table of contents - ccbc faculty web serverfaculty.ccbcmd.edu/~jzelinsk/phys102_labmanual.pdfthe...

Table of Contents

About the Laboratory Component…..3

0 – Ohm’s Relationship…..6

1 – Electric Field Mapping…..11

2 – Millikan Oil Drop Experiment…..14

3 – Build a Capacitor…..16

4 – Combinations of Capacitors…..21

5 – Combinations of Resistors …..25

6 – Kirchhoff’s Rules…..29

7 - Electrical Equivalent of Heat…..35

8 – Build a Voltmeter/Ammeter…..41

9 – Specific Charge of the Electron…..47

10 – Magnetic Fields….50

11 – RC Circuits…..55

11a – RC Circuits……58*

12 – LRC Circuits and Resonance…..62

13 – Properties of Light…..67

14 – Thin Lenses…..73

15 – Interference…..79

16 – Atomic Spectra…..83

Sample Lab Report…..89

*Not available at all campuses

3

Laboratory Exercises

About the Laboratory Component -

The scheduled laboratory periods may be used for lab exercises, as question sessions before the exams, or if necessary as additional lecture time. A student who misses a lab will be given an opportunity to perform a substitute exercise during the semester at a time arranged with the consent of the instructor. The average of the lab grades will count as 25% of the student's final course grade, unless the course instructor indicates otherwise. Lab partners will be assigned and rotated several times during the semester. If your instructor uses a sign-in sheet or attendance sheet, be certain that your name is included.

The student will keep a notebook (e.g. Ampad #26-251) of all laboratory work. Notebooks will be written neatly and clearly, and in ink. All laboratory objectives, equipment lists (include model and serial numbers), procedures, techniques, data, results, and conclusions will be written in the notebook (see below for guidelines). The notebook will then form the outline for any formal reports required. No loose sheets may be used as scrap. Any errors or changes must be struck out with a single, light stroke with the corrected value written nearby. No pages are to be removed, and the information is not to be recopied later into a 'cleaner, neater' notebook. Graphs printed by computer or drawn on loose leaf graph paper should be glued or stapled into the book, one graph per page. The instructor will examine and sign each notebook before it leaves the laboratory classroom; it is the student's responsibility to ensure that this is done. Never disassemble your apparatus until your notebook has been checked; your instructor may require you to take new or additional data, and be able to check for problems with the apparatus. While all this may seem rather AR, the student must realize that, at the least, a notebook must be capable of reminding the author of his procedures and results in case he must repeat them or if his work is questioned, and at the other extreme could be the factor determining who gets credit for a patent or other discovery. A good self test if enough information has been included is to ask whether a friend at some other school could duplicate the experiment using just the notebook and lab manual.

Construct a table similar to the one below on the first page of your notebook.

Lab # Date Title Instructor’s Signature

01

02

03

The grade for the lab portion of the course will be based on formal reports (5 points, due typically one week after the exercise) and the notebook checks (5 points). If a

4

laboratory exercise is performed, but no report is submitted by the due date, present the signed notebook as your proof that you did the lab and half credit may be awarded. Notebooks and formal reports will follow the general format given below, although some sections may be combined if it seems better to do so. Laboratory reports are due one week after the exercise is performed. Slightly late reports may be accepted at the instructor’s discretion, provided this allowance is made equally for all students. Once the reports are returned, you have one week to bring any questions or complaints to the instructor’s attention; after that, the grades are finalized.

Reports for Summer Session classes will be somewhat less formal and will be due without exception at the end of the lab period. Once the reports are returned, you have two class days to bring any questions or complaints to the instructor’s attention; after that, the grades are finalized. You may be asked to use the Physics Laboratory Report Form available separately on line; if so, remember to bring a copy of the Physics Laboratory Report Form with you to Lab Class. Otherwise, word processing facilities will be made available for the final hour of lab classes.

• Student Name - Title - Date - Names of Partners • Objective of Experiment - The objective is often to verify some relationship which was

presented in class. In these cases, a brief discussion of the concept is required, along with an outline of how this experiment will support (or disprove) it.

• Description of Experimental Apparatus - A labeled schematic sketch is often enough for the reports. Artistic renderings of the apparatus are inappropriate. Notebooks should include model and serial numbers, scale settings, et c.

• Procedure(s) – If the procedure corresponds exactly with that given in the lab manual, then write ‘The procedure in the manual was followed exactly.’ Any deviations from the given procedure should be included in the report. The goal is that the available information should be specific enough that another student taking PHYS I could reproduce the experiment. In particular, any steps with may be considered novel or unusual should be documented in detail.

• Data (if appropriate) - For reports, it is a judgment call as to how much raw data are included. Often, data can be presented in the form of a graph more efficiently than as columns of numbers. In the notebooks, however, all data should be recorded in some way, if at all possible. All measurements must be accompanied by an estimate of the uncertainty in that measurement. It may be that the student will not be asked to propagate the uncertainty through to the result, but at least the necessary information will be available. Again, do not disassemble your apparatus until your instructor gives permission.

• Results - Results often call for comparison of the student's answer to some accepted value; generally a per cent difference can be calculated, or a check can be made to see if the accepted value is within the uncertainty of the experimental result. Other times, a particular relationship among variables may be found by graphing. Results should be clearly indicated.

5

• Conclusions - This can often be combined with the results section. Did the experiment support whatever hypothesis was discussed? What mathematical relationship connects two or more variables? What are the implications of these results? Were there any problems with the experiment that could be corrected?

The reports should be typed, although figures may be hand-sketched and graphs may be hand-plotted on commercial graph paper. Obviously, Summer Session reports can be handwritten. Formal reports do not need to be overly long; just include what’s necessary. Reports will be written in third-person passive voice (e.g., not ‘We dropped the ball from a height of two meters,’ but rather ‘The ball was dropped from a height of two meters.’). The language should be clear, concise, and natural, without the pretentious use of synonyms (e.g., 'use' and 'utilize' do not mean the same thing). Philosophical digressions into the nature of the universe or questions about whether the reports are actually read are not appropriate. Do not blame poor results on 'human error' unless there is a reaction time effect or something similar; poor experimental technique should not be explained away, it should be corrected before you leave. Now, on occasion, it may be that an apparatus will not yield good results, either because the equipment is worn or broken, or because the experiment is truly ill-conceived. We can only assure the student that the instructor has performed each experiment and obtained reasonable results, and that the equipment was all present and in working order before the student arrived. Notebooks will not be signed until all apparatus have been stored properly.

In addition, note that there will be no food or drink allowed in the lab room, electronic

devices will be off and put away, and that appropriate dress is required (covered shoes required, no sandals; occasionally, long pants are required). Lab groups will be assigned and will comprise no more than four students. Attendance at and participation in laboratory exercises is mandatory; students more than a few minutes late to lab will be asked to leave and perform a make-up instead. Students are responsible for returning the lab equipment to its original state. Students must sign into the lab and be certain to have the instructor sign notebooks before leaving. Violations of these and other general classroom policies may result in ejection from the classroom under the College’s Code of Conduct. Avenues for appealing any such sanctions are outlined in the Code of Conduct.

6

Lab 0 - Ohm’s Relationship (non-Pasco)

OBJECTIVE

To determine the current v. voltage relationships for resistors and diodes.

META-OBJECTIVE

To acquaint (or re-acquaint) students with using Excel to plot graphs in order to analyze data. The

Physics concepts used to accomplish this will be covered in greater detail at a later point in the

course.

BACKGROUND

Let’s make use of an analogy. Consider a fluid in a pipe. In order to make the fluid flow through the

pipe, a pressure difference ΔP must exist between the ends of the pipe. As a result, the fluid will

move at a rate F (amount of mass passing a given point per unit time) proportional to the pressure

difference as described by Poiseuille’s Law:

� � ��

where H is a constant of proportionality that depends on characteristics of the pipe, e.g., its

diameter and length, and on the properties of the fluid.

In the same way, the electric current (symbol: I; unit: the Ampère) can be defined as the rate at which

electric charge moves past a given point. The electric potential (symbol: V or φ; unit: the Volt) will

be defined later in this course, but for now can be thought of as analogous to fluid pressure. A

difference in potential (ΔV) between two ends of an object in which charges are free to move will

create a current that is often (but not always) proportional to the potential difference: � � ��

where S is the conductance (unit: the Siemens). An object that exhibits this proportional or linear

behavior is said to obey Ohm’s Relationship and is referred to as an ideal resistor.

Diodes do not follow Ohm’s Relationship. Ideal diodes allow current to flow without limit, but in one

direction only. Real diodes have a more complicated behavior that can be approximated with this

relationship: � � � �� where Vo is a number that depends on the temperature, composition, and construction of the

diode, but is in theory approximately equal to 0.026 Volts.

7

PROCEDURE

1) Be sure that everything is turned off and unplugged.

2) Connect the circuit as shown in the figure. Use

component A on the Component Board as the

resistor. One Cen-Tech multimeter will be set to

act as the voltmeter and the other to act as the

ammeter to measure current. The devices in the

circuit are connected using banana plug cables.

Place one wire into the + (red) terminal of the

power supply and connect it to the banana-lug

adaptor on the black component board, as

shown in Figure 1. Connect the other side of component A to the VΩmA plug on the ammeter.

Connect the COM plug of the ammeter to the – (black) terminal of the power supply. Now,

connect wires from each side of component A to the COM and VΩmA plugs of the voltmeter, as

shown. Before you turn on the power supply, turn the COARSE and FINE voltage control knobs

completely counter-clockwise (CCW) and the CURRENT knob completely clockwise (CW). Make

sure that there is a metal bar connecting the two black connector posts on the right of the supply.

Have your instructor check your circuit.

3) Review the use of a multi-meter before proceeding. Turn the knob on the ammeter to the DCA

200μ setting; this means that the largest current you can measure is 200 micro-Ampères, and that

you should multiply the numerical values you read on the meter by 10-6

A. Turn the knob on the

voltmeter to the DCV 2000m setting; this means that the largest voltage you can measure is 2000

milli-Volts (or 2 Volts) and that you should multiply the numerical values by 10-3

V. Determine and

record in your notebook the Least Count1 (LC) values for these scales.

4) Plug in the power supply. Turn on both meters and the power supply. Using only the FINE knob,

vary the applied potential difference between 0.1 and 1.0 volts in approximately 0.1 Volt intervals,

as measured on the voltmeter (ignore the meter on the power supply). Do not try to adjust the

voltages exactly, just adjust the voltages fairly close to the target values and then record the actual

values from the Cen-Techs. For each value of ΔV, record the corresponding current. For this

portion of the lab, you should be able to get all of your current values on the 200μ setting of the

ammeter.

1 Underlined quantities are to be recorded in your notebook.

Figure 1 - Set-up for determining the conductance, S.

8

5) Turn the FINE knob completely CCW and turn off the power supply. You will obtain negative

potential differences by reversing the connections to the power supply. Repeat Step 4 above.

6) Replace the resistor with a diode (B on the Component Board) by moving the connections on the

black board down one position on each side. Have your instructor check your circuit before the

power supply is turned on. Repeat Steps 4 and 5 above, but vary the voltage in steps of 0.1 Volt to

no larger than ± 0.7 V. Record your measurements of ΔV and I. For the diode, you will certainly

have to change the scale of the ammeter; do so in such a way as to obtain the greatest number of

digits on the readout without overloading the meter, and remember to record the LC values on

each scale. When you are done, turn the power supply and the meters off, but do not dismantle

your circuit until your instructor has signed your notebook.

ANALYSIS

1) For the resistor measurements, which quantity is your independent variable, current or voltage?

Which is the dependent variable? Plot your data using Excel so as to obtain a straight line. Perform

a least-squares linear fit. What does the slope of the line represent? Determine the experimental

value of the conductance.

2) Ask your instructor to determine the expected value of the conductance; you will learn how to do

this later, using the colored bands on the resistor. Look at the color of the fourth band on the

resistor; this indicates how closely the manufacturer claims to have hit the intended value. A gold

band means that the conductance should be within 5% of the intended value, silver 10%, and no

band 20%. Record this tolerance value for your resistor. Calculate the percent difference between

the value of S you determined from your graph and the manufacturer’s expected value. Is it within

the expected tolerance? Share your percent difference and tolerance value with the rest of the

class. Are all of the class resistance values within the given tolerance?

3) For the diode, which quantity is your independent variable? Which is the dependent variable? Plot

your data (using Excel); what shape curve results? Re-plot only the positive voltage points in such a

way as to obtain a straight line (review Lab 1 from Physics 1). Perform a least-squares linear fit and

determine Io and Vo. Compare Vo to the accepted value given above by calculating a percent

difference.

9

4) Comment on how well each formula ((Eq. 1) and (Eq. 2) above) models the behavior of the

corresponding device.

APPENDIX - Using Excel 2007 to plot a graph.

1) Open Excel: START → PROGRAMS → MICROSOFT OFFICE → EXCEL.

2) Enter your data in two columns with the independent variable (x) on the left and the dependent

variable (y) on the right. Highlight both columns and click the INSERT tab at the top. Choose

‘Scatter with only Markers.’ The graph should appear.

3) Clean up the graph by removing any unneeded features such as the legend or gridlines. Click the

LAYOUT tab. Generally, we don’t want GRIDLINES, so remove them. Adjust the scaling of the

graph, if necessary, by clicking the AXES button.

4) Label the axes by clicking the AXIS TITLES button. Be sure to include units.

5) When the graph is ready, be sure that it has a blue border around it (if not, just click once on the

graph) and PRINT.

There is no worksheet for this lab exercise. Remember to write a full formal report.

10

On the Use of Multimeters

There are a number of specialized meters used to measure various quantities in electricity. You will

use some of them during the course of the semester. However, most measurements can be

made using a multimeter, which, as the name suggests, can measure many things.

Take a look at the CEN-TECH meter on your table. There are three connectors near the bottom.

Every use of a multimeter requires that two of the sockets are connected to the circuit under

study. One of them is always the COM socket. For the CEN-TECH meters, the other connection

is almost always the VΩmA socket. If a very large current is to be measured, then the other

connection is the one at the top, labeled ‘10ADC.’ In Lab 0, you will use the CEN-TECH to

measure what is called DC Voltage, so turn the dial to the DCV with the two lines over it. Now,

you will want as much precision as possible, so turn the selector knob so that you obtain as

many digits as possible without overloading the meter (usually indicated by a ‘1’ on the left of

the display). To measure DC currents, turn the knob to the DCA settings.

Take a look at the Fluke 111 meter on your table. There are three connectors near the bottom.

Every use of a multimeter requires that two of the sockets are connected to the circuit under

study. One of them is always the COM socket. If current is to be measured, then the other

connection is the one on the left, labeled ‘A.’ Everything else, including potential (or voltage), is

measured by connecting to the right hand socket (labeled with a V and some other strange

symbols). In Lab 0, you will use the Fluke to measure what is called DC Voltage, so turn the dial

to the V with the two lines over it. Now, you will want as much precision as possible, so press

the RANGE button until you see four digits and the words ’Manual Range 6.’ Similarly, to

measure DC current, move the connection to the ‘A’ socket and select the symbol A with a solid

and dotted line above it.

Now, here is an additional concern that must be addressed. The current measuring section of most

meters contains a fuse that will burn out if the current exceeds a given If you are getting no

readings except zero, you should first have your circuit checked, and if that is O.K., then have

your instructor check the fuse.

Other specialty meters will be used throughout the semester; your instructor will guide you in their

use.

11

Lab 1 – Electric Field Mapping

OBJECTIVE

To determine the shapes of equi-potential surfaces in the region of charged conductors. To determine

indirectly the appearance of the electric field.

BACKGROUND

Any charged object has associated with it a vector quantity called the electric field (symbol: E; units:

N/C or V/m) that exists in the space surrounding the object. Generally, the greater the distance

from the object, the weaker the electric field. If the object is positively charged (e.g., if electrons

are removed from a neutral object), the electric field vector points away from the positively

charged object. The field points towards the object if the object is negatively charged.

The electric potential (symbol: V or φ; unit: the Volt) is a scalar quantity that is related to the electric

field. An equi-potential curve or surface is the set of

points all having the same potential; equi-potential

surfaces are always perpendicular to the electric field

lines. Figure 1 shows the pattern of the E-field

(radiating lines) and the corresponding equi-

potentials (circles) in the plane of a charged disc.

In this experiment, you are to plot the equi-potential

curves established in the vicinity of two equally, but

oppositely, charged conductors maintained at a

constant potential difference. You will be provided with

a board, a source of potential difference (the

battery eliminator), a galvanometer, appropriate

probes, and some white paper. Your lab instructor will

describe how to assemble and use the circuit.

Figure 2 - E field and equi-potential lines in the

plane of a charged disc.

12

PROCEDURE:

1. Do not plug anything in or turn anything on until your apparatus has been approved by your

instructor. Place a sheet of white paper under the spring clamps on the top side of the apparatus.

Each set of conductors is attached to a plastic sheet which you must fasten to the bottom of the

apparatus. You should also have been given a set of templates, each of which corresponds to one

of the conductor arrangements; place the template on the paper and trace out the shapes, then

remove and store the templates in the correct envelope. The probe for measuring potential is

mounted at the end of a long handle with a slit down its length (sometimes called ‘the salad tongs’

by students); the probe goes on the bottom side and the arm with a small hole corresponding to

the probe’s location is placed on the upper side of the apparatus.

2. Place the board so that the banana connectors are along the top side. Connect the potential

difference device (in this case, a battery eliminator) to the apparatus; one wire should go from the

negative (black) terminal of the battery eliminator to the left side of the board, while another wire

connects the positive (red) terminal to the right side of the board. Connect one terminal of the

galvanometer to the probe handle. The other terminal will plug into each of the sockets at the top

of the board in turn (see below for more details).

3. Have your instructor check your set-up and show you how to zero the galvanometer. If the set-up

is approved, turn the knob on the battery eliminator to 6V and turn it on. At this point, the circuit

along the top of the board becomes a voltage divider, and each banana connector corresponds to a

particular reference voltage from zero to 6V in 0.75 Volt increments. Now, a galvanometer, we

shall see later in the semester, is a device for measuring very small electrical currents. As you saw

in the last lab exercise, currents can be caused by potential differences. So, you will connect the

galvanometer to one of the reference voltage connectors (let’s say 2.25V, as an example) and move

the probe around on the plate containing the conductors. If the potential at the location of the

probe is different than 2.25V, the galvanometer will detect a current; contrarily, if the

galvanometer reads zero, then the potential at that spot must be 2.25V, and you can mark the

position on the paper by making a dot through the little hole. The procedure, then, is to choose a

reference potential, find the points in the region of the conductors that are at that potential, and

record their locations. Repeat for all possible reference potentials, then, repeat the entire

procedure for the other conductor arrangement. Of course, it is impossible to record all of the

points at a given potential, there are after all an infinite number of them. Just record the locations

of points that are spaced from each other by about 1cm. Don’t forget to look in the regions

‘behind’ the conductors. Don’t forget to label which potential corresponds to which points, and

also don’t forget to indicate on the paper which electrode is positive and which is negative.

4. At this point, your group should have two pieces of paper each with an outline of the conductors’

shapes and many points of labeled potential values. Photocopy these so that each member of the

group has a copy of each.

13

5. Each student will individually draw in the equi-potential surfaces (curves, in this case) and label the

potential values on his papers. The metal surfaces of the electrodes are also equi-potential

surfaces.

6. Use these equi-potential surfaces to sketch in the electric field lines. Indicate the correct direction

by placing arrows on each line. Photocopy these results one more time so that you have a record

in your notebook.

Your report will present these diagrams of the equi-potentials and the corresponding E-fields, along

with a very brief report. Be sure that the diagrams are neat, clear, and carefully labeled.

There is no worksheet for this lab. Be sure to hand in a full formal report.

14

Lab 2 – Millikan Experiment

OBJECTIVE

To determine the elementary charge of an electron and demonstrate that electric charge is quantised.

META-OBJECTIVE

To provide practice with Excel.

BACKGROUND

The Millikan ‘Oil Drop’ experiment showed that the charge is quantised, that is, it only occurs as an

integer multiple of some given fundamental value. The experiment is extremely tedious to

perform, so you will make use of Millikan’s own data.

The essentials of the experiment are given here. A small spherical drop of oil of radius r is given an

electric charge q (by either adding or removing some small number of electrons through exposure

to a radio-active source) and then allowed to fall through air while between two charged metal

plates. Since the drop is so small, it achieves its terminal velocity (due to drag from the air) in a

very short time. As may have been discussed in Physics 1, the magnitude of the drag force D acting

on the drop moving at speed v is given by Stokes’s Law:

��

where μ is the viscosity of the air. The other possible external forces include the weight W of the

drop, a buoyant force B on the drop due to the air, and an electric force FE:

� � ! � "#$ �%&�'()*� + � "#$ �%&�',)-

�. � � � �/0

where ρOIL is the density of the oil, ρAIR is the density of the air, q is the

charge on the drop, and ΔV and d are the potential difference and

physical separation between the metal plates. A particular drop is chosen

and viewed through a microscope. With the electric field off, the drop

falls distance y in time tF at constant speed vF = y/tF. Making use of

Newton’s Second Law, we then have that

1��2 ��3+ 4� 3 5 � !6 � 7 Figure 1 - Forces on a

falling drop (left) and

on a rising drop (right)

15

"#$ �%&�',)- 4 � "#$ �%&�'()* 3 �� 89: � 7��

Re-arrange Eq. (2) to get the radius r; we need to do this because there is no easy way to measure r:

% � �; <=>�?@ � ��'()* 4�',)-�

Then, the electric field is turned on and the same drop is watched while it rises distance y in time tR at

constant speed vR = y/tR. Newton’s Second Law now looks like this:

1��2 ��3+ 4� 4 5 3 �. � !6 � 7

"#$ �%&�',)- 4 � "#$ �%&�'()* 4 �� 89A �3 ��B/C �� 7��

Now, substitute the expression for r above into Eq. (3) and solve for q:

� �D#0 E FGHGIJ�KLMNOKPMQ�RST� UVQWVXVQ�VX

GT Y Z[� (Eq. 3)

Note that only the last two terms will change from trial to trial, so long as the temperature is

constant.

Here are some values you will need from the experiment:

Plate separation, d 1.60 x10-2

m

Distance to fall or rise, y 1.010 x10-2

m

Density of oil at 25oC, ρOIL 896.0 kg/m

3

Density of air at 25oC, ρAIR 1.184 kg/m

3

Viscosity of air at 25oC, µ 1.862 x10

-5 Ns/m

2

Program an Excel sheet to calculate from Eq. 3 the charge values for each of the data sets given. Plot

the resulting values of the charge to shown the quantisation effect, and then estimate the value of

the fundamental charge (how will you do this?).

There is no worksheet for this lab exercise. Be sure to hand in a full formal report.

16

Lab 3 – Build a Capacitor

OBJECTIVE

To confirm the relation derived in class for parallel plate capacitors.

META-OBJECTIVE

To demonstrate that ‘doing Physics’ does not always require expensive equipment.

BACKGROUND

In class, it was shown that the capacitance C of a parallel plate capacitor is given approximately by

\ � �] ^�_0

where A is the surface area of the plates, d is the plate separation, and κ is the dielectric constant of

the material between the plates. In this exercise, you will construct parallel plate capacitors of

various areas and separation and investigate how well this formula models the behavior of real

capacitors.

PROCEDURE

1) The capacitor plates will be formed from sheets of aluminum foil placed between the pages of

your Physics textbook. Cut two pieces of Al foil slightly larger than the page of your book,

insert each tightly against the spine of your open book, close the book, and crease the foil

where it emerges from the pages of the book. Remove the foil and then either fold the foil or

cut it along the creases, leaving a very small extra tab to which you will connect the capacitance

meter leads. Measure and record the dimensions of your foil sheets1 and determine the area,

A.

2) To determine conveniently the spacing of your sheets, we shall use the page numbers in the

textbook. However, we must be able to convert these numbers to actual plate separations.

Collect up a large number of pages (preferable a multiple of 100), press them together to

remove as much air as possible, and measure the thickness with the vernier calipers. Calculate

and record the thickness of, say, 100 pages and record this value.

1 Underlined quantities should be recorded in your notebook.

17

3) Place one aluminum sheet between pages 50 and 51 of your textbook; be sure that it is aligned

with the edges with only a small tab protruding to which to connect the capacitance meter

alligator clip leads. Similarly, place the other sheet between pages 100 and 101. The tabs of

each sheet of aluminum should be on opposite sides of the book and be bent away from the

other sheet. Connect the two leads of the capacitance meter together and zero the meter; the

meter must be zeroed every time the scale is changed. Then, attach the leads to each sheet at

the tabs and measure and record the capacitance. Repeat this procedure for different spacings

of the plates. In each case, be sure to compress the pages to eliminate as much air as possible;

use the page numbers to measure the spacing of the plates, but be sure to convert back to

actual distances before plotting your data.

4) Return the sheets to their 50-51/100-101 spacing. Measure the capacitance again (it should be

very close to your first measurement). Now, keeping the sheets a constant distance apart, fold

only the top sheet in half as accurately as you can, replace it into the book, then measure and

record the capacitance again. Continue to halve the top foil and measure C until you have at

least five data points.

5) Turn off the meter, but do not disconnect the apparatus until your notebook is approved.

ANALYSIS

1) Consider the data collected in Part 3 above. Which quantity is your independent variable and

which is the dependent variable? Plot your data (Capacitance C as a function of plate

separation d) in such as way as to obtain a straight line. What would be the physical meaning

of the slope of this line? Explain any deviations from linear behavior (HINT: what assumptions

were made in class during the derivation of the formula at the top of this page?).

2) Consider the data collected in Part 4 above. Which quantity is your independent variable and

which is the dependent variable? Plot your data (Capacitance C as a function of plate area A) in

such as way as to obtain a straight line. What is the physical meaning of the slope of this line?

Explain any deviations from a straight line.

3) Use the slopes of your two lines to calculate values for the dielectric constant of the paper

composing your textbook. Compare these two values, first to each other, then to the value for

paper given in your book. Explain any discrepancies.

19

WORKSHEET for LAB 3 – BUILD A CAPACITOR

Name__________________________ Date _________________

Instructor_____________________________________________

OBJECTIVE:

Sheet dimensions: ________ x ________ Area = __________ Thickness of 100 Pages: __________

Constant Area

Number of Pages Plate separation d Capacitance

Slope of Line: __________ Value for κ: __________

Continue to next page.

20

Constant Plate Separation

Number of Pages: __________ d = __________

Area Capacitance

Slope of Line: __________ Value for κ: __________

Per cent difference in values for the dielectric constant, κ: __________

CONCLUSION:

If requested so to do, turn in this sheet with your two graphs. Otherwise, submit a full formal report.

21

LAB 4 – Combinations of Capacitors

OBJECTIVE

To verify the rules for calculating equivalent capacitances.

BACKGROUND

In class, it was shown that the equivalent capacitance CEQ of a combination of two capacitors C1 and C2

is given by

\.` ��\Z 3�\I��a6%6bb�b�� \.` �� \Z 3� �\I ��c�%d�c�

Find the equivalent capacitance of all possible combinations of three capacitors.

PROCEDURE

1) Since the marked values1 of capacitors are usually only within about twenty percent of the actual

values, use the Fluke multimeters to measure the actual values. Set the switch on the -| (- symbol.

2) How many ways are there to combine three different capacitors in either series or parallel? Does

the order matter for series capacitors (e.g., -A-B- or -B-A-)? Use banana cables to connect the

capacitors; also remember that these are electrolytic capacitors, and so the positive ends need to

orientated in the same direction. Lastly, be sure to connect the capacitance meter with the correct

polarity during the measurements.

ANALYSIS

For each possible combination of the three capacitors, calculate the theoretical value of CEQ using the

actual values previously measured, and then measure the experimental value of CEQ. Calculate a

percent difference. Construct a chart and comment on how well the theory matches the measured

values.

1 Underlined values should be recorded in your notebook.

23

WORKSHEET for LAB 4 – Combinations of Capacitors

Name__________________________ Date _________________

Instructor_____________________________________________

OBJECTIVE:

A B C

Nominal Value

Actual Value

Schematic Diagram of

Combination

Theoretical Value Measured Value Per cent difference

24

CONCLUSION:

If requested so to do, turn in this sheet. Otherwise, submit a full formal report.

25

LAB 5– Combinations of Resistors

OBJECTIVE

To verify the rules for calculating equivalent resistances.

BACKGROUND

In class, it was shown that the equivalent resistance REQ of a combination of two resistors R1 and R2 is

given by

e.` ��eZ 3�eI��c�%d�c�� e.` �� eZ 3� �eI ��a6%6bb�b�

Find the equivalent resistance of all possible combinations of three resistors.

PROCEDURE

1) Determine the nominal values of the three resistors1 you have been given. These values are

indicated by the color bands on the resistor. Orient the resistor so that the gold or silver band is on

the right. Record the colors in order from the left. Use this chart to determine the values:

Black 0

Brown 1

Red 2

Orange 3

Yellow 4

Green 5

Blue 6

Violet 7

Grey 8

White 9

Write down the number corresponding to the first band’s color, then write down the number of

the color of the second band, then multiply by as many powers of ten as indicated by the color of

the third band. Lastly, if the fourth band is gold, then the manufacturer claims that the actual value

is within 5% of the nominal value, silver indicates 10%, and the absence of a band indicates 20%.

For example, if the bands are green, orange, yellow, and silver, then the nominal value is 53x104 ±

10% Ohms.

1 Underlined values should be recorded in your notebook.

26

2) Since the nominal values of resistors are usually only within about five or ten percent of the actual

values, use a resistance meter to measure the actual values.

3) In a series pair, does which resistor the current enters first have an effect on the equivalent

resistance? For a parallel pair, does it matter which resistor is on the right or on the left? How

many electronically independent ways are there to combine three different resistors in either

series or parallel? For each possible combination of the three resistors, calculate the theoretical

value of REQ using the actual values measured previously. Then, measure the experimental value of

REQ. For each resistance measurement made, be sure to record the LC of the meter. Calculate a

percent difference. Construct a chart and comment on how well the theory matches the measured

values.

27

WORKSHEET for LAB 5 – Combinations of Resistors

Name__________________________ Date _________________

Instructor_____________________________________________

OBJECTIVE:

A B C

Nominal Value

Actual Value

Schematic Diagram of

Combination

Theoretical Value Measured Value Per cent difference

28

CONCLUSION:


29

Lab 6 – Kirchhoff’s Rules

OBJECTIVE

To confirm Kirchhoff’s Rules for DC circuits.

META-OBJECTIVE

By confirming Kirchhoff’s rules, we verify the concepts of conservation of charge and the conservatism

of the electric field.

BACKGROUND

As discussed in class, the sum of all charges entering a node in a given period of time must equal the

sum of the charge leaving, or

Z2��2 � 7�

The fact that the electric field is conservative requires that the sum of all potential rises and drops

around a closed loop be zero, or

12e2�2 ��12f2��

In both cases, a particular sign convention is used.

PROCEDURE

1) Record the nominal values1 of each of your resistors. Once again, these values are determined

from the color coded bands on the resistor (see Lab 7). Measure the actual resistances of each

of the resistors using a Cen-Tech multimeter.

2) Turn all equipment off and unplug the power

supplies until your circuit is approved by your

instructor. Construct the circuit shown in

Figure 1. Use power supplies as the emfs (‘red’

is positive and ‘black’ is negative) and insert

the Cen-Tech multimeters (use the 20mA DCA

setting, ‘COM’ is the negative connection and


Figure 1 - Circuit for Kirchhoff's Rules

30

‘VΩmA’ is the positive). By carefully observing the conventions for hooking up these

components, the signs of the quantities measured will be consistent with those in the diagram.

Be sure the powers supplies are turned off. Turn the CURRENT knob of the power supplies

completely clockwise (CW), set the FINE knob to the middle of its range, and the COARSE knob

completely counter-clockwise (CCW). Have your instructor check the circuit before you turn

anything on.

3) Assume that you will adjust one power supply (E1) to 8 Volts and the other (E2) to 5 Volts (don’t

do it yet). Write an appropriate set of equations using Kirchhoff’s rules and solve for the

expected current in each branch of the circuit. When you solve, use resistance values that are

11 Ohms higher than the measured values of the resistances to account for the resistance of

the ammeters. Show all work in your notebook. Record the theoretical values of the currents

in each branch.

4) Turn on the power supplies and carefully adjust each to the values given above (monitor the

outputs with the fourth multimeter set to 20 DCV; do not rely on the built-in meters). Record

these power supply voltages.

5) Measure and record the actual current in each branch.

6) Use your fourth multimeter on a voltage setting (2 or 20 DCV, whichever gives you more digits)

and measure and record the voltages around each of the three loops. In order to make sure

that the polarity of the meter is maintained, always lead to the next circuit element with the

red probe.

ANALYSIS

1) Compare each measured current value to the theoretical value you found previously by

calculating a percent difference.

2) Generate a figure of merit that tests how close to zero the sum of the currents is. Take the sum

of the currents from Step 4 above and divide by the sum of the absolute values of the currents

and form a percentage:

31

12�212g�2g h �77i

3) For each loop in Part 6 above, calculate the sum of the voltages (keep track of the signs). How

close to zero is your sum? Generate a figure of merit by dividing the sum of the voltages by the

sum of the absolute values of the voltages:

Z22Z2g2g h �77i

Record this value for each of the three loops.

4) If requested, adjust E1 to 2 Volts (or whatever value your instructor gives you) and repeat the

experiment.

5) When you have obtained good results and your notebook is signed by your instructor, turn the

COARSE knob of the power supplies completely CCW, turn off the supplies and all of the

meters, and return the equipment to its place of origin.

33

WORKSHEET for LAB 6 – KIRCHHOFF’S RULES

Name_________________________________ Section___________________________

OBJECTIVE:

RESISTORS Nominal Value Measured Value Effective Value

= Measured + 11 Ohms

R1

R2

R3

Ɛ1 = __________ Ɛ2 = __________

CURRENTS I1 I2 I3

Theoretical Value

Measured Value

Per cent Difference

Node Law:

Sum of Currents

Figure of Merit

Loop Law:

Sum Voltages in Loop 1 Figure of Merit



CONCLUSION:


35

Lab 7 – Electrical Equivalent of Heat

OBJECTIVE

To confirm that electrical potential energy is converted to thermal energy in a resistor.

BACKGROUND

Consider a resistor with a potential difference ΔV across its ends. As a result, the net motion of

electrons (from low potential to high potential) results in a change in their potential energy, qΔV

(note that this quantity will be negative for electrons). Since the drift speeds of the electrons

entering and exiting the resistor are about the same, there is no increase in the electrons’ kinetic

energies. The potential energy is ‘lost’ during collisions among the electrons and with the atoms of

the resistor, eventually taking the form of thermal energy, U, resulting in an increase in the

temperature of the resistor. Heat (symbol: Q, unit: the calorie) is the transfer of thermal energy

due to a difference in temperature, in this case between the warm resistor and a water bath in

which it is immersed. By measuring the increase in the water’s temperature, you will be able to

determine the energy dissipated in the resistor as heat.

The charge q passing through a resistor in time Δt will be

� 4��?,

where I is the electrical current. The energy ‘lost’ by this charge and converted to thermal energy is

then

j*�kV � 4 �� 3��?��

Assuming no losses to the environment so that all of the energy goes into warming the resistor,

water, and the container, we have that

j*�kV � l ��!mnVopqmnVop�rmnVop 3�!stuqstu�rstu 3�\*2v�r*2v

where the ‘lid’ is the cover for the cup that comprises the connectors, the resistor, and the stirrer.

Since we expect that all components will reach the same final temperature, and given that the heat

capacity1 of the lid is 2.5 cal/°C, this becomes

��?�� !mnVopqmnVop 3�!stuqstu 3�\snu��r�� 1 Note that C represents the heat capacity, the number of calories required to raise the temperature of a particular object

one degree. The specific heat capacity, c, is the number of calories required to raise the temperature of one gram of a

material by one degree.

36

PROCEDURE:

1) Determine the mass of the inner calorimeter cup.1

2) Fill the cup 2/3 full of water and determine the mass of water.

3) Place the coil in the water, mix thoroughly to allow the coil and water to reach equilibrium, and

record the initial temperature of the water.

4) Make sure that the power supply is

unplugged and that all devices are

turned off. Connect the circuit as shown

in the diagram.2 Set the Cen-Tech

voltmeter to the 20 DCV range and

connect the Welsh ammeter to the 25 A

range. Have your instructor check the

circuit before you turn anything on.

5) Simultaneously, turn on the power supply and start the timer. The voltage and current should stay

approximately constant and you should continuously stir the water gently. Record the current

through and the voltage across the resistor at two minute intervals. Simultaneously, record the

temperature of the water. At the end of ten minutes, shut everything off, but do NOT dissemble

the equipment until you have gone through a preliminary calculation to ensure that your data are

reasonable.

ANALYSIS

1. For each time interval (i.e. 0 → 120s, 120s → 240s, et c.), compute the energy released by the

current carrying coil using the left side Equation 2. Note that the units of the expression (I Δt ΔV)

are (Amps)(seconds)(Volts) = Joules.

2. Using the right hand side of Equation 2, compute the energy absorbed by the calorimeter system

for each time interval. Convert your results from calories to Joules by multiplying by 4.184 (1 cal =

4.184 J).


2 Figure adapted from Sopka and Bartnick.

37

3. For each time interval, calculate a percent difference between the electrical energy lost by the

resistor and the thermal energy gained by the complete system. Evaluate the conservation of

energy for this system. Does the agreement get better or worse with time?

39

WORKSHEET for LAB 7 – ELECTRICAL EQUIVALENT OF HEAT

Name_____________________________________ Section___________________________________

OBJECTIVE:

Time

(sec)

Current

(Amps)

Voltage

(Volts)

Temperature

(°C)

0

120

240

360

480

600

CONCLUSION:


41

Lab 8 - Build a Voltmeter/Ammeter

OBJECTIVE

To apply knowledge of circuits to construct a voltmeter and an ammeter.

BACKGROUND

Modern multimeters are very convenient to use and have many applications. However, scientists and

engineers should always have an understanding of how their equipment works. In this exercise,

you will convert a galvanometer into a voltmeter and into an ammeter.

The galvanometer is a device that measures small currents. The current passes though a coil (mounted

on a gimbal) that is located between the poles of a permanent magnet. The current in the coil

causes a magnetic moment which then experiences a torque due to the magnetic field. A spring

attached to the coil provides an opposing toque, and equilibrium is reached when the coil has

turned far enough so that the torques cancel. A dial is then marked off in arbitrary current units.

The full-scale current (IFS) is the current necessary for full-scale deflection of the coil. Necessarily,

the galvanometer also has its own resistance, RG.

PROCEDURE (for characterizing the Galvanometer)

1) First, you must characterize the galvanometer. Check to

see if the galvanometer is zeroed; if not, ask your

instructor to zero it.

2) Next, determine IFS and RG. To determine the resistance

of the galvanometer, RG, you may use a commercial

multimeter (e.g., a Mastech 3900) to measure directly.

Connect the two terminals of the galvanometer to the

COM and V/Ω sockets on the meter and turn the dial to

the Ω setting; adjust the scale to obtain the maximum

number of digits. The process for finding IFS is more complicated. Be certain that the power supply

is off and unplugged, that the voltage knob is turned completely CCW, and the current knob is

completely CW. Connect the galvanometer as shown in Figure 1 with a power supply, a safety

resistor (Resistor C on the resistor board), and commercial micro-ammeter (e.g., the Mastech 3900

using the 2A and COM sockets) in series. The safety resistor is present merely to limit the current

to small values so as not to burn out the galvanometer; its exact value is not critical, but should be

about 20kΩ. Turn the power supply on and slowly adjust the voltage so that the needle on the

Figure 1 - Setup to determine full-scale current

(Method A).

42

galvanometer reads exactly a full scale deflection; measure this full-scale deflection current1 on the

commercial meter and record. Turn the voltage on the power supply back to zero and turn it off.

BACKGROUND (for the Voltmeter)

A voltmeter measures the potential difference

between two points, and so must be placed in

parallel with the circuit element for which ΔV is to

be measured. The resistance of the voltmeter

should be as high as possible so as not to draw off

much current from the circuit, but low enough to

allow sufficient current through the galvanometer

for a reasonable deflection. This resistance is

usually much higher than RG, so an additional resistance RVM must be added in series with the

galvanometer (see Figure 2).

Decide what the range of measurable voltages will be for the voltmeter; different desired ranges will

require different values of RVM. Since the galvanometer is marked off in tens to ± 50, it might be

convenient to let full scale deflection correspond to VMAX = 5 V. So, for the situation of full-scale

deflection,

w,x �� e�w 3�ey��@z

Solving for RVM,

e�w ��w,x�@z �4�ey

Calculate and record this value for RVM.

PROCEDURE (for the Voltmeter)

Disassemble the circuit used previously. Construct

your voltmeter by wiring the resistance box in series

with the galvanometer (see Figure 3). Set the

resistance box to the calculated value of RVM.

Connect your new voltmeter across the terminals of

the power supply in parallel with the commercial

voltmeter (using the V/Ω and COM sockets and the

V--- settings; set for as many digits as possible). Once your set-up is approved by your instructor, turn

on the power supply and set it to some random voltage between zero and five volts. Measure and


Figure 2 - Schematic of a voltmeter

Figure 3 – Testing the voltmeter

43

record the voltage using your voltmeter and the voltage measured by the commercial meter. Repeat

for a total of ten different voltages between zero and five volts. Turn the voltage down slowly and

turn off the power supply.

ANALYSIS (for the Voltmeter)

Compare your results by constructing a graph and drawing a best-fit line. What should this line look

like? Comment on whether the graph meets your expectations; if it doesn’t, find out why not.

BACKGROUND (for the Ammeter)

An ammeter measures the current in a

branch of a circuit, and so must be

placed in series with the circuit

element for which I is to be

measured. The resistance of the

ammeter should be as low as

possible so as not to reduce the

current in the branch, but large

enough that a sufficient voltage

difference appears across the

galvanometer to produce deflection;

this resistance is usually much lower

than RG, so an additional resistance RSHUNT must be added in parallel with the galvanometer.

Decide what the range of measurable currents will be for our meter. Since the galvanometer is marked

off in tens to ± 50, it might be convenient to let full scale deflection correspond to IMAX = 5 mA. So,

for the case of full-scale deflection,

z{|}~ ��y ��6�0��w,x �� z{|}~ 3��@z� �z{|}~ez{|}~ �� @zey

��w,x 4��@z�ez{|}~ �� @zey

ez{|}~ �� @zey�w,x 4��@z

Calculate and record this value for RSHUNT.

Figure 4 - Schematic of an ammeter

44

PROCEDURE (for the Ammeter)

1) Disassemble the circuit. Construct your ammeter

by wiring the resistance box in parallel with the

galvanometer and setting the resistance box to the

value of RSHUNT calculated above. Note: You should

double check the value of the resistance box with

a multimeter. Connect your new ammeter to the

power supply in series with a commercial ammeter

(e.g., the Mastech; us the 2A and COM sockets and

set the dial on the A--- scale so as to obtain the

maximum number of digits) and a second

resistance of about 100 Ω (Resistor D on the

resistor board). The exact value of the resistor is

not critical, it only acts to limit the current to a few milli-amperes.

2) Once your circuit is approved by your instructor, turn the voltage knob on the power supply

completely CCW. Turn on the power supply and slowly set it to some random voltage between

zero and five volts. Measure and record the current values measured by your ammeter and by

the commercial meter. Repeat for nine other current values between zero and five milliamps.

ANALYSIS (for the Ammeter)

Compare your results by constructing a graph and drawing a best-fit line. Assess the accuracy of

your ammeter.

Once good results have been obtained and your instructor has signed your notebook, turn off and

disassemble all equipment and return it to its original state.

Figure 5 - Testing the ammeter

45

WORKSHEET for LAB 9 – BUILD A VOLTMETER/AMMETER

Name__________________________________ Section_____________________________

OBJECTIVE:

IFS = __________ RG = __________ Calculated RVM = __________ Calculated RSHUNT = __________

VYour Meter VCommercial Meter IYour Meter ICommercial Meter

CONCLUSION:

If requested so to do, staple this sheet to your graphs and turn them in. Otherwise, submit a full

formal report.

47

Lab 9 – Specific Charge of the Electron (e/me)

OBJECTIVE

To determine the charge to mass ratio (specific charge) of the electron.

META-OBJECTIVE

To observe directly the effect of the Lorentz force, FM.

BACKGROUND

In this experiment, you will generate a stream of

electrons of charge q by heating a wire (the

electrons ‘evaporate’ from the surface of the wire)

and accelerate them through a potential

difference, V, to a final velocity, v. The electrons

will then enter a region with a magnetic induction

field (symbol: B; unit: the Tesla) perpendicular to

the direction of the velocity. The magnetic field is

produced by a set of Helmholtz coils and is therefor

extremely uniform. The discharge tube is filled

with a vapor at a very low pressure; since the

quickly-moving electrons ionize the gas, the beam

appears as a luminous streamer. The magnetic force exerted on the electrons causes the beam to

follow a circular path. So,

�s ��!6s

�w � g � h �g � � �+ � �!�I%

The velocity v is found from conservation of energy:

� � ZI�!�I

Combining these relationships results in

! � �+I%I

Figure 1 - Apparatus for determining the specific charge of

the electron.

48

For Helmholtz coils, the magnetic induction field strength is related to the current in the coils by

+ ��7��=��6

with B in Tesla, N the number of turns in each coil (here N = 130), I the current in Amps, and a the

radius of the coil (here a = 0.150 m).

PROCEDURE:

1. Be sure that the main switch on the power supply is set to OFF. Carefully set the Helmholtz coil

device and the Discharge Tube Power Supply side by side on the tabletop so that the length of the

cabinet runs in a North-South direction. Connect the wire leads as shown in Figure 2 (at the end of

this write-up). Do not plug in the power cord of the power supply. Turn all knobs on the power

supply down to zero by rotating them counterclockwise (CCW). Have your instructor approve your

wiring before you turn anything on.

2. Now that the leads are connected, plug in the power supply's main power cord to an AC wall socket

and turn the power supply switch to ON. The filament in the discharge tube should begin to glow.

3. Move the VOLTAGE MONITOR SELECT switch on the power supply to the left.

4. Increase the ANODE VOLTAGE by using the leftmost knob on the power supply (the one labeled "0-

500Vdc / 10mA") until a blue beam emerges from the gun inside the discharge tube. This should

happen at just under 200 V. Once you are satisfied with the brightness of the beam, record this

anode voltage.1

5. Set the COIL CURRENT ADJ knob on the Helmholtz coil front panel to the middle of its range, i.e., so

that the white indicator points upward. Gradually increase the current through the Helmholtz coils

by turning the right hand knob on the power supply (the one labeled "0-20 Vdc 5A MAX"). As the

coil voltage increases, you should see the electron beam bend into a circular pattern. The more coil

voltage applied, the smaller the circular pattern will become.

6. It may be necessary to adjust the position of the tube so that the electron beam will hit the glass

rod. Your instructor will show you how. Ideally, the beam should be ‘cut in two’ by the rod. This

rod is marked off in centimeters and is used to measure the diameter of the electrons’ orbits.

7. Record the coil current (that is, the magnetic field strength, see above) required for collapsing the

circular pattern to at least 6 different diameters over the range of 0.105 to 0.050 meters, as


49

measured on the etched glass scale. Since the beam has thickness, choose a convenient portion of

the beam as the reference for making all measurements. For example, the center of the beam as

indicated by the greatest luminosity of the scale etching. This technique reduces one source of

systematic error.

ANALYSIS

1. For each coil current value above, calculate and record the corresponding magnetic field strength.

Double check and record the value of the accelerating potential, V.

2. For each diameter above, calculate the specific charge for the electron. Calculate the average of

these values, and compare the average to the accepted value by computing a percent difference.

Suggested Data Table

Diameter (m) Coil Current (A) B (T) V (V) e/m (C/kg)

0.100

0.090

0.080

0.075

0.070

0.060

0.050

Average --- --- ---

Per cent

Difference

3. Use the results you obtained in Lab 2 to calculate the mass of an electron. Compare this value to

the accepted value given in your textbook.

There is no worksheet for this lab exercise.

50

Lab 10 – MAGNETIC FIELDS

OBJECTIVE

To determine the fundamental magnetic constant, μo.

META-OBJECTIVE

To make and interpret relative measurements, rather than absolute measurements.

BACKROUND

In class, we made use of the Biot-Savart Law to find the magnetic field B at the center of a circular loop

of current:

+s�2� ��=��e

where R is the radius of the loop, N is the number of turns in the loop, I is the current in the loop,

and μo is the permeability of free space with a value of exactly 4π×10-7

m kg s-2

A-2

. You will

measure the B-field of the coil in terms of the horizontal component of the Earth’s field, BEarth; your

instructor will give you a value for your lab room that was determined without using the value of

μo.

The Earth’s field will be oriented along the 0o mark, and the coil’s

field will be perpendicular to that. A compass located at the

center of the coil will align with the total field, BEarth + BCoil.

The tangent of the angle θ will be BCoil/BEarth. Combining this

with the relation above, we obtain

�� 9��

9��

PROCEDURE

1. Carefully record the number of turns in the coil, (usually, N = 15). The diameter of the coil is 12.5

cm.

51

2. Place the compass securely on the pedestal within the coil. Turn the compass so that the 0o-180

o

line is in the plane of the coil. Rotate the whole apparatus so that the compass points at 0o. At this

point, the compass should be aligned with the Earth’s magnetic field.

3. Be sure that the power supply is turned off and that both knobs are turned completely counter-

clockwise. Attach cables from the power supply to the outside (N = 15) plugs on the coil. Ask your

instructor to approve your set-up.

4. Turn on your power supply. Turn the Voltage knob all the way up. Slowly turn the Current control

until you start to see the compass needle move. At approximately 10 degree intervals, record the

current and the deviation angle, θ. Do not let the current exceed 5A!

5. Turn the current back to zero, turn off the power supply, reverse the cables at the power supply,

and repeat Step 4. These currents and angles will be considered to be negative. When finished,

turn the current to zero and turn off the power supply, but do not disassemble your apparatus.

ANALYSIS

1. What was your independent variable? What was your dependent variable? Plot these in such a

way as to obtain a straight line. What is the meaning of the slope of your line? Solve for µo, the

permeability of free space.

2. Compare your value for µo with the accepted value and compute the percent difference.

53

WORKSHEET for LAB 10 – MAGNETIC FIELDS

NAME__________________________________ SECTION____________________________

OBJECTIVE:

N = __________ Diameter = __________

Current I Angle θ Tan θ

Slope of graph:__________ Experimental value for μo:__________

Actual value of μo:__________ Per cent Difference:__________

CONCLUSION:

55

Lab 11 - RC Circuits (Pasco)

OBJECTIVE

To confirm the predicted behavior of RC circuits.

BACKGROUND

In class, we wrote Kirchhoff’s Loop Rule for a charging RC circuit with DC emf as

f � �e 3�l\ � �e 0l0? 3� �\ �l � e\ 0q0? 3�s �� d?��c�b�?d��s�?� � �f�� 4 �OV�-s��%�s�7� � �7

and for a discharging RC circuit as

7 � �e 3�l\ � e 0l0? 3� �\ �l � �e\ 0q0? 3�s �� d?��c�b�?d��s�?� � s��OV�-s

The quantity RC is called the time constant, τ (tau), and represents the time required for the

potential difference across the capacitor to rise from zero to 63% of its full value or to fall to 37% of

its initial value.

PROCEDURE

1. Measure the actual values of the resistors and capacitors using the LRC meters. Don’t forget to

estimate the uncertainties of each measurement you make. Before you measure each capacitor,

short the ends with a spare cable to ensure that it is uncharged; during the measurement, wait

about a minute for the reading to stabilize. Make a data table showing the marked values 1 and

measured values of your resistors and capacitors. Generally, the actual values are between 5 and

20 percent off the nominal marked values, so you will use the marked values only to identify the

components, and the measured values in any calculations.

2. Calculate the product RC (= τ the time constant) for each resistor-capacitor pair you will test. How

many combinations are possible with your apparatus?

1 Underlined text denotes data to be recorded in your notebook.

56

3. Make sure that your power supply is off and that both

control knobs are turned CCW. Assemble the apparatus as

follows. Use a banana cable to connect points C and D; this

will short out the inductor, thereby removing it from the

circuit. Connect the wires from the switch box as labeled:

insert the wire labeled A into one of the three resistor

connectors, the wire labeled B into one of the capacitor

connectors, and the wire labeled ‘+” into the positive side

of the power supply. Your choice of A and B connectors determines which resistor and capacitor

are in the circuit. The switch box allows you to charge or discharge the capacitor. Connect a wire

from the negative side of the power supply to your B connector. Lastly, place a cable from the

Pasco 750 Input A with the positive (red) plug at point D and the negative (black) plug at your point

B; this will allow the 750 to record the voltage across the capacitor.

4. Have your instructor check your circuit.

Discharging the Capacitor:

1. Turn on the Pasco 750. On your computer desktop, find and open RCCircuits.ds. This program will

graph the voltage across the capacitor as a function of time, but will not start until the voltage

drops below a specific value. That is, you will not see all of the discharge curve. Turn on the power

supply and adjust the current control all the way CW and the voltage to approximately 5 volts (the

exact value is not critical). The trigger level on the graph should already be set somewhat above

4.5V. The time scale on the graph can be adjusted using the arrows at the bottom; the number

between the arrows indicates how much time each horizontal interval on the graph represents.

2. Flip the switch box to CHARGE and wait a few seconds. Click START on DataStudio. Gently move

the switch box to DISCHARGE. You should now see an exponentially decaying curve on the screen.

If necessary, adjust the time scale on the graph so that the curve fits nicely on the screen.

3. Use the cursor to determine the time at which the voltage passed 4.0 Volts. Now move the cursor

to determine the time at which the voltage was equal to 1.472 Volts (= 4.0/e = 0.37x4.0), i.e., when

one time constant has passed. How many times should you repeat your measurements?

4. Repeat Steps Two and Three for the other combinations of R and C.

57

5. When you are finished, turn both control knobs completely CCW and turn off the power supply, but

do not disassemble your apparatus until your results are approved by your instructor.

ANALYSIS

1. Construct a graph. What is your independent variable? What, then, is the dependent variable?

What should your curve look like?

2. Discuss whether your results support the theory discussed in class.

There is no worksheet for this lab exercise. Submit a full formal report.

58

Lab 11a - RC Circuits (non-Pasco)

OBJECTIVE

To confirm the predicted behavior of RC circuits

BACKGROUND

In class, we wrote Kirchhoff’s Loop Rule for a charging RC circuit with DC emf as

f � �e 3�l\ � �e 0l0? 3� �\ �l � e\ 0q0? 3�s �� d?��c�b�?d��s�?� � �f�� 4 �OV�-s��%�s�7� � �7

and for a discharging RC circuit as

7 � �e 3�l\ � e 0l0? 3� �\ �l � �e\ 0q0? 3�s �� d?��c�b�?d��s�?� � s��OV�-s

The quantity RC is called the time constant, τ (tau), and represents the time required for the

potential difference across the capacitor to rise from zero to 63% of its full value or to fall to 37% of

its initial value.

PROCEDURE

1. Measure the values of the resistors and capacitors using the LRC meters. Don’t forget to estimate

the uncertainties of each measurement you make. Before you measure each capacitor, short the

ends with a spare cable to ensure that it is uncharged; during the measurement, wait about a

minute for the reading to stabilize. Make a data table showing the marked values 1 and measured

values of your resistors and capacitors. Generally, the actual values are between 5 and 20 percent

off the nominal marked values, so you will use the marked values only to identify the components,

and the measured values in any calculations.

2. Calculate the product RC (= τ the time constant) for each resistor-capacitor pair you will test. How

many combinations are possible with your apparatus?

1 Underlined text denotes data to be recorded in your notebook.

59

3. Choose a resistor value R by connecting the

uppermost yellow socket to one of the other

yellow sockets (labeled ‘Resistor Selection’)

with a banana plug wire. Choose a capacitor

value C by connecting the nearest green

connector to one of the other green connectors

(labeled ‘Capacitor Selection’). Without

turning anything on yet, connect the power

supply to the terminals on the left side of the

board, making absolutely certain that the

positive terminal of the power supply is

connected to the positive terminal on the

board (red to red), and similarly for the

negative terminal (black to black). Put the DC

voltmeter across the capacitor by connecting

the corresponding inputs (V and COM) to the

labeled connectors on the board; this reading

will be VC.

4. Place the switch SW1 into its center, disconnected position.

5. Have your instructor check your circuit.

Charging Circuit:

1. Turn on the voltmeter. Turn the Voltage setting of the power supply all the way CCW, put the Fine

Voltage control to the 12 o’clock position, and turn the Current setting all the way CW (this allows

the supply to provide the necessary current for this experiment). Turn on the power supply.

2. Put SW1 into the discharging position (down). Press SW2 on the right side of the board and slowly

increase the power supply voltage until the meter reads about 10 Volts; use the Fine Voltage

control to make any final adjustments to the output. This is the value for the emf, E. Release SW2.

Don’t worry if the voltage immediately starts to decrease. N.B.: SW2 is a ‘cheat’ circuit added to

the main circuit that allows quick charging and discharging of the capacitor.

3. Calculate and record: s� � E� 4 Z�R f

60

4. Flip SW1 to the charging position and press SW2. The capacitor should discharge to within a few

millivolts of zero within a few seconds. Release SW2 and simultaneously start the timer. Measure

and record the time required for VC to reach s�. Once the measurement has been made, you do

not need to wait for the circuit to charge fully; just press SW2, wait for VC to return to zero, and

repeat the process. How many times do you think this measurement should be made? Record

your time values, the average of the values, and the standard deviation of the values.

5. Place SW1 into its center disconnected position and rewire the board to investigate a different

combination of R and C values. Repeat Step Four for the other combinations of R and C.

Occasionally, repeat Step Two above to re-adjust the power supply voltage.

Discharging Circuit:

1. Calculate and record: s�� Zo f

2. Place SW1 in its center, disconnected position. Choose values of R and C once again by wiring the

board as above.

3. Place SW1 into the discharge position and press SW2. Adjust the power supply so that the voltage

across the capacitor is 10 Volts.

4. Release SW2 and start the timer simultaneously. The capacitor should begin discharging. Measure

and record the time necessary for VC to reach s��. It is not necessary to wait for the capacitor to

discharge completely; simply press SW2 and recharge the capacitor to 10 Volts. How many times

do you think this measurement should be made? Record your time values, the average of the

values, and the standard deviation of the values.

5. Place SW1 into its center disconnected position and rewire the board to investigate a different

combination of R and C values. Repeat Step Four for the other combinations of R and C.

Occasionally, repeat Step Three above to re-adjust the power supply voltage.

6. When all data have been collected, turn off the voltmeter, turn the Voltage knob on the power

supply completely CCW, reset the Fine Voltage control to 12 o’clock, and turn the Current control

61

completely CCW. Turn off the power supply, but do not disassemble your apparatus until you have

analyzed your data.

ANALYSIS

1. Construct a graph. What is your independent variable? What, then, is the dependent variable?

What should your curve look like?

2. Discuss whether your results support the theory discussed in class.

There is no worksheet for this lab exercise. Submit a full formal report.

62

Lab 12 - LRC Circuits and Resonance

OBJECTIVE

To verify the theoretically predicted behavior of an LRC Circuit.

META-OBJECTIVE

To investigate resonance. To be introduced to the process of normalization.

BACKGROUND

An alternating current circuit (AC) is one in which the power supplied changes polarity at some

selected frequency, f. AC power is used in most industrial and household applications because it is

easier to produce and transmit. In an AC circuit, the current is determined by the capacitive

reactance (symbol: χC; unit: the Ohm) and the inductive reactance (symbol: χL; unit: the Ohm), as

well as resistance (R). The definitions of these reactances are:

�s �� #�\ ��* � ��#�

where f is the current frequency in Hertz (cycles per second), C is the capacitance, and L is the

inductance in Henries (H). Reactance and resistance are each an inhibition to AC current flow and

are examples of impedance, Z. Because of the differing phase relationships between current and

voltage in capacitors, inductors, and resistors, the total impedance of an AC circuit is not a simple

sum of the individual impedances. In a series LRC circuit, the impedance is described by the

equation:

¡ � �¢eI 3��* 4��s�I

Ohm's relationship for AC circuits may be written:

£p¤k � �p¤k¡��

So, the current in the circuit will be greatest (that is, resonance with the driving agent occurs) at the

frequency when Z is least, i.e., when XL = XC, or equivalently, when

�� # �¥ \��

assuming that the resistance R is small.

63

Note also that the voltage drop across the inductor and the current through the inductor are

related by an Ohm’s Relationship-like formula:

*�p¤k �� p¤k�*��

and for capacitor, s�p¤k �� p¤k�s ��

At resonance, then, VC rms = VL rms.

In this experiment, the resonant frequency of a series LRC circuit will be determined by graphing the

rms current as a function of the driving frequency.

PROCEDURE:

1. Measure and record the actual values of the resistance, inductance, and capacitance.

2. Calculate and record the theoretical resonant frequency of the circuit, fo.

3. Be certain that all devices are off and that the signal

generator is unplugged. Construct the circuit

shown in the Figure. You may choose either

capacitor, but use the 10 Ohm resistor. Insert the

BNC cable into the output connection of the signal

generator. Connect the other ends to the open

connectors of the circuit board (polarity doesn’t

matter). Attach a multi-meter to the same two

connectors and set it to read AC voltages; this

meter monitors the output of the signal generator,

which does not remain constant as a function of

frequency. The other multi-meters are used to measure the rms voltage drops across the resistor,

the capacitor, and the inductor simultaneously.

4. Ask your instructor to check your circuit before turning anything on. Set the waveform switch on

the signal generator to SINE, disable both attenuation circuits (buttons out), set the output switch

to INT, and turn the output control knob all the way to the left. Select the ‘C’ range, and then turn

on the signal generator. Adjust the frequency to approximately 50 Hz. Turn the output up until the

VTOTAL multi-meter reads 0.5V. NOTE: as you adjust the frequency, you will notice that the voltage

output from the signal generator will change. So long as the output is between about 0.1V and 0.5

V, the circuit will be operating well enough; there is no need to continually re-adjust the output.

64

However, what you will do is record the signal generator’s output and normalize the other voltages

to the output value. That is, when you do your graphs later in the exercise, you will plot VR/VTOTAL.

5. Record the actual driving frequency f of the circuit. Measure and record the rms voltage drops

across the LRC combination (VTOTAL) and VR. Put your data in a table in your notebook.

6. Increase the frequency by about 10 Hz, readjust the signal generator output if necessary, and

repeat the measurements. Continue in this way in 10 Hz steps until 300 Hz is reached. Remember

to re-adjust the signal generator voltage to about 1V as necessary.

ANALYSIS

Construct a graph of VR/VTOTAL (which is proportional to the current Irms) v. the driving frequency f.

Determine the frequency corresponding to the largest Irms. How well does this value compare with

the theoretical value fo calculated earlier? Calculate and record a percent difference.

65

WORKSHEET for LAB 12 – LRC Circuits and Resonance

Name __________________________________ Section __________________________

OBJECTIVE:

Actual values for R = __________ C = __________ L = __________ fo = __________

Driving Frequency f VTOTAL VR VR/VTOTAL

66

Observed resonant frequency = __________ Per cent difference __________

CONCLUSION:

If asked so to do, staple this sheet to your graph and turn them in. If not, be sure to submit a full,

formal report.

67

Lab 13 – Properties of Light

OBJECTIVE

To confirm the laws of reflection and refraction (Snell’s Law)

BACKGROUND

In this laboratory exercise, the optical phenomena (reflection and

refraction) that are the basic means by which most optical devices

work are investigated. The law of reflection states that the angle of

incidence of a light ray, as measured from a normal to the reflecting

surface, is equal in size to the angle of reflection, measured in the

same manner (see Figure 1).

The law of refraction (Snell’s Law), in its modern form, states that the

angles formed by a ray (relative to a normal) passing from one

material to another meet this condition:

n1 sin θ1 = n2 sin θ2

where n1 and n2 are each the index of refraction of the respective

materials. The index of refraction of a material is the ratio of the

speed of light in vacuum to the speed in the material (n = c/v) and is

equal to the square root of the material’s dielectric constant, κ

PROCEDURE and ANALYSIS

I REFLECTION

1. Mount the Light Source Box near one end of the magnetic rail. Place the Slit Plate on the front of

the Light Source with the slits vertical. Place the Parallel Ray Lens on a magnetic holder and mount

it on the rail, approximately 9 cm in front of the Source. Place the White Angle Table on the tilted

bracket and mount that at about the middle of the rail. Adjust the position of the lens and the bulb

in the light source until several parallel rays fall across the white angle table. Next, place the Slit

Mask over the slit plate so that only one ray energies. Lastly, adjust everything so that the one ray

is incident along the 0o

line of the angle table and so that it is as thin as possible.

2. Place the flat side of the mirror so that it aligns exactly along the ±90o line.

Figure 2 - Refraction

Figure 1 - Reflection

68

3. Rotate the angle table by ten degrees at a time and record the incident and reflected angles.1

Which is your independent variable and which is the dependent variable? Graph the values in such

a way as to obtain a straight line. Is the Law of Reflection valid?

II REFRACTION

1. Remove the mirror and replace it with the Cylindrical Lens. Place the flat side of the lens toward

the light source and align it exactly along the ±90o line. Adjust the table and slits so that the incident

ray comes in exactly along the 0o line.

2. Rotate the table by ten degrees at a time and record the incident and refracted ray angles. Which

is your independent variable and which is the dependent variable? Graph the values in such a way

as to obtain a straight line. Is Snell’s Law valid? How is the index of refraction of the plastic

represented on the graph? What is the index of refraction, n, for this particular plastic?

III TOTAL INTERNAL REFLECTION

1. Set up the cylindrical lens as in Part II, except have the flat side of the lens away from the light

source, so that the light will emerge from the plastic at the flat surface. Slowly, rotate the lens until

the refracted ray appears to emerge parallel to the flat surface. Record the critical incident angle.

Calculate the index of refraction again. Compare this value with the one obtained in Part II by

calculating a per cent difference.

IIII DIFFRACTION

1. You will return to diffraction with much more detail in a later exercise. For now, this is an

experiential exercise. Remove the cylindrical lens from the angle table and adjust the apparatus

again so that only one ray falls on the table. Remove the parallel ray lens and replace it with the

diffraction grating. The grating is an array of many very narrow slits.

2. Describe, in words or perhaps with a sketch, what you see. How many ‘rays’ are there now? How

are the rays different?


69

V POLARIZATION

1. Remove the angle table and its bracket. Remove the diffraction grating, but leave the magnetic

holder in place. Put two more holders on the rail, one perhaps two inches away from the original

holder, and the other perhaps two or three inches further down. On the last holder, place the

white screen.

2. Note how bright the light appears to be on the screen. Now place one polarizer on the first holder

so that 0o is up in the notch. Once again note the brightness of the light on the screen and describe

it in words.

3. Place the second polarizer on the middle holder so that its 0o mark is in the notch. Again,

qualitatively describe the brightness of the light you see.

4. Now, rotate the second polarizer in 10o increments. Describe what happens to the brightness of

the light seen on the screen after each rotation. At what angle does the screen go dark? What

happens as the angle continues to increase? Find the angles for which the transmitted light is

brightest (tough to do exactly) and darkest (much easier).

71

WORKSHEET for Lab 13 - Properties of Light

Name: _________________________________ Section: ________________________

OBJECTIVE:

I REFLECTION ANALYSIS:

θIncident θReflected

10o

20 o

30 o

40 o

50 o

60 o

70 o

80 o

II REFRACTION ANALYSIS:

θ1 θ2

10o

20 o

30 o

40 o

50 o

60 o

70 o

80 o

Index of refraction of plastic: ___________

III TOTAL INTERNAL REFLECTION:

θCritical = __________ Index of refraction = __________ Per cent difference = __________

72

IIII DIFFRACTION

Describe what you see.

V POLARIZATION

Describe what you see. At what angles is the transmitted light brightest? At what angles is it darkest?

CONCLUSION:

If requested so to do, staple this sheet to your graphs and turn them in. Otherwise, a full formal report is required.

73

Lab 14 – Thin Lenses

OBJECTIVE

To confirm the Thin Lens Equation and investigate several types of aberrations.

BACKGROUND

The behavior of light passing through a lens may be explained in terms of the principle governing the

refraction of light; i.e., the path of light traveling from one medium to another bends upon entering

the new medium. If the new medium is optically denser (n2 > n1) than the original, the light bends

toward the normal at the interface. If n2<n1, the light path will bend away from the normal.

Lenses are categorized according to what effect they have on light passing through them, namely

converging and diverging lenses. These categories may be further subdivided according to the

curvatures of the two surfaces:

Converging (f > 0) Diverging (f < 0)

meniscus )) meniscus ))

plano-convex |) plano-concave |(

double-convex () double-concave )(

The following is a summary of the properties of thin lenses with which you should become familiar.

More detail on each topic is found in the textbook. Keep in mind that the effects of real lenses are

more complicated.

A. The relationship among the object distance, o (the distance from lens to object), the image distance

i (the distance from lens to image), and the focal length of the lens, f, is

�� 3��d � � ��

The object distance is positive for objects in front of the lens and the image distance is positive for

objects behind the lens.

B. The magnification is the ratio of the image size to the object size (hi/ho); this can be shown to be

equal to the ratio of the image distance to the object distance:

!� � �4d� �

If the magnification is the positive, the image is upright; if it is negative, the image is inverted.

74

C. Chromatic aberration is a defect in the focal properties of a lens due to dispersion, or the spreading

out of a beam of refracted light due to the fact that the index of refraction varies with wavelength

(color).

D. Spherical aberration is a defect in the focal properties of a lens due to the fact that rays passing

through the outer portion of the lens are refracted more than those which traverse the central

portion. For example, the rays passing through the outer parts of a converging lens are brought to

a focus closer to the lens than are the central rays.

E. Coma is the aberration which affects rays from parts of the object which are not on the axis of the

lens; the consequence of this is that all rays are not focused at the same point.

F. Astigmatism is a defect in the focal properties of a lens or lens system due to a lack of symmetry

about the line from the center of a lens to an object. Horizontal and vertical lines in an object are

brought to a focus in different planes.

PROCEDURE

A. Converging Lens

1. Place the light source at one end of the optical

rail. Clip the object slide to the front of the light

source. Set up the optical bench using the 75mm

converging lens as in Figure 1. Look through the

lens and find the image. Approximately, where

does the image appear to be? 1

2. Attach the screen holder with screen to the

optical rail (Figure 2). The frosted side of the

glass screen should face the lens so that the

image will form on the front surface, but you may

still observe it from the backside. Locate the

image on the screen and record the following

information: object distance (measured from the

plate with the arrow-shaped hole, not from the

1 Underlined quantities are to be recorded in your notebook.

Figure 1 - Looking at the Image through a

Converging Lens

Figure 2 - Projecting the Image onto the Screen

75

center of the lamp), image distance, image real or virtual, object size, image size, and image upright

or inverted.

3. Compute and record the focal length fC of the converging lens.

4. Compute and record the magnification of the image (from hi/ho). Calculate a predicted value for

the magnification based on the object and image distances and do a percent difference between

the predicted value and the actual value.

5. *Construct a ray diagram using the object distance and image distance in Step 1. Determine the

focal length and magnification from your diagram and compare with values found in Steps 3 and 4

by performing percent difference calculations.

6. Using the same object distance as in Step 1, place a red filter in the light path. Focus the image of

the screen and record the image position. Compare this value with the original image position.

Repeat this step using a blue filter; record the image position. Comment on how chromatic

aberration affects the image position.

7. Using the same object distance as in Step 1, place a circular disc over the center of the lens. Re-

focus and record the image position. Replace the disc with an aperture, refocus, and again record

the image position. What can you conclude about spherical aberration?

B. Diverging Lens

NOTE: The image of a real object formed by a diverging lens is always virtual. A virtual image cannot

be focused on the screen; it can, however, be seen by eye if you sight through the lens at the

object. It is always upright, reduced in size, and appears to ‘hang’ in mid-air between the object

and the lens. There are a number of ways to determine the position of a virtual image.

1. Remove the screen and replace the converging lens

with a diverging lens. Can you see an image through

the lens? Describe its approximate position.

2. Mount the Virtual Image Locator on another magnetic

holder so that it is above the opening in the holder.

Place the locator at the approximate position of the

image. Now, you will make use of an effect known as parallax; move your head left and right,

watching the arrow on the locator and the image as seen through the lens. Most likely, the arrow

and the image will shift back and forth differently. Adjust the location of the arrow locator until the

arrow and image move together, i.e., they are in the same spot. Record the location of the image.

Figure 3

76

Calculate the focal length of the diverging lens and

compare with the given value with a per cent

difference.

Figure 4

77

WORKSHEET for Lab 14 – THIN LENSES

Name: _________________________________ Section: ________________________

OBJECTIVE:

I CONVERGING LENS

Image location (by eye)

Image location (on screen)

Object distance

Image distance

m ( = - i/o)

Real/Virtual

ho

hi

M (= hi/ho)

Upright/Inverted

fC Calculated

Per cent difference

II ABERATIONS

Image location red light

Image location blue light

Image location w/disc (outer edge of lens passes light

Image location w/aperture (center of lens passes light)

III DIVERGING LENS

Image location ( by eye)

Image location (by parallax)

Object distance

Image distance

fD Calculated

Per cent difference

If requested so to do, turn this sheet in. Otherwise, a full formal report is required.

79

Lab 15 - Interference

OBJECTIVE

Determine the wavelength of the light from a laser using interference.

BACKGROUND

Interference is an effect that directly supports the

wave nature of light. When coherent light

from two (or more) sources arrives at a

particular point, the waves can add

constructively (always in phase), completely

destructively (always out of phase), or

somewhere in between. In this exercise, you

will make use of a gas laser as both sources of

light by passing the light perpendicularly

through a double slit; the two resulting

sources are therefor exactly in phase with one

another. The light then continues on until it

hits a screen. If the two beams are in phase on arrival at a particular spot on the screen, then the

waves add constructively and a bright spot is seen. If the beams are 180o out of phase (and of the

same intensity), a dark spot will appear. As derived in class, the condition for these two cases are

0�cd�¦ � !§��q��c?%�q?d��0�cd�¦ � E! 3�ZIR §��0�c?%�q?d��

Now, because the slits themselves are not infinitely thin, as was assumed in the derivation, there is

also a diffraction effect. This appears in the interference pattern as an alternating decrease, then

increase, in the brightness of the spots.

Let’s simplify the relationship for destructive interference, since the angles are small. The sine of theta

should be about the same as the tangent of theta, which is x/Y, so that

0�?6�¦� ¨ E! 3�ZIR § �0�?6�¦ ¨ ��! 3 ��§

0� �©ª ¨ ��! 3 ��§

« � ¬�ª§0 ! 3 ¬ª§0

Figure 1 - Interference of Light Set-up

80

In this expression, X is the distance along the screen between a dark spot on the left side of the

central maximum and the corresponding dark spot on the right side (X = 2x), while N is the number

of bright spots between the dark spots, i.e., m = (N-1)/2.

PROCEDURE:

1. Be very careful to avoid looking at the laser light!

2. Cover the screen with white paper. Mount the laser, slit plate, and screen on the optical rail. The

plate should be about 6 cm from the laser, but the screen should be as far as possible from the slits

while still showing a clear interference pattern. Measure this distance from slits to screen, Y.1

Watch out for reflected laser light!

3. The slits to be used are D and E. Align the laser and slits so that a clear pattern is seen on the

screen.

4. For Slit Set D, measure the distance X from a dark spot on one side of the central maximum to the

corresponding dark spot in the other side. Count how many bright spots appear between the

marks; this is N. It might be easier to mark the spots with a pencil and measure the distance after

removing the paper from the screen. Repeat for as many dark spot pairs as possible. For each,

calculate the corresponding value for m.

5. Repeat for Slit Set E.

ANALYSIS

Separately for each slit set, plot your data is such a way as to obtain a straight line and perform a least-

squares best fit. What is the physical meaning of the slope of the best fit line? What is the value

you obtain for the slit separation, d for each set? Check your results with your instructor.

1Underlined quantities should be recorded in your notebook.

81

WORKSHEET for Lab 15 – DIFFRACTION

Name: _________________________________ Section: ________________________

OBJECTIVE:

Sit Set D Slit Set E

X N m X N m

Slope Slope

Slit Separation Slit Separation

Accepted value for d 0.125 mm Accepted value for d 0.250 mm

Per cent difference Per cent difference

CONCLUSION:

If requested so to do, staple this sheet to your graphs and turn them in. Otherwise, a full formal report is required.

83

Lab 16 – Atomic Spectra

OBJECTIVE

To measure the wavelengths of several optical transition lines of mercury.

META-OBJECTIVE

To investigate the properties of diffraction.

BACKGROUND

A diffraction grating provides an example of interference using many sources. In this case, light from a

single source is passed through many slits (not just two as in a previous lab). As discussed in class,

there are many interference maximums, but the brightest interference maximums occur when the

following condition is met:

mλ = d sin θm

where

m is the order of the maximum (waves from adjacent slits are in phase but the distance traveled to

the screen differ by m wavelengths),

d is the separation between two successive lines or slits on the grating (usually on the order of a

few wavelengths),

λ is the wavelength of the light, and

θm is the angle at which the mth

maximum occurs.

In this experiment, you will determine the wavelengths of the four principal lines in the emission

spectrum of the element mercury.

PROCEDURE

1. Note the slit spacing d of your grating. It will probably be written as the number of lines per

millimeter. Convert this to nanometers per line.

84

2. Mount the diffraction grating in its magnetic holder at one end

of the optical bench. Position the optical bench so that that end

hangs slightly over the edge of the table in such a way that it will

be comfortable to look through the grating. Mount the mercury

lamp at the other end of the optical rail. Adjust the heights of

the grating and lamp to be approximately the same. Mount the

two-meter stick on its stands and blocks well behind the optical

rail (see Figure 1); be sure that it is reasonably well centered and

perpendicular to the optical bench. Record the distance

between the grating and the meter stick1 as D (you may use the

horizontal distance).

3. Turn on the lamp by plugging it in. Mercury has a number of ultra-violet lines, so avoid looking

directly at the lamp; looking at the lamp through the glass grating should present no problem. Look

through the grating to observe the diffraction maximums; you should see a violet line (405 nm), a

blue line (436 nm), a green line (546 nm), and two yellow lines (577 & 579 nm), then the pattern

should repeat. You should be able to see two complete orders and part of the third order on each

side of the mercury lamp. Adjust the grating so that the lines are sharp and clear and appear in a

horizontal line.

4. Measure the apparent positions (XLeft and XRight) of as many first order lines as you can. Partner A

should look through the grating at a given line so that the line appears near the meter stick.

Partner B will move the edge of a sheet of white paper along the meter stick until A says that the

edge and the line under observation are aligned. Partner C will then shine the flashlight onto the

stick and record the position of the paper’s edge. Be sure to make measurements of the lines on

each side of the lamp. Measure the locations of as many lines as you can. Simply record the

positions of the lines on the meter stick; do not bother to measure the distance from the center.

This will be taken care of in the next step.

ANALYSIS

1) Calculate X, the difference of the apparent positions of the corresponding lines on each side

divided by two (X = (XRight- XLeft)/2); this process helps to reduce errors by averaging the distances of

the lines from the central axis. Find and record the angles between each line and the optical axis

(Hint: what is the relationship among X, D, and the angle θ?).


Figure 1

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2) Calculate and record the wavelength of each line. Compare your values to the values given above

in Part 3 by computing a percent difference. As an aside, the wavelengths of these lines can be

measured with spectrometers to within a few parts per thousand.

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WORKSHEET for Lab 16 – Atomic Spectra

Name: _________________________________ Section: ________________________

OBJECTIVE:

D = __________ d = __________

Violet Blue Green Yellow-1 Yellow-2

XLeft

XRight

X

(= XRight – XLeft)/2

Θ

λMeasured

λAccepted

Per cent

difference

CONCLUSION:

If requested so to do, turn this sheet in. Otherwise, a full formal report is required.

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APPENDIX - SAMPLE LAB HANDOUT, NOTEBOOK, and REPORT

Lab 100 - Output Power of a Microwave Oven

OBJECTIVE

To measure the output power of a commercial microwave oven.

BACKGROUND

Microwave ovens operate by exposing water molecules to an alternating electric field; since water is

an electric dipole, the field exerts torques on the water molecules that cause them to spin. As the

water molecules ‘bump’ into other types of molecules, such as sugars, proteins, and fats, these other

molecules acquire thermal energy.

PROCEDURE

1) Determine the mass of a Styrofoam cup1 for use as a calorimeter. Fill the cup approximately ¾

full with water and find the mass of the combination to determine the mass of the water alone.

2) Allow the water to come to room temperature.

3) Place the cup at the center of the oven, stir is gently, and make a temperature reading.

4) Close the oven door and switch the microwave on for 30 seconds. Measure the actual time the

oven is on with a stopwatch. As soon as the oven switches off, open the door, stir the water

gently with the thermometer, and take a temperature reading.

5) Repeat Step 4 until the water reaches about 90oC (i.e., don’t let it boil). Be sure to record the

time that the oven is actually running, not the total time from the start of the experiment.

6) Let the apparatus cool. Dismantle it only after you have performed the analysis below.

ANALYSIS

1) Assume that all of the energy output of the oven is absorbed as heat by the water and the cup.

Conservation of energy then requires that

Pt = Q = (mc∆T)water + (mc∆T)cup ,

where P is the power output of the oven, t is the total time over which that power was

supplied, Q is the heat flow into the water and cup, and m, c, and ∆T are the mass, specific

heat, and temperature change experienced by the water and the cup. In this particular


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exercise, the mass of the styrofoam cup is less than one-one hundredth the mass of water and

the specific heat of styrofoam is approximately one-fifth that of water. Therefore, the (mc)cup

term is small enough compared to (mc)water that it can be ignored, and the equation becomes

Q = [(mc)water] ∆T = Pt (Eq. 1)

Plot your data in such a way as to obtain a straight line. What will be your independent variable

and what will be the dependent? What is the physical significance of the slope of the line?

Determine the power output of the oven in Watts and compare your value with the

manufacturer’s advertised value of 650 W by performing a per cent difference calculation.

2) It is very difficult to do the propagation of uncertainty calculation for this lab; a good estimate is

about 3%. Does your result overlap with the given power value? If not, what might account for

the discrepancy?

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Note the correction made: the student didn’t realize that the thermometer was digital and so required a least count rather than an estimated scale uncertainty. The procedure from the manual was followed exactly, so there was no need to copy it into the notebook. Also, a lab partner apparently added some vital information.

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Here, the student has made an error in recording some values. The 44.4 has been crossed out with a single stroke and the correct value written nearby. He should have left a blank spot, or perhaps a zero, at the top of the right hand column; the correction is fairly clear. Note that the student has neglected to record the mass of the empty Styrofoam cup; even though the value was not used in the calculations, it should have been included in the notebook.

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Here, the graph was printed using Excel, then cut out and glued into the notebook.

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PHYS 101 - Lab Report – Output Power of a Microwave Oven

Steve Zodiac Partners: Marla Oaks, Sarah Jane Smith, & Fred Friendly January 21st, 2065 Instructor: Dr Milligan

Objective:

In this experiment, the power output of a particular microwave oven will be measured.

Apparatus:

Microwave oven - Caloric Model 750A9; Mercury Thermometer; Styrofoam cup calorimeter; Stop

watch; Triple Beam Balance

Procedure: The procedure was the same as given in the lab manual. Results and Analysis:

The data were measured as described above and recorded in the lab notebook. Assuming that all of

the energy output of the oven (Pt) is absorbed as heat (Q) by the water and the cup, conservation of

energy requires that

Pt = Q = (mc∆T)water + (mc∆T)cup ,

where P is the power output of the oven, t is the total time over which that power was supplied, and

m, c, and ∆T are the mass, specific heat, and temperature change experienced by the water and the

cup. In this particular exercise, the mass of the styrofoam cup is less than one-one hundredth the mass

of water and the specific heat of

styrofoam is approximately one-fifth

that of water. Therefore, the (mc)cup

term is small enough compared to

(mc)water that it can be ignored:

Q = [(mc)water] ∆T = Pt

This has the form of a linear equation,

so a plot of the calculated values of Q

versus t will allow for a determination

of P. The graph was plotted using

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Excel. The slope of the best fit line is 110.5 Cal/second. Since each Calorie is 4.19 Joules, this converts

to 463.9 Watts. No propagation of uncertainty was required for this laboratory exercise.

Conclusion:

The accepted value for the power of the microwave is 650 Watts, a percent difference of -29%. Since

the given estimate of the uncertainty in our measurements is 3%, it is most likely that either not all of

the microwave energy was actually absorbed by the water or the manufacturer’s asserted value was

incorrect.

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