Download Interactive Physics Laboratory — Experiments in Electricity

WDS'10 Proceedings of Contributed Papers, Part III, 91–96, 2010.
ISBN 978-80-7378-141-5 © MATFYZPRESS
Interactive Physics Laboratory — Experiments in Electricity
Z. Šabatka
Charles University Prague, Faculty of Mathematics and Physics, Prague, Czech Republic.
Abstract. The main goal of this paper is to present three laboratory experiments in a
form which is suitable for an Interactive Physics Laboratory. The type of these
experiments is common and one may find them both in literature and internet. We
prepared, verified and quantitatively measured their new variants. The article also
presents the form of an assignment of a lab experiment.
Introduction
The department of physics education is starting an interactive physics laboratory (IPL) 1 . It will be a place
where students can come and do their own experiments. A class or group of students will be divided in pairs
which will work on different tasks given by us. Only the topic will be the same for the whole class.
To do experiments interesting for students we try to use tools, which are not from some reason so common
in our schools (expensive tools, experiments supported by a computer …).
Our idea is that students should (and it also comes out from a questionnaire asking teachers about their
opinions 2 ) work with some worksheet, which should be a reminder what they did and learned.
We think about how to outline the physical problem which should be solved by students. How to guide
students while working on the task seems to be also very hard question. What we really don‘t want to do is to
give students an instruction manual. Much rather we would like to give them tips and hints in a moment when
they don‘t know what to do next.
Experiments
The most wanted topic in the questionnaire was Electricity and Magnetism. So the first experiments
prepared by us are from the field of Electricity. Here we present three of them, especially from Electrostatics.
Verifying Coulomb’s law
Coulomb’s law quantitatively describes the force acting between two electrically charged particles. It was
first published by Charles Augustin de Coulomb. High school students are familiarized with its scalar form
Fe =
Q1Q2
,
4πε r 2
1
⋅
(1)
where Q1, Q2 are charges of particles, ε is the permittivity of dielectric media surrounding the particles and r is a
distance between those particles. One has to add that the positive force implies a repulsive interaction and a
negative force implies an attractive interaction.
Such dependence of force on charges and their distance could be verified using similar apparatus (using a
principle of a torsion balance) as Coulomb used, e.g. [2]. You can also use an apparatus produced by PASCO
(see [3]) or you can built your own apparatus just like us.
The main principle of the verification is that you have to somehow determine a magnitude of the acting
force. To do it you may use simple scales, as described in [4]. However our experiment was inspired mainly by
[5] using electronic scales.
Apparatus
Our apparatus (see Fig. 1) consists of three ping-pong balls painted using conductive ink. Each of those
balls is fixed to a straw witch makes together with a small plastic slab a stand of the ball. Balls could be charged
using a high voltage power source (25 kV). There are also electronic scales with resolution 0,01 g, a stand and
of course wires and a metre.
Tasks, measuring methods and results
The general task “to verify the Coulomb’s law” is divided into few steps. There is a work sheet for students
containing following tasks/questions:
1
2
More information about the IPL may be found in [1].
Data gathered from the questionnaire were published and commented also in [1].
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ŠABATKA: INTERACTIVE PHYSICS LABORATORY — EXPERIMENTS IN ELECTRICITY
Figure 1. Apparatus of Coulomb’s law experiment.
1.
2.
3.
4.
Verify that two electrically charged balls attract or repel each other according to their charge.
Determine a dependence of an acting electrical force on a quantity of charge.
Determine a dependence of an acting electrical force on a distance of charged balls.
(Bonus :) Observe what happens if we put conduction body (e.g. your hand) near the charged ball.
We think it should be easier for students to work in clear steps. It is done so they go from easier to harder
tasks. In the first one they get know the principle of measurement. To proof, that two balls charged by the
same/opposite polarity of charge repulse/attract each other, let’s stand one ball with its stand on the scales and
other above it. The repulsion/attraction of balls will be detected by scales as an increment/decrement of a ball’s
mass. It is very easy to charge the balls at the same potential (they will have also the same charge). Harder
question is how to charge a ball with an opposite charge using the same power source. It has to be done using an
electrostatic induction.
The second task could be fulfilled in two ways. First and simpler possibility is to charge the balls with the
same charge. The next step is to place them to a constant distance. And then one will observe how the force
(weight) is changing by dividing the charge of one ball into halves using the third ball. Students will see that
also the force is the half size. The second possibility is to measure the acting force by charging the balls (or one
of them) at different potential (and also with different charge).
To fulfil the third task students should measure the acting force versus balls’ relative distance. They let one
ball staying on the scales and move with the adjustable stand in which the second ball is fixed. The fourth task
should push students forward the idea of the method of mirror charges.
Determination of capacitor’s capacity
In this task students should become familiar with a capacitor and possibilities how to measure its capacity.
First of all they will measure capacity of two “small” capacitors using common multimeter. They may also try
what is the total capacity of those two capacitors connected in parallel or in series.
The main part is to determine the capacity using measuring voltage and current by discharging the
capacitor. We offer to students three following methods based on work with the discharge curve.
Experiments determining a capacity may be also find in literature, e.g. [6], [7].
A discharge curve
A discharge curve of a capacitor is a graph of time dependent current (or voltage, or charge) when
discharging a capacitor. The current i in time t is expressed as
⎛ t ⎞
i = I 0 exp⎜ −
⎟,
⎝ RC ⎠
(2)
where R is a resistance connected to the capacitor, C is the capacity and I 0 is an initial current.
To measure the current and the voltage in time we use current and voltage probes from Vernier connected
via the LabQuest to a computer. The scheme of such circuit is at the Figure 2. Gathered data are processed by a
program LabPro. This program is also able to integrate (to count) an area under a graph.
Determination the capacity from the area under the discharge curve
Current I is defined as charge Q flowing through a cross-section of a wire per time t
I=
Q
.
t
92
(3)
ŠABATKA: INTERACTIVE PHYSICS LABORATORY — EXPERIMENTS IN ELECTRICITY
Figure 2. Scheme of a circuit.
How could one determine charge from the discharge curve? For constant current it is clear. Charge would
be count as Q = I·t. Thanks to the shape of a curve we have to count the charge using Newton’s integral as
t2
Q = ∫ i (t ) ⋅ dt .
(4)
t1
So the current corresponds to the area under the discharge curve. It is true that it would be hard for majority
of high school students to use integral in their third year of high school studies. But on the other the idea, that
the charge is the area under the curve and that there is a program which is able to count it, is pretty
understandable. An example of such measurement you may see at Graph 1. For this measurement we used a
resistor with the resistance 10 Ω and a capacitor C = 500 μF.
Using the determined charge and knowing the initial voltage on the capacitor we may count the capacitor’s
capacity from its definition as
C=
Q
.
U
(5)
There is the charge Q = (3,1 ± 0,1) mC 3 in the presented graph. The initial voltage was approx.
U 0 = (4,62 ± 0,03) V 4 . So the capacity is count as C = (680 ± 30 ) μF .
Determine the capacity from the time of the discharge
Using the equation (2) of a discharge curve and knowing the capacity we may count the current (or voltage)
in given time. It is also easy to express the capacity from the same equation as
Graph 1. An area under the discharge curve of a capacitor.
3
The error was estimated from an inaccuracy of both current measurement and determination of the point
when the current is zero.
4
U0 is the voltage of the fully charged capacitor. The error was estimated from an inaccuracy of voltage
measurement.
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ŠABATKA: INTERACTIVE PHYSICS LABORATORY — EXPERIMENTS IN ELECTRICITY
C=
t
I
R ln 0
i (t )
=
t
U
R ln 0
u (t )
.
(6)
For measurement using this method we use the same circuit as at the Figure 2 (R = 1 kΩ and C = 500 μF).
In this case we use the second form of the formula, because the current is too close to resolution of the current
probe. From gathered data one may find out, that the capacity is C = (740 ± 20 ) μF .
Determine the capacity from the discharge curve equation
The last method we offer to students for measuring capacity is based on determination of a discharge equation. If we know the equation of discharge curve of a specific capacitor, we will be able to determine the product
C ⋅ R [see equation (2)]. And if we know also the resistance in the circuit, we will determine the capacity C.
At the Graph 2 we may see an example of such determination. It is very important that we could discuss
with students about what do all of letters in an equation (A, B, D, E) mean. It is very good that they may set e.g.
coefficients A, B and D (which are pretty clear from measured data) and a computer will calculate the wanted
coefficient E, which is the product C ⋅ R . And if you know the resistance (in our case R = 1 kΩ), you will be
able to count the capacity as C = (721,6 ± 0,2) μF .
The next step of students’ work will be of course to compare their experimental results obtained by
different methods and also with the capacity marked by a producer of the capacitor. They will definitely find out
the real capacity used to be higher.
A capacitor as a power source; VA characteristic of a bulb and a resistor
This task also concerns about capacitors. But the main part is focused on “playing” with Ohm’s law.
Students should verify that the dependence between current and voltage is in case of constant temperature linear.
We have two ways how to measure such dependence.
VA characteristics point by point
The first very well known method is measuring point by point. An experimenter registers current through a
resistor (or a bulb) at given voltage. Both of them are written into a table and a graph is constructed (see
Graph 3).
A capacitor as a power source of variable voltage
Very nice variant of this experiment is with a capacitor as a power source. If we use a “small” capacitor (in
our case C = 200 μF is used), the bulb will have not enough time to be heated and its VA characteristics will be
linear (see Graph 4). An inspiration for this variant of an experiment was an apparatus made by PASCO [8].
On the other hand if one take a capacitor with higher capacity (we use C = 2 mF), the bulb will be heated
and its resistance will change, so the dependence won’t be linear. This is shown at Graph 5.
Graph 2. An equation of a discharge curve.
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ŠABATKA: INTERACTIVE PHYSICS LABORATORY — EXPERIMENTS IN ELECTRICITY
Graph 3. VA characteristics of bulb (6 V, 0,1 A), point by point method. Thanks to increasing temperature of
the bulb the graph is not linear.
Graph 4. VA characteristics of a bulb (6 V, 0,1 A), using a capacitor C = 200 μF as a power source.
Graph 5. VA characteristic of a bulb (6 V, 0,1 A), using a capacitor C = 2 mF as a power source.
Consider that data were recorded by decreasing voltage.
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ŠABATKA: INTERACTIVE PHYSICS LABORATORY — EXPERIMENTS IN ELECTRICITY
The main point students should learn in this task is that Coulomb’s law is not only U = RI. One has to think
also about the temperature of the wire. If the temperature is constant, the resistance will be constant, too. One
concrete example of such situation is shown at Graph 4 – the process was short and the wire “had no time to
warm up”.
On the other hand the higher is the temperature the higher is the resistance of the wire. From the Graph 3
one can see that the current is increasing slower and slower – the resistance is increasing together with the
temperature. The second example of such situation (see Graph 5) is more complicated. Comparing with Graph 3
we may see that the Graph 5 looks unfamiliarly. It is done by the decreasing voltage during which the data were
gathered.
Conclusions
We have presented some of many experiments which will take a part in our Interactive Physics Laboratory.
Up to now we have prepared “normal” worksheets, which may be used. But as said in an introduction we would
like to give students hints and not a manual how to do it.
So we decided to use the computer for assignment of tasks. We would like to prepare a database of our lab
experiments in a form of guides, which could give a hint if students don‘t know how to continue. To fulfil this
plan we will use a proved interface of a web www.physicstasks.eu.
References
[1] ŠABATKA Z., Interactive Physics Laboratory for High School Students (Experiences and Teachers' Opinions), in
WDS'09 Proceedings of Contributed Papers: Part III – Physics (eds. J. Safrankova and J. Pavlu), Prague, Matfyzpress,
Prague, Matfyzpress, pp. 134–137, 2009, ISBN 978-80-7378-103-3, available at
<http://www.mff.cuni.cz/veda/konference/wds/contents/pdf09/WDS09_344_f12_Sabatka.pdf>
[2] MARTÍNEZ A. A., Replication of Coulomb's Torsion Balance Experiment, in Archive for History of Exact Sciences,
2006, vol. 60, no. 6, pp. 517-563.
[3] PASCO: Coulomb’s Law Experiment [online], [cit. 2010-06-09], available at
<http://www.pasco.com/featured-products/coulombs-law-experiment/index.cfm>.
[4] LARSON C. O., GOSS E. W., A Coulomb's Law Balance Suitable for Physics Majors and Nonscience Students, in
American Journal of Physics, 1970, vol. 38, no. 11, pp. 1349-1352.
[5] CORTEL A., Demonstrations of Coulomb’s Law with an Electronic Balance, in Physics Teacher, 1999, vol. 37, no. 7,
pp. 447-48.
[6] Vybíjecí křivka kondenzátoru (In Czech), [online], [cit. 2010-06-09], available at
<http://www.ises.info/old-site/experim/labuloh/lu3/lu3.html>
[7] Ukázka laboratorních prací měřených soupravou ISES (In Czech), [online], 2002, [cit. 2010-06-09], available at
<http://kdf.mff.cuni.cz/veletrh/sbornik/Veletrh_07/07_25_Vicha.html>
[8] PASCO Ohm’s Law Experiment [online], [cit. 2010-06-09], available at
<http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=55933&groupID=282&Detail=1>
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