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Transcript
Circuit Electricity Experiment 3
Constructing a DC power supply
Prelab questions for this experiment can be found on page E-24.
Safety
Make sure that you have read the safety notes in the introductory section of this manual before
beginning any practical work.
Do not, under any circumstances, attempt to repair any of the equipment should you think it to be
faulty. Rather, turn off the apparatus at the power-point and consult your demonstrator.
The capacitors you will use for this exercise are electrolytic capacitors, so it is essential that they
are connected in the correct fashion. Connect the black end or ‘-’ of capacitor to the earth side of
the circuit as shown in the circuit diagram in Experiment (i). If in doubt, ask your demonstrator.
References
121/2:
Sections 27.1, 29.7, 36.3 and 44.5.
141/2:
Sections 26.2, 27.5, 28.8, 29.3, 42.6 to 42.8.
Introduction
In the Electricity and Measurement laboratory, the basic experiments were all concerned with
direct current (D.C.) circuits. These are circuits with continuous conducting paths, in which only
unchanging E.M.F.'s and currents and only the resistance of circuit elements are studied.
When a circuit contains time varying or alternating E.M.F.'s (eg. the mains power supply) or
contains elements with inductance (eg. a coil of wire) or capacitance (eg. a capacitor, which acts as
a break in the circuit) - then we need to study the changes in voltages and currents with time. In
this experiment, you will learn how to use a cathode ray oscilloscope (CRO) to investigate timevarying waveforms. In particular, you will examine the properties of capacitors and diodes and
how they can be used to construct a direct current (DC) power supply from an alternating supply.
The following experiment concerns features of capacitors and diodes as used in simple circuits. If
you are unfamiliar with the basic concept of capacitance or diodes, read Appendices A and B first.
The CRO:
Today we will be using the Cathode Ray Oscilloscope (CRO) which displays a voltage-time graph
on a screen. For our purposes it will only be necessary to know what the CRO shows us, not how
(the “hows” of the CRO will be investigated in one of the experiments in the Projects laboratory).
The CRO displays potential difference vertically on the screen. That is, “the dot” moves an
amount up or down on the screen depending on the potential difference applied to the input. The
central line (or any other line) of the screen can be set to represent 0 volts. If the scale (labelled Ygain) is set to 2 volt/cm the dot moves up or down a cm for every 2 volts applied to the input. For
example, when the CRO is attached to a six-volt battery in the forward direction the dot would
move 3 cm up the screen. If the connections of this battery to the CRO input terminals were
swapped over the dot would move down 3 cm. These situations are shown on the next page.
Physics 121/2 and 141/2 Laboratory Manual
C-21
Settings:
Settings:
Settings:
Timebase: off
timebase:
off
timebase:
off
Y-gain:
2 V/cm
Y-gain:
2 V/cm
Y-gain:
2 V/cm
Input:
not connected
Input:
connected to a 6 V
battery, forward
direction
Input:
connected to a 6 V
battery, reverse
direction
The advantage of the CRO over a voltmeter is that it can move the dot from left to right at a
steady speed while measuring a potential difference, and so the variation of potential difference
with time can be observed. For example, suppose the dot is moved in the horizontal direction at
one cm per second (this is called the time-base) and the Y-gain is set to 1 V/cm. If the input
voltage begins at 0 V, reaches 3 V in 2 seconds and then 0 V again a further 2 seconds later, we
would see the dot start on X-axis of the screen on the left hand side, then move up three cm while
moving 2 cm to the right, then go down three cm while moving another two cm to the right.
If the dot is moving sufficiently fast from left to right, it will appear as a line on the screen. If you
then apply a sinusoidally varying potential, at a frequency of 1 kHz (that is 1000 cycles per
second) with an amplitude of 6 volts and the time base is on, you would see a sine function since
the CRO shows us a graph of potential difference versus time.
Settings:
Settings:
Settings:
Timebase: 0.1 mSec/cm
timebase:
0.2 mSec/cm
timebase:
0.05 mSec/cm
Y-gain:
2 V/cm
Y-gain:
2 V/cm
Y-gain:
2 V/cm
Input:
1 kHz, 6 V
amplitude
Input:
1 kHz, 6 V
amplitude
Input:
1 kHz, 6 V
amplitude
C-22
Physics 121/2 and 141/2 Laboratory Manual
We can measure the frequency of the signal from the CRO screen. From the leftmost diagram we
see that in the time that it takes the input voltage to go through one complete cycle (that is,
increase, decrease and return to the original voltage), the dot has moved 10 cm horizontally. The
timebase is set on 0.1 mSec/cm, hence the time required for the input voltage to move through one
cycle (ie. the period of the input) is 1.0 mSec. The frequency is the inverse of the period, ie. 1.0
kHz. The middle diagram shows that the dot travels 5 cm horizontally as the input voltage
returns to the starting position. The timebase for this diagram is 0.2 mSec, hence the period is
again 1.0 mSec. The same analysis can be followed for the rightmost diagram.
There are some sophisticated “tricks” that the CRO uses to enable it to “show” this sort of time
dependence but for the time being you need not worry about them. At first it is sufficient to be
able to interpret what is shown on the CRO screen.
Shown below is a diagram of a CRO control panel. Don't panic. You will be using only a few of
these controls. For example, a stereo system can be operated effectively without ever using the
graphic equaliser!
Time Base
Power
Horizontal
Position
Intensity
Triggering
Focus
Channel 1 OR Y
MODE
Channel 2 OR X
Coupling
Coupling
POS.
Y input
POS.
Y Gain
X Gain
X input
The two controls that have been discussed so far are the Y-gain and the timebase. The signal is
sent to the CRO through a co-axial cable connected to the Y input. A control that is discussed
later is this laboratory exercise is the coupling switch.
Physics 121/2 and 141/2 Laboratory Manual
C-23
Prelab Exercise:
Read the CRO screens and the information given below and briefly describe in the space
provided the input voltage that is applied to the CRO to give the picture shown.
For the input signal shown on the rightmost diagram, determine how long it takes for the
voltage to increase from 0 V to 12 V.
Settings:
Settings:
Settings:
Timebase: off
timebase:
0.1 mSec/cm
timebase:
0.01 mSec/cm
Y-gain:
Y-gain:
1 V/cm
Y-gain:
5 V/cm
2 V/cm
Input:
Input:
Input:
Section A:
The Capacitor
Introduction:
The two circuit components you have used in the laboratory so far are the light globe and resistor.
Both of these devices have the property of conducting DC currents. If a constant potential
difference is established across them, there will be a steady current.
The capacitor behaves quite differently. It often takes the form of two parallel plates with no
conducting path between them. It is not possible for a steady DC current to be carried by a
capacitor.
metal plates
Capacitance,
C
Capacitor
Symbol for a
capacitor
C =
Q
V
Q = charge on plates
V = voltage on plates
However, capacitors have the property of being able to accumulate and store charge. When
connected across a battery, the plates become charged. The rate of charging (ie. current)
decreases as the charge on the plates increases (in the same way that the rate of parking cars
in a car park decreases as the car park fills up - since it is harder to find a spot!).
C-24
Physics 121/2 and 141/2 Laboratory Manual
In Section A of this exercise, the CRO will be used to investigate the charging and discharging of
capacitors.
Charging and discharging a capacitor
Experiment A1:
Uncertainties:
There are many possible sources of error in experimental work. Read through the section in your
lab manual Notes on Confidence Limits in Experimental Physics and identify two such sources of
error that could be found when measuring the discharge of a capacitor as described in Experiment
A2. Find an expression for the error. Check with your demonstrator if you are unsure of how to
do this.
One way to study the charging and discharging characteristics of the capacitor is to repeat the
charging and discharging process and display these processes on a CRO. This is done by
supplying a square wave voltage to the resistor and capacitor in series.
Connect up the circuit below. Use the resistor code given at the start of the Electricity section of
these notes to find the correct resistor.
Note:
When setting up this circuit it is important that the earth connections of the signal
generator and CRO are common - ie. there is no circuit element between them. Make
sure that the black earth terminal of the signal generator is on the same side of the
circuit as the earth lead of the CRO. Remember to connect the black end or ‘-’ of
capacitor to the earth side of the circuit as shown.
1 k
Signal
Generator
0.27 F
CRO
Set the signal generator to 200 Hz, 6 volts peak to peak square wave (check it with the CRO - get
your demonstrator to set up the CRO properly). Now connect the CRO leads across the capacitor.
Adjust the frequency of the signal generator so that two cycles of charging and discharging curves
are displayed. Adjust the Y-gain of the CRO so that the charging and discharging curves are
displayed as large as possible on the CRO screen.
The voltage across the capacitor as it is rapidly charged and discharged is now shown on the CRO
screen. Sketch the charging and discharging curves, making careful note of the voltage and time
scales. Your demonstrator will show you how to set the Coupling Switch to "Ground" to check
where zero volts is. You should do this occasionally to check that you haven't accidentally
changed some settings.
Physics 121/2 and 141/2 Laboratory Manual
C-25
Measuring the discharge of a capacitor
Experiment A2:
It can be shown that the discharge curve is described by the equation:
V = Vmax e–t/RC
where R = value of resistance and C = value of capacitance.
From the above expression we can see that after a time interval of magnitude R C, the voltage
across the capacitor is:
V = Vmax e–RC/RC
= Vmax/e
Vmax/3
We call this time interval (t = R C) the time constant.
The discharge curve of a capacitor is shown below:
V
Vmax
~Vmax/3
0
(i)
RC
t
Using the above approximation, measure the time constant for your circuit with the CRO by
measuring the time it takes the capacitor to discharge to 1/3 of its starting value.
Use the value of the time constant together with the resistance of the circuit to obtain the
capacitance value for your capacitor. The resistance of the circuit includes both the 1 k
resistance and the internal resistance of the signal generator. The internal resistance of the
signal generator is approximately 600  The uncertainty in the 1k resistor can be found
by looking at the coloured bands on the resistor and comparing with the values given on
page EM-4.
Compare the resulting value for the capacitance with the value given on the body of the
capacitor (consider uncertainties, of course).
(ii)
Repeat this time constant measurement using a resistance of 10 k. You may find that with
this resistance the extended time of decay will mean that only a small section of the curve is
seen in each cycle of the square wave. If this occurs, then decrease the frequency of the
signal generator to extend the period of the square wave in order to give the voltage time to
drop to 1/3 of its original value. For this reason it is important that you check where
zero volts is on your screen. Sketch the charging and discharging curves, taking careful
note of the voltage and time scales. Compare the charging and discharging curves for this
case with those obtained in (i). Account for the differences.
Ask your demonstrator for advice if this is not clear.
(iii)
What change would you expect to observe in the discharging characteristics if C were
increased by the factor of 10? decreased by a factor of 10? Explain. (You can check your
predictions by plugging in a couple of the other capacitors on the board. Have a quick look.)
C-26
Physics 121/2 and 141/2 Laboratory Manual
Section B:
The Diode
Introduction:
The diode is the electrical equivalent of a valve. Like the valve in a bicycle tyre which only allows
air to flow into the tyre and not out, the diode (ideally) allows current to flow one way only. In
practice there is a very small current in the reverse direction, but for our purposes we can
approximate this to zero.
In this experiment you will gain some practical experience in the use of a solid state diode. This
type of diode is made from a semiconductor such as germanium or silicon. These materials are
neither good conductors like metals nor poor conductors like insulators. When impurities are
added to the material it can take on unusual properties.
The following explanation of how a diode operates is useful but is not required in order to use a
diode. See 44.5 (121/2) or 27.5, 41.6 to 41.8 (141/2) for more details.
Germanium (or silicon) has four valence electrons (that is, it is a group IV element). If an
impurity with three valence electrons (that is one belonging to group III of the periodic table) such
as indium is added to germanium then the composite material has an ability to attract electrons
that makes it appear positively charged and is called a p-type material.
Similarly if an impurity having five valence electrons (that is an element of group V) is added to
germanium then the composite material has a tendency to give up electrons. It has free negative
charges and is called an n-type material. We say that the charge carriers are negative. (See
Appendix B for an extended introduction to the diode.)
A piece of semiconductor which has had impurities introduced so that one side is n-type, and the
other p-type, is called a diode and has particular properties when connected in a circuit
containing a battery.
no current flows
current flows
+
+
-
-
circuit (a)
circuit (b)
(forward biased)
(reverse biased)
In circuit (a) current will flow and the diode is said to be 'forward biased' while in circuit (b) no
current flows and the diode is said to be 'reverse biased'. Consequently, the resistance of the diode
in circuit (a) is small and is called the forward resistance. The reverse resistance is high (ideally
infinite) since no current flows in circuit (b).
The symbol for a diode is
and on an actual diode the short line is marked by a band (often white or red). The arrow is in the
direction of current flow.
white or
red line
Physics 121/2 and 141/2 Laboratory Manual
C-27
Characteristics of a Diode
Experiment B1:
The diode you have has the following nominal characteristics:
6V
Forward resistance of the diode:
about 10 ohm
Reverse resistance of the diode:
about 106 ohm
+
6V
-
+
-
Circuit 1
Circuit 2
(i)
Predict what will happen when the switch is closed, for the circuits shown above.
(ii)
Connect up these circuits and check your predictions. Explain any discrepancy between
your predictions and observations.
The Diode as a Rectifier (part 1)
Experiment B2:
Our main source of electrical energy, the mains, provides us with an AC (Alternating Current)
signal of 240 volts RMS, 50 Hz. Many household devices, however, require a DC (Direct Current)
Signal to run them, (radios, TV's, etc.).
The first step in converting AC to DC is to rectify it, ie. make the signal uni-directional so that
the voltage output is always positive, or always negative. This can be done simply with a diode.
(i)
Set up the circuit shown below (the 10 k resistor is there merely to complete the circuit
and represent the 'load' which the circuit is powering).
240V a.c.
Warning:
(ii)
C-28
12 V RMS
10 k 
CRO
Switch off the transformer when not in use
Examine the output on the CRO when the diode is in the circuit (switch open) and when the
diode is shorted out of the circuit (switch closed). Sketch the curve shown on the CRO
screen, carefully labelling the voltage and timebase scales. Is the waveform rectified?
Physics 121/2 and 141/2 Laboratory Manual
The Diode as a Rectifier (part 2)
Experiment B3:
The previous circuit rectified the signal over half the input cycle. We can construct a circuit using
diodes that will give rectification over the whole cycle.
(i)
On the circuit diagram show the path taken by the current when point A is more positive
than C. Now, using a different colour, show the path taken by the current when point C is
more positive than A.
(ii)
Predict the output when an alternating current is provided by the transformer.
(iii)
Set up the circuit shown below (the 10 k resistor is there merely to complete the circuit
and represent the 'load' which the circuit is powering).
Check with your demonstrator before turning the circuit on.
A
240V a.c.
12 V RMS
B
D
C
Warning:
(ii)
10 k 
CRO
Switch off the transformer when not in use.
Examine the output on the CRO. Sketch the curve shown on the CRO screen, carefully
labelling the voltage and timebase scales. How does the output of this circuit differ from the
output of the circuit used in Experiment B2?
Physics 121/2 and 141/2 Laboratory Manual
C-29
Smoothing
Experiment B4:
The previous two experiments showed that rectification alone does not give us a DC signal. We
need to smooth out the 'bumps'.
(i)
Set up the following circuit:
A
240V a.c.
12 V RMS
B
D
C
10 k 
CRO
+
C
(ii)
Close the switch and observe the effect of the capacitor upon the rectified output. Repeat
this for various values of capacitance (0.27; 4; 100 µF). Explain how the capacitor achieves
this effect.
(iii)
Sketch the observed waveforms to scale, superimposing the smoothed waveform on the
rectified output as follows, being careful about the actual peak values.
}
"ripple"
Set the coupling switch on the CRO to the DC setting, then change this to the AC setting to
measure the ripple voltage. (When the coupling switch is on the AC setting, a capacitor is in
series with the CRO input, so only AC signals will show up on the CRO screen.)
Note:
C-30
Although the above power supplies are rather crude, they are actually used in
commercial devices. For example, many 'battery-saver' type power packs (6V, 9V
output) simply use the circuit of experiment B3 to provide their so-called 'DC' output
Physics 121/2 and 141/2 Laboratory Manual