissipated in a resistor is given by the product of the current and voltage.

THE EXPERIMENT:

1. APPARATUS:

Your lab station should be equipped with: three 6 Volts DC batteries, resistors, two

mutimeters, variable DC power supply, breadboard, banana cables, flat cables, and lamps.

1. 1 The multimeter

In our experiment we will use the multimeter as an instrument for measuring voltage (i.e.

voltmeter), current (i.e. ammeter), and resistance (i.e. ohmmeter).In general multimeter is

composed of different part shown in figure 4.

Figure 4. The multimeter (a) palaced for measuring voltage (b) and current (c).

2. PROCEDURE:

Examine the multimeter. Notice that it has a positive and negative terminal. When

you measure the emf of a source you must be careful to observe these polarities; the positive

terminal (or probe) should be connected to the positive terminal of the source. Likewise, the

negative probe should be connected to the negative terminal of the source. The function key

should be set to the desired V range. The polarity is also important when measuring the

potential difference across a resistor. The positive probe must touch the end of the resistor

with the highest potential (remember the current flows from plus to minus, with the potential

decreasing at each resistor). Figure 4b shows the correct use of the voltmeter.

As with the voltmeter, the polarity of the ammeter is also important. Current has to

flow through the ammeter, so the circuit should be broken and the ammeter inserted into the

circuit. Like the voltmeter, the positive probe goes to the point of highest potential. See

Figure 4c. Note that in a series circuit it doesn’t matter where you place the ammeter, but in a

parallel circuit each branch could have a different current, so placement of the meter is

important. NOTE: Failure to observe the correct polarity for either meter result in the

destruction of the meter. Check with your lab instructor if you are uncertain.

With the three batteries mounted in their battery holders, measure the emf of one

battery, then the emf of two batteries in series and then the emf of three batteries in series.

43

When connecting batteries in series, connect them with the terminals as shown in Figure 5a.

Repeat with two and three batteries in parallel. Batteries connected in parallel are joined with

the positive and negative terminals with common connections, as shown in Figure 5b.

Summarize the results of these measurements on the worksheet in Table 1.

⇒ ⇒ ⇒

(a) (b)

Figure 5: Terminal Connections for: a) Batteries in Series, b) Batteries in Parallel.

Next, construct the circuit of Figure 6a, but complete the connections only when ready

to take measurements. Note in the figure that when more than one battery is connected in

series the wire connecting the batteries is not drawn. Open the circuit at point A to insert the

ammeter in the circuit. Observe the proper polarity as discussed above. Then connect the

voltmeter across the resistor at points B and C, again being careful of the polarity. Double

check your work, referring to Figure 4. Before completing the connections have your lab

instructor inspect the circuit. Measure and record the potential difference of the resistor and

the value of the current.

Repeat this measurement three more times, adding a resistor in series each time.

Leave the voltmeter across the first resistor; refer to this resistor as R1. Record the results in

Table 2.

With the four resistors in series measure the voltage drop (potential difference) across

the four resistors all together (i.e. VR1+R2+R3+R4), then for each resistor alone, that is VR1, VR2,

VR3, and VR4. Report these values in Table 3.

Connect a single battery to two resistors in parallel as shown in Figure 7. Connect the

voltmeter and ammeter as shown. Again, have your circuit inspected by the lab instructor.

Record the current and voltage measurements in Table 2. Adding one resistor at a time (and

leaving the instruments in the same place), repeat this measurement two times. Record your

results in Table 2.

With the four resistors in parallel record the current going through the four branches of

the circuit. That is connect the ammeter in series with each one of the four resistors and

record the values of I1, I2, I3, and I4 (the currents flowing through R1, R2, R3, and R4

respectively) in Table 3. When you are finished completely disconnect the batteries and

resistors and using the ohmmeter measure the resistance of each resistor in the order used

throughout the experiment and record your values in Table 4.

Figure 6: Experimental Set-Up for Series Circuit.

44

Figure 7: Experimental Set-Up for Parallel Circuit.

Analysis:

From Table 2 make the following graphs: on the first sheet of graph paper, plot current

I-versus-the number of resistors for both the series and parallel circuits. Use as much of the

paper as possible.

On the second sheet, graph the potential difference for the single resistor (R1) versus

the number of resistors for both the series and parallel circuits. Use the same arrangement of

axes as in the first graph.

Summarize the results of these two sets of graphs. In particular, what qualitative

statements can be made about the relationship between current and resistance in a series and a

parallel circuit? What about current and voltage? In both experiments, you increased the

number of resistors. Did both circuits respond in the same way? Discuss any differences.

Write your answer in the space provided of your answer sheet.

From Table 3, add the values of VR1+ VR2 + VR3 + VR4 and compare the results with

VR1+R2+R3+R4. Do the same thing for I1 + I2 + I3 + I4 and compare this value with the total

current leaving the battery which you have in Table 2.

Calculate the total resistance for the series connection.

Calculate the total resistance for the parallel connection.

Give the total power dissipated in the series circuit and in the parallel circuit.

QUESTIONS:

1. Following are a set of statements about series or parallel circuits. Using the information

from you data, indicate which statement applies to series and which statement applies to

parallel.

a) resistance is additive

b) the potential difference is numerically the same as the emf of the source (no matter

how many resistors)

c) as resistors are added the resistance of the circuit decreases

d) the sum of the potential differences of the resistors is equal to the emf of the source

e) as resistors are added the total current (through the source) increases.

2. How would you insert an ammeter into a circuit to measure current? How would you

insert a voltmeter into a circuit to measure potential difference?

3. When three cells are connected in series, one cell is accidentally connected with reversed

polarity. What is the effect on the total emf? On the total internal resistance?

45


EXPERIMENT 4

RESISTANCE AND POWER IN ELECTRICAL CIRCUITS

NAME: . . DATE: . .

SECTION: . .

* * *





46



No. of EMF (V)

Batteries SERIES PARALLEL

1

2

3


No. of SERIES PARALLEL

Resistors Potential Difference

Across R1

Current Potential Difference

Across R1

Current

1

2

3

4

TABLE 3: (5 points)

Potential Difference in Series Connection Current in Parallel Connection

VR1 VR2 VR3 VR4 VR1+R2+R3+R4 I1 I2 I3 I4 I1+2+3+4

TABLE 4: Resistors Values as Measured With the Ohmmeter. (5 points)

Measurements with R1 R2 R3 R4

OHMETER

COLOR CODES

Summary and Discussion of the two graphs: (5 points)

Resistors in Series Analysis: (5 points)

47

VR1+ VR2 + VR3 + VR4 =

Comparison between VR1+ VR2 + VR3 + VR4 and VR1+R2+R3+R4

Resistors in Parallel Analysis: (5 points)

I1 + I2 + I3 + I4 =

Comparison between I1 + I2 + I3 + I4 and the total current leaving the battery

Calculations of total resistance for series connection: (5 points)

Calculations of total resistance for parallel connection: (5 points)

48

4. CONCLUSIONS: (5 points)


49

GRAPH (10 points)

50

GRAPH (10 points)

51

EXPERIMENT 5

THE TEMPERATURE COEFFICIENT OF RESISTANCE WHEATSTONE

BRIDGE METHOD

INTRODUCTION:

The ohmic resistance of a given resistor varies with a change in its temperature. The

rate at which the resistance changes with temperature for a particular material is called the

temperature coefficient of resistance and is usually quite constant over a wide range of

temperature. Suppose we have a resistor which has a resistance R0 at a reference temperature

T0, and, when heated up to a temperature T it has a resistance RT. We define the temperature

coefficient of resistance for this resistor as follows:

α =−−

=R R

R T T

the slop of R versus T

R

T 0

0 0 0( )

Henceα , is the change in resistance per unit resistance per unit change of temperature

and has the units °C-1. (α copper = 3.93x10

-3/°C.)

Our goal in this laboratory exercise is to become familiar with the wheatstone bridge

as an instrument for measuring electrical resistance and to use the bridge method to determine

the temperature coefficient of resistance of a metallic conductor.

THEORY:

Experiment shows that in many instances, the current I flowing through a conductor is

directly proportional to the potential difference V across the conductor. We say that I is

proportional to V, or V = constant x I. The constant is given the symbol R and called the

resistance of the conductor. R is defined by R (ohms) = V/I.

Figure 1: General Method for Measuring I and V in a Circuit.

In the voltmeter-ammeter method, R is measured by using the circuit shown above,

reading V and I from meters and calculating R = V/I. Note that if the negative terminal of the

voltmeter is connected at point a, the voltmeter is measuring the potential difference across

the ammeter as well as R, and an error is introduced. On the other hand, if the volt-meter is

attached at a point b, the ammeter reads the current flow through the voltmeter as well as

through the resistance R, and again an error is introduced. These errors are inherent in the

voltmeter-ammeter approach, but do not occur when a bridge is used.

The most convenient and accurate method of measuring resistance of widely different

values is by means of the wheatstone bridge. The operation of a wheatstone bridge can be

52

explained as follows: an unknown resistance X, a variable but calibrated resistance R, and two

known resistance R1 and R2 are connected in a series-parallel combination across the battery

as shown.

Figure 2: General Diagram of a Wheatstone Bridge.

A galvanometer (with protective resistance, RG) is then bridged across the parallel

circuit. In general, point 2 and 3 in the circuit will be at different potentials, and a current will

flow through the galvanometer. Proper adjustments of R will reduce the galvanometer current

to zero-- hence the potentials to 2 and 3 must now be the same.

When the bridge is balanced, the potential difference across X must equal the potential

difference across R1. If we denote the current through R and X as I1 and the current through

the lower branch as I2, Ohm’s law tells us that

i X i R1 2 1= (1)

Similarly,

i R i R1 2 2= (2)

Dividing the second equation into the first results in the bridge relationship: X/R = R1/R2, or

X=R(R1/R2), from which X can be calculated.

XR R

R= 1

2

(3)

In the slide-wire from of the bridge, the resistance R1 and R2 are replaced by a uniform

wire AB with a sliding contact key at C. Since the wire is uniform, the resistance’s of the two

portions are proportional to the lengths; hence, the ratio R1/R2 is equal to the ratio AC/CB. If

R is a known resistance, and the unknown resistance is denoted by X, we have

X

R

AC

CB

LL

= = 1

2

(4)

From this, the value of X is easily calculated:

XR L

L= 1

2

(5)

53

This type of bridge is convenient since the length segments can be easily measured. The

resistance R1 and R2 of the length segments may be quite small relative to X and R because the

bridge formula depends only on the ratio of R1/R2 or L1/L2. It is this fact which allows us to

use a wire as one side of the bridge.

Figure 3: The Slide-Wire Wheatstone Bridge.

THE EXPERIMENT:

1. APPARATUS:

Your lab. station should be equipped with: galvanometer, variable resistance box, hot

plate, calorimeter vessel, test coil of wire, and thermometer.

The specimen to be used for the measurement of temperature coefficient of resistance

is a copper wire. It is wound on an insulated cylinder, within a thin brass tube filled with oil.

This tube is immersed in a calorimeter vessel containing water to which heat is applied.

2. PROCEDURE:

1. Hook up the slide-wire from of the bridge as shown above. For X, use the copper wire

filament immersed in the oil bath. The whole tube is than placed in a deionized water

bath. For RG, use the provided resistance, and use the decade resistance box for R. Before

closing any switches, have the circuit approved by your instructor.

2. Start with the contact key (C) in the middle of the slide wire, such that L1 is equal to L2.

Set R so that the galvanometer shows no deflection.

NOTE:

• Do not let the deflection of galvanometer go off scale. that will damage the

instrument.

• Do not slide the key along the wire while it is pressed down. This will scrape

the wire, causing it to become non-uniform

3. There should only be one point along the slide-wire at which the galvanometer shows no

deflection. This is called the balance point. Repeat step 3 until you are sure you’ve found

the balance point to within a millimeter or so.

54

4. Record the values of R, L1, L2, and the water bath temperature in your data table on the

worksheet of the write-up. DO NOT CHANGE THE VALUE OF R THROUGHOUT

THE REST OF THE EXPERIMENT.

5. Repeat the resistance measurement for at least 8 different temperatures between room

temperature and about 95 °C. Heat the water bath slowly, remove the heat source, and

wait at least 1 minutes for temperature equilibrium each time.

6. For each temperature, make sure that the galvanometer deflection stay within its permitted

scale and record values of R, L1, L2 and T.

Analysis of Results:

Plot a graph of resistance in ohms versus temperature. Start the temperature axis at

zero.

Extrapolate the curve to 0°C. Using the value of resistance at 0 °C as R0 , calculate

the temperature coefficient of resistance of the sample. Compare with the standard value

given in your experimental write-up. Show your work.

QUESTIONS:

1. Why, when constructing a bridge, it is important to use short, heavy wires for connecting

the resistance but not so important for connecting the galvanometer or battery?

NOTE: R LA∝

2. What is advantage of using a Wheatstone bridge for measuring resistance as opposed to

using a sensitive ammeter and voltmeter and applying Ohm’s law?

3. Could the method developed in the laboratory experiment be used to measure the

resistance of lamp filament in operation at high temperature? Explain.

55


EXPERIMENT 5

THE TEMPERATURE COEFFICIENT OF RESISTANCE

WHEATSTONE BRIDGE METHOD

NAME: . . DATE: . .

SECTION: . .

* * *





56



Temp (°C) R L1 L2 L1/L2 Unknown (X)

TEMPERATURE COEFFICIENT CALCULATION: (10 points)

% Error Calculation: (5 points)


57

QUESTIONS (10 points)

GRAPH: (25 points)

58

EXPERIMENT 06

MEASUREMENT OF CAPACITANCE BY THE BRIDGE METHOD

INTRODUCTION:

A capacitor consists of two conductors placed near each other but separated by an

insulating material. It may take numerous forms, for example, that of a conducting sphere on

an insulating stand placed in the middle of a room. The sphere is one conductor; the walls and

other objects in the room serve as the second. One of the most useful forms for a capacitor is

that of two large metal sheets, close together, and separated by a thin layer of paper, oil, or

other insulating material.

The most common application of capacitors is that of storing an electric charge.

Charges of equal magnitude and opposite sign placed on the two conductors forming the

capacitor will attract each other and remain in position for long periods of time or until the

two conductors are connected together via an external conducting path. Other applications of

capacitors are related with their properties in AC electrical circuits. Some of these will be

shown in this experiment and, together with other electrical elements, in the RCL circuit

experiment. Capacitors in electrical circuits are marked with symbol . Note that the

lengths of the two vertical lines are equal (in contrast of a battery symbol, where one of them

is shorter than the other).

In this experiment, the capacitance of capacitors and that various combinations of

capacitors will be measured in terms of capacitance of a standard capacitor and two known

resistance’s by the bridge method.

THEORY:

The capacitance of a capacitor is defined as the ratio of charge on one of the two

conductors to the potential difference measured between the two conductors. The unit of

capacitance is the farad.

Capaci ce farad C Q Vtan ( ) = = (1)

The farad is a very large unit of capacitance. In most practical circuits, we are

concerned with either microfarads (10-6 farad) or picofarads (10

-12 farad). The capacitance of

a capacitor depends upon its geometry, i.e., on the size and separation of its conductors and

the nature of the intervening insulating material.

When a capacitor is placed into a DC circuit the initial current gradually builds up

charges on the conducting plates and a corresponding potential difference (V) is built up

between them. When this potential (V) is equal to the voltage provided by the battery, the

process stops. In an AC circuit, the charge alternately builds up and discharges on the plates

so that there is an effective current in the circuit. A capacitor in AC circuits represents a

barrier of the current flow, similar to a resistor. This barrier, named impedance, (ZC) is

inversely proportional to the capacitance:

Zf C

C =1

2π (2)

where f is the frequency of the AC. This feature allows the measurement of capacitance in a

bridge circuit.

59

The measurement of the capacitance of capacitors and that various combinations of

capacitors by the bridge method is carried by using the connections as shown in Figure 1

which is the same as for the measurement of resistance with the Wheatstone bridge. A source

of audio-frequency alternating current is used as the source in place of the DC source. A

cathode ray oscilloscope is used as the detector in place of the galvanometer.

In the balanced condition (i.e., when the oscilloscope shows zero potential difference),

the voltages across the capacitor Cx and the resistance R2 must be equal. Call this voltage V.

We know from equation (1) and Ohm’s law that

V Q C and V IR= = 2 (3)

Similarly, the voltage across the capacitor C1 and the resistor R1 must be equal. We can call

this voltage V’.

V Q C and V I R' ' ' '= =1 1 (4)

Since the capacitors Cx and C1 are connected in series, Q’ = Q. Similarly, the current through

the resistor R1 and R2 must also be equal since they are connected in series (I’ = I).

Combining equations (3) and (4), we obtain

Q C IRx = 2 (5a)

Q C IR1 1= (5b)

Figure 1: Circuit For The Measurement of Capacitance by The Bridge Method.

60

These two equations can be combined to give the condition-of-balance relation between the

resistances and capacitances.

C C R Rx 1 1 2= (6)

Hence, if Cx is an unknown capacitance, and C1 is a standard capacitance, with known

resistances R1 and R2, the net value of unknown capacitance is given by

C C R RX = 1 1 2 (7)

CAPACITORS IN PARALLEL AND SERIES:

Capacitors may be used in combinations. When the capacitors are combined in

parallel arrangement (Figure 2a), the effective capacitance (Ceq) of the combination is

calculated by adding the capacitances of the individual capacitors, thus:

C C C Ceq n= + + +1 2 L (8)

C1

C2 C1 C2 Cn

Cn

(a) (b)

Figure 1: Parallel (a) and Series (b) Combinations of Capacitors.

In a series combination (Figure 1b) the effective capacitance (Ceq) is calculated by

adding the reciprocals of the individual capacitances, thus:

1 1 1 11 2/ / / /C C C Ceq n= + + +L (9)

THE EXPERIMENT:

1. APPARATUS:

The apparatus consists a known capacitor, unknown capacitors, a fixed resistance, a

variable resistance, a voltmeter, a function generator, and connection cables. All of these

parts should be available on your work banch.

2. PROCEDURE

1. Connect the apparatus as shown in Figure 1. Connect the elements of the bridge first; then

connect the oscillator and the voltmeter to the bridge. Use as C1 the standard capacitor.

R2 is fixed at 2000Ω. (This value seems to give good results, although it can in principle have any value.). Set R1 at zero.

2. Set the Oscillator (Function generator) frequency to 1000 Hz, and amplitude to 20 V on

the oscillator dial..

3. After your instructor has checked your circuit, you are in business.

61

4. Adjust the resistance of R1 until you get the minimum voltage . At this point, the bridge is

balanced. Record the value of R1, R2 and C1 and find the net capacitance, Cx, for C2 as Cx.

Repeat this procedure for C3 and C4.

5. Repeat to find the capacitance of C2 and C3 when they are connected in series. Again use

as C1 the standard capacitor, and use the same value of R2. Record the new value of R1 for

the position of balance.

6. Measure the capacitance of the combination of C2 and C3 in parallel. Use the same C1 and

R2 as before. Record the value of R1 for the position of balance.

7. Repeat steps 4 and 5 using all three capacitors (C1, C3, and C4).

8. Now connect C2 and C3 in series forming an effective capacitor as in step 5. To this

connect C4 in parallel and measure the net capacitance by finding the value of R1 that

balances the bridge.

9. Now connect C2 and C3 in parallel forming an effective capacitor as in step 6. To this

connect C4 in series and again measure the net capacitance.


Using the measured net Cx values for C2, C3, and C4, calculate the value of Cx for

capacitors in parallel and in series for the connections used in steps 6-10 and compare these

with the values that you measured. Show your work on the worksheet by drawing the circuit

diagrams for Cx and by writing out the algebraic expression for Cx. Put your results in the

table.

QUESTIONS

1. Given 3 capacitors, 0.25 µF, 0.5 µF, and 1.0 µF, how many different values of capacitance can be obtained using 1 or more capacitors and what are they?

2. How is the capacitance bridge balanced, and what are the expressions for the potential

differences across the circuit components in this condition?

3. Could this experiment be done using a DC power supply instead of an AC oscillator

source? Explain why or why not.

62


EXPERIMENT 6

MEASUREMENT OF CAPACITANCE BY THE BRIDGE METHOD

NAME: . . DATE: . .

SECTION: . .

* * *





63



Capacitors

Measured

R1

R2

Standard

C1

Net

Capacitance

Cx

Calculated

Value

for Cx

%

Differenc

e

C2

C3

C4

C2 and C3 in

Series

C2 and C3 in

parallel

C2, C3 and

C4 in Series

C2, C3 and

C4 in

Parallel

(C2 and C3

in Series)

with C4 in

Parallel

(C2 and C3

in Parallel)

with C4 in

Series

WORK SPACE: (use the back of the data table if needed) (10 points)

64



65

EXPERIMENT 07

INDUCTION AND LR CIRCUITS

INTRODUCTION:

The production of induced currents is one of the most important branches of the study

of electricity, since it forms one of the foundations of the electrical industry. The present

experiment deals with some of the fundamental principles involved.

In this experiment you will examine the phenomena of induction and Faraday’s Law;

and examine a simple LR circuit, and verify the time dependent behavior of the current and

the property of inductance.

THEORY:

INDUCTION

Michael Faraday and Joseph Henry are generally given credit for the discovery for the

Electromagnetic Induction. Faraday discovered that if there is a change in the magnetic flux

passing through a coil of wire, then a voltage (an emf) is induced in the wire. The idea is

pictured schematically below.

Figure 1: Induced emf.

Here a magnetic field B passes through a loop of wire of area A. The magnetic flux φ is thus φ = BA. If there is a change in the strength of the field (i.e. the flux φ changes) - due, for example, to a magnet being moved into or out of the loop - then an emf is induced in the loop.

The size of the emf, Ε, is dependent upon the rate at which the flux changes with respect to time, and can be calculated from Faraday’s Law which states:

ΕΦ

= −d

d t (1)

If there is more than one loop, then the total emf is just the sum of all the emfs induced in

each loop. Thus, for a coil consisting of N loops we have a total emf of

ΕΦ

= −

Nd

dt (2)

66

The SI unit of magnetic field is the Tesla (T); the SI unit of magnetic flux is the weber (W),

where 1 weber = 1 Tesla-square; the SI unit of emf is the volt (V).

INDUCTANCE AND LR CIRCUITS

In figure 1 magnetic field comes from an external source (e.g. a magnet). However,

the magnetic field does not need to come from an external source for Faraday’s law to work.

For Example, if you take a coil, as in Figure 2 below, and pass current I through that coil by

connecting it to a voltage source V, a magnetic field B will be induced inside the coil.

Figure 2: N Loops With a Current I Passing Through the Coil.

(This is the principle by which electromagnets work.) If now the voltage is varied (e.g. if it is

an AC source, or if it is suddenly switched off, or on) then the current subsequently the

magnetic field B will also change. This changing magnetic field itself produces its own emf

in the same circuit as the coil, according to Faraday’s Law (equation 2). The effect in which a

changing current in a circuit induces an emf in the same circuit is called self-induction. Since

the magnetic flux φ in the coil is proportional to the current I through the coil, we may write:

Nφ = LI (3)

where L is the constant of proportionality and is known as the self-inductance, or simply

inductance. The SI units of L are henries (H).

Rewriting equation 2 we now have:

Ε∆Φ∆

∆ Φ∆

∆∆

= − = − = −nt

n

t

LI

t

( ) ( )

or, simply:

Ε∆∆

= − LI

t (4)

which says that the induced emf, Ε, due to inductance L is proportional to the rate of change of current I through the circuit. Furthermore, from Lenz’s Law we know that the induced emf

opposes the voltage which induces it. (For this reason, the induced emf is sometimes called a

“back emf”.)

The coil of wire discussed above is known as an inductor. In addition to having the

property of inductance, an inductor also has resistance (since it is usually a long length of wire

wrapped into a coil). An inductor is thus described by its inductance L, and its resistance RL.

So, imagine applying a voltage V to an inductor in series with another resistor RR, as

shown in Figure 3 (an example of an “LR circuit”).

67

Figure 3: LR Circuit.

If the voltage V is steady (for example, from a battery) the maximum current Imax in the

circuit is given by Ohm’s Law, namely:

(5)

where RL + RR is the total resistance of the circuit. However, when we first connect the circuit

to the battery, i.e. when we close switch S, we find that the current takes some time to reach

this value because, according to Faraday’s law (equation (4)) a “back emf” is induced when

the voltage is suddenly changed.

In fact, the current changes exponentially with time according to:

(6)

which looks like Figure 4a

(a)

(b)

Figure 4: The change of Current in an Inductor As (a) The Switch is Closed, and (b) The

Switch is Opened.

Conversely, if the voltage is suddenly switched off, then the current exponentially

decays to zero according to:

I I e t= −max

τ (7)

which looks like figure 4b.

)1()1( max

)(

max

τtLrt eIeII −− −=−=

RL RR

VI

+=max

68

In the above equations, R is the total resistance of the circuit and is equal to RL+RR,

and τ is known as the time constant of the circuit. It is given by

τ = =+

L

R

L

R RL R

(8)

It is defined as the time taken for the current to rise (or fall) to 63% of its final value. (Note

Units: 1 Henry/ 1 ohm = 1 second)

The time taken t1/2 for VR to fall (or rise) to 50% (half) of its maximum value is related

to the time constant by:

t1 2 2 0 693/ ln( ) .= =τ τ (9)

THE EXPERIMENT :

1. APPARATUS

The apparatus consists of magnetic bars, an inductor L (Solenoid), a resistor RR, a

circuit board holder, a function generator, a computer operated in the oscilloscope mode, rods,

laboratory fingers and electrical cables. Identify these on your workbench.

2. PROCEDURE:

To start the computer operated in the oscilloscope mode, you need to:

• Turn the computer on.

• From the DOS (C:\>) prompt type WIN

• Get the Windows icons on the computer screen

• Double-click on the MPLI Program icon.

• Click on the OK button in the About box to continue.

• From the Menu Bar choose the File menu to open the VOLTS.EXP file.

• select the vertical axis by double clicking on the POTENTIAL label, then select

CHANNEL A (you should click on the box showing B so that the X sign does not appear

anymore, and do the same thing with the box for channel C).

• Connect the measuring probes to the solenoid as shown in Figure 5.

Now that the computer oscilloscope is set to record traces; follow these steps:

1. Take the air cooled solenoid and clamp it with the aid of the lab fingers to the rod as

shown in Figure 5

Input MPLI BOX Pulley Block

Lab. Table

Output Magnet

to The Computer

Solenoid Coil

Measuring Probes

Rod with Stand Laboratory Fingers

Figure 5: Experimental Set-Up for Faraday’s Law

69

2. Attach the magnets together with the string.

3. Attach one end of the string to the wooden block and pass the other end of the string

through the hole in the solenoid and over the pulley. Don’t let the block slide.

4. Experiment with adding different weights on the block and releasing it, thus letting the

magnet pass through the solenoid at different speeds.

5. Once the magnet starts moving, press the start button on the oscilloscope, so that you can

record the signature of the induced emf.

6. When you are satisfied with the results get two good traces at different magnet speeds and

save them under file names TRACE1.EXP and TRACE2.EXP

Now you have finished collecting the data for the first part of the laboratory, that is the

part that deals with Faraday’s law or the law of induction.

Next with the Function Generator DISCONNECTED from the circuit. Select the

square wave output; select 100 Hz; switch on an adjust the output to 5 V. Switch off the

Function Generator

Connect the LR circuit shown in Figure 6, using the 10Ω resistor and the provided inductor (solenoid). We will use the Function Generator as a voltage source. The square

wave output form the function generator will act as if we are switching a DC source on and

off in rapid succession. To Channel B

Inductor

Function

Resistor Generator

To Channel C

To Channel A

Figure 6: Experimental Set-Up For LR Circuit.

Connect banana plugs from the Channel B cable across the Inductor, Channel A across

the 10 Ω resistor, and Channel C across the voltage source (function generator). Select the Computer Oscilloscope Timing button and set the experiment length to 0.5 s

and the data collection rate to 25000 reads/s.

IF THE LAB. INSTRUCTOR HAS CHECKED YOUR CIRCUIT. Observe the

different wave you see for the different channels. You will need to adjust both the time scale

and the voltage scale in order to observe a nice clean signal. You do this by selecting the

maximum range on either axis and adjusting to the value you like to have for the maximum

range. If you have any trouble figuring this check with your lab instructor for help.

We wish to monitor the growth and decay to the current in the circuit as it responds to

the on-off voltage source. Since the current through the resistor I is related to the voltage VR

across the resistor by Ohm’s law (VR = I RR) then in order to monitor current I we just need to

monitor voltage VR. To do this we need to turn on Channel A alone (you should turn off

channels B and C).

Once you get a nice signal for channel A input, choose one wavelength and save it

under the file name LR1.EXP. Using the cursors on the screen measure the time constant τf for the falling part of the voltage across the resistor. Enter the value in your lab report.

70

According to the theory section the time constant for the rise τr or fall τf of the voltage across the resistor is given by equation (8), i.e.:

τ τ τf r L

R= = =

Thus, if we decrease the value of R, we increase the time constant. If you are given

three resistors of values 10 Ω, 33 Ω, and 100 Ω; how could you combine these 3 resistors to give the smallest value for the resistance RR? What is the value of this resistance? Enter the

value in your lab report.

Construct a circuit in which the resistance RR is used in place of the 10 Ω resistor and save the one wavelength trace of the voltage drop across this resistor under a file with name

LR2.EXP. Using the cursors on the screen measure the time constant τf for the falling part of the voltage across the resistor. Enter the value in your lab report.

You have one final task. To calculate the coils inductance you need to know the coil

resistance. Remove all leads from the circuit board and use the multimeter set to the

maximum range to measure the resistance of the coil. Switch off the multimeter and enter the

measured value in your lab report.


From the saved files get a hard copy of each trace and attach to your lab report.

Using File TRACE1.EXP, select the first peak area by dragging the mouse over it;

then go and click on the Integral button on the toolbar. This will allow you to integrate under

the first peak. Report the area value in Table 1 of your lab report. Do the same for the second

peak.

Repeat the same analysis as above for the TRACE2.EXP file. Report your results to

Table 1 of your lab report.

What physical quantity does the integrated area represent?

Explain the general shape of the curve trace in TRACE1.EXP and TRACE2.EXP.

Why are the two peaks in opposite directions (i.e. one positive, one negative)? Discuss in

terms of Faraday’s Law?

How did the speed with which the magnet passed through the coil affect the result?

From the LR1.EXP file (LR circuit with R = 10 Ω), estimate the following as best as you can and enter the values in Table 1 in your lab report.

1. The maximum value of VR.

2. The beginning times tr0 and t

f0 for the rise and fall of the voltage VR.

3. The times at half-maximum, tr1/2 and t

f1/2, for the rise and fall of VR.

4. The time constant τr and τf, for the rise and fall of VR.

Compare the two time constants τf measured for the falling part of the voltage -one using the 10 Ω resistor and one using the combined resistor. Using Equation (8) find the value of the coil inductance, for the two cases of

resistance. Find the percent difference between the calculated inductance from the two

resistance’s’ values.

71

QUESTIONS:

1. If you reverse the polarity of the magnet in the Faraday’s Law experiment; would the shape

of the trace change? Explain.

2. Are the two areas of the peaks in the Faraday’s Law experiment always the same? Suggest

reasons for why they may be different (if so)?

3. In the LR experiment give a description of what is causing the observed rise and fall of the

voltage across R.

72


EXPERIMENT 07

INDUCTION AND LR CIRCUITS

NAME: . . DATE: . .

SECTION: . .

* * *





73


Computer traces of TRACE1.EXP and TRACE2.EXP (5 points) -Attach to report-

TABLE 1: Integrated Areas of the Computer Traces (5 points)

TRACE1.EXP TRACE2.EXP

FIRST PEAK AREA

SECOND PEAK AREA

Physical quantity represented by the peaks area: (5 points)

General shape of the TRACE1.EXP and TRACE2.EXP curves and analysis: (5 points)

Effect of the magnet speed on the results of TRACE1.EXP and TRACE2.EXP; (5 points)

74

Computer Traces for LR1.EXP and LR2.EXP (10 points) -Attach to report-

Lowest combined value of the 3 resistances (5 points)

Time constants (5 points) τf with 10 Ω resistor

τf with combined resistors

Resistance of coil: (5 points)


Maximum voltage, VR.

The beginning time (rise), tr0

The beginning time (fall), tf0

The time at half-maximum (rise), tr1/2

The time at half-maximum (fall), tf1/2

The time constant (rise), τr

The time constant (fall), τf

Comparison between the values of τf using the 10 Ω resistor and combined resistors:(5 points)

Calculation of the coil’s inductance: (5 points)

with the 10 Ω resistor L =

with the combined resistors L =

Comparison between the calculated values of L: (5 points)

75



76

EXPERIMENT 08

RCL CIRCUITS

INTRODUCTION:

In this experiment, we will learn some of basic properties of alternating current

circuits.

BACKGROUND

In a direct current (dc) circuit, the electrons always move in the same direction.

Moreover, the emfs and the potential differences are the same value at all times. There are,

however, emfs which vary sinusoidally in time. In fact, the most common source of current, a

wall socket, provides a sinusoidal emf with a frequency of 50 Hz (50 cycles/ second) and an

amplitude of 220 volts. In general, an alternating emf can be written as follows:

E t V f tab ( ) sin( )= −0 02π θ (1a)

or alternatively,

E t V tab ( ) sin( )= −0 0ω θ (1b)

In the above, V0 is called the amplitude (the maximum value of Eab), φ ω θ( )t t= − 0 is

called the time dependent phase angle, or simply the phase, f is the frequency measured in

hertz (Hz), or cycles per second, ω π( )≡ 2 f is the angular frequency in radians per second, and

θ 0 is the phase shift. A sketch of Eab(t) versus ω is given below. We shall use radians for

angular measure ( , , , ).902180 270 3 2 360 20 0 0 0= = = =π π π π

Remember that Eab(t) is a measure of the potential at point a minus the potential at point

b as a function of time. Suppose, for example, that θ 0 0= . When t = (1/4)f, Eab = V0, and

when t = (3/4)f, Eab = -V0. At the earlier time, the potential at a is higher than b, while at the

later time, b is at higher potential than a.

Since the imposed emf varies sinusoidally with frequency f, it is not surprising that the

potential differences across the circuit elements as well as the current also oscillate

sinusoidally at the same frequency. This is called an alternating current (AC) circuit.

Describing the potential difference across the elements of an AC circuit is more complex than

the steady state DC circuit. These potential differences are oscillating at the same frequency

as the imposed emf. However, they are not generally in phase with the emf. Phasor diagrams,

77

discussed in your text, are a convenient way to represent these oscillating voltages and

currents.

A phasor is a vector whose tail is at the origin. Its length, or amplitude, represents the

maximum value of the voltage across (or current through) a circuit element. The direction of

the phasor represents the phase. For this reason, a phasor is through of as rotating

counterclockwise about the origin at the same frequency as the voltage applied to the circuit.

The projection of the phasor along the y axis gives you the instantaneous value of the voltage

(or current) of the circuit element. For example, in the figure of a phasor diagram on the next

page, we see the projection of the current I on the y-axis. We could do the same for all the

other phasor in the diagram to find their instantaneous values. Since all the phasors drawn for

a single circuit will rotate at the same frequency f, the angle between the phasors will always

remain constant as they rotate.

There are three basic circuit elements: resistors, capacitors and inductors. We need to

know how to draw phasors for the voltage across each of these elements. The amplitude of

the voltage phasor is found by using the equation V = IZ, where V and I are the voltage and

the current, and Z is a quantity called impedance, which acts much like the resistance in a DC

circuit. The impedance of a resistor (ZR) is, in fact, just the resistance R. The impedance of a

capacitor (ZC) or an inductor (ZL) is slightly more complicated. Using V = IZ, we can find the

amplitude of the voltage phasor for a resistor (VR), capacitor (Vc) or inductor (VL):

V IZ I R

V I Z I c

V I Z I L

R R

c C

L L

= == == =

( )

( )

1 ωω

(2)

Note that the amplitude of VC and VL depend on ω as well as C and L. Since phasors are vectors, we also need to know their direction. We know, of course,

that they all rotate with frequency f. We are interested in the angles between the phasors. In a

series circuit, the direction of the phasor VR is always the same as that of the phasor

representing the current in the circuit. This means that the current across a resistor is always

in phase with the voltage across it. The direction of the phasor VC is always 90° less than that

of the current. This means that the voltage across a capacitor lags the current by 90°. The

direction of VL is always 90° greater than that of the current. This means that the voltage

across an inductor leads the current by 90°.

An example of a phasor diagram for an RCL circuit is

Shown at right. Kirchhoff’s laws tell us that the sum of the

voltage s around loop must be zero. This holds true even in an

ac circuit, where the voltage are changing with time. If we call

the voltage that drives the circuit Eab, then

E V V Vab R C L= + + (3)

This means that Eab is the vector sum of the phasors VR, VC, and VL.

This is shown in the figure at right.

We have seen that phasors add like vectors. Thus, we can use the

law of cosines to fined the amplitude of the sum; of two phasors of

arbitrary direction V1 and V2:

V V V V V COStot

2

1

2

2

2

1 22= + + θ (4)

78

where Vtot is the amplitude of the sum of the phasors V1 and V2 and θ is the angle between the two phasors. You will use Equation (4) in this experiment to add phasors.

EXPERIMENT:

1. APPARATUS:

The RLC circuit consists of a resistance, a capacitor, an inductance, a function

generator, and an oscilloscope. All of these components should be provided in your work

station.

2. PROCEDURE

I. RC Circuit

Note that it is very important that both black terminals be connected to a common point since

each is grounded inside the oscilloscope.

This presents no problem since it is only potential differences being measured. On the other

hand, if the black terminals were connected at two different points in the circuit, then in fact

all points between them, including the circuit elements, would be maintained at ground

potential contrary to our intentions.

CH1 now monitors VR and CH2 monitors V0. The mode switch should be set to BOTH

and the scale dials set on 2 volts/div. Set the oscillator frequency at f = 4000 Hz and adjust its

output to that the amplitude V0 = 6 volts (or 12 V peak to peak). V0 will have to be set to 6

volts at each frequency. Also make sure the calibration knobs are set all the way clockwise so

that the scaling (fudge) factor is 1.0. Change the MODE switch to CH1, and measure and

record the value of VR in table 1. Change the MODE to CH2, and measure and record the

value of V0 in table 1. To measure θ θR − 0 , change the MODE to BOTH. Put trigger to

CH2. Adjust the sweep time so that two or three cycles at most appear on the screen. By

using the cursor find the wavelengthλ and then find the number X (time per division) between corresponding phase (e.g. ϕ = 0) on the V0 and VR traces. The final result is

( ) ( deg )X

in reesRλθ θ360 0°= −

where X and λ are the distances shown in the figure.

determine θ θ0 − C

Now, switch the leads connecting the RC

components to the function generator, so that the

capacitor is connected to the negative terminal of the

genrator and the resistor is connected to the positive

terminal. Folowing the same procedures,

Connect the two terminals of the audio oscillator

across the RC pair as Shown in the figure. Connect

the oscilloscope as follows: CH1 across the resistor

and CH2 across the function generator as shown.

79

Determine the algebraic sign of θR - θC : Make sure you know which trace is VC and which is

VR. Simply use the ground switch at the input terminals to eliminate one of traces. Thereby

establishing the identity of the two. If VR is leading VC then the sign is (+).

Now repeat the procedures outlined above by seeping the frequency range from 4000 Hz

to 11,500 Hz in increments of 1500 Hz, each time adjusting V0 to 6 volts. Again record the

results in table 1 on the worksheet.

RC CIRCUIT CALCULATIONS

From equation (2), one can show that the impedance

Z V V Rc C R= ( ) .

1. Compute ZC in units or the resistance R for the various frequencies and record the results

in table 1 on the worksheet. Draw a graph of ZC as a function of f. Does equation (2)

predict the trend of your graph of ZC?

2. Add the two phasors VR and VC to compute V0 (Use equation (4))

3. Compare this with the measured value of V0 at 4000 Hz and 10,000 Hz.

4. Calculate percent difference.

5. Discus this in the space below Table 1 on the worksheet.

II. RCL Circuit; Resonance

Connect the audio oscillator across RCL. Monitor Vac(t) on CH1 and Vab(t) on CH2 by

connecting the circuit as shown in the figure below.

By varying the frequecy continuously starting from 1000 Hz, find the resonance frequency and

compare it to the its theoretical counterpart.

At the resonance frequency f0 02= πω , the impedance Z R( )ω 0 = . Consequently,

VR=V and θ R =0. Also, ZC=ZL. Place your value for f0 in the space provided on the

worksheet.

QUESTIONS

(1) What is the impedance of an inductor when we approaches 0 (i.e., a dc circuit)? Explain

why your answer is reasonable. (HINT: Look at Equation 2 and your graph of ZL.)

(2) What is he impedance of a capacitor when we approaches 0? Explain why your answer is

reasonable. (HINT: Look at Equation 2 and your graph of ZC.

80


EXPERIMENT 08

RCL CIRCUITS

NAME: . . DATE: . .

SECTION: . .

* * *





81


TABLE 1 (30 points)

f V0 VR VC θ θR − 0 .

(degrees)

θ θ0 − C .

(degrees)

θ θR C− .

(degrees)

ZC

4000

5500

7000

8500

10000

11500

Comparison (10 points)

82

The resonance frequency (20 points)

(f0)experimental = Hz as found when θ R

Theoritical resonance frequency

(f0 )Theoritical= Hz

Comparison between the (f0)experimental and (f0 )Theoritical (10 points)



83

GRAPHS: (10 points)

84

EXPERIMENT 09

OBSERVATION OF SPECTRA

INTRODUCTION:

In physics, as in very other area of study, one of the most valuable questions a student

can learn to ask is, “How do they know that?” Thus, when you read that Wolf-457 has a

density of 20.000 tons/in3, or the universe is 18 billion years old, or that a gravitational black

hole has been observed, you should always stop to ask the question, “How?”

Practically everything we know about universe beyond the earth results from an

analysis of the spectrum of the light coming to us. Likewise, the spectrometer is one of the

most powerful instruments available to the scientist and engineer in studding laboratory

phenomena.

THEORY:

Two instruments are available for the purpose of forming a spectrum of visible light.

The first, a prism spectrometer, consists of (1) a collimator which forms a parallel beam of the

light radiated from a source, (2) a prism which uses the phenomenon of refraction to separate

the light into its various components (colors), and (3) a telescope to enhance viewing of the

spectrum.

Figure 1: Prism - Spectroscope

The second device is similar to the prism spectroscope except that a grating replaces the prism

and produces a spectrum through the phenomenon of diffraction.

The two general classes of spectra are emission (a series of bright lines or bands of

color against a dark background) and absorption (a series of dark lines or bands against a

bright background) spectra. There are three types of emission spectra: continuous, bright line,

and band spectra. Continuous spectra, looking like a cross section of the rainbow, are usually

produced by incandescent solids and liquids. Generally, bright line spectra are atomic spectra

produced by incandescent gases and vapors as electrons make downward transitions from

higher, more energetic orbits to the ground state. Band spectra ordinarily have an origin

which may be traced to molecular effects. An absorption spectrum is just what its name

implies -- a spectrum in which some parts are missing are due to part of the light energy

having been absorbed by passage through an absorbing medium. It may be of the dark band

or the dark line type. The light filters used in photography produce absorption bands. Almost

every liquid has an absorption band somewhere within the spectrum of visible light. The

Fraunhofer lines of the sun’s spectrum are the most noted example of dark line spectrum.

85

THE EXPERIMENT:

1. APPARATUS:

In this experiment you will use a Spectroscope (a replica diffraction grating) to

observe the spectrum of the different discharge tubes. The tubes are powered with a high

power voltage supply. All of these components are provided in your laboratory station.

2. PROCEDURE:

2.1 The Dispersion Curve

Dispersion is the process of separating light into various wavelengths. This is done,

primarily, with the use of a prism or grating. In the case of a prism, the light is divided

according to its wave lengths because the glass has a different index of refraction for each

color, the index becoming larger as the wavelength gets smaller. This means that when light

passes through a prism, the red end of the spectrum is refracted less than the blue end of the

spectrum. If one plots a curve showing the amount of deviation for each wavelength of light,

he will obtain a dispersion curve for that particular instrument. Having plotted such a curve, it

may be used to determine unknown wavelengths when their deviations are measured. Each

curve is characteristic of the instrument for which it was drawn and cannot be used for any

other instrument. The accuracy with which unknown wavelengths can be determined depends

largely on the instrument for which the dispersion curve is drawn. Your dispersion curve will

be quite crude. It will be only a few inches in length. Accurate curves, sometimes several feet

in length, are useful in rapid spectrum analysis.

Illuminate the slit of the spectroscope with the provided spectrum tube light. The tube

containing the scale should be pointed toward a window or an artificial light. IT SHOULD

BE UNNECESSARY TO DISTURB THIS TUBE. Looking into the telescope, focus it until a

clear image of the slit is seen. IF THE SCALE IS NOT VISIBLE AT THIS TIME, HAVE

AN INSTRUCTOR MAKE PROPER ADJUSTMENT FOR YOU. Focus the telescope until

the yellow doublet is quite distinct. Read and record the positions of these two lines on the

scale. Do likewise for other lines listed on the card at your lab station. Replace the mercury

lamp with the other tube provided by your instructor and take the scale readings of the spectral

lines listed on the card. Record the scale reading for three or four other lines not listed.

Go to the bulletin board and study the chart of spectra posted there-- this will aid you in

identifying the mercury lines.

Use the space provided on the worksheet to record the information requested.

Use the graph paper on the worksheet to plot wavelength versus your scale reading; i.e., make

a singe dispersion curve using the provided tubes spectra.

(b) OBSERVATION OF SPECTRA

For the remainder of this experiment you are to observe and chart the spectra of various

sources on the worksheet. Each chart should be one cm high and each division on the

horizontal scale is to represent one of the numbered units on the scale of the spectroscope.

Place the wavelength in Angstrom units at the top of the charts. Use the colored pencils

provided and see that they are returned at the end of the period.

86

CAUTION: You can get a nasty shock from the high voltage required to excite the spectral

tubes. BE SURE ALL POWER IS OFF BEFORE HANDLING TUBES IN ANY WAY.

QUESTIONS:

1. The Doppler effect in sound manifests as a rise or fall in pitch (i.e., an increase or decrease

in frequency) as a sound source approaches or recedes from an observer. How could be

Doppler effect be observed in the light from a star and what kind of information can be gained

from a study of the effect?

2. Fraunhofer lines are dark lines on the continuous spectrum of the sun. What is the origin

of these lines? How might one determine something about the atmosphere of the Mars by

observing sunlight reflected from the planet?

3. A board beam of light from a sodium vapor lamp flame of a Bunsen burner. A small

screen is placed on the other side of the burner. Salt is sprinkled into the flame and brilliant

yellow light is observed. What is the origin of this light? When salt is sprinkled into the

flame, a shadow of the flame appears on the screen. In the absence of salt, no shadow is seen.

Explain.

87


EXPERIMENT 09

OBSERVATION OF SPECTRA

NAME: . . DATE: . .

SECTION: . .

* * *





88



SPECTRAL LINES OF: SPECTRAL LINES OF:

wavelength scale reading wavelength scale reading

GRAPH (25 points)

SPECTRA (25 points)

89

SPECTRUM OF:

SPECTRUM OF:

SPECTRUM OF:

SPECTRUM OF:

SPECTRUM OF:

SPECTRUM OF:

SPECTRUM OF:


90


91

92

EXPERIMENT 10

PRECISE MEASUREMENT OF THE INDEX OF REFRACTION

INTRODUCTION

When light passes from one transparent medium to another, it usually changes

direction at the surface separating the two media. This change in direction is due to the fact

the velocity of light is greater in one medium than in the other. The degree of binding

depends upon the ratio of these velocities. This ratio is known as the index of refraction of

one medium relative to another. Thus, the index of refraction of glass relative to air is

understood to mean the velocity of light in air divided by the velocity of light in glass. In

mathematical symbols, n = c/v.

In this experiment we will measure the index of refraction of a glass prism by using

the spectrometer.

THEORY:

In Figure 1, a-b is a beam of light of small width passing through air and falling upon a

glass prism at b. Because light travels more slowly in glass than in air, the lower part of the

beam falls behind as it enters the glass. This results in the deviation of the beam from its

original direction to the direction b-c. The amount of deviation will depend upon the ratio of

velocities; i.e., upon the index of refraction of the glass. In fact, your textbook shows that the

index of refraction n is: n = sin i/sin r, where i and r are the angles shown in Figure 1. When

the beam of light passes out of the prism at c, its direction is changed again for the same

reason as at b.

Figure 1: A Ray of Light Passing From Air Through Glass and Back to Air.

Thus, passage through the prism causes the beam to deviate from its original direction

by an angle ∠dod’. This angle is known as the angle of deviation. Its magnitude (for a given prism) depends only on angle i and wavelength of the light used. It has a minimum value for

a certain value of I and particular wavelength of light. The definite relationship between the

prism angle A, the angle of minimum deviation D, and the index of refraction n is

[ ]

nA D

A=

+sin ( ) /

sin( / )

2

2 (1)

93

Since A and D can readily be measured experimentally, this relationship provides an easy and

accurate method for measuring the index of refraction of the glass which forms the prism.

This is the method to be used in the experiment.

THE EXPERIMENT:

1. APPARATUS:

The experimental set-up is composed of a discharge tube with its high voltage power

supply, a Griffin spectrometer, and a glass prism. All of these parts are provided in your lab

station. BE GENTLE WITH THIS EQUIPMENT.

READ THIS PART BEFORE TOUCHING THE EQUIPMENT

1.1 The Spectrometer:

A spectrometer is a delicate and expensive instrument. Considerable care should be

exercised when using it. Many adjustments should never be attempted by the student. An

experienced instructor should be called when something needs to be done you are not given

authority to do. In order that the student may safely carry out the necessary adjustments

for performance of experiments, careful study of the instrument should be made. The

picture in Figure 2 will aid you in doing this.

Figure 2: Griffin Spectrometer.

The chief parts of the spectrometer are collimator, the vernier scale, the telescope, and

the prism of grating. Identify each in the picture. Also, identify each means of adjustment

and practice doing these adjustments on the instrument.

Remember all parts are delicate. In tightening the screws only sufficient pressure

(usually quite small) should be applied to accomplish the purpose. A gentle twist will suffice.

The slit never should be opened more than a millimeter. In fact, this is far more than is

necessary.

The spectrometers you will use in this laboratory have a divided circle on which the

smallest divisions are 30’. Study the vernier carefully and you will be correct to less than five

minutes. This requires much care.

The prism or grating should not be moved from its position on the prism table without

the consent and supervision of an instructor.

Note that the eyepiece of the telescope is arranged to slide in or out of the telescope

tube. Such motion permits one to focus on the cross-hairs in the telescope tube just in front of

94

the eyepiece. This should be done before the telescope focusing screw is used to focus on the

slit. No attempt by the student should be made to adjust the length of the collimator tube.

The same precaution should be observed relative to the leveling screws for the prism table and

for the alignment screws for the telescope and collimator.

A careful study of the spectrometer is recommended before any experiment is started.

2. PROCEDURE

Begin by reading the NOTE ON THE SPECTROMETER. Equation 1 indicates that

only two angles need to be measured to determine the index of refraction of the glass. Angle

A is independent of the kind of light used. Since angle D depends upon the index of refraction

of the glass, it will have different values for different wavelengths of light. Angle D will be

measured and n is determined for red light (wavelength will be given by your instructor) and

for a blue light.

Start by adjusting the telescope. Slide the eyepiece in or out to obtain a clear image of

the cross-wires. If necessary rotate the eyepiece so that one sire is vertical. Direct the

telescope at a distant object and adjust the focus control to give a clear image which has no

parallax with respect to the cross-wires if your eye is moved slowly form side to side. When

this is done the telescope will be adjusted to receive parallel light and produce an image in the

plane of the cross-wires. The telescope adjustments should not be touched during the

experiment.

PART I: Measurement of the Prism Angle.

C

a a’ Figure 3: Measurement of the Prism Angle, A

b b’

A

c 2A c’

T T’

To measure A, rotate the prism table so that the angle A of the prism is pointed in the

direction of the collimator lens C as shown in Figure 3. With the provided lamp in front of

the slide and the slit open never more than one millimeter, the beam falling on the prism will

be sufficiently wide so that part will be reflected along b-c and part along b’-c’. Move the

telescope to the position T so the b-c beam will produce an image of the slit in the eyepiece.

You may have to move your prism slightly to see the image reflected off of both sides of the

prism. Narrow the slit so that its image in the eyepiece in the center of the slit image. Read

the angle from the vernier, and record it.

Rotate the telescope to position T’ where it intercepts the ray b’-c’, and repeat these

observations. The difference in the readings vernier A will be the angle through which the

telescope was rotated. A little plane geometry will prove to you that half the angle through

which the telescope rotates is the value of angle A.

Measure angle A. Show your vernier readings and the result in some systematic way in

the space provided on the worksheet.

PART II Measurement of the Index of Refraction, n:

95

In this task you will be working with the lamp provided in your work banch, this lamp

might emit strongly in the UV. Do not look directly into the lamp and keep hands away.

Start the discharge tube by turning on high power supply switch. With the source in

front of the slit, rotate the telescope so that it is parallel with o-d’ when the collimator is

parallel with a-b (References are to Figure 1). Set the cross-hairs on the slit image ( enough

light will pass over the prism to permit this), and read a vernier. This specifies the direction

of the ray before entering the prism and is used as a reference point. Rotate the telescope

about 52° toward the o-d. While looking into the telescope and observing the right hand side

spectrum of the prism (b’c’), rotate the prism table (letting the prism rotate with it).

Eventually, the red line will appear from the left in the field of the eyepiece. Soon the line

will cease going to the right and start toward the left. At the instant this line starts back

toward the left, stop the prism table and gently clamp it into place. The prism is now set for

the angle of minimum deviation for that particular wavelength. Set the cross-hairs on this red

line and read a vernier. The difference between your two measurement is the angle D.

Record D for this wavelength, and calculate the corresponding value of the index of

refraction of the glass. Note that it will be necessary to use a minimum of four significant

figures throughout the calculation. Show your work in some systematic manner on the

worksheet.

Rotate the telescope to the left until you find the blue line. Find and measure the angle

of minimum deviation for this line and calculate n as you did for the red line.

QUESTIONS:

1. Suppose you were called upon to measure n for a liquid. How might you proceed?

2. Prove the statement in Part I that angle A is just one-half of the angle through which the

telescope was rotated.

3. Which color of light is deviated most (or least) in passing through the prism? Which color

has the greatest (and least) speed in glass? What is the speed of 4047Å light in glass?

4. Would it be a correct statement to say “light slows down when it enters a material with a

greater index of refraction”? Explain.

96


EXPERIMENT 10

PRECISE MEASUREMENT OF THE INDEX OF REFRACTION

NAME: . . DATE: . .

SECTION: . .

* * *





97


PART I: Measurement of Angle A (25 points)

PART II Measurement of minimum deviation angles for both wavelengths (25 points)

98

Calculation of indices of refraction for both wavelengths (25 points)

99



100

EXPERIMENT 11

THE SIMPLE LENS

INTRODUCTION

A lens is an optical system formed by two or more refracting surfaces. Examples of

simple lens systems are eyeglasses, magnifying glasses, and telescopes. These simple systems

may comprise either converging or diverging lenses or a combination of both. A lens is said

to be converging (positive) if the rays from an infinitely placed object converge after passing

through the lens. Conversely, in the case of a diverging (negative) lens, the rays diverge after

passing through the lens.

THEORY:

A converging lens is thicker at the center than the periphery, and the incident parallel

rays converge to form a real image on the opposite side of the lens from the object, Figure 1.

A diverging lens is thinner at the center than at the periphery, and the incident parallel rays

diverge to form a virtual image on the same side of the lens as the object, Figure 2.

The principle axis of a lens is a line through the center of the lens, perpendicular to

both faces. The focal point of a lens is that point on the principal axis through which the

incident rays parallel to the principal axis pass ( for a converging lens) or appear to originate

(for a diverging lens) when refracted by the lens.

focal point focal point

Principal

Axis

f (+) f (-)

Figure 1: Converging Lens. Figure 2: Diverging Lens

The lens formula,

1 1 1p q f+ = (1)

gives the relation between the object distance p, the image distance q and the focal length f

(see Figure 3). The lens should be placed with rays from the object incident on the lens from

the left, and the object distance is considered positive. When the image is to the right of the

lens, the image distance is positive; if the image is to the left, the image distance is negative.

A positive value of q indicates a real image, and a negative value of q indicates a virtual

image.

To find the focal length of a thin lens, it is only necessary to measure p and q by some

method. In the special case of Figures 1 and 2, p is very large and 1/p is approximately equal

to zero; therefore, f = q.

101

Image

Object Object

Image

F1 F2 F2 F1

f (+) f (+) q

f (+) f (-)

p (+) q(+) p (+)

(a) (b)

Figure 3: Object, Image, and Focal Length for Lenses: a) Converging, b) Diverging.

When two thin lenses are placed in contact, the combined focal length f can be

expressed as,

1 1 11 2f f f= + (2)

where f1 and f2 are the focal length of the respective lenses. If one of the lenses is diverging,

the negative value of f must be used for that lens. The magnification m produced by a lens is

given by

m = q/p (3)

The above formulae are valid for all thin lenses. Remember, from your textbook the

image is either larger than or smaller than the object, it is either real or virtual, and it is either

upright or inverted.

THE EXPERIMENT:

1. APPARATUS:

Thin converging and diverging lenses with their lens stands will be used on the

laboratory optical bench in order to find the real image of a lamps. In your laboratory station

you should find the above mentioned equipment in addition to a DC power supply and

electrical cables.

2. PROCEDURE:

2.1 Lens A

1. Call the thinner of the converging lenses lens A. Measure its focal length by arranging the

apparatus to yield a real image of a very distant object on the screen.

2. Mount the illuminated object, lens A, and the screen on the bench so that a real, inverted,

reduced image is formed on the screen. Measure the image and object distances as well as

the image and the object heights. Compute the focal length of lens A using equation 1.

Compare the measured magnification with the prediction of equation 3.

3. Keep the object and screen fixed and move the lens to produce an enlarged image. Repeat

the measurement of step 2.

2.2 Lens B

102

1. Call the thicker of the converging lenses lens B. Measure its focal length by arranging the

apparatus to yield a real image of a very distant object on the screen.

2. Mount the illuminated object, lens B, and the screen on the bench so that a real, inverted,

reduced image is formed on the screen. Measure the image and object distances as well as

the image and the object heights. Compute the focal length of lens B using equation 1.

Compare the measured magnification with the prediction of equation 3.

2.3 Lens C

The diverging lens must be treated a little differently since it is not possible to obtain a

real image on a screen using a single diverging lens alone. Call the diverging lens lens C.

Use lenses B (the thicker of the converging lenses) and C together. Mount them in contact

with one another, keeping a distance between them and repeat the procedures (1) and (1).

QUESTIONS:

1. By the aid of a ray diagram explain the operation of a simple magnifier.

2. Draw a graph to show the variation of 1/p with 1/q for a converging lens. What is the

significance of the horizontal and vertical intercepts of this curve?

103


EXPERIMENT 11

THE SIMPLE LENS

NAME: . . DATE: . .

SECTION: . .

* * *





104


Lens A (20 points)

1) f = . cm

2) p = . cm

q = . cm

f = . cm

Object height = . cm

Image height = . cm

Magnification = .

Calculated Mag. = .

Percent difference = .

3) p = . cm

q = . cm

f = . cm


Image height = . cm

Magnification = .

Calculated Mag. = .


Lens B (20 points)

1) f = . cm

2) p = . cm

q = . cm

f = . cm


Image height = . cm

105

Magnification = .

Calculated Mag. = .


Lens C (20 points)

1) Combination f = . cm

Lens C f = . cm

2) p = . cm

q = . cm

Combination f = . cm

Lens C f = . cm


Image height = . cm

Magnification = .

Calculated Mag. = .


Telescope (20 points)

a) Make a sketch of your telescope showing the lenses, the distance between them, and

the positions of the object and the observer. Discuss the details of the image you observed.

b) Calculate the magnification using Equation.(4). Does this magnification agree with what

you see in your telescope? Describe how you determine the magnification experimentally.

106



107

EXPERIMENT 12

THE WAVELENGTH OF LIGHT; THE DIFFRACTION GRATING

INTRODUCTION:

One of the most fascinating chapters in the history of physics has been the search for

an understanding of the “true nature of light.” The search to discover whether light is a

particle or a wave, which extended over three centuries, has been in large part abandoned-- not

because the answer is known, but rather because most physicist now agree that the question is

meaningless. In this experiment you will observe the formation of spectra by a diffraction

grating-- an experiment which was once considered positive evidence that light is a wave.

THEORY:

A grating consists essentially of a large number of fine, evenly spaced, parallel slits.

There are two types, transmission gratings and reflection gratings. In the former type, used in

this experiment, lines are ruled on glass, the unruled portions acting as slits; in the latter type,

lines are ruled on a polished metal surface and the incident light is reflected from unruled

portions, effecting by reflection the same results as is secured by transmission in the other

type. Gratings are usually ruled with from 10,000 to 20,000 lines to an inch.

Consider a parallel beam of monochromatic light falling on the grating from the left.

Huygen’s principle asserts that each of the grating slits can be considered a new source of

light as shown by the wavelets to the right of the grating in Figure 1. A new wave front is

constructed by drawing the envelope that connects these wavelets. This new wavefront

propagates directly ahead ( as shown by the dotted waves and rays) and is brought to a focus

by the telescope at C. This is called the central image of the grating.

However, other wavefronts can also be constructed from the original Huygen’s

wavelets. One such set is shown by the solid waves and rays in the region to the right of the

grating. This set of waves will be focused by the telescope to a point displaced from C, the

angular position being given by,

sinθ λ= d (1)

108

where d is the distance between adjustment slits in the grating (called the grating constant),

and λ is the wavelength of light used. Since λ varies of different colors of light, a spectrum is formed in this region.

Other wavefronts can be constructed by choosing every second (or third) wavelet from

adjacent slits, so that the general form of equation (1) is

n λ = d sinθ (2)

where n is called the order number.

The angle between the ray emerging from the grating and the ray incident up on the

grating is called the angle of deviation. The value of this angle depends, among other things,

upon the angle of incidence. If the angle of incidence is zero degrees, that is, if the grating is

normal to the ray of light, equation (2) applies.

There is a certain angle of incidence, however, for which the deviation produced has a

minimum value. When this condition exits, the grating is said to be in a position of minimum

deviation. Measurements of wavelength are somewhat simplified by using the grating in this

position. When so used, the wavelength is given by the relation

n λ = 2 d sin(D/2) (3)

where all quantities have the same meaning as before and D is the minimum value of the

deviation.

THE EXPERIMENT:

1. APPARATUS:

The experimental apparatus consists of: a discharge tube with its high voltage power

supply, a spectrometer, and a diffraction grating (600 lines/mm). All of these parts are

provided in your laboratory station.

2. PROCEDURE:

CAUTION: Be sure not to touch the grating surface.

Study the spectrometer and follow the instruction described in the previous experiment

for the measurement of the index of refraction. Locate the collimator, the telescope, the

grating table, and the slit, as well as the set and slow motion screws for each. Place the

telescope and the collimator approximately in line. Be sure you know how to read the scales.

The main scale is graduated in degrees and half degrees, and the vernier reads to minutes.

Now that you are familiar with the spectrometer, you should follow the following

experimental procedures:

1. Switch on the discharge tube.

2. After the arc has been lighted, see that the slit is opened but never more than one

millimeter. Focus the telescope so that you have a distinct and well-illuminated image of

the slit.

3. Turn the grating table so that the incident light is approximately normal to the grating.

You will see an image of the slit and use this same edge throughout the experiment.

Obtain and record the scale reading.

4. Rotate the telescope left (approximately 18°) until the intense green line is approximately

in the center of the field of view.

109

5. Rotate the grating table in the same direction. You will notice that the green line rotates in

the opposite direction for a short distance and then, after further rotation of the grating, the

line moves in the same direction. Set the grating table at the point of reversal. Set the

cross-hair on the line by means of slow motion screw. Check the setting of the cross-hair

by small rotations of the grating in both directions. You now have the grating set at the

angle of minimum deviation. For accurate work, the slit should be moderately narrow.

6. Read the vernier and record the angle.

7. Rotate the telescope in the same direction as before until this green line appears a second

time. This is the second order and is about 36° from the central image. This line is very

faint and, therefore, you may have to widen the slit if possible and set the cross-hair on the

line. Record your data on the worksheet.

8. Repeat steps (4) through (7), this time going to the right. Record your data on the

worksheet.

ANALYSIS OF RESULTS

Calculate the angle of minimum deviation for each of the four observations.

Use the Equation (3) to calculate the wavelength of the light. Give the final answer in

Angstroms. Five-place accuracy is suggested. Show your work in the space on the worksheet

with explanatory remarks as required.

QUESTIONS:

1. The central image at C is sometimes called a “white image”. Why?

2. What is the maximum order number you might expect to see with the grating you have at

your station with λ = 4500Å and 8000Å? Explain.

3. What advantages might you expect to result from using a grating to form a spectrum

opposed to using a prism?

4. Using Equation (2) can you judge whether the first order or the second order measurements

seem more accurate than the other?

110


EXPERIMENT 12

THE WAVELENGTH OF LIGHT; THE DIFFRACTION GRATING

NAME: . . DATE: . .

SECTION: . .

* * *





111


Grating Spacing (lines/mm) .

Grating Constant (mm/line) . (10 points)

(35 points) TABLE 1:

n central vernier reading minimum deviation (D) λ

left

right

Calculations of Minimum Deviation and λ ( show your work) (25 points)

112

4. CONCLUSION: (5 points)

QUESTIONS (15 points)

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