Florida International University
GENERAL PHYSICS
LABORATORY 2
MANUAL
Florida International University
Department of Physics
Physics Laboratory Manual for Course
PHY 2049L
Manual revised by Brian Raue, Fall 2007
Originally compiled by Richard A. Bone and Laird Kramer
Contents
Syllabus
Sample Lab Report
The Vernier
Graphing and Tables with Microsoft Excel
Estimation of Uncertainties
2
5
7
9
11
Experiments
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Electrostatic Demonstrations
Electric Field Mapping
Force that Charged Parallel Plates exert on each other
Capacitors
The Oscilloscope
Direct Current Circuits
The Charge to Mass Ratio of an Electron
Magnetic Fields
Faraday’s and Lenz’s Laws
Electrical Resonance
Plane Reflection and Refraction
Mirrors, Lenses, and the Telescope
Double Slit and Thin Film Interference
1
15
18
20
23
28
32
37
40
48
51
54
57
61
SYLLABUS
Welcome to the exciting world of physics. This course is part of the two-semester sequence of
the introductory undergraduate physics labs. Students in this class should have taken or be taking
Phy2049 or Phy2054.
NOTE: If you drop the lecture class during the semester you are taking the lab, you will
automatically be dropped from the lab. There are no exceptions.
Physics is an experimental science and, while it is true that progress in physics has always relied
upon the contributions of theorists, the ultimate test of their theories takes place in the laboratory.
The experiments in this course cover most of the topics you will encounter in your lecture course.
They will be invaluable as an aid to deeper, conceptual understanding of those topics.
Fundamental laws and relationships will be put to the test and (hopefully) verified. The meaning
of an equation will be clarified so that it is not merely a collection of symbols. You will learn the
use of several instruments, and how computers can be interfaced with physics experiments.
In order to take maximum advantage of what this course can offer, read about your assigned
experiment in this manual before coming to class. Pay attention to the instructor and/or the
instructional video that will be played at the start of each class. Question your instructor if things
are unclear.
LAB COORDINATOR
Brian A. Raue
Office: CP 217
Phone: 305-348-3958
Email: baraue@fiu.edu
CLASS MEETINGS
 Classes start the first week of each semester and end the week prior to the final exam
week.
 Make-up labs must be completed during the same week as the missed lab by attending
one of the other sections. Consent of both the instructor of your regular section and the
section you wish to attend must be obtained. Permission from the second instructor will
only be granted if space is available.
 Students must sign in each class meeting to verify attendance.
COURSE WEBSITE
The website for all sections of this course is at www.fiu.edu/~baraue/teaching/2049L.html. The
website has important links to weekly pre-lab assignments, the schedule for labs, and
supplemental materials that will help you with your lab.
WEEKLY PRE-LAB ASSIGNMENTS:
Each week before the class meets you are required to download and read the manual for the
week. Before coming to class, you will be required to do an online assignment related to that
2
week's lab (except the first week). The online assignment will consist of a series of questions
related to the lab. To do the online assignment, you need to:
1. Point your browser to http://capa.fiu.edu/teacher.
2. Choose phy2049Lab from the pop-up menu.
3. Enter your Student Number followed by 00 and your CAPA ID. Get your CAPA ID
number at http://www.fiu.edu/~baraue/teaching/2049L/capaid.txt. There is a different
CAPA ID number for each set.
4. Click on the appropriate button to try your set.
Special notes and helpful hints
 Most problems are multiple choice and you will get one chance at answering them
correctly. Other problems may require numerical calculations for which you may
get more chances to get right.
 Entering the wrong units and the wrong number of significant figures won't count
against your four attempts but you have to get them right to get the problem right.
 Do not open multiple sessions or browsers. Be sure to exit properly each time to
terminate a session.
 You don't have to do the whole set at one sitting. You can log in as many times as
needed to get the set done before class.
 Avoid using your browser's RELOAD button as it may re-submit an incorrect
answer and use up one of your tries. Use the RELOAD button at the top the
assignment if needed.
 Always use basic SI units unless otherwise specified. Units such as "micrometers" are entered as "um", "kilograms" are entered as "kg", "newtons/meter" are
entered as "N/m", and "meters per second squared" are entered as "m/s^2".
 Answers requiring scientific notation such as 3.010-8 can be entered as "3.0E-8".
 Hints may come up for some problems if you submit an incorrect answer.
 If you ended up getting an answer wrong, you can log onto the set after lab and
find the right answer by clicking on the "view previous set" button on the login
page.
LAB REPORTS
In addition to the weekly pre-lab assignments, you will be required to turn in a "lab report" at the
start of class of the following week. The format of the report is somewhat different from
previous years, as we won't require you to write up a procedure. A short introductory paragraph
is required. You should answer all questions, do all calculations, and make all of the required
tables and graphs as stipulated in the manual. You should also provide a concluding paragraph
or two in which you discuss your results, any uncertainties, and make comparisons between your
results and "known" values. Proper use of grammar and punctuation is expected.
GRADES
 The weekly pre-lab assignments count for 20% of your grade.
 Lab reports count for 80% of your grade. Each lab report will be graded on a 20-point
scale. Points are taken off for each of the following:
o No introduction.
o Missed preliminary or analysis questions.
3
o
o
o
o
o
o




Improper use of significant figures.
Improper use of units.
Failure to label graphs.
Missing measurements/data.
Lack of experimental uncertainties.
Data analysis problems such as lack of trendlines on graphs, calculation of
required quantities, etc.
o Missing conclusion.
A missed assignment or lab will receive a ZERO grade.
Lab reports are due within the first five minutes of the next class meeting. After that, they
are considered late. Late reports will be docked 5 points each week that they are late. If
you are going to miss a lab, the report from the previous week is still due by the start of
your regularly scheduled class. You should make arrangements to turn your report in
early.
The lowest lab score will be dropped from your grade. A missed lab can be counted as
your lowest score.
The grading system is based on the following scale although your instructor may apply a
"curve" if it is deemed necessary. The upper three points of each scale will be given a "+"
and the bottom three points will be assigned a "-".
o A: 90-100%
o B: 80-90%
o C: 70-80%
o D: 60-70%
WHAT YOU NEED TO PROVIDE
1. Science Notebook (optional) with lined pages alternating with graph pages. Print your name
and lab section on the front cover. Otherwise submit individual lab reports on stapled paper.
2. Calculator with trig. and other math functions such as mean and standard deviation.
3. Computer memory device. Many labs will use the computer interface and produce tables or
graphs that must be included in your lab report. To transfer the data to your own computer
you must bring either a floppy disk or memory stick (flash drive) to download the data.
4. Access to a word processor and spreadsheet program.
AT THE END OF CLASS
1. Switch off and unplug any electrical equipment.
2. Disconnect all electrical circuits that you have connected.
3. Report any broken or malfunctioning equipment.
4. Arrange equipment tidily on the bench.
4
SAMPLE LAB REPORT
Young’s Modulus for Steel
(Lab partner - Michael West)
June 25, 1998
Introduction The purpose of the experiment was to determine the value of Young’s modulus of
elasticity for steel.
Results
Length of wire, l = 3.4650.005 m
Diameter of wire = 0.800.02 mm
Table of mass and corresponding extension
Mass (kg)
Extension (mm)
0.5
1.0
1.5
2.0
0.174
0.352
0.498
0.704
etc.
The data from the above table are plotted in Fig. 1
Calculations
mg
gl
A = mgl =
l
Al
slope  A
l
where m = suspended mass, l = original length of wire, l = extension, A = cross-sectional area
of wire, g = accel. due to gravity.
Young’s modulus, Y = stress/strain =
Now slope of graph = (0.330.01)x10-3 m/kg
Also A = r2 = (0.4x10-3) m2 = 5.0x10-7 m2
Y=
3.465  9.8
N/m2 = 2.06x1011 N/m2
0.33  10  3  5  10  7
5
Uncertainty calculations
2
l 2 slope  A 2
0.005 2 0.012 0.02 2
Y
    





  
  
  0.047

 l   slope   A 
3.456  0.33 0.80 
Y
 Y = 0.058x2.06x10-11 N/m2 = 0.1x1011 N/m2
 Young’s modulus for steel = (2.10.1)x1011 N/m2
Conclusions
The value obtained for Young’s modulus was consistent with the value of 2.0x1011 N/m2
reported in the textbook. The method used was reasonably accurate and produced an uncertainty
in the result of about 5%.
Max.s
lope
e
tlin
s
e
B
1
4
e
p
lo
.s
in
M
1
2
1
0
Extensio(m)

8
6
4
2
3
4
5
6
M
a
s
s
(
k
g
)
F
i
g
.
1
G
r
a
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o
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e
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v
s
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m
a
s
s
6
7
The Vernier
In order to measure lengths to a higher degree of precision than 1mm, for example, a vernier
scale is used. In Fig. 1 a vernier scale V is used to increase the accuracy with which a millimeter
scale M (e.g. on a meter rule) may be read. The total length of V is 9mm, having 10 divisions
each of length 0.9 mm. Thus each division on V is shorter than each division on M by 0.1 mm.
V
M
3
0
4
0
Fig. 1
Suppose now we wish to measure the position on the meter rule of the dashed line in Fig. 2. The
vernier scale is positioned as shown.
A
20
B
C
D
V
M
30
Fig. 2
Clearly the required reading is somewhere between 24 and 25 mm. To obtain the fractional part,
we note which graduation on V coincides (or comes closest to coinciding) with a graduation on
M. In Fig. 2 it is the 7th, labeled B, and the required reading is 24.7 mm. The reasoning is as
follows: The graduation on V to the immediate left of B is 0.1 mm in front of its counterpart on
M. Therefore if we move 7 divisions from B until we reach the zero graduation A, we conclude
that A will be 7 x 0.1 mm = 0.7 mm in front of the graduation D on scale M. (The value of
graduation C is immaterial.)
A common instrument used to measure linear dimensions is the vernier calipers. This consists of
a scale M graduated in millimeters and attached to a fixed jaw A, and a vernier scale V engraved
on a movable jaw B. This is shown in Fig. 3.
7
0 cm
1
3
5
M
V
A
C
B
Fig.3
When the jaws are closed, the zero graduations on M and V coincide. The object, C, to be
measured is placed snugly between the jaws by sliding B. Its length can then be read from scales
M and V. In Fig. 3 the reading is 2.57 cm.
Not all vernier scales are straight scales. Circular vernier scales are used on instruments that
measure angles accurately, such as the spectrometer. The main circular scale M (corresponding
to the millimeter scale above) is graduated in half-degree divisions. The fractional part of a
degree (in minutes) is read from the vernier scale V that rotates relative to M. In Fig. 4, the
reading is 10.5o + 12’, i.e. 10o 42'.
0’
30’
15’
30 o
20
Fig. 4
8
o
M
V
o
Graphing and Tables with Microsoft Excel
Unless the lab manual instructs you otherwise, tables and graphs are to be generated by
computer. Doing so will save you time, particularly when you are trying to determine the slope,
and the uncertainty in the slope, of a straight-line graph. (See “Estimation of Uncertainties.) The
computers are equipped with Microsoft Excel. You can open this program by clicking on
“Programs” in the Start menu and then clicking on “Microsoft Excel”. There are Excel
templates for many of the tables and graphs you will need to make at
www.fiu.edu/~baraue/teaching/2049L/schedule.html.
Tables: Begin by entering column headings, using your mouse to specify a particular cell, or
cells, for each heading. If, for example, column A is too narrow for the heading, highlight the
column by clicking on “A”. Then click on “Format”, “Column”, and “AutoFit selection”. Next
enter your data in the appropriate columns. To improve the appearance of the table, highlight the
column headings and click the boldface (“B”) button on the toolbar. To print the table, highlight
all the cells that you have used, then click on “File”, “Print area”, and “Set print area”, then
“File” and “Print”.
Spreadsheet calculations: You can save considerable time on repetitive calculations using
Excel. For example, in the table below, measurements have been made of velocities v0 and v, and
entered in columns C and D. From these values, it is required to calculate the accelerations, a,
using the equation a  v 2  v 02 /2x , and record them in column E. Here's how. Click on cell E4.
Note that E4 then appears in the window to the left of the equals sign. Click on the window to
the right of the equals sign and then type =(D4*D4-C4*C4)/2/0.25 (In this example, x = 0.25 m).
Press the Enter key, and the result, 0.71, will appear in cell E4. Click on E4 then place the cursor
 square in the lower right-hand corner of E4 and drag downwards. Calculated values
on the black
of acceleration, a, will appear in each cell of column E.
9
Graphs: Highlight the data in one of the two columns of data to be used in the graph. Hold
down the Control key and highlight the data in the second column. Click on the Chart Wizard
button. Select X-Y Scatter. Click on “Next”. Check whether the graph has your x data on the x
axis and your y data on the y axis. If it does, click “Next”. If not, click on “Series”. Highlight
the window labeled “X Values:”, then highlight all cells which contain your x data. Similarly
highlight the window labeled “Y Values:”, then highlight all cells which contain your y data.
Click on “Next”.
In the window that appears, add a chart title (e.g. Fig. 1 Graph of load versus extension) and
labels for your axes (e.g. Extension [mm]). Click on “Gridlines” and add or remove gridlines
according to your needs. Click “Next” followed by the button “as new sheet” followed by
“Finish”.
Click on “Chart” followed by “Add Trendline”. For a straight line graph select “Linear”. For a
parabola (as in Rectilinear Motion experiment), select “Polynomial” with the default Order of 2.
Click “Options” and check the box labeled “Display equation on chart”. Click “OK”.
To print your graph, click on “File” followed by “Print”. You can also cut and past your graph
into your Word generated
To determine the uncertainty in the slope (and intercept), click on the appropriate sheet (probably
sheet 1) in order to display your data. Click on “Tools” then “Data analysis”. Select
“Regression”. Check whether the “Input X range” and “Input Y range” are correct. If not, make
appropriate corrections (as for “X Values” above). Click “OK”. The slope (termed “X
Variable”) and intercept will appear, together with their uncertainties.
10
Estimation of Uncertainties
The purpose of this section is to provide you with the rules for determining the uncertainties in
your experimental results. All measurements have some uncertainty in the results due to the fact
you can never do a perfect experiment. The rules for estimating these uncertainties must be
adhered to in all experiments that you perform. We begin with the rules for estimating
uncertainties in individual measurements, and then show how these uncertainties are to be
combined to produce the uncertainty in the final result.
The “absolute uncertainty” in a measured quantity is expressed in the same units as the quantity
itself. E.g. length of table = 1.65 + 0.05 m or, symbolically, L + L. This means we are
reasonably confident that the length of the table is between 1.60 and 1.70 m, and 1.65 m is our
best estimate. If L is based on a single measurement, it is often a good rule of thumb to make L
equal to half the smallest division on the measuring scale. In the case of a meter rule, this would
be 0.5 mm. Other considerations, such as a rounded edge to the table, may make us wish to
increase L. For example, in the diagram, the end of the table might be estimated to be to be at
35.3 + 0.1 cm.
If the same measurement is repeated several times, the average (mean) value is taken as the most
probable value and the “standard deviation” is used as the absolute uncertainty. Therefore if the
length of the table is measured 3 times giving values of 1.65, 1.60 and 1.85m, the average value
is
165  160  185

 170 m
3
The deviations of the 3 values from the average are -0.05, -0.10 and +0.15m, and the standard
deviation

sum of squares of deviations
number of measurements
So now we express the length of the table as 1.7+ 0.1 m.
Note: Your calculator should be capable of providing the mean and standard deviation
automatically. Excel can also be used to calculate these quantities.

0.052  010
. 2  015
. 2
3
11
 01
. m
Generally it is only necessary to quote an uncertainty to one, or at most two, significant figures,
and the accompanying measurement is rounded off (not truncated) in the same decimal position.
“Fractional uncertainty” or “percentage uncertainty” is the absolute uncertainty, expressed as a
fraction or percentage of the associated measurement. In the above example, the fractional
uncertainty, L/L is 0.1/1.7 = 0.06, and the percentage uncertainty is 0.06 x 100 = 6%.
Rules for obtaining the uncertainty in a calculated result.
We now need to consider how uncertainties in measured quantities are to be combined to
produce the uncertainty in the final result. There are 2 basic rules:
A)
When quantities are added or subtracted, the absolute uncertainty in the result is equal to
the square root of the sum of the squares of the absolute uncertainties in the quantities.
B)
When quantities are multiplied or divided, the fractional uncertainty in the result is equal
to the square root of the sum of the squares of the fractional uncertainties in the
quantities.
Examples
1.
In calculating a quantity x using the formula x = a + b - c, measurements give
a = 2.1 + 0.2 kg
b = 1.6 + 0.1 kg
c = 0.8 + 0.1 kg
Therefore, x = 2.9 kg
Absolute error in x, x  0.22  01
. 2  01
.2
 0.2 kg
The result is therefore x = 2.9 + 0.2 kg
2.
In calculating a quantity x using the formula x = ab/c, measurements give
a = 0.75 + 0.01 kg
b = 0.81 + 0.01 m
c = 0.08 + 0.02 m
Therefore x = 7.59375 kg (by calculator).
0.012 0.012 0.02 2
x
 
  
  
  0.25
0.75  0.81 0.08 
x
Absolute uncertainty in x, x = 0.25  7.59375
= 2 kg (to one significant figure)
The result, therefore, is x = 8 + 2 kg

Fractional uncertainty in x,
Note: the value of x has to be rounded in accordance with the value of x. If x had been
calculated to be 0.003 kg, the result would have been x = 7.594 + 0.003 kg.
3.
The following example involves both rule A and rule B.
12
In calculating a quantity x using the formula x = (a + b)/c, measurements give
a = 0.42 + 0.01 kg
b = 1.63 + 0.02 kg
c = 0.0043 + 0.0004 m3
Therefore x = 476.7 kg/m3
Absolute uncertainty in a  b  0.012  0.02 2  0.02 kg
Fractional uncertainty in a + b = 0.02 / 2.05 = 0.01
Fractional uncertainty in c = 0.0004 / 0.0043 = 0.093
Fractional uncertainty in x  0.0932  0.012  0.094
Absolute uncertainty in x, x = 0.094 476.7 = 40 kg/m3 (to one significant figure)
The result is therefore x = 480 +40 kg/m3
Note that almost all of the uncertainty here is due to the uncertainty in c. One should therefore
concentrate on improving the accuracy with which c is measured in attempting to decrease the
uncertainty.
Uncertainty in the slope of a graph
Often, one of the quantities used in calculating a final result will be the slope of a graph.
Therefore we need a rule for determining the uncertainty in the slope. As described above, Excel
can do this for you. Another way to do this is “by hand” as follows: In drawing the best straight
line (see figure on following page),
1.
The deviations of the data points from the line should be kept to a minimum.
2.
The points should be as evenly distributed as possible on either side of the line.
3.
To determine the absolute uncertainty in the slope:
a. Draw a rectangle with the sides parallel to and perpendicular to the best straight
line that just encloses all of the points.
b. The slopes of the diagonals of the rectangle are measured to give a maximum
slope and a minimum slope.
max slope - min slope
c. The absolute uncertainty in the slope is given by:
, where n
2 n
is the number of data points.

13
Max.s
lope
e
tlin
s
e
B
1
4
e
p
lo
.s
in
M
1
2
Extensio(m)
1
0
8
6
4
2
3
4
5
6
7
M
a
s
s
(
k
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)
F
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1
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m
a
s
s
What has been described above is known as “standard uncertainty theory”. In this system, a
calculated result, accompanied by its uncertainty (the standard deviation s), has the following
properties: There is a 70% probability that the “true value” lies within the +s of the calculated
value, a 95% probability that it lies within the + 2s, a 99.7% probability that it lies within + 3s,
etc. We may therefore state that the “true value” essentially always lies within plus or minus 3
standard deviations from the calculated value. Bear this in mind when comparing your result
with the expected result (when this is known).
Some final words of warning
It is often thought that the uncertainty in a result can be calculated as just the percentage
difference between the result obtained and the expected (textbook) value. This is incorrect.
What is important is whether the expected value lies within the range defined by your result and
uncertainty.
Uncertainties are also sometimes referred to as “errors”. While this language is common practice
among experienced scientists, it conveys the idea that errors were made. However, a good
scientist is going to correct the known errors before completing an experiment and reporting
results. Erroneous results due to poor execution of an experiment are different than uncertain
results due to limits of experimental techniques.
14
Electrostatic Demonstrations
Introduction
In the first part of this experiment, an electroscope will be used to demonstrate the existence of
two types of charge and a few of their basic properties. In the second part, a Van de Graaff
generator will be used to impart a large charge to a hollow conductor and the electric field inside
this conductor will be investigated.
Procedure Part 1: Demonstrations with the electroscope
The existence of two types of charge, positive and negative, may be demonstrated with an
electroscope, shown in Fig. 1. It consists of a metal conducting rod with a metal ball at the upper
end and a pair of light, hinged, conducting leaves at the lower end. The rod is insulated from the
electroscope’s metal case by an insulating stopper. If both leaves acquire either a net positive
charge or a net negative charge, they will separate due to the repulsive forces that the leaves exert
on each other.
Before attempting each demonstration, touch the knob of
the electroscope with your finger to remove any excess
charge it may posses. For each demonstration, draw
sketches indicating the location of charges on the
different parts of the electroscope and describe and
explain your observations.
Insulator
Metal rod
a) Charge the hard rubber rod by rubbing it with a
felt cloth, and then bring it close to the
electroscope’s metal ball without touching it. The
Conducting
rubber will have acquired a negative charge by the
rubbing process.
leaves
b) Repeat with the glass rod rubbed with either silk
or tissue paper. In this case, the rod acquires a
positive charge.
c) Bring both the charged rubber rod and glass rod
near the metal ball and see if you can adjust their
Figure 1:
relative distances from the ball to produce no
Electrometer
divergence of the leaves.
d) Touch the knob with the charged rubber rod then remove it.
e) What happens if, after touching the knob with the charged rubber rod you bring the felt
cloth near the knob?
f) To charge the electroscope by “induction”, bring the charged rubber rod near the metal
ball, but not touching it, and then touch the ball with your finger. Remove your finger
and afterwards withdraw the rod.
15
g) To test the sign of the induced charge on the leaves, once again bring the charged rubber
rod near the ball and see if the leaves collapse or diverge further. Repeat with the glass
rod.
Van de Graaff Generator
The Van de Graaff generator works on the principle that charge accumulates only on the surface
of a conductor. The metal sphere in Fig. 2 is charged by a rubber belt that runs over two pulleys,
P1 and P2. The pulleys are made of different insulating materials. The lower pulley, P1, is motor
driven. The movement of the belt results in the top pulley acquiring a slight positive charge due
to friction while the lower one acquires a negative charge. The negative charge on the lower
pulley repels electrons on the outer surface of the belt, which then pass through the metal comb,
M1, to earth. This leaves the outer surface of the belt with a net positive charge. When this
charge arrives at the upper pulley, electrons are attracted to the belt from the sphere through the
metal comb, M2, from the hollow metal sphere leaving it with a net positive charge. Examine the
construction of the Van de Graaff generator in your classroom noting the features mentioned
here.
Metal sphere
Rubber belt
Earth
Figure 2: Van de Graaff Generator
16
Procedure Part 2: Electric field inside a charged, hollow conductor
In what follows, do not allow any part of your body within six inches of the spheres or the
cylinder since the voltages developed may be as high as 30,000 volts.




Place the large, grounded metal sphere approximately 1 inch from the generator sphere.
This prevents the voltage on the generator sphere from becoming too large.
Place the hollow wire-mesh cylinder on top of the generator sphere. This is your hollow
conductor.
Under your instructor’s supervision, suspend a pith ball inside the cylinder from a silk
thread, and then switch on the generator. Move the pith ball around, allowing it to touch
the bottom of the cylinder.
Now remove the pith ball from the cylinder and suspend it close to the generator sphere.
Describe and explain your observations and state your conclusions concerning the electric field
inside and outside a charged, hollow conductor. Note: An electric field is a region of space
where a charged object will experience a force of electrical origin. Such a field is produced by
other charges.
17
Electric Field Mapping
Introduction
An “Electric Field Mapping Apparatus” will be used to investigate the electric fields of a number
of pairs of oppositely charged conductors. The apparatus will allow you to draw the
equipotential lines. As the word implies, equipotential lines are lines where the electric potential,
or voltage, is the same. From these it will be possible to construct the electric field lines, which
indicate the direction of the field. You will determine the electric fields for three configurations
of conductors: a) two oppositely charged parallel plates, b) two oppositely charged small
spheres, and c) a small sphere near an oppositely charged flat plate.
Apparatus
The apparatus provides a two-dimensional analog of each of the three situations above. For
example, the parallel plates are represented by two bars, as shown in Fig 1, and may be
considered as a cross section through the plates.
V/8 2V/8 3V/8 4V/8 5V/8 6V/8 7V/8
A
Galvanometer
B
Probe
Power
supply
Figure 1
These “plates” are connected to a low voltage power supply, which is also connected between
terminals A and B. If terminal A is arbitrarily assigned a potential of zero, terminal B will be at a
potential, V, that will be indicated by the voltmeter on the front of the power supply. A chain of
8 resistors, alternating with seven terminals, is connected between A and B, providing seven
reference potentials of V/8, 2V/8, 3V/8, ... 7V/8 volts.
A center reading galvanometer is connected between, say, the 3V/8 terminal, as shown in Fig. 1,
and a moveable probe that can be placed anywhere in the electric field created by the charged
18
plates. The needle will deflect to the left or right depending on whether the potential at the
position of the probe is greater or less than 3V/8 respectively. The procedure is to locate a series
of points where the deflection is zero, these points lying on an equipotential line at 3V/8 volts.
Similarly we can construct the V/8, 2V/8,....equipotential lines.
Procedure
1. Setting up.
a. Place the selected pattern (graphite side outwards) on the underside of the field
mapping board, securing it with the two knurled screws.
b. Connect the power supply between terminals A and B (Fig. 1) with the negative
terminal of the supply connected to A.
c. Set the power supply to four volts.
d. Fasten a sheet of plain paper under the four rubber mushrooms on the upper side of
the board, and, using the appropriate transparent plastic template, trace the selected
pattern on the paper.
e. Connect the galvanometer between the probe and the V/8 terminal.
2. Make the measurements.
a. Now move the probe over the board until a position is found where the galvanometer
deflection is zero. The circular hole in the top arm of the probe is directly above the
contact point of the probe, thus allowing the position to be marked on the paper.
b. Move the probe to another nearby position where the galvanometer reading is zero,
and continue this process across the whole board.
c. Connect these equipotential points by a smooth curve. Since V = 4 volts, the potential
along this line is V/8=0.5 volts. Label the line with this potential.
3. Repeat the above procedure for the remaining six reference potential terminals.
4. Remove the paper and, using dashed lines, sketch a few electric field lines. Remember that
these lines always originate on a positive charge and terminate on a negative charge. Also
they intersect equipotential lines at right angles and meet the surface of a conductor at right
angles because that surface is an equipotential surface.
Now repeat all of the above procedures for the other pairs of conductors.
Q1.
What is the magnitude of the electric field intensity in the central region between the
parallel plates? Comment on the uniformity of the field (or lack of it) between the plates.
Q2.
How can you tell qualitatively from your diagrams where the value of the electric field is
large and where it is small?
19
Force that Charged Parallel Plates Exert on Each Other
Introduction
This experiment is an indirect test of the validity of Coulomb’s Law, which concerns the force
which one charged particle exerts on another. You will be determining the force that a charged
conducting plate exerts on a second, parallel, oppositely charged plate. This, essentially, is a
charged capacitor.
We can use Gauss’s Law, itself a consequence of Coulomb’s Law, to show that the electric field,
E, of one of the plates, carrying a charge q, is
q
E
2 A 0
where A is the area of the plate and 0 is the permittivity of free space. This field then exerts a
force on the other plate, which carries a charge –q. The magnitude of the force is
q2
2 A 0
Now recall that the charge q is proportional to the potential difference, V, between the plates,
namely q = CV. The capacitance C is given by
F   q E
C
0 A
q
0 A
V
d
d
where d is the distance between the plates. Substituting into the expression for F,
 AV 2
F 0 2
2d
The validity of this equation, which is based on Coulomb’s Law, will be examined, and you will
obtain a value for 0 to be compared with the accepted value of 8.85 10-12 F/m.
Figure 1
20
Apparatus
The apparatus is shown schematically in Fig. 1. The lower plate is fixed whereas the upper plate
is pivoted on a knife edge about an axis, XX, a distance a from the center of the plate. A mirror,
M, is rigidly connected to the upper plate and therefore also pivots about this axis. The mirror
makes it possible to measure the distance, d, between the plates very accurately using a laser and
scale as shown in Fig. 2. Further details of the use of this arrangement are given below.
Figure 2
+
Power
supply
1 M
Plates
V
Figure 3
Procedure
1. Locate and mark lightly with a pencil the exact center of the upper plate. Determine the plate
area, A.
2. Set up the circuit shown in Fig. 3, with the 1 M (1000,000 ) resistor included as
protection for the power supply in the event that the parallel plates touch. DO NOT
SWITCH ON THE POWER SUPPLY UNTIL THE CIRCUIT HAS BEEN CHECKED BY
YOUR INSTRUCTOR.
3. Arrange the laser and scale so that the distance b (Fig. 2) is about 1.5 m. Adjust the mirror,
M, so that the laser hits the scale.
21
4. Gently raise and lower the pivoted assembly by means of the beam-lift attachment provided
for this purpose. This ensures that the knife-edges are correctly positioned with respect to the
rest of the apparatus and should be done before any reading is taken.
5. Adjust the counterbalance until the gap, d, between the plates is approximately 4 or 5 mm.
(The lower plate may need some adjustment to ensure that it is parallel with the upper one at
this separation.) Again operate the beam-lifter.
6. Having shielded the apparatus from air currents, record the reading s', of the laser spot on the
scale. Don’t try to use the center of the laser spot but rather the upper edge of the laser spot.
Although this reading is not used in future calculations, it will be necessary to recheck it
periodically, as described below, to ensure that the apparatus has not accidentally been
disturbed.
7. Place a 10 mg mass at the center of the upper plate and record the new scale reading, s.
8. Repeat step 7 for masses of 20, 30, 40, 50 and 60 mg. You should have a different value of s
for each mass.
9. Carefully remove the masses and check that the value of s' has not changed. If it has, use the
beam-lifter to reset the apparatus.
10. Turn on the power supply and gradually increase the potential difference between the plates
until you obtain the same scale reading, s, that was obtained with the 10 mg mass.
11. Record the voltmeter reading, V.
12. If the separation, s, has been carefully reproduced, the electrical force of attraction, F, will be
equal to the weight of the 10 mg mass.
13. Repeat steps 10-12 for the separations corresponding to the other masses.
14. If the value of s' is seen to change at any stage, it will be necessary to use the beam-lifter to
reset the apparatus. If you cannot reproduce s', it will be necessary to start again from step 7.
REMEMBER TO SWITCH OFF THE POWER SUPPLY before adding or removing masses.
15. With the power off, place a small coin, or other weight, at the center of the upper plate to
bring it into contact with the lower one, and record the scale reading, so. The distance, d,
between the plates can be shown by simple geometry to be given by
d  s  s0 a / 2b .
16. Prepare a table similar to the one below
Mass, m
(kilograms)
Scale
reading, s
(meters)
Pot. Diff., V
(volts)
Electrical
force, F
(newtons)
Plate
separation, d
(meters)
V2/d2
17. Plot a graph of F (y axis) vs V 2/d 2 (x axis) and, from the slope, determine 0 (value and
error). Compare your value with the accepted value given in the Introduction.
22
Capacitors
Introduction
A capacitor is any two conductors separated by an insulator. If equal and opposite charges are
placed on the two conductors, a potential difference is established between the conductors. The
relationship between the charge q on the conductors and the potential difference V between the
conductors is given by
q  VC ,
where C is a proportionality constant known as the capacitance. C is measured in units of farads,
F, (1 farad = 1 coulomb/volt). The capacitance of the capacitor depends on size, shape, and
location of the conductors as well as the insulating material. In this lab, we first build a capacitor
and then investigate the charging/discharging characteristics of capacitors.
The simplest capacitor to build and study is a parallel plate capacitor. It consists of two flat plates
placed next to each other, separated by an insulator. The capacitance of a parallel plate capacitor
is given by
 A
C 0
d
where  is the dielectric constant of the insulator, 0 is the permittivity of free space, A is the area
of the plates, and d is the separation distance between the plates.
To study the charging/discharging properties of a capacitor, we’ll build an RC circuit with a
capacitor, resistor, switch, and battery. We’ll connect the battery to the resistor and capacitor in
series and monitor the charge on the capacitor as charge builds up by measuring the potential
difference across the capacitor. We’ll also connect a charged capacitor to a resistor and monitor
the charge flowing off the capacitor. The flow of charge (i.e. current) follows an exponential
distribution in both cases. Figure 1 illustrates the charging circuit.
Figure 1
When the capacitor is charged, the potential across it approaches the final value exponentially,
modeled by
V(t)  V0 (1 e
23

t
RC
)
where V0 is the applied potential difference, R is the resistance, C is the capacitance, and t is the
time. The product RC, known as the time constant of the circuit, determines the rate of charging.
A large time constant means that the capacitor will charge slowly.
If the switch is thrown into the other position, the capacitor will discharge, the potential across
the capacitor is reduced, which in turn reduces the current. This process creates an exponentially
decreasing voltage, modeled by

t
V(t)  V0 e RC
where the same time constant RC describes the rate of charging as well as the rate of discharging.
Objectives





Build and investigate the capacitance of a parallel plate capacitor.
Measure an experimental time constant of a resistor-capacitor circuit.
Compare the time constant to the value predicted from the component values of the resistance
and capacitance.
Measure the potential difference across a capacitor as a function of time as it discharges and
as it charges.
Fit an exponential function to the data. One of the fit parameters corresponds to an
experimental time constant.
Part I: Build A capacitor
You can build a parallel plate capacitor out of two rectangular sheets of aluminum foil separated
by a piece of paper. We’ll use a textbook as the foil separator since it is easy to slip the foil
between any number of pages, thus varying the separation distance. To ensure the pages have
equal separation, place a weight on top of the book. Be careful not to “short out” the pieces of
foil when you connect the meter leads to the foil. That is, don’t let them touch each other.
Procedure Part I
1. Take two pieces of aluminum foil approximately the size of your textbook and place them in
your textbook separated by 10 pages. You may want to add small “tabs” for connecting to the
multimeter leads. Place the weight on the textbook.
2. Attach two leads with alligator clips to your tabs on the foil. At your station is a meter that
can measure capacitance. Put two small wires into the input for capacitance measurement
and select the capacitance measurement function on the meter. Attach the other ends of the
leads to the two small wires that you plugged into the meter and take a measurement of the
capacitance. The meter will measure capacitances from 2 nF up to 20 F. You will need to
adjust the range selection on the meter to get your measurement.
3. Fill in the data table below with your values.
4. To explore the relationship of capacitance to the separation distance, change the number of
pages between the foils. You want to make an additional four (or more) measurements and
record them in the table. Make sure to place the weight on the book for each measurement.
24
Decide how to vary the numbers of pages, considering how the capacitance depends on
separation distance.
5. To explore the relationship of capacitance to area, reduce the area of both pieces of foil
equally, insert them into the book, and record your measurements in the table. Note that the
foils need to be aligned on top of one another for a useful measurement. You should carry out
at least an additional two measurements to study the trend. You decide how to vary the size
of the foil. Again, consider how to optimize the measurements.
6. Estimate the thickness of the pages by using a vernier caliper to measure a large number of
pages and then determine the average values for the thickness. You may want to make several
measurements and average the results.
Separation (m)
Length (m)
Width (m)
Area (m2)
Capacitance
Analysis Part I
1. For the data as a function of separation, plot the measured capacitance vs. separation.
2. How does the capacitance depend on separation? Does it follow a straight line? Does it
follow the trend you expect? Why or why not?
3. For the data as a function of area, plot the measured capacitance as a function of area.
4. How does the capacitance depend on area? Does it follow a straight line? Does it follow the
trend you expect? Why or why not?
5. Using the slope from your graph, determine the dielectric constant of paper. Find a value for
the dielectric constant of paper in your textbook and compare to your measured value.
Part II: Measure the Time Constant of A capacitor
Preliminary Questions
1.
2.
To better understand exponential decay—like the discharging of a capacitor—consider a
candy jar, initially with 1000 candies. You walk past it once each hour. Since you don’t
want anyone to notice that you’re taking candy, each time you take 10% of the candies
remaining in the jar. Sketch a graph of the number of candies for a few hours.
How would the graph change if instead of removing 10% of the candies, you removed
20%? Sketch your new graph.
25
Procedure Part II
1. Use the meter to measure the capacitance of the capacitor at your work station. Be sure to
connect the positive lead of the capacitor to the positive input on the meter. Record the value
of the capacitor in your data table.
2. Connect a series circuit of the variable resistor, 100-F capacitor, and a battery. For now,
leave one lead off of the battery. Then connect the LabPro Voltage Probe leads across the
capacitor with the red lead on the positive side of the capacitor. Your setup will look similar
to Figure 1 but we are just going to connect the battery instead of using the switch. Set
variable resistor box to 100-k. Note that the capacitor has a polarity and must be connected
to the battery correctly. The negative side is marked and this must be connected towards the
negative lead of the battery. Record the values of your resistor in your data table, as well as
the tolerance value of the resistor marked on back.
3. Connect the Voltage Probe to Channel 1 of the LabPro or Universal Lab Interface.
4. Open the file in the Experiment 27 folder of Physics with Computers. A graph will be
displayed. The vertical axis of the graph has potential scaled from 0 to 4 V, which must be
changed to 0 to 9 V by clicking on the “4” and typing in 9. The horizontal axis has time
scaled from 0 to 10 s. Change this by clicking on the Data Collection tab and setting the
upper limit to 25 s.
5. Click
to begin data collection. As soon as graphing starts, connect the remaining lead
to the positive terminal of the battery. Your graph should show zero voltage for a few
seconds and then a gradual increase with time.
6. To compare your data to the model, select only the data after the potential has started to
increase smoothly by dragging across the graph. Click the curve fit tool , and from the
function selection box, choose the Natural Exponential function, A*(1-exp(–C*x )) + B. Click
, and inspect the fit. Click
to return to the main graph window.
7. Record the value of the fit parameters in your data table. Note that the C used in the curve fit
is not the same as the C used to stand for capacitance. Compare the fit equation to the
mathematical model for a capacitor discharge proposed in the introduction,
V  V0 (1  e

t
RC
)
8. Cut and paste your graph into a Word document for your report. Choose Store Latest Run
from the Data menu to store your data. You will need this data for later analysis.
9. Your capacitor is now fully charged so again click the
to begin data collection. As
soon as graphing starts, connect the positive lead to the battery to the negative lead. This will
cause the capacitor to discharge through the resistor box. Your data should show a constant
value initially, then a decreasing function. Note that you need to make the connection quickly
because the capacitor will discharge through the resistance of the voltage probe.
10. To compare your data to the model, select only the data after the potential has started to
decrease smoothly by dragging across the graph; that is, omit the constant portion and the
initial decrease from moving the banana plug. Click the curve fit tool , and from the
function selection box, choose the Natural Exponential function, A*exp(–C*x )) + B. Click
, and inspect the fit. Click
to return to the main graph window.
V(t)  V0 e
26

t
RC
11. Record your parameters again in your data table and cut and paste your graph into a Word
document for your report. Choose Store Latest Run from the Data menu to store your
data.
12. Hide your first runs by choosing Hide Run Run 1 from the Data menu. Remove any
remaining fit information by clicking the gray close box in the floating boxes.
13. Now you will repeat the experiment with a resistor of lower value—say 50 k How do you
think this change will affect the way the capacitor discharges? Repeat Steps 4 – 11.
Be sure to do step 5 of the analysis before leaving the lab as it requires you to make an
additional plot.
Data Table
Fit parameters
Trial
A
B
C
1/C
Resistor
Capacitor
Time
constant
R
()
C
(F)
RC
(s)
Charge 1
Discharge 1
Charge 2
Discharge 2
Analysis
1. In the data table, calculate the time constant of the circuit used; that is, the product of
resistance in ohms and capacitance in farads. (Note that 1F = 1 s).
2. Calculate and enter in the data table the inverse of the fit constant C for each trial. Now
compare each of these values to the time constant of your circuit. Are they equal? Should
they be?
3. Note that resistors and capacitors are not marked with their exact values, but only
approximate values with a tolerance. If there is a discrepancy between the two quantities
compared in analysis step 2, can the tolerance values explain the difference?
4. What was the effect of reducing the resistance of the resistor on the way the capacitor
discharged?
5. How would the graphs of your discharge graph look if you plotted the natural logarithm of
the potential across the capacitor vs. time? Sketch a prediction. Show Run 1 (the first
discharge of the capacitor) and hide the remaining runs. Click on the y-axis label and select
ln(V). Uncheck the boxes for the Potential column. Click
to see the new plot.
6. What is the significance of the slope of the plot of ln(V) vs. time for a capacitor discharge
circuit?
7. What percentage of the initial potential remains after one time constant has passed? After two
time constants? Three?
27
The Oscilloscope
Introduction
One of the most versatile and important instruments found in research labs, industry and
medicine is the oscilloscope. In the research lab, it is used mainly as a device for monitoring
voltages and electrical signals. Industry uses the oscilloscope for the design, construction and
maintenance of electronic equipment. Hospitals use oscilloscopes for monitoring vital signs,
such as a patient’s heart-beat.
Electron gun
Figure 1
The essential internal features of the oscilloscope are shown in Figs. 1 and 2. Fig. 1 shows
electrons being generated “thermionically” from a hot filament (cathode), and accelerated
towards a positive anode. Some of the electrons pass through a small hole in the anode and form
a beam that is directed towards a fluorescent screen at the front of the instrument where it forms
a bright spot of light. On its way to the screen, the beam passes between two sets of parallel
metal plates. A potential difference applied between the Y plates causes the beam to be deflected
vertically in the resulting electric field, as shown in Fig. 2. Similarly the X-plates control
deflection in the horizontal direction. A potential difference, which may be constant or varying
with time, can be applied through input sockets on the front of the oscilloscope, after which it is
amplified before being fed to either the X-plates or Y-plates. The degree of amplification may be
varied by a “gain” control, and the whole trace may be shifted horizontally or vertically by
“position” controls. Some of the controls are illustrated in Fig. 3. Note that most oscilloscopes
are “dual-trace”, meaning that they can handle two signals simultaneously. Therefore several of
the controls on the front panel are duplicated.
Figure 2
Y-plates
X-plates
Fluorescent screen
Electron beam
28
INTENSITY FOCUS
POSITION
POWER
POSITION
AC
GROUND
TIME BASE
Y-GAIN
(VOLTS/CM)
DC
INPUT SOCKET
Figure 3
Procedures
Familiarization and preliminary adjustments
Turn on the power to the oscilloscope and wait about 15 seconds for it to warm up. Set the
intensity control to the middle of its range, and then switch off the “time base”. You should now
see a stationary spot of light. Adjust the focus to obtain the smallest spot. Note how its position
may be varied manually with the horizontal and vertical position controls. Switch on the timebase and set the trigger control to “auto”. The time base applies a saw-tooth voltage to the Xplates, causing the beam to sweep uniformly from left to right, and then flip rapidly back to the
left before repeating the sequence. Note the effect of different time-base settings.
The time base setting tells you the rate at which the trace sweeps horizontally across the screen.
For example, if the time base setting is 1 ms/cm means it takes the scope 1 ms to sweep across
the screen 1cm. Therefore, you can tell how much time has elapsed between two events that
occur on the screen. The Y-gain tells you the voltage difference between to parts of the trace.
For example, if the Y-gain is set at 2 volts/cm, and you see the trace at 3 cm above some
reference point, this corresponds to 3x2=6 volts.
NOTE: Some of the scopes have controls that are time/division (such as 5 ms/DIV) and V/DIV.
Voltage measurement 1.
1. Adjust the time base setting to 1 ms/cm and use the vertical position control to position the
trace on a grid line near the bottom of the screen.
2. Now connect a battery to the input socket via a switch, with the positive battery terminal
going to the central conductor. See Fig. 4.
3. Set the Y-gain to 2 volts/cm with the continuously variable control in the “calibrate” position.
4. Close the switch and note how far the trace jumps.
5. Calculate the terminal potential difference of the battery.
6. Now repeat with the Y-gain set at 1 and 5 volts/cm.
Q1. Which one of these three settings is most suitable? Why?
29
Figure 4
Voltage measurement 2.
1. Now set up the circuit in Fig. 5, observing the polarities (+ and - signs), if any, on the 100 F
capacitor and the unknown capacitor whose capacitance, C, is to be determined.
2. Before taking readings, discharge the capacitors as follows: Disconnect the battery and,
using a piece of connecting wire, momentarily connect the two terminals of each capacitor in
turn.
3. Reconnect the battery and, holding the switch closed as briefly as possible, measure the
voltage across the 100 F capacitor.
4. Subtracting this from your measured value of the battery voltage gives you the voltage across
the unknown capacitor. Also, applying the relation q = CV to the 100 F capacitor gives its
charge q. Recalling that two capacitors in series carry the same charge, apply the same
relation to the unknown capacitor to determine C.
C
100 F
+
+
Figure 5
Frequency measurement
The oscilloscope will be used to determine the frequency of the alternating current supplied by
FP&L.
1. Set the time base to 5 ms/cm and adjust the continuously variable control to the calibrate
position. Set the Y-gain to 0.2 volts/cm.
30
2. To measure the AC frequency, we will use a simple antenna to pick up a signal radiating
from the oscilloscope’s power cable. Connect a co-axial cable to the oscilloscope input, hold
the central conductor in one hand and touch the oscilloscope’s insulated power cable with
your other hand. You should now observe a sinusoidal wave on the screen. If necessary,
adjust the Y-gain until a wave amplitude of about 2 cm or more is obtained. Now adjust the
“trig level” until the trace appears to be stationary.
3. Position the trace such that the fine scale divisions on the screen may be used to measure the
horizontal distance between two adjacent peaks. From this measurement and the time base
setting, determine the period of the wave and hence its frequency.
Investigation of a power supply’s output
In this section, you will use the oscilloscope to determine the AC and DC outputs from a power
supply. DC outputs are typically derived from AC by means of diodes, which are like one-way
valves for current. The power supply has a half-wave rectified DC output, and a full-wave
rectified DC output. In the case of a half-wave rectified output, the power supply takes an AC
signal and simply cuts off the negative output. In the case of a full-wave rectified output, the
negative part is inverted and added back to the output. It is easy to visualize this if you take a
sinusoidal wave and simply erase the bottom half (half-wave) or invert it and add it to the
positive part.
Connect each output of the power supply in turn directly to the input socket on the oscilloscope
and sketch the resulting waveform. Adjust the Y-gain to obtain a convenient trace amplitude.
For the full-wave rectified DC output, measure the maximum (peak) voltage. The equivalent
steady DC voltage is given by the maximum voltage divided by 2. Determine what this voltage
is and compare it with the value obtained with a voltmeter in place of the oscilloscope.
Determine the frequencies of the half- and full-wave rectified DC outputs.
Q2. How are these two frequencies related? How are they related to the frequency of FP&L’s
AC power?
31
Direct Current Circuits
Introduction
This lab investigates the relationship between current, voltage, and resistance as well as series
and parallel circuits. We begin with Ohm’s Law where a voltmeter and an ammeter will be used
to carry out measurements of resistor/light-bulb circuits. Resistance, R, of a conductor is defined
as the potential difference, V, applied between its ends divided by the corresponding current, I,
through the conductor:
R=V/I.
A material whose resistance is constant and does not depend on applied voltage is said to obey
Ohm’s Law.
To clarify the meaning of these electrical quantities, one can make the comparison between
electrical circuits and water flowing in pipes. Here is a chart of the three electrical quantities we
will study in this experiment.
Electrical Quantity
Description
Unit
Water Analogy
Voltage or Potential
Difference
Difference in potential energy
per unit charge when a unit
charge is located at two points
in a circuit.
Volt (V)
Difference in water pressure
between two points in a
pipe.
Current
A measure of the rate of flow
of charge along a conductor.
Ampere (A)
A measure of the rate of
flow of water in a pipe.
Resistance
A measure of how difficult it is
for current to flow along a
conductor.
Ohm ()
A measure of how difficult
it is for water to flow
through a pipe.
Next we will investigate series and parallel circuits. Components are in series when they are
connected one after the other, so that the same current flows through all of them. Components are
in parallel when they are connected between the same pair of points in a circuit, so they are
subjected to the same potential difference. Series and parallel circuits function differently. When
using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps
goes off. These lamps are in series. When a light bulb burns out in your house, the other lights
stay on. Household appliances and light bulbs are normally in parallel.
Objectives




Determine the mathematical relationship between current, potential difference, and resistance
for simple electrical components.
Compare the potential difference vs. current behavior of a resistor to that of a light bulb.
Study current flow and potential differences in series and parallel circuits.
Use Ohm’s Law to calculate equivalent resistance of series and parallel circuits.
32
Part I: Investigation of Voltage, Resistance, and Current
In this first part of this lab, we will construct the circuit shown in Figure 1 to measure current
through a device as a function of potential difference between its ends. The voltmeter, V,
measures the voltage across a circuit competent—a resistor in this case—and must be placed in
parallel with it. The ammeter, A, measures the current through a particular part or component of
the circuit and is placed in series with the component. The other item in the circuit is a variable
power supply indicated by the battery symbol with an arrow through it.
Figure 1
Procedure Part I
1. With the power supply turned off, make the circuit shown above using a 10  resistor. Have
your instructor check your circuit before turning on the power supply.
2. Make sure the power supply is set to 0 V with the range switch set to 6 V. Record the voltage
and current readings in Table 1.
3. Now turn the power supply up so that you get approximately 0.5 V across the resistor.
Again, record the voltage and current in your table.
4. Repeat this procedure for 0.5 V steps until you reach the 6 V limit of your power supply.
5. Repeat steps 1-4 using a 50  resistor.
6. Repeat steps 1-4 using the light bulb supplied with your lab equipment.
NOTE: The table below is a sample only. You will have 12 entries for each resistor and 12 for
the light bulb for a total of 36 entries.
R1
V (Volts)
Table 1
33
I (A)
Analysis Part I
1. Plot a graph of voltage vs. current for each resistor/light bulb. All three plots can be on the
same graph if you wish.
2. Fit a straight line on each plot and find the slope. You should set the y-intercept to zero in
each case.
3. What is the value of the slope? Compare it to the resistor value. Do they agree? Note that
resistors are manufactured such that their actual value is within a tolerance. For most resistors
used in this lab, the tolerance is 5% or 10%. Check with your instructor to determine the
tolerance of the resistors you are using. Calculate the range of values for each resistor. Does
the constant in each equation fit within the appropriate range of values for each resistor?
4. Do the resistors obey Ohm’s law? That is, do they all give you a straight line? If not,
propose an explanation.
5. Describe what happened to the current through the light bulb as the potential difference
increased. Was the change linear? Since a change in the slope of the linear regression line is a
measure of a change in resistance, describe what happened to the resistance as the voltage
increased. Since the bulb gets brighter as it gets hotter, how does the resistance vary with
temperature?
6. Does your light bulb follow Ohm’s law? Base your answer on your experimental data.
Part II: Investigation of Series and Parallel Circuits
Figure 2
Preliminary Question
For each of the resistors you are using, note the tolerance rating. Tolerance is a percent rating,
showing how much the actual resistance could vary from the labeled value. This value is labeled
on the resistor or indicated with a color code. Calculate the range of resistance values that fall in
this tolerance range.
Labeled resistor
value ()
Tolerance (%)
Minimum
resistance ()
34
Maximum
resistance ()
Procedure Part II
Section II-A: Series Circuits
1. Connect the series circuit shown in Figure 3 using the 10- resistors for
resistor 1 and resistor 2. Notice the voltmeter is first used to measure the
voltage applied to both resistors.
2. Set the power supply to 3.0 V and record the voltage and current in the
data table.
3. Now measure the voltage across each resistor separately.
4. Now move the ammeter so that it measures the current through R1 and
then R2 separately. Record the currents in the table.
Figure 3
5. Replace resistor 2 with a 50- resistor and repeat the measurements of voltage and current
and record the results in the table.
Section II-B: Parallel circuits
1. Connect the parallel circuit shown below using 50- resistors for both
resistor 1 and resistor 2. As in the previous circuit, the voltmeter is
used to measure the voltage applied to both resistors. The ammeter is
used to measure the total current in the circuit.
2. Again set the power supply to 3.0 V and record the voltage and current
in the data table.
3. Now measure the voltage across each resistor separately.
4. Move the ammeter so that you can measure the current going only
through R1 alone.
Figure 4
5. Move the ammeter again so that you measure the current going only through R2.
6. Replace resistor 2 with an 82- resistor and repeat the measurements of voltage and current
and record the results in the table.
Data Tables
Section II-A: Series circuits
R1 ()
R2 ()
1
10
10
2
10
50
I (A)
V1 (V)
I2 (A)
V2 (V)
I2 (A)
Req () VTOT (V)
I (A)
V1 (V)
I1 (A)
V2 (V)
I2 (A)
Req () VTOT (V)
Section II-B: Parallel circuits
R1 ()
R2 ()
1
50
50
2
50
10
35
Analysis
Section II-A: Series Circuits
1. What is the relationship between the three voltage readings: V1, V2, and VTOT?
2. Using the measurements you made for I and VTOT and your knowledge of Ohm’s law (V=IR),
calculate the equivalent resistance (Req) of the circuit for the two series circuits you tested.
3. Study the equivalent resistance readings for the series circuits. Can you come up with a rule
for the equivalent resistance (Req) of a series circuit with two resistors?
5. For each of the series circuits, compare the experimental results with the resistance calculated
using your rule. In evaluating your results, consider the tolerance of each resistor by using the
minimum and maximum values in your calculations.
6. Examine the currents you measured for the series circuits. What is the relationship between
the total current and the currents through each of the resistors?
Section II-B: Parallel Circuits
1. Using the measurements you made for I and VTOT and your knowledge of Ohm’s law,
calculate the equivalent resistance (Req) of the circuit for the two parallel circuits you tested.
2. Study the equivalent resistance readings for the parallel circuits. Devise a rule for the
equivalent resistance of a parallel circuit of two resistors.
3. What do you notice about the relationship between the three voltage readings V1, V2, and
VTOT in parallel circuits?
4. Examine the currents you measured for the parallel circuits. What is the relationship between
the total current and the currents through each of the resistors?
5. If the two measured currents in your parallel circuit were not the same, which resistor had the
larger current going through it? Why?
6. Compare the total currents through the parallel circuits to the total current flowing through
the series circuits. Which has the largest total current? Why?
36
The Charge to Mass Ratio of an Electron
Introduction
This classic experiment was first carried out by J.J. Thomson in 1897. It involves the use of an
electric field to accelerate electrons up to high velocity, and a magnetic field to then steer the
electrons in a circular trajectory. The electrons are released by thermionic emission from a
heated filament (cathode) and are accelerated towards a cylindrical anode by a potential
difference, V, which is maintained between the cathode and anode. See Fig. 1. This is a similar
situation to the electron gun used to generate the electron beam in the oscilloscope.
Electron trajectory
Anode
Connecting wires
Graduated
rod
Filament
Figure 1
As the electrons accelerate from the cathode to anode, the electrons lose potential energy, eV, and
gain an equal amount of kinetic energy, ½mv2. Therefore they arrive at the anode with a velocity
v given by
2eV
……………………………………………….(1)
v
m
Some of the electrons escape with this velocity through a narrow aperture in the anode into a
region where a uniform magnetic field exists. In Fig. 1, this field, which is not shown, would
point outwards, perpendicular to the plane of the diagram. The field exerts a centripetal magnetic
force of F= evB on each electron causing it to move along a circular path. From Newton’s 2nd
Law,
mv 2
evB 
,…………………………………………….(2)
r
where r is the radius of the path. Eliminating v between equations (1) and (2), we obtain the
charge to mass ratio,
37
e
2V
 2 2 …………………………………………….(3)
m B r
The magnetic field is produced by current flowing in a pair of “Helmholtz coils”. The distance
between these circular coils is equal to their radius, an arrangement that results in a reasonably
uniform, axial magnetic field midway between the coils. The magnitude of the magnetic field, B,
in this region is given by
8 0 NI
B
…………………………………………...(4)
125 R
where N = # of turns per coil (130 for the Daedalon apparatus)
I = current in coils
R = radius of coils
µo = permeability of free space = 4 x 10-7 Wb/A.m
Procedure
These instructions are for the apparatus made by Daedalon. In the unlikely event that you have
on made by Sargent Welch or by Nakamura a separate set of instructions will be provided. and
one by Daedalon. The Daedalon apparatus has all power supplies and meters built-in so no
there will be no need to make any electrical connections besides just plugging in the AC power
cord. One power supply provides a DC current that flows through the coils to produce the
magnetic field. Another power supply provides a DC voltage to accelerate the electrons.
Switch on the apparatus and wait as the 30-second warm up delay counts down. Set the
accelerating voltage to approximately 200 V. With the room lights switched off and current
provided to the Helmholtz coils, the circular trajectory of the electron beam should be visible.
The beam is made visible by a small amount of helium gas in the bulb, which is excited by
collisions with the high-speed electrons. The plane of the coils should be pointing northward in
order to minimize the effect of the earth’s magnetic field. If the beam does not intersect the
graduated rod, adjust the orientation of the apparatus until it does.
Adjust the coil current until the electron beam intercepts, the 5 cm indicator mark on graduated
rod (closest to the filament). Readjust the accelerating voltage, if necessary, to obtain direct
interception. Note the accelerating voltage, V, and the current, I, in the Helmholtz coils.
Readjust the coil current until the beam impinges on the second, third, etc. crossbars/indicator
marks, in each case making the fine adjustment by altering the accelerating voltage. For each
case record V and I.
Analysis
Present your results in tabulated form as shown below. Here you are given the distances from the
filament to each crossbar/indicator mark, these representing the diameters of the circular orbits of
the electrons.
38
To obtain B, you will need to determine the average radius of the Helmholtz coils. To do this,
measure both the inside and outside diameters of both coils on at least three different axes and
then average them. The coils may not be quite round, and they may be of slightly different
diameters.
Average value of R=____________________m
Calculate the average value of e/m and the standard deviation. Compare your result with the
known value, which can probably be found in your textbook or calculated from e and m values in
your textbook.
Diameter of beam
orbit (m)
0.05
r (m)
I (A)
B (Eq. 4)
(T)
V (V)
0.06
0.07
0.08
0.09
0.10
0.11
average
Std. Dev.
39
e/m (Eq. 3)
(C/ kg)
Magnetic Fields
When an electric current flows through a wire, a magnetic field is produced around the wire. The
magnitude and direction of the field depends on the shape of the wire and the direction and
magnitude of the current through the wire. If the wire is wrapped into a loop, the field near the
center of the loop is perpendicular to the plane of the loop. When the wire is looped a number of
times to form a coil, the magnetic field at the center increases. Another possible configuration is
wire wrapped helically around a tube, known as a solenoid. When a current passes through this
configuration, a uniform magnetic field is present inside the solenoid while there is almost no
field outside the solenoid. Solenoids are used in electronic circuits or as electromagnets.
In the first part of this lab, you will examine how the magnetic field is related to both the number
of turns in a coil and the current through the coil. A Magnetic Field Sensor will be used to detect
the field at the center of the coil. In the second part of the lab, you will study the solenoidal
magnetic field created by a metal Slinky®. This will lead to a measurement of 0, the
permeability of free space. One complication that must be considered is that the magnetic field
sensor will also detect the Earth’s field and any local fields due to electric currents or some
metals in the vicinity of the sensor.
Objectives






Use a Magnetic Field Sensor to measure the field at the center of a coil.
Determine the relationships between magnetic field and both the number of turns and current
in a coil.
Determine the relationships between magnetic field and both the current and the number of
turns per meter in a solenoid.
Study how the field varies inside and outside a solenoid.
Determine the value of 0, the permeability of free space
Explore the Earth’s magnetic field in the laboratory.
Part I: Magnetic field of a Coil
Initial setup Part I
1. Connect the Vernier Magnetic Field Sensor to Channel 1 of the LabPro Interface. Set the
switch on the sensor to Low.
2. Using the long piece of wire, loop the wire ten times around the PVC pipe creating a coil of
ten turns. You should wrap the wire near, but not covering, the hole in the center and secure
the wire with a piece of tape.
3. Connect the coil, switch, and ammeter in series with the power supply. The leads should be
connected to the 3 A input of the ammeter.
4. Open the file in the Experiment 28 folder of Physics with Computers. A graph will
appear on the screen. The vertical axis has magnetic field scaled from –0.10 to
+0.10 millitesla. The horizontal axis has time scaled from 0 to 20 s. The Meter window
displays magnetic field in (mT). You may adjust the scale by clicking on the end of the scale
and entering a new value.
40
Preliminary questions and additional setup Part I
1. Hold the plastic rod containing the Magnetic Field Sensor vertically and move it completely
away from the coil. Click
to begin data collection. Rotate the rod around a vertical
axis. Look at the graph. What do you observe? What is causing the variation of field reading?
2. Determine the orientation of the sensor when the magnetic field is at a maximum, and
compare the direction that the dot on the sensor is pointing with the direction that the
magnetic compass needle points. What did you discover? How much does the reading change
in one rotation?
3. Set the power supply so that the current will be the maximum
possible (~ 1.8 A) when the switch is closed. Place the sensor
through the hole in the pipe near the center of the coil, with the
white dot facing along the axis of the coil as shown here. Click
. Wait 2 to 3 seconds and then close the switch. What did
you observe? Warning This lab requires fairly large currents to
flow through the wires. Do not leave the switch on except when
taking measurements. The wire and possibly the power supply
may get hot if you leave current flowing continuously.
Sensor
(Rotate about vertical axis)
Axis of
coil
Figure 1
4. Repeat Step 3, but this time rotate the Magnetic Field Sensor while you are holding the
switch closed. Determine the orientation of the sensor that gives the maximum reading. How
much does the reading change in one rotation of the sensor?
Procedure Part I
Part I-A: How Is The Magnetic Field In A Coil Related To The Current?
In this part of the experiment you will determine the relationship between the magnetic field in
the center of a coil and the current through the coil. Use the loop with all ten turns for all of Part
I-A. As before, leave the current off except when making a measurement.
1. Set the power supply so that the current will be the maximum possible (~1.8 A) when the
switch is closed.
2. Place the Magnetic Field Sensor in a vertical position so that the flat end is at the center of
the coil. With the switch closed, rotate the sensor about a vertical axis and observe the
magnetic field values in the Meter window. Find the position that indicates a maximum
positive magnetic field. The flat end of the sensor should be in the plane of the coil. Keep the
sensor in the same position for the remainder of the experiment.
3. We will first zero the sensor when no current is flowing; that is, we will remove the effect of
the Earth’s magnetic field and any local magnetism. With the switch open, click
.
4. Click
to begin data collection. Wait a few seconds and then close the switch for the
rest of the run.
5. View the field vs. time graph and determine when the current was flowing in the wire. Select
this region on the graph, by dragging over it. Determine the average field while the current
was on by clicking on the Statistics button, . Record the average field and the current
through the coil in the data table.
6. Briefly close the switch and decrease the current by 0.3 A and repeat Steps 4 and 5.
7. Repeat Step 6 down to a minimum of 0.3 A.
41
Part I-B How Is The Magnetic Field In A Coil Related To The Number Of Turns?
For this part of the experiment you will determine the relationship between the magnetic field at
the center of a coil and the number of turns in the coil. The Magnetic Field Sensor should be
oriented as before. Use a maximum current (~1.8 A) for all of part I-B. Leave the current off
except when making a measurement.
1. We will first zero the sensor when no current is flowing. That is, we will remove the effect of
the Earth’s magnetic field and local magnetism. With the switch open, click on
.
2. Set the power supply so that the current will be 1.8 A when the switch is closed. Click
. After a few seconds, close and hold the switch for at least 10 s during the data
collection.
3. View the field vs. time graph and determine when the current was flowing in the wire. Select
this region of the graph by dragging over it with the mouse cursor. Determine the average
field while the current was on by clicking on the Statistics button, . Record the average
field and the number of turns on the coil (10) in the data table.
4. Remove one loop of wire from the frame to reduce the number of turns by one and repeat
Steps 1–3. If you move the frame or the sensor, make sure that you get it back to the
same orientation as for the previous measurement.
5. Repeat Step 4 until you have only one turn of wire on the frame. Keep the current at 1.8 A.
Data Table Part I
Part I-A
Current in coil
(A)
Magnetic field
(mT)
1.8
1.5
1.2
0.9
0.6
0.3
42
Part I-B
Number of turns
Magnetic field
(mT)
Number of turns
10
5
9
4
8
3
7
2
6
1
Magnetic field
(mT)
Analysis Part I
Part I-A
1. Use Excel to plot a graph of magnetic field vs. current through the coil.
2. What is the relationship between the current in a coil and the resulting magnetic field at the
center of the coil?
3. Determine the equation of the best-fit line (trendline) through the data points. Explain the
significance of the constants in your equation. What are the units of the constants?
Part I-B
1. Use Excel to plot a graph of magnetic field vs. the number of turns on the coil.
2. How is magnetic field related to the number of turns?
3. Using the linear regression tool in Graphical Analysis, determine the best-fit line through the
data points. Explain the significance of the constants in your equation. What are the units of
the constants?
4. Remember that you zeroed the sensor before taking data in this lab. Should the line you fit in
Step 6 go through the origin?
Part II: Magnetic field of a Slinky
Figure 2
43
Initial setup Part II
1. Make sure the Vernier Magnetic Field Sensor is connected to Channel 1 of the LabPro
Interface. Set the switch on the sensor to High.
2. Stretch the Slinky until it is about 1 m in length. The distance between the coils should be
about 1 cm. Use a non-conducting material (tape, cardboard, etc.) to hold the Slinky at this
length.
3. Connect the coil, switch, ammeter, and power supply, as shown in Figure 2. The leads should
be connected to the 3 A input of the ammeter. You do not need to use a power resistor. Wires
with clips on the end should be used to connect to the Slinky.
4. Turn on the power supply and adjust it so that the ammeter reads ~1.8 A when the switch is
held closed.
Warning: This lab requires fairly large currents to flow through the wires and Slinky. Only
close the switch so the current flows when you are taking a measurement. The Slinky, wires,
and possibly the power supply may get hot if left on continuously.
5. Open the file in the Experiment 29 folder of Physics with Computers. A graph will
appear on the screen. The vertical axis has magnetic field scaled from –0.3 to +0.3 mT. The
horizontal axis has time scaled from 0 to 20 s. The Meter window displays magnetic field in
millitesla, mT. The meter is a live display of the magnetic field intensity.
Preliminary questions Part II
1. Hold the switch closed. The current should be ~1.8 A. Place the Magnetic Field Sensor
between the turns of the Slinky near its center. Rotate the sensor and determine which
direction gives the largest magnetic field reading.
2. What happens if you rotate the white dot to point the opposite way? What happens if you
rotate the white dot so it points perpendicular to the axis of the solenoid?
3. Stick the Magnetic Field Sensor through different locations along the Slinky to explore how
the field varies along the length. Always orient the sensor to read the maximum magnetic
field at that point along the Slinky. How does the magnetic field inside the solenoid seem to
vary along its length?
4. Check the magnetic field intensity just outside the solenoid. Does it agree with what you
expect?
Procedure Part II
Part II-A How Is The Magnetic Field In A Solenoid Related To The Current?
For this part of the experiment you will determine the relationship between the magnetic field at
the center of a solenoid and the current flowing through the solenoid. As before, leave the current
off except when making a measurement.
1. Place the Magnetic Field Sensor between the turns of the Slinky near its center.
2. Close the switch and rotate the sensor so that the white dot points directly down the long axis
of the solenoid. This will be the position for all of the magnetic field measurements for the
rest of this lab.
44
3. Click
to begin data collection. Wait a few seconds
and close the switch to turn on the current.
4. If the magnetic field increases when the switch is closed, you
are ready to take data. If the field decreases when you close
the switch, rotate the Magnetic Field Sensor so that it points
the other direction down the solenoid.
5. With the Magnetic Field Sensor in position and the switch
open, click on the Zero button,
, to zero the sensor and
remove readings due to the Earth’s magnetic field, any
magnetism in the metal of the Slinky, or the table.
Figure 4
6. Adjust the power supply so that 0.5 A will flow through the coil when the switch is closed.
7. Click
collection.
to begin data collection. Close the switch for at least 10 seconds during the data
8. View the field vs. time graph and determine the region of the curve when the current was
flowing in the wire. Select this region on the graph by dragging over it. Determine the
average field strength while the current was on by clicking on the Statistics button, . Record
the average field in the data table.
9. Increase the current by 0.5 A and repeat Steps 7 and 8.
10. Repeat Step 9 up to the maximum allowed by the supply (~1.8 A).
11. Count the number of turns of the Slinky and measure its length. If you have any unstretched
part of the Slinky at the ends, do not count it for either the turns or the length. Calculate the
number of turns per meter of the stretched portion. Record the length, turns, and the number
of turns per meter in the data table.
Part II-B: How is the Magnetic Field in a Solenoid Related to the Spacing of the Turns?
In this part of the experiment, you will determine the relationship between the magnetic field in
the center of a coil and the number of turns of wire per meter of the solenoid. You will keep the
current constant. Leave the Slinky set up as shown in Figure 3. The sensor will be oriented as it
was before, so that it measures the field down the middle of the solenoid. You will be changing
the length of the Slinky from 0.5 to 2.0 m to change the number of turns per meter.
1. Adjust the power supply so that the current will be 1.5 A when the switch is closed.
2. With the Magnetic Field Sensor in position, but no current flowing, click
to zero the
sensor and remove readings due to the Earth’s magnetic field and any magnetism in the metal
of the Slinky. Since the Slinky is made of an iron alloy, it can be magnetized itself. Moving
the Slinky around can cause a change in the field, even if no current is flowing. This means
you will need to zero the reading each time you move or adjust the Slinky.
3. Click
to begin data collection. Close and hold the switch for about 10 seconds during
the data collection. As before, leave the switch closed only during actual data collection.
4. View the field vs. time graph and determine when the current was flowing in the wire. Select
this region on the graph by dragging over it. Find the average field while the current was on
by clicking on the Statistics button, . Count the number of turns of the Slinky and measure
its length. If you have any unstretched part of the Slinky at the ends, do not count it for either
the turns or the length. Record the length of the Slinky and the average field in the data table.
45
5. Repeat Steps 13 – 15 after changing the length of the Slinky to 0.5 m, 1.5 m, and 2.0 m. Each
time, zero the Magnetic Field Sensor with the current off. Make sure that the current remains
at 1.5 A each time you turn it on.
Data Table Part II
Part II-A
Current in solenoid I
(A)
Magnetic field B
(mT)
0.5
1.0
1.5
1.8
Length of solenoid (m)
Number of turns
–1
Turns/m (m )
Part II-B
Length of solenoid
(m)
Turns/meter n
–1
(m )
CCurrentCC
Magnetic field B
(mT)
Number of turns in Slinky
Analysis Part II
1. Use Excel to plot a graph of magnetic field B vs. the current I through the solenoid.
2. How is magnetic field related to the current through the solenoid?
3. Determine the equation of the best-fit line, including the y-intercept. Note the constants and
their units.
4. For each of the measurements of Part II-B, calculate the number of turns per meter. Enter
these values in the data table.
5. Use Excel to plot a graph of magnetic field B vs. the turns per meter of the solenoid (n).
6. How is magnetic field related to the turns/meter of the solenoid?
46
7. Determine the equation of the best-fit line to your graph. Note the constants and their units
8. From Ampere’s law, it can be shown that the magnetic field B inside a long solenoid is
B   0 nI
where 0 is the permeability constant. Do your results agree with this equation? Explain.
9. Assuming the equation in the previous question applies for your solenoid, calculate the value
and uncertainty of 0 using your graph of B vs. n.
10. Look up the value of 0, the permeability constant. Compare it to your experimental value.
11. Was your Slinky positioned along an east-west, north-south, or on some other axis? Will this
have any effect on your readings?
47
Faraday’s and Lenz’s Laws
Introduction
In 1831, Michael Faraday made a discovery with enormous technological consequences. He
discovered that for an electric current in one wire to induce a current in a second wire, the current
in the first wire must be changing with time. The induced current is caused by the changing
magnetic field generated by the changing current in the first wire. This changing field induces an
emf in the second wire, which in turn generates an induced current. The technological
consequence of all this is our whole system of electrical power generation.
Faraday’s Law summarizes this quantitatively; stating that the magnitude of the induced emf in a
conducting loop is equal to the rate at which the magnetic flux through the area bounded by the
loop is changing with time. That is:
    or, more correctly,    d .
t
dt
The negative sign is related to a sign convention for the direction of the induced current.
Alternatively this direction is given by Lenz’s Law, which states that an emf or current is induced
in a conducting loop in a direction such as to oppose the change that produced it.
A series of mainly qualitative experiments will be performed to illustrate the validity of
Faraday’s and Lenz’s Laws.
Procedure Part I
1. Connect the terminals, labeled A and B, of the large solenoid to the terminals of the center
reading galvanometer. Push the north end of the bar magnet into the end of the solenoid
remote from the terminals, observing the galvanometer during the process. Now hold the
magnet steady for several seconds and then pull it out of the coil. Repeat these procedures
varying the speed of the magnet.
Q1. Does the galvanometer deflect to the left or the right when
a. the magnet is being pushed in
b. the magnet is being pulled out
c. the magnet is being held stationary?
Q2. How does the maximum deflection of the galvanometer appear to depend on the speed
with which the magnet is moved? Why?
Q3. How do your observations lend support to the statement: “A steady magnetic field
cannot induce currents in a stationary conductor”?
2. Connect the terminals of the larger-diameter solenoid to the galvanometer and those of the
smaller coil, via a switch, to a power supply as shown in Fig. 1. Beware of accidental
shorting between the solenoid terminals.
48
Figure 1
When the switch is closed, the current through the smaller coil creates a magnetic field, as should
be observed by the deflection of a nearby compass needle. Open the switch and place the smaller
solenoid inside the larger. Adjust the power supply to give minimum output and close the
switch. Turn the voltage control knob rapidly from the minimum to the maximum setting while
observing the galvanometer. Leave it at the maximum setting for several seconds and then turn it
rapidly to the minimum setting, again while observing the galvanometer.
Q4. Does the galvanometer deflect to the left or right while the current in the smaller coil is
a. increasing?
b. decreasing?
c. held constant?
Q5. State, giving reasons, whether the answers given to Q4. are to be expected on the basis of
those given in Q1.
3. Insert the metal rod fully into the smaller solenoid and repeat the operations of increasing,
holding steady and decreasing the current in the smaller solenoid. Also try varying the rate
with which the current is increased and decreased. The effect of the rod, which you will
observe, is due to a process called “magnetization”. The magnetic field of the current in the
inner solenoid causes the magnetic dipole moments of the atoms in the rod to become
aligned. The magnetic fields of these dipoles then add to the field of the inner solenoid
resulting in a considerably stronger magnetic field and a correspondingly greater flux through
each turn of the outer solenoid.
Q6. What is the effect of the presence of the rod on the current induced in the larger
solenoid?
Q7. How does the induced current depend on the rate with which the current in the smaller
solenoid is altered?
4. With the rod still inserted, place an ammeter in the circuit in series with the power supply.
With the switch closed, adjust the power supply to give a current of 200 mA. Now open the
switch and close it again and observe the maximum galvanometer deflection when the
switch is closed. Repeat with currents of 300, 400, 500 and 600 mA. Plot a graph of
galvanometer deflection vs. current.
Q8. What does the graph indicate?
Procedure Part II: Verification of Lenz’s Law
In this section you will verify that when a magnet is pushed into a solenoid, the induced current
creates a magnetic field that exerts a repulsive force on the magnet, as indicated in Fig. 2. To
49
show that this is the case, you must first determine the direction of the induced current, and then,
while driving a larger current through the solenoid in the same direction, check the direction of
the magnetic field, which should now be large enough to be detected.
N
S
Direction of motion
Figure 2
1. Connect the galvanometer to the larger solenoid and push the north pole of the bar magnet
into the end farthest from the terminals as shown in Fig. 3 (a). Note whether the
galvanometer deflects to the right or left. Also note which terminal of the solenoid is
connected to which terminal of the galvanometer.
10,000 
N
A
B
S
Right terminal
Power
supply
Left terminal
b)
a)
Figure 3
2. Disconnect the solenoid and set up the circuit shown in Fig. 3 (b). Set the power supply
output to 2 volts. The 10,000  resistor is to protect the sensitive galvanometer. Alter the
connections to the galvanometer, if necessary, to obtain the same direction of defection as in
(i). Reproduce the circuit diagram of Fig. 3 (b) and mark on it the direction of the current.
You are now in a position to reproduce Fig. 3 (a) and also to mark on it the direction of the
(induced) current.
3. Adjust the power supply output to 4 volts and connect it to the solenoid in such a way that the
current passes through the solenoid in the same direction as indicated in Fig. 3(a). You have
now created a magnetic field in the same direction as that due to the induced current, but one
which is much stronger.
4. Use the compass to determine whether the end of the coil remote from the terminals behaves
as a north or south pole. Label the poles on your figure of the coil.
Discuss your results in the light of Lenz’s Law.
50
Electrical Resonance
Introduction
When you adjust the tuning control on a radio, you are altering the capacitance of a capacitor in
an RCL circuit (a circuit containing a resistor, capacitor and inductor). When correctly tuned, the
circuit “resonates” at the same frequency, say 93.1 MHz, as the electromagnetic waves being
transmitted from the radio station. Under resonance conditions, the oscillating current in the
circuit becomes relatively large and can then be further amplified and decoded before being sent
on to the speakers. In this experiment, the phenomenon of resonance in an RCL circuit, powered
by an alternating current generator, will be examined.
Theory
We first consider the relationship between AC voltage and AC current for resistors, capacitors
and inductors. The resistor obeys Ohm’s law just as it does under DC conditions, i.e. the
instantaneous voltage across the resistor is always proportional to the instantaneous current
through it. Therefore the voltage and current are “in phase” with each other, as shown in Fig. 1
a).
Voltage
Voltage
Voltage
Current
Current
Time
Current
a) Resistor
Time
Time
t
t
b) Capacitor
c) Inductor
Figure 1
For a capacitor, the voltage between the plates is proportional to the charge on either plate, so the
peak voltage will occur when the charge is a maximum. In Fig. 1 b), current will be flowing in
one direction only during the interval t, thereby building up charge on one of the plates. Thus
the charge, and therefore the voltage, will be a maximum at the end of that interval. Note that the
peak voltage occurs a quarter cycle after the peak current. Also, the peak voltage, Vmax, is related
to the peak current, Imax, by the relationship,
Vmax  I max X C ,
where XC is the capacitive reactance and depends on the angular frequency, , namely
1
XC 
C
For an inductor, such as a solenoid, the voltage between its ends is just the induced emf, which,
by Faraday’s Law, is proportional to the rate of change of current through it. In Fig. 3 c) this rate
51
is seen to be a maximum at time t, so this is when the voltage will be a maximum. Thus, the
peak voltage occurs one quarter cycle before the peak current and the relationship between them
is
Vmax  I max X L
XL is the inductive reactance, and also depends on frequency:
X L  L
AC generator
C
R
A
L
B
Figure 2
In an RCL series circuit like that shown in Fig. 2, the currents in the resistor, capacitor and
inductor are in phase with each other. Therefore the voltages across the capacitor and inductor
are a half cycle out of phase with each other. At a frequency where the two reactances are equal,
these voltages have equal magnitudes but opposite signs. So the potential difference VAB (see
Fig. 2) is zero and the AC generator does no work in driving current from A to B. The only thing
impeding the flow of current is the resistor. This is the condition for maximum current in the
circuit, that is, for resonance. Equating the reactances, the resonant angular frequency, 0, is
given by
1
,
0 
LC
with a corresponding frequency in hertz of
1
……………….………………………(1)
f0 
2 LC
Procedure Part I
1. The Circuit: The RCL circuit is set up on a circuit board, which already has a 33 mH
inductor in place.
a. Put the AC generator in the circuit making sure that that the resistor is connected to
the ground of the generator.
b. Set the AC generator to produce a sine wave with a frequency of 2000 Hz and a
maximum voltage.
c. Set the variable resistor to 100  and the variable capacitor to 0.01 F.
2. Current Measurement: To demonstrate resonance, you will be determining the current as a
function of frequency. To obtain the current, you will connect the oscilloscope across the
resistor, which will allow you to measure voltage across the resistor and then obtain the
52
3.
4.
5.
6.
7.
8.
9.
current by applying Ohm’s law. The oscilloscope will also allow you to measure the
frequency of the AC generator.
a. Attach the input to the oscilloscope across the resistor making sure that the ground of
the scope is connected to the same side of the resistor as the AC generator.
b. Adjust the Y gain and the time-base to produce a sinusoidal trace on the screen. If you
don’t see the trace, try reversing the AC generator connections. Be sure that the
continuously variable controls for the Y gain and time-base are both in the calibrate
position.
c. Measure the vertical distance between the peak and trough and then calculate the
corresponding peak-to-peak voltage. Divide this by 22 to obtain the “root mean
square voltage”. Since this is the voltage across the 100  resistor, the root mean
square current, from Ohm’s law, is found by dividing the voltage by 100 .
Frequency Measurement: The AC generator displays the frequency of the signal. You may
use this displayed value, however, you should verify that the display agrees with the
frequency of the signal first. To find the frequency, measure the horizontal distance between
adjacent peaks and multiply this by the time-base setting to get the period.
Tabulate your measurements of frequency, peak-to-peak voltage, rms voltage and rms
current.
Repeat the voltage and frequency measurements at roughly 2000 Hz intervals between 2000
and 14000 Hz.
By inspecting your results you should be able to determine the approximate resonance
frequency. In order to more accurately determine it, take several more readings in the vicinity
of the highest current reading at approximately 500 Hz intervals.
Plot a graph of current (on the y axis) versus frequency (on the x axis).
Repeat the entire experiment with the capacitor set to 0.02 F and everything else the same.
Repeat the entire experiment with the capacitor set back to 0.01 F but with the resistance
box increased to 1000 .
Analysis Part I
Comment on the three curves obtained. Compare the resonant frequencies obtained
experimentally with the theoretical predictions. Recall that there is an approximate 10%
tolerance for each component of the circuit. Include this tolerance in your comparison.
Procedure Part II
Replace the inductor in the RLC circuit with the large solenoid. Set the capacitor at 0.01 F and
the resistance box at 100 . Adjust the frequency of the AC generator until the voltage across
the resistor (thus the current) is a maximum and then use equation (1) to calculate the inductance,
L, of the solenoid. Compare this with the theoretical prediction (based on an ideal, infinitely
long solenoid) given by
L   0 n 2 Al ,
where n is the number of turns per meter, l is the length and A is the cross-sectional area of the
solenoid. Obtain A from a diameter measurement using vernier calipers.
53
Plane Reflection and Refraction
Introduction
Image formation by reflection and refraction is best described using a graphical construct called a
light ray, which is basically a line indicating a path along which light is traveling. The nearest
physical approximation to a light ray is a narrow beam of light like you get from a laser. When
such a beam of light, or ray, strikes a boundary separating two transparent media, for example an
air-water interface, it is partially reflected and partially refracted. In this experiment the laws
governing these processes will be investigated.
Procedure Part I: The Law of Reflection
Place a sheet of white paper on the cardboard provided with the mirror positioned near the center
of the paper.
1. Outline the rear surface of the mirror with a pencil and place a pin at a point A approximately
10 cm from the mirror, as shown in Fig. 1. This pin is the object. Rays from A are reflected
by the mirror in such a way that they appear to be coming from A', the virtual image of A.
2. Place a second pin B close to the mirror such that a ray traveling from A to B will strike the
mirror at about 45o. The corresponding reflected ray may now be found by lining up the
images of A and B in the mirror and placing two locating pins C and D so that all four appear
to be in line.
3. Mark the position of the pins and join AB and CD to meet the mirror as in Fig. 1. Also mark
in the normal PN. The angle APN is the “angle of incidence” and DPN is the “angle of
reflection”. Measure these two angles with a protractor and compare them.
N
A
D
~10cm
C
B
P
A'
Figure 1
54
4. Trace another ray in exactly the same way but with an angle of incidence of about 30o. See
Fig. 1. Both reflected rays appear to originate at the same point (the image) behind the
mirror. Extend the rays backward to locate A'.
Q1. Where is A' in relation to A? Compare the distance from the mirror to A to the distance
from the mirror to A'.
Procedure Part II: Snell’s Law of Refraction
Snell’s Law states that
n1sin 1  n2 sin  2
where n1 (1.00029) is the refractive index of air and n2 is the refractive index of the glass block.
1. Adjust the ray box to produce a narrow beam of light. Place a sheet of white paper on the
board with the transparent rectangular block at the center of the paper.
2. Draw the outline of the block on the paper and make a small mark on the paper near the
midpoint of one of the long sides.
3. Direct the light beam towards the mark making the angle of incidence about 30o.
4. Mark two points on the incident ray and two on the emerging ray.
5. Remove the block and trace the path of the ray as in Fig. 2. Note that you will probably not
be able to see the ray within the block but can still tell it’s trajectory by connecting the point
where it entered to the point where it left the block. Measure and record the angles of
incidence and refraction at the first surface.
6. Repeat this procedure for five different angles of incidence between 10o and 60o. (Rotate the
block and paper together to vary the angle. You may need to change where the ray enters the
block.)
7. Plot a graph of sin1 (y axis) vs. sin2 (x axis) and, from the slope, calculate n2. Look up the
value of the index of refraction for glass in your textbook and compare it to your result. Note
that different types of glass may have different indices of refraction.
Emerging ray
2
1
Incident ray
Figure 2
55
Procedure Part III: Critical Angle
When light passes from a material with a high index of refraction to a material with a lower
index of refraction, the ray bends away from the normal. It is possible in this situation to have an
angle of incidence such that no light leaves the first material. This can be seen by rearranging
Snell’s law:
n1sin 1
 sin  2 .
n2
If n1sin1> n2, then sin2>1, which is not possible. Therefore no light will exit the first material.
This is a condition call “total internal reflection”. It will occur for all incident angles greater than
the critical angle, 1=C, given by
n
sin  C  2 .
n1
In this part of the lab, you will find the critical angle for a glass semicircle.
1. Direct the narrow beam of light from the ray box through the curved surface of the semicircular block towards the center of the flat face.
2. Rotate the block about this center until the angle of refraction at the flat face is 90o. Mark the
positions of the incident ray and the flat face and hence find the critical angle.
Q2. What do you observe happening to rays incident at angles of incidence greater than the
critical angle?
Q3. From your determination of the critical angle, determine the index of refraction for the glass.
Compare this value to a known index of refraction for glass.
56
Mirrors, Lenses, and the Telescope
Introduction
Lenses and mirrors are the basic building blocks of such optical instruments as cameras,
binoculars, telescopes, microscopes, magnifying mirrors, movie projectors, etc. In this lab, you
will begin by measuring the basic properties of lenses and mirrors. In the last part of the
experiment you will construct and examine the properties of an astronomical telescope.
Throughout the lab, you will be using the lens/mirror formula:
1 1 1
  ,
f s s'
where f, is the focal length of the mirror or lens, s is the distance from the object to the lens or
mirror (object distance), and s’ is the distance from the lens or mirror to the image (image
distance). The magnfication, M, of an image created by a lens or mirror is given by
s ' h'
M   ,
s h
where h and h’ are the object and image sizes, respectively.
Procedure Part I: Concave Mirror
Figure 1
1. The “object” for this part of the lab is a lightbox that projects through a crossed arrow on the
front.
a. Setup your concave mirror so that it reflects back onto a screen alongside the object as
shown in Fig. 1.
b. Now adjust the position of the concave mirror until a clear, sharp image is obtained on
the screen. The object and image distances are then equal (s = s’) to one another and also
equal to the radius of curvature, r, of the mirror.
57
c. Measure the distance and draw a ray diagram showing why this is the case.
Q1.
What is the magnification for the image in this situation?
Figure 2
2. In this part you will reflect the light from a distant object (s =∞) onto a screen as shown in
Fig. 2. Use the cardboard screen with a cutout held up to the window to select your object.
Make sure the window shade is pulled down so that there is only enough of a gap to fill the
cutout in your screen.
a. Adjust the mirror-screen distance until you get a sharply focused image.
b. Measure the distance between the mirror and the screen when the image is in sharp
focus. This is the focal length, f, of the mirror.
Q2.
What is the apparent relationship between f and r?
Procedure Part II: Converging Lens
The lens equation given in the introduction may be used to determine the focal length of a
converging lens.
1. Mount a lens in a holder on the optical bench at a distance of approximately 20 cm from the
illuminated crossed arrow.
2. Move a screen back and forth (on the other side of the lens from the object) until a sharp
image is formed. Measure the object and image distances.
3. Repeat for 4 different object distances.
4. Using equation (1), calculate the focal length for each set of readings. Calculate the average
focal length and the average deviation.
5. Check your average value by comparing it with the image distance obtained by focusing light
from a distant object onto the screen. This is best done by using an object from outside the
window as you did for the concave mirror.
58
Virtual object
Lens A
|s|
s'
Lens C
Real image
Figure 3
Procedure Part III: Diverging Lens
In Fig. 3, converging lens A (the one you used in Part II) by itself would produce a real image at
the point of convergence of the refracted rays. If diverging lens C is interposed between lens A
and this real image, a new real image will be formed as shown. The original real image formed
by lens A becomes a virtual object for lens C. According to the sign convention, the
corresponding object distance for lens C will be negative.
1. First reproduce the set-up in Fig. 3 but without lens C. Adjust the position of the converging
lens A to give a real image on a screen with a relatively short image distance—less than 20
cm. Measure this image distance.
2. Next, insert the diverging lens between lens A and the screen, and reposition the screen until
the image is in sharp focus.
3. Measure the new-image distance relative to lens C, and calculate the focal length of the
diverging lens using equation (1). Note that |s| in this case is the distance from lens C to
where the image was formed by lens A alone.
Procedure Part IV: The Telescope
The final part of the experiment is to construct a simple telescope. You will use the converging
lens from the previous section as the objective (lens A) and a second converging lens with a
smaller focal length for the eyepiece (lens B). The setup is shown in Fig. 4 with the equation for
the angular magnification given by:
Angular magnification =
Objective
f
f
O
E
Eyepiece
f
O
Figure 4
59
f
E
Q1.
Why would you want the focal length of the objective to be larger than the focal length of
the eyepiece?
1. Measure the focal length of lens B like you did for lens A.
2. Mount lens B on a meter rule about 20 cm from one end.
3. Mount lens A at a distance from lens B equal to the sum of their focal lengths.
4. If you look through lens B at a distant object, you should see an enlarged, inverted image,
though you may need to slide lens B back and forth to obtain a well-focused image.
5. In the lab there is a large graded scale on one wall. Take your telescope to the other end of
the lab from the scale and look at the scale through your telescope with one eye. With the
other eye, look at the scale directly. Estimate how many divisions of the scale seen through
the telescope correspond to the entire ten divisions of the scale as seen with the unaided eye.
6. From this observation, determine the magnification and compare with the theoretical
prediction.
60
Double Slit and Thin Film Interference
Introduction
Until the beginning of the 19th century, the question of whether light propagated as a type of
wave, or as a beam of particles had not been answered. Isaac Newton favored the particle theory
to explain why light appeared to travel in straight lines, whereas Robert Hooke and Christian
Huygens were able to explain refraction by assuming that light traveled as a wave with different
speeds in different media. Then in 1801, Thomas Young performed his crucial two-slit
interference experiment, which clearly demonstrated the wave nature of light.
y = L
d
d
L
Figure 1
In Young’s experiment, light waves spread out from each slit as shown in Fig. 1. Along the
directions where the crests reinforce each other, as indicated by the gray lines, the wave intensity
is high. Along the directions where a crest is cancelled by a trough, as indicated by the black
lines, the intensity is low. If a screen is positioned to intercept the waves, an interference pattern
of bright and dark regions is obtained. The condition for maximum brightness at a point on the
screen is that the distances from the slits to that point differ by a whole number of wavelengths,
m, where m is an integer. The distance y between the centers of two adjacent bright fringes is
given by the formula in Fig. 1.
Procedure Part I: Double slit interference
CAUTION: In reproducing this experiment, you will be using a helium-neon laser that produces
a narrow, low divergence beam of highly monochromatic light of wavelength 632.8 nm. The
beam is of high intensity and eye damage could result from looking directly into the laser.
Beware of accidentally directing the beam into your own or other people’s eyes either directly or
by reflection from a shiny object.
61
1. At your work station you are provided with a photographic negative that has several sets of
double slits inscribed on it. The spacing for each pair of slits should be given.
2. Place the laser about 5 cm from the slits and switch on the laser. Direct the beam through
one of the pair of slits and project the image on a piece of white paper place about 3 m from
the slits. Make sure to accurately measure and record this distance, L, and note the slit
spacing, d.
3. Mark the position on the paper of the centers of the bright fringes at the extreme left and right
of the pattern. Measure this distance, y, and record it in the table. Also count the number, N,
of spaces between the extreme bright fringes. The average fringe spacing can then be
determined by taking the ratio: y = y/N.
4. Repeat the measurement for all pairs of slits on your film.
5. Plot a graph of y on the y axis versus L/d on the x axis. According to the equation, the slope
of a straight trendline should give . Determine the wavelength and uncertainty of the laser.
Compare this with the value given in the introduction.
L (m)
d (m)
L/d
y (m)
N
y (m)
Procedure Part II: Thin film interference
Interference may also be observed when light is partially reflected from the upper and lower
surfaces of a thin transparent film, such as a soap bubble or a layer of oil on water. With laser
light, the film can be relatively thick. Here you will be using a glass microscope slide. Set up
the apparatus as in Fig. 2 with the position of the beam-expanding lens adjusted so that the
expanded beam fills most of the microscope side.
Beam expanding
lens
Laser
Microscope
slide
Figure 2
62
The microscope slide should be clamped rigidly at 45o to the beam and positioned so that the
reflected beam is directed vertically downwards onto the floor. Observe the interference fringes
produced by irregularities in the slide. Make a rough tracing of the pattern.
Q1.
What can you say about the variation in thickness of the slide along any bright or dark
fringe?
Q2.
Roughly where on the slide is the thickness changing most rapidly? Least rapidly?
Indicate these positions on your sketch.
63
64