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Physics Lab 212P-4
How Capacitors Work
NAME:
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LAB PARTNERS:
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LAB SECTION:
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LAB INSTRUCTOR: __________________________
DATE:
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Physics Lab 212P-4
Equipment List (all items marked with * are in the student kit, others are supplied at the time of
the lab)
Science Workshop Interface + voltage probes
1 µF capacitor.
A two position switch.
*1 F "super-capacitor"
*Two 1.5 V batteries + a battery holder
*Flashlight bulb (use one of the "long" bulbs in your kit) + bulb holder
*Hookup wires with alligator clips
Lab Activity: How Capacitors Work.
This lab involves three separate activities:
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An experiment in which you examine how a capacitor stores energy.
An experiment in which you examine how capacitors in series behave.
Modeling exercises in which you examine how real capacitors are made.
At this point in the course, we still have not studied circuits and batteries in any detail. However,
you can use qualitative physical reasoning to understand your experimental observations. Treat a
battery as a "black box" with the following properties:
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A battery ideally provides a fixed potential difference across its terminals.
A battery can supply charge (electrons); the negative terminal sends electrons out while
the positive terminal pulls electrons in.
A battery converts chemical energy into electrical energy.
Important note: for now, we would like you to think about electrons moving around a circuit
since this is what really happens. Later, when we learn about circuits, we will treat current as the
flow of "positive" charge -- this is an unfortunate convention used by engineers and physicists!
Always remember that it is actually electrons that move around in wires!
Activity 1: How capacitors store energy
You have been told that capacitors are used to store energy. Let's now see this happen. For the
experiment, you need to use:
 A 1 Farad capacitor;
 Two batteries, placed in a battery holder (from your kit);
 One of the long bulbs placed in its holder (from your kit).
 A two way switch provided to you;
 Wires with alligator clips (from your kit);
 Science Workshop Interface and voltage probes.
CAUTION: the 1 Farad capacitor in your lab kit has a “polarity” i.e the casing indicates a
“+” and a “-“ for each lead. Whenever you connect a battery or a power supply across the
capacitor, always make sure you connect the positive terminal to the “+” terminal of the
capacitor else you may be in for an unpleasant surprise (the capacitor might start
leaking or could even burst).
In this lab, we will examine how capacitors are used to store energy by studying the charging and
discharging process at a qualitative level. For the experiments, we need to use the software
program called "Science Workshop" located in the "Physics" group on the Start menu. This
program allows us to measure and store the time variation of the voltage across any two points in
a circuit by sending the signal through an interface. The measured data can then be displayed in a
table and/or as a graph. Before we proceed to the actual experiments, take some time to refamiliarize yourself with Science Workshop by following the procedure below:
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Start Science Workshop: You should see the active window shown below.
Drag this symbol to
ANALOG CHANNEL A.
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Click & drag the "analog plug" icon shown above to analog channel A.
Click & drag the "Graph" icon shown above to analog channel A.
Click & drag the "Table" icon shown above to analog channel A.
Click & drag the "Digits" icon shown above to analog channel A.
When you do this, you should see the screen shown on the following page.
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Select the "clock" icon (next to the  icon) in the table window. Clicking on this changes
the "Voltage(V)" column to one that will contain pairs of data (time, volts) when you
make measurements.
Double click anywhere on the x-axis of the graph. When you do this, you will get a
screen that allows you to set the parameters for the x-axis. You can leave the settings
unchanged for now: but remember that you will need to change them later in this lab.
Double click anywhere on the y-axis of the graph. When you do this, you will get a
screen that allows you to set the parameters for the y-axis. Since the maximum voltage of
your two batteries in series is around 3 V, set the maximum value of the voltage for 4 V.
Connect the terminals of the 1 F capacitor to each other for a few seconds using some
wire.
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Set up the circuit shown below, making sure that you connect the batteries to each other with
the correct polarities (i.e. "positive" end of one battery connected to the "negative" terminal
of the second battery)! Do NOT complete the circuit yet -- i.e. leave the switch OPEN. Note
that the switch has two possible closed positions, labeled A and B in the diagram above. Note
that the voltage probes from the Science Workshop interface box should already be
connected to Analog Channel A.
Interface
box
bulb
I1 FF
A
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B
Make sure that the voltage probes are properly connected to measure the voltage across the
capacitor, VC.
Now, click on the "REC" icon on your program screen and complete the circuit by closing
the switch in position A. You will see your data getting recorded in the table and it will also
be displayed on the graph.
After the capacitor seems to have charged completely, flip the switch to position B.
 Stop recording data by clicking the "STOP" icon when the capacitor has discharged
completely.
 Note now that you have (a) a graph that displays VC vs. t and (b) a table that shows the
actual voltage readings (in volts) at different times (in seconds).
 You might wish to do this a few times in order to get a reasonable set of data. Note that
you can delete any set of data simply by highlighting the name of the data set in the data
window and then pressing the "delete" key.
Q1. Described what you observed during the experiment and sketch (or print and attach) the
potential difference across the capacitor vs. time, assuming that you started the experiment at
t = 0. In the sketch below, indicate when the switch was thrown from position A to position B.
Also indicate the numerical value of the voltage when the capacitor is completely charged.
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Potential
difference (V)
TIME (seconds)
Q2. How much energy was stored in the capacitor when it was fully charged?
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Q3. Creative exercise: use the idea of energy conservation to describe the entire process of
charging and discharging that you observed. Remember that energy can take on different forms:
chemical energy, light, heat, electrical energy (i.e. electric field)…
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Activity 2: Capacitors in Series
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First, discharge completely both the 1 F and the 1 F capacitors -- you can do this by
hooking up a wire across the terminals of each capacitor. Remember from activity 1 that the
1 F capacitor can take a few minutes to discharge completely.
Connect the circuit shown below.
Convert the Science Workshop interface into a voltmeter by clicking on the monitor “MON”
icon and reading the voltage from the digital display window for analog channel A.
With the switch in the open position, measure the initial potential difference across each
capacitor to make sure the capacitors do not have any charge.
Then, throw the switch to position A, while watching the bulb and measuring the potential
difference across the smaller (1F) capacitor.
Measure the final potential difference across each capacitor after the switch has been in
position A.
bulb
I1 FF
A
B
Q4. What is the total capacitance of the two capacitors in series?
1 F
Q5. Based on your observations of the bulb, did the capacitors in series get charged slower or
faster than when you had only a 1 F capacitor in the circuit? (You do not have to explain
anything here -- just report your empirical observations.)
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Q6. What is the final potential difference that you measured across each capacitor?
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Q7. Use your understanding of capacitors in series to explain your observation in Q6.
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Activity 3: How are capacitors designed?
The aim of this activity is to get you to think about how capacitors are made. A "dielectric" is
placed in between the plates of the capacitor so as to enhance the capacitance. Dielectric
materials are insulators, so an applied electric field does not actually make charges move from
one point in a dielectric to another. However, the molecules in a dielectric act like dipoles that
are free to rotate and line up in an applied electric field. The result is that the "effective" electric
field inside the dielectric medium is reduced by a factor called the "dielectric constant" . The
dielectric constants for some common materials are listed below. Refer to this table when
answering questions in this lab activity.
MATERIAL
Air
Polystyrene
Paper
Pyrex
Silicon (a semiconductor)
Water (close to room temperature)
Titanium-based Ceramic
Strontium titanate
DIELECTRIC CONSTANT
~1
2.6
3.5
4.7
12
~80
~130
~310
Another important consideration is the breakdown electric field of a dielectric: if the electric
field across the plates of a capacitor is too large, the molecules get "torn apart," charges move
from one place to another and the dielectric is no longer an insulator! For instance, if you make
the plates of a parallel plate capacitor too close together, then for a given applied voltage, the
electric field can become huge and lead to breakdown. This is why the casing of a capacitor has a
maximum rated voltage listed on it.
Your goal is try to make a model of the 1 F capacitor.
Q8. First, model the capacitor by a parallel plate capacitor, as depicted below. You have to
make some intelligent estimates of the distances A and d from the external appearance of the
capacitor. How large a dielectric constant is needed to produce the measured capacitance? Is this
realistic?
Plates of area A
d
Here is the equation we used to model this parallel plate capacitor:
Estimated value of A:
Estimated value of d:
Based on values of C, A & d, we obtain the following value for the dielectric constant:
Is this reasonable or not? Justify your answer.
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Q9. So, you've probably figured out by now that the parallel plate model does not work! Model
the capacitor by a cylindrical capacitor instead. As in the pre/post lab, this should consist of an
inner cylinder of radius R1, an outer radius R2 and a length L. How large a dielectric constant is
needed to produce the measured capacitance? Is this realistic?
Expression used for calculating capacitance of cylindrical capacitor:
Estimated values of geometrical parameters in above expression:
Radius of inner cylinder:
Radius of outer cylinder:
Based on values of C, R1 and R2, we obtain the following value for the dielectric constant:
Is this reasonable or not? Justify your answer.
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Q10. Creative exercise: Hmmm… Neither the simple parallel plate nor the cylindrical
capacitor schemes seem to work. So, how on earth are these capacitors constructed?? Design an
alternative scheme that can produce the measured capacitance in the given compact
package/geometry. Think creatively but remember that your scheme should be amenable to
large-scale manufacturing and hence cannot be extremely intricate! (Hint: look at the expression
for the capacitance of a parallel plate capacitor. What geometrical factor should you maximize to
increase capacitance? What geometrical factor should you minimize to increase capacitance?
How would you make a package that is compact but meets these requirements?)