Experiment No. 1 Sine Wave For Single Loop Generator: Objective

AC Circuit Analysis Experiment No.
Experiment No. 1
Sine Wave for Single Loop Generator
Objective:
• Construct sine wave generated by a simple single loop generator.
Apparatus:
• Internet Based Simulation
Theoretical Background:
When a single wire conductor loop is rotated within a stationary magnetic field, it induces an
"EMF" within the conductor due to the conductor's movement through the magnetic flux. This
is the fundamental principle used by electrical machines and generators to produce a Sinusoidal
Waveform for our mains supply.
No lines of flux are cut and no EMF is induced into the conductor if the conductor moves
parallel to the magnetic field; however, if the conductor moves at right angles to the magnetic
field, the maximum amount of magnetic flux is cut and the maximum amount of induced EMF
is generated. The movement of a single loop conductor through a magnetic field is shown in
figure 1. The left-hand side diagram shows the movement of conductor as it cuts the magnetic
flux lines at 90° and the diagram on the right-hand side shows the movement of the conductor
as it moves parallel (0° angle)° to the magnetic flux lines.
Figure 1: Conductor movement through magnetic flux

Furthermore, since the conductor cuts the magnetic field at various angles between these two
positions (0° and 90°), the quantity of induced EMF would be anywhere between zero and
maximum. The amount of emf induced in a conductor is then determined by the angle between
the conductor and the magnetic flux, as well as the magnetic field strength.
A simple single loop AC generator is made up of two permanent magnets that create a fixed
magnetic field between the north and south poles. A single rectangular loop of wire can be
rotated around a fixed axis within this magnetic field, allowing it to cut the magnetic flux at
different angles.
AC Circuit Analysis Experiment No. 1
Figure 2: Single Loop AC Generator

The conductor loop cuts the magnetic field lines at various angles as the coil rotates
anticlockwise around the central axis, which is perpendicular to the magnetic field. At any
given moment, the total EMF induced in the loop is proportional to the angle of rotation of the
loop of conductor.
Electrons in the wire loop flow in one direction around the loop as it rotates. When the wire
loop has rotated past 180 degrees and is moving in the opposite direction past the magnetic
field lines, the electrons in the wire loop shift and flow in the opposite direction. The polarity
of the induced voltage is then determined by the direction of electron movement.
One full sinusoidal waveform is generated when the conductor loop physically completes one
whole revolution, or 360°, with one cycle of the waveform being produced for each revolution
of the coil. The electrical connections to the coil are made as the coil rotates inside the magnetic
field, using carbon brushes and slip-rings to draw the electrical current generated in the coil.
The amount of induced emf depends on the speed of rotation of the coil, the length of the coil
and the magnetic field strength. The frequency of the produced sine wave is also proportional
to the speed of rotation. Increasing the number of pole pairs will also increase the number of
cycles of sine wave produced for each revolution. A single pair of poles results in a single cycle
of sine wave per revolution of coil, two pole pairs result in two cycles of sine wave per
revolution and so on. As a result, frequency is proportional to the number of magnetic pole
pairs. Considering these two points, frequency in Hertz is given by the formula:
𝑁𝑃
𝑓= 𝐻𝑧 (1)
60
where ‘N’ is the speed of rotation r.p.m and ‘P’ is the number of pole pairs.
The amplitude of a sinusoidal AC waveform is continuously changing; the value of emf at any
point in time would be different from the next point in time. The value of voltage or emf at any
specific instant in time is known “Instantaneous Value”. The waveform's instantaneous value,
as well as its direction, varies depending on the coil's location within the magnetic field. This
instantaneous value of voltage 𝑉𝑖 is given by the formula:
𝑉𝑖 = 𝑉𝑚𝑎𝑥 sin 𝜃 (2)
Where, Vmax is the maximum induced voltage induced θ is the rotational angle of the coil with
respect to time. The rotational angle is given by:
𝜃 = 𝜔𝑡 = 2𝜋𝑓𝑡 (3)
Where 𝜔 is the angular velocity in degrees/sec or radians/sec and t is the time and f is the
frequency.
The formula for instantaneous voltage can be re-written as:
𝑉𝑖 = 𝑉𝑚𝑎𝑥 sin(2𝜋𝑓𝑡) (4)
The instantaneous values at different points along the waveform can be determined using the
formulas above if we know the maximum or peak value of the waveform.
Procedure:
1. Set the rotation speed of the coil.
2. Connect a voltmeter to the coil output to measure the induced voltage
3. Note the maximum value of voltage as observed on the voltmeter
4. Using the formula of instantaneous voltage in eq 2, calculate value of voltage at various
angles.
5. Plot the waveform on a graph. ( 𝑉𝑖 on y-axis and θ on x-axis)
6. Using the relation (eq 1) between rotational speed, pole pairs and frequency, calculate
frequency f of the sine wave.
7. Use formula in eq 4 to calculate instantaneous voltage at various values of time.
8. Plot the waveform on a graph ( 𝑉𝑖 on y-axis and t on x-axis)
9. Repeat step 6-8 for another value of rotational speed.
Calculations and Results:

Case 1:
Coil Rotation Speed: ___________________________
Table 1:
𝜃 0 30 60 90 120 150 180 210 240 270 300 330 360
(x-axis)
𝑉𝑖
(y-axis)
Table 2:
𝑡
(x-axis)
𝑉𝑖
(y-axis)
Waveform Plot (Voltage vs Rotational Angle):
Waveform Plot (Voltage vs Time):
Case 2:
Coil Rotation Speed: ___________________________
Table 1:
𝜃 0 30 60 90 120 150 180 210 240 270 300 330 360
(x-axis)
𝑉𝑖
(y-axis)
Table 2:
𝑡
(x-axis)
𝑉𝑖
(y-axis)
Waveform Plot (Voltage vs Rotational Angle):
Waveform Plot (Voltage vs Time):
Conclusion:
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Experiment No. 1 Sine Wave For Single Loop Generator: Objective

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Experiment No. 1 Sine Wave For Single Loop Generator: Objective

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AC Circuit Analysis Experiment No.

Figure 1: Conductor movement through magnetic flux

Figure 2: Single Loop AC Generator

Calculations and Results:

Waveform Plot (Voltage vs Rotational Angle):

Waveform Plot (Voltage vs Time):

Waveform Plot (Voltage vs Rotational Angle):

Waveform Plot (Voltage vs Time):

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