TOPS Physics
Capacitance and Plate Separation
Parallel Plate Capacitor
A parallel plate capacitor is a device used to study capacitors. It reduces to barest form
the function of a capacitor. Real-world capacitors are usually wrapped up in spirals in
small packages, so the parallel-plate capacitor makes it much easier to relate the function
to the device.
A capacitor works by building up opposite charges on parallel plates when a voltage is
applied from one plate to the other. An electric field exists between the plates, which
allows the capacitor to store energy. The surface area of the plates and the spacing
between them determines the amount of charge, which may be stored per volt applied.
The larger the plates and the more closely they are spaced, the more charge can be stored
for every volt of potential difference between the plates.
The amount of charge that can be
stored in a capacitor is measured by
its capacitance. A capacitor of one
Farad (F) can store one Coulomb of
charge for every Volt that is applied
to the capacitor. The formula for
this is:
C = q/v
Capacitor with charges
+
+
+
+
+
+
+
+
-
Where C is the capacitance in
Farads, q is the charge in
Coulombs, and v is the electric
potential in Volts.
+
Voltage Source
For a parallel plate capacitor, the capacitance is given by the following formula:
C = ε0A/d
Where C is the capacitance in Farads, ε0 is the constant for the permittivity of free space
(8.85x10-12), A is the area of the plates in square meters, and d is the spacing of the plates
in meters.
A Farad is a very large quantity of capacitance, so we will use metric prefixes to produce
more usable numbers. Capacitance is normally measured in microfarads (µF), which is
1.0x10-6F, or picofarads (pF), which is 1.0x10-12F. 1.0F = 1,000,000µF =
1,000,000,000,000pF! Be very careful with your calculations!
TOPS Variable Capacitor Capacitance and Plate Separation.doc
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TOPS Physics
Purpose:
The purpose of this lab is to investigate the relationship between plate separation and
capacitance of a parallel plate capacitor.
Equipment:
Variable capacitor
Digital multimeter
Capacitance Tester (short leads that plug into
multimeter)
Graph Paper
Cautions:
This equipment is delicate. Everything should go together with the lightest of touches.
Do not force anything!
Procedure to set up the variable capacitor
1. Place the variable capacitor in the middle of the lab table, with the 0cm mark to
your left. Don’t put the capacitor too close to the edge of the table!
2. Place the multimeter close to the capacitor plates. You will find it most convenient
to put the meter behind the capacitor.
3. Plug the capacitance tester into the Cx socket on the multimeter. One pin of the
tester goes into each of the slots of the Cx socket
4. Put the plates at 5 mm separation (Align the left edge of the plastic tab that
extends toward the scale with the 5mm mark on the scale). Note that the scale is
calibrated in cm, so the 5mm mark will be halfway between 0cm and 1cm.
5. Clip the leads of the capacitance tester to the plates of the capacitor. The best
place to clip them is onto the radial flanges on the backside of the plates. There
are binding posts present, but the flanges work better!
The meter and leads themselves have some capacitance (about 4pF), so the leads have
to be kept short. Try to keep the leads as far away from each other as you can. This
value will have to be subtracted out of all your experimental readings.
6. Turn the big dial on the multimeter to “2000p”. This turns the meter on and
adjusts it to read in picofarads (pF). A picofarad is 1.0x10-12 farads.
7. Get everyone away from the apparatus; let the meter settle to a constant reading
and record the reading in the “Experimental Capacitance” column in the 5mm
row.
8. Repeat this procedure moving the plates 5 mm further apart for each measurement
until you reach 65 mm. Record each measurement in the table. When the reading
becomes less than 15pF, you should change to the 200pF scale for more accuracy.
TOPS Variable Capacitor Capacitance and Plate Separation.doc
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TOPS Physics
Plate separation
( mm )
Experimental Capacitance
Minus 4 pF
( pF)
Theoretical
Capacitance
( pF)
Difference in
Capacitance
(pF)
% Error
5
10
15
20
25
30
35
40
45
50
55
60
65
Data analysis:
You must calculate the theoretical capacitance for each spacing. We’ll do the first one, and
then you can do the rest! The hardest part of this is getting the units right. The easiest way to
proceed is to put everything in meters for the calculations:
1. The diameter of the capacitor plates in centimeters should be 17.8cm.
2. Divide the diameter by 100 to put the measurement in meters. The result is 0.178m.
Divide this by two to get the radius: 0.089m
3. The area of the plate is determined by the common formula A=πr2. Plug in the numbers
to get A = π(0.089)2 = 0.0249m2
4. Convert the plate spacing (5mm) to meters by dividing by 1000. 5/1000 = .005m.
5. Use these numbers in the formula C = ε0A/d to determine the theoretical capacitance
thus: C = 8.85x10-12(.0249)/.005 = 4.40x10-11. This is equal to 44.0x10-12F or 44.0pF
6. Write this result (44.0pF) in the “Theoretical Capacitance” column and the 5mm row.
7. Repeat this process for the other plate spacings. Note that the plate area is the same for
all, so all you need to do is repeat steps 5 and 6, inserting the correct values for the
spacing in each case.
8. For each plate spacing in the table, find the difference between the experimental and
theoretical values by subtracting each theoretical value from each experimental value.
Record the difference in the table.
9. Now you will calculate the experimental error for each spacing. Just use the formula:
E=(Theoretical Value-Experimental Value) x100/Theoretical Value. For example, at the
5mm setting, if your theoretical value is 44.0pF and your experimental value is 61.1pF,
you just plug these into the formula:
E = (44.0-61.1) x100/44.0 = -38.9%. Take the absolute value of this number (38.9%) and
record it in the “% Error” column of the table.
TOPS Variable Capacitor Capacitance and Plate Separation.doc
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TOPS Physics
10. On graph paper, plot the plate spacing on the x (horizontal) axis versus the
capacitance on the y (vertical) axis. Plot both the theoretical value and the
experimental value, using either different colors or line styles to distinguish the
two curves. Make sure that you choose appropriate scales and label the axes and
scales clearly. It is best to orient the paper with its long axis in the horizontal
direction (“landscape mode”).
11. Examine your graph and answer the following questions:
a. Does your experimental data support the theoretical values? Why?
b. Can you explain the experimental error?
c. Which set of data is more helpful in understanding the reasons behind the
experimental error, the difference between the experimental and
theoretical values or the percentage of error? Explain why you feel this
way.
d. Is it possible to change the value of the capacitor without changing the
size or spacing of the plates? (Hint: think about what happened to the
reading when you were physically close to the capacitor!)
TOPS Variable Capacitor Capacitance and Plate Separation.doc
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