```Researcher: Lewis Ellway
AC Circuits
Demonstrator:
EM04
Sunday, 01 November 2009
Introduction
Nathanial Bowditch in 1815 worked on what was then called a Bowditch
curve, until in 1857 Jules Antoine Lissajous, developed what is now more
commonly known as Lissajous figures. Lissajous Figures are used as a
method of seeing whether two oscillations have the same phase.
Experimental-equipment
 Oscilloscope.
 Oscillator (contained in a single circuitry box).
 A 3.1V and 50Hz AC supply.
 A 25kΩ and a 10kΩ resistor, along with 0.22μf capacitor and a 20H
inductor, all housed in a single circuitry device.
Diagram of experimental equipment: Lissajous figures/experiment 1.
Plan of measurements: Lissajous Figures experiment.
Connect the oscillator to the Y or ch.2 input plates of the oscilloscope via the
BNC or ‘T’ connector, and set the amplitude of the oscillator to 1V and the
wave signal to a sinusoidal wave type. It is advisable to adjust the time base
accordingly on the oscillator so as to check the correct AC signal is obtained
on the oscilloscope. Use of the ‘Trig Level’ control will aid the user to
synchronise the time base. Using further BNC or ‘T’ connectors, it is now
available to complete the experimental set up, by connecting the equipment
as shown in the left hand diagram, making sure that the connector is plugged
into the X plates or ‘ExtX/Trig’ input. Adjust the Y gain control along with the
potentiometer, to ensure equal deflections on the oscilloscope. Next adjust
the frequency on the oscillator between frequencies of 10Hz and 1000Hz, and
observe the relative patterns formed on the oscilloscope. When a ratio of 3:2
is set the pattern observed has been sketched into the researcher’s laboratory
book [refer to Lab book, under Lissajous Figures/ Experiment 1]. Finally in this
experiment it can be observed that when the frequency of the oscillator is a
Researcher: Lewis Ellway
Demonstrator:
integer multiple of 50Hz, then the pattern displayed by the Cathode ray
oscilloscope should be a stationary wave. The ratio of the frequencies
to
Is determined by how points of intersection there are on the curve. Use this
ratio and the pattern observed to calculate the error in the frequency due to
the dial settings on the oscillator.
Diagram of Experimental equipment: Phase Ellipse/ Experiment 2.
Oscillator
25kΩ
10kΩ
0.22μF
Earthed
Earthed
Plan of measurements: Phase Ellipses Experiment.
Once the circuit displayed in the diagram above has been set up accordingly.
Adjust the oscilloscope and oscillator, so that the amplitude of the X and Y
deflections are of a similar magnitude. Thus making the oscilloscope
convenient for taking measurements, it is also possible that the potentiometer
may need adjusting. When connected simultaneously into the X and Y plates
a phase ellipse should be seen on the Oscilloscope display screen. By using
the graticule rotation knob on the oscilloscope it is possible for the
experimenter to record and see whether the ratios of minor to major axes on
the ellipse are consistent with theory. Repeated readings at various
frequencies will further help to test the results against the associated theory.
Diagram of Experimental equipment: Transients/Experiment 3
Researcher: Lewis Ellway
Demonstrator:
Circuitry Diagram LR
Circuit.
Circuitry Diagram CR Circuit.
Oscillator
Oscillator
10kΩ
0.22μF
10H
10kΩ
Earthed
Earthed
Oscilloscope
Oscilloscope
Circuitry Diagram for LCR Circuit
Experiment
Oscillator
20kΩ
0.002μF
20H
Earthed
Plan of measurements: Transients Experiment.
In a CR and LR Circuit.
By switching the oscillator to the square wave function mode and setting up
the circuit according to the circuitry diagram above for CR and LR circuits. An
inspection of the oscilloscope as the square wave form is initiated on the
oscillator, should display a square wave function on the screen. When either
of the above circuits are connected the wave pattern displayed should be
revolutionised into a new wave display that is shown later in the report in the
results section. The experimenter is recording the time taken for the wave to
rise to 63% or 1/e of its maximum value or alternatively for the wave to fall by
33% or 1-(1/e) of the wave’s maximum value. Use of the time base and the
time base calibration control will ensure that the measurement of the time
taken for the wave to rise or fall is as accurate as possible.
Researcher: Lewis Ellway
Demonstrator:
In a LCR Circuit.
First the researcher must adhere to the lower value capacitor which has the
value of 0.002μF, opposed to the value of 0.22μF used in the previous
experiments. Initially start by setting up the circuit according to the diagram
above for the LCR circuit. The time base on the oscillator here will be
essential to making sure the researcher is able to read the results with ease,
while enabling the results to withstand a scale of accuracy. Furthermore the
oscillator frequency should be kept low to ensure that the observer or
experimenter is able to distinguish between wave peaks during decaying
oscillations.
Safety Procedures.
For the three experiments, the commonality between them is that mains
electricity is being used and therefore standard electrical safety precautions
should be taken. But in addition to this the researcher, should ensure that
always where the circuits have been earthed or grounded to make sure that
this is done so, to avoid the user being electrocuted. Other devices that may
cause interference should try to be removed, as it may endanger the safety of
the experimenter, while also causing inaccuracies in the results.
Results.
Lissajous Figures Experiment
The results for the frequency ratio of 3:2 are on display in my laboratory book.
When the oscillator frequency was an integer or multiple of the 50Hz mains
frequency, a stationery pattern was obtained, however the pattern was distort
and this is discussed in the discussion section.
Phase Ellipse Experiment
x/time (s)
ω/frequency(Hz)
300
1.50
500
1.55
700
1.60
900
1.50
1100
1.50
1300
1.50
1500
1.50
1700
1.45
1900
1.50
y/ voltage
(V)
1.10
1.50
1.80
2.05
2.20
2.00
2.10
2.10
2.20
Φ/2-Phi/2
(degrees)
56.58
42.27
33.00
26.80
22.45
19.27
16.86
14.97
13.45
Φ-Phi
(degrees)
113.16
84.54
66.00
53.60
44.90
38.54
33.72
29.94
26.90
Above is a table of the results obtained from the phase ellipse experiment, it
displays the frequency of the oscillator, along with the time period (t) and the
voltage (v), from this using the equation
, and then by
adjusting the equation to obtain the phase difference or phi, by:
Researcher: Lewis Ellway
Transient Experiment
Demonstrator:
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