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FOUNDATION EXP 4 – CAPACITORS AND CAPACITANCE
EXPERIMENT 4
CAPACITORS AND CAPACITANCE
1.0 INTRODUCTION
1.1 WHAT IS A CAPACITOR?
A capacitor is a little like a battery. Although they work in completely different
ways, capacitors and batteries both store electrical energy. As you know a battery
has two terminals. Inside the battery, chemical reactions produce electrons on one
terminal and absorb electrons at the other terminal. A capacitor is a much simpler
device, and it cannot produce new electrons - it only stores them.
Like a battery, a capacitor has two terminals. Inside the capacitor, the terminals
connect to two metal plates separated by an insulator called a dielectric. The
dielectric can be air, paper, plastic or anything else that does not conduct
electricity and keeps the plates from touching each other. You can easily make a
capacitor from two pieces of aluminium foil and a piece of paper. It won't be a
particularly good capacitor in terms of its storage capacity, but it will work.
1.2 WHAT A CAPACITOR DOES
The symbol for a capacitor in an electronic circuit is shown in Figure 1.1.
Figure 1.1
If a capacitor were to be connected to a battery, as in Figure 1.2, the plate on the
capacitor that is attached to the negative terminal of the battery accepts electrons
that the battery is producing.
Figure 1.2
The plate on the capacitor that is attached to the positive terminal of the
battery loses electrons to the battery.
Dr. Daniel Nankoo
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FOUNDATION EXP 4 – CAPACITORS AND CAPACITANCE
Once it is charged, the capacitor has the same voltage as the battery (1.5 volts
on the battery means 1.5 volts on the capacitor). For a small capacitor, the
capacity is small. But large capacitors can hold quite a bit of charge. You can
find capacitors as big as soft drink cans, for example, that hold enough charge
to light a torch bulb for a minute or more. When you see lightning in the sky,
what you are seeing is a huge capacitor where one plate is the cloud and the
other plate is the ground, and the lightning is the charge being released
between these two plates. Obviously, in a capacitor that large, you can hold a
huge amount of charge.
1.3 EXAMPLE OF DISCHARGING
Figure 1.3
Suppose a capacitor, light bulb and battery were connected as in Figure 1.3. If
the capacitor was quite large, what you would notice is that, when you
connected the battery, the light bulb would light up as current flows from the
battery to the capacitor to charge it up. The bulb would get progressively
dimmer and finally go out once the capacitor reached its capacity. Then on
removing the battery and replacing it with a wire, current would flow from one
plate of the capacitor to the other. The light bulb would light and then get
dimmer and dimmer, finally going out once the capacitor had completely
discharged, i.e. when there are the same number electrons left on both plates.
One way to visualize the action of a capacitor is to imagine it as a water tower
connected to a pipe. A water tower "stores" water pressure - when the water
system pumps produce more water than a town needs, the excess is stored in
the water tower. Then, at times of high demand, the excess water flows out of
the tower to keep the pressure up. A capacitor stores electrons in the same
way, and can then release them later.
1.4 CAPACITANCE
The unit of capacitance is the farad, F. A capacitance of 1 farad is very large,
and it is much more common to encounter microfarads (µF – 10-6), nanofarads
(nF – 10-9) or picofarads (pF – 10-12). All capacitors have a maximum working
voltage, which should not be exceeded. Care must be exercised when working
on circuits containing capacitors. If the capacitor is inadvertently shorted or
connected to ground, a rapid discharge may occur which may cause the
capacitor to explode or may give a lethal shock.
Dr. Daniel Nankoo
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FOUNDATION EXP 4 – CAPACITORS AND CAPACITANCE
2.0 PROCEDURE
2.1 CIRCUIT AND SET UP
Connect up the circuit as shown in Figure 2.1. Set the Function Generator to
produce a square wave (50) output with an amplitude of 5.0V. The Function
Generator’s DC offset should be zero, i.e. the OFFSET dial should be pushed
in. Use the oscilloscope and the appropriate BNC cables to verify this. Set the
scope’s VOLT/DIV to 1volt/div. Calculate the RC product, and hence set the
frequency to about 1/gRC Hz, where g is a constant between 8 and 12.
A
R = 1.0k
D
B
C = 0.1µF
Figure 2.1
2.2 MEASUREMENTS
Voltage axis as % of maximum
100%
y
63.2%
50%
0.0%
x
T=
Time Constant
Time axis
Figure 2.2
Dr. Daniel Nankoo
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FOUNDATION EXP 4 – CAPACITORS AND CAPACITANCE
Connect the output from the Frequency Generator to the input of your circuit,
and use the oscilloscope accordingly to observe the waveform across points A
– D and B – D, where the scope’s earth is connected to D.
Adjust the generator amplitude controls and the scope’s VOLTS/DIV and
SEC/DIV settings to obtain clear waveforms as outlined in Figure 2.2. Use the
scope controls to obtain a suitable trace – make good use of the VOLTS/DIV,
SEC/DIV and HORIZONTAL POSITION dials. Check your settings with a
member of staff, and note down your settings before accurately sketching the
two waveforms in your lab book.
2.3 TIME CONSTANT MEASUREMENTS
You should have recorded an output waveform (across B-D) similar to that
shown in Figure 2.2. You should be able to observe that the waveform does
not rise immediately to the full 100% of the input, but it is delayed. This delay
is related to the Time Constant of the circuit. There are two ways of finding
the time constant.
1. It can be calculated from the values of R and C using the formula
T = RC, where R is in Ohms, C is in Farads and T is in seconds.
2. It can also be calculated using the property of an exponential
waveform, that the circuit’s time constant occurs after reaching 63.2%
of the final voltage value.
Before performing the measurement as described in 2, check the set up of your
oscilloscope for the input (across A-D) so that the top (100%) and bottom
(0.0%) of your waveform take up a large area of the screen. If you use the
scope controls to view one pulse that takes up the full area of the vertical
screen (i.e. 8 divisions), then each division represents 12.5%, and then it is
relatively straightforward to work out how many divisions correspond to
63.2%). Connect the oscilloscope input across points B-D, and measure the
time constant along the horizontal (time) axis. You may use the MEASURE
function to aid taking readings.
Calculate the time constant using both methods, and note this down in your lab
books, along with the % difference between the two figures.
Dr. Daniel Nankoo
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FOUNDATION EXP 4 – CAPACITORS AND CAPACITANCE
3.0 CAPACITORS IN SERIES AND PARALLEL
3.1 PREREQUISITE
Capacitors, like resistors, may be connected in a combination of series or
parallel layouts. The purpose of this part of the experiment is to estimate the
combined values of two capacitors by means of a measurement of the time
constant using the scope and the 63.2% principle. As the resistance is held
constant at a known value, these measurements can be used to suggest a
formula for capacitors in series and parallel.
3.2 PROCEDURE
Connect the circuit as shown in Figure 3.1.
A
B
R = 1.0k
D
C
0.1µF
C
0.1µF
Figure 3.1
Using the 63.2% principle, measure the time constant. Draw an accurate
diagram of the waveform observed across points B-D, making a note of the
scope settings, which you should adjust accordingly in order to have a
reasonable display. Once you have worked out the time constant, use T = RC
to estimate the value of the total effective capacitance, Ctot, of the combination
of the capacitors.
A
B
R = 1.0k
D
C = 0.1µF
C = 0.1µF
Figure 3.2
Dr. Daniel Nankoo
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FOUNDATION EXP 4 – CAPACITORS AND CAPACITANCE
Repeat the above procedure for the circuit shown in Figure 3.2.
From your calculated values for the effective capacitances for both circuits,
suggest formulae to allow the total value of capacitance to be estimated for
capacitors in series and parallel.
4.0 COMMENTS AND CONCLUSIONS
When writing the comments and conclusions in your lab books, you may want
to consider discussing the following.
i)
ii)
iii)
iv)
v)
Using the waveform observed in Section 2.2, determine the initial
slope, in Volts/sec units, of the output waveform (i.e. the slope of the
tangent shown as the dotted line between x and y in Figure 2.2).
Explain why it is important to set up the scope properly when taking
measurements.
List possible reasons for any differences between the calculated and
measured values for T.
Discuss the results from the tests with added capacitance. Compare
with the expressions for resistors in series and parallel from
Experiment 2.
Explain why it is important for the earth lead from the scope to be
connected to point D. What would happen if it were connected to some
other point in the circuit?
Dr. Daniel Nankoo
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