Topic 1 sinusoidal alternating voltage and current topic a1

Solve Problems in Single and Three
Phase Low Voltage Circuits  Part A

Content
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Sinusoidal Alternating Voltage and Current
Phasor Representation of Voltage and
Current
Resistance in AC Circuits
Inductance in AC Circuits
Capacitance In AC Circuits
Analysis of AC Circuits
Resonance in AC Circuits
Nathan Condie

1


Solve problems in single and
three-phase low voltage circuits
Topic 1: Sinusoidal Alternating Voltage
and Current

Generation of a Voltage
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Conductor
Magnetic Flux
Relative Motion

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Induced Current or EMF in a Conductor

Current flowing AWAY from viewer

Current flowing TOWARD from viewer

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Fleming’s Right-Hand Rule (for
generators)
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Thumb – Indicates the direction of relative
motion or TRAVEL
First Finger – Indicates the direction of the
flow of magnetic FLUX
Centre Finger – indicates the direction of
induced CURRENT therefore induced EMF

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Fleming’s Right-Hand Rule (for
generators)

Nathan CondieCopyright  2003 McGraw-Hill Australia Pty Ltd
PPTs t/a Electrical Principals
for theCondie
Electrical Trades 5e by Jenneson
Nathan
Slides prepared by Anne McLean

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In each of the following examples, determine the direction of induced EMF

1.

2.

North
Conductor
Motion

S

N

South
4.
N
3.

N

S

Magnetic
Field
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Motion

S

Magnetic
Field

Motion
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Answers: Direction of induced EMF
1.

2.

North
Conductor
Motion

S

N

South
4.
N
3.

N

No Induced EMF –
travels parallel to flux

S

Magnetic

Field
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Motion

S

Magnetic
Field
Motion
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Further exercises using Fleming’s Right-Hand Rule (for Generators)

?
S

N

Direction of relative
motion of
conductor?

?

?
Polarity of magnetic
field poles?

?

N

Polarity of magnetic
field poles?
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S

Direction of relative
motion of magnetic
field?

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Answers: Fleming’s Right-Hand Rule (for Generators)

North
S

N

Direction of relative
motion of
conductor?

N

South
Polarity of magnetic

field poles?

S
N

Polarity of magnetic
field poles?
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S

Direction of relative
motion of magnetic
field?

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Fleming’s Right-Hand Rule (for Generators):
A single conductor formed into a loop

North

South

Front
View

Conductor Loop

Magnetic
Field
Poles

South

North

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Top View

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Generation of an AC Voltage

Copyright  2003 McGraw-Hill Australia Pty Ltd
PPTs t/a Electrical Principals
for theCondie
Electrical Trades 5e by Jenneson
Nathan
Slides prepared by Anne McLean

12


Generation of an AC Voltage

Voltage

1

2

3

4

5

N

N

N

N

N

S

S

S

S

S

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Time

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AC Waveform: Vertical Axis


The height the waveform reaches above (or below) the
horizontal axis represents its AMPLITUDE. Amplitude is
expressed as a:
 Peak or Maximum Value
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

The distance from the zero value to the highest value on the curve
(either above or below the horizontal axis)
For a Voltage waveform, symbol VPk or VMax
For a Current waveform, symbol IPk or Imax

Peak-to-Peak Value
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The distance between the top (crest) and bottom (trough) of the
waveform
For a Voltage waveform, symbol VP-P
For a Current waveform, symbol IP-P
VP-P=2VPk
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AC Waveform: Vertical Axis
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Instantaneous Value




The value at any point along the waveform
For Voltage waveform, symbol “v” (lowercase)
For Current waveform, symbol “i” (lowercase)
Sine Wave Only v = VmaxSinθ

Where
v is the instantaneous value of the sinewave at a specified point
Vmax is the maximum value of the sinewave
Sin is a function applied to the phase angle
Θ is the phase angle in degrees Electrical (indicates the rotation of loop)

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AC Waveform: Vertical Axis
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Average Value
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

A measure of the average energy available in an
AC waveform.
This value is only valid when the AC waveform is
RECTIFIED into DC (average for AC is zero).
Applicable mainly in electronics, and some
analogue meters.
Sine Wave Only

VAve = 0.637 Vmax

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AC Waveform: Vertical Axis
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RMS Value (Root-Mean-Square)



Represents the EFFECTIVE value of the AC waveform.
An RMS value represents the DC equivalent in terms of
electrical energy potential.


The RMS value of an alternating current (AC) waveform will
cause the same heat dissipation as that value of direct current
(DC).
Sine Wave Only

VRMS = 0.707 Vmax

ALL AC values given are considered to be RMS values, unless
otherwise specified

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AC Waveform: Vertical Axis

Instantaneous values

Copyright  2003 McGraw-Hill Australia Pty Ltd
PPTs t/a Electrical Principals
for theCondie
Electrical Trades 5e by Jenneson
Nathan
Slides prepared by Anne McLean

18


AC Waveform: Horizontal Axis
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Represents the Time Domain for an AC
waveform


Period, or Periodic Time
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

The time taken for the AC waveform to complete one full
cycle (360oE)
Symbol t, measured in Seconds (s)

Frequency
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The number of cycles per second
Symbol ƒ, measured in Hertz (Hz)

ƒ = 1/t
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AC Waveform: Horizontal Axis
one cycle

one cycle
Periodic Time

one cycle

Periodic time is measured between two EQUIVALENT points of the
waveform
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AC Waveform: Electrical Degrees
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Waveforms are only observed on
oscilloscopes where the horizontal axis is
normally given as a time base (in seconds)
rather than as an angle (in degrees).
To apply the instantaneous value formula,
any specified time value will need to be
converted to an angle (Electrical Degrees).

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AC Waveform: Electrical Degrees


Conversion of Time to θ (theta) in Electrical
Degrees:
θ = tinstantaneous x 3600
tperiodic

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AC Waveform: Exercises



Given a sinusoidal waveform with an RMS
value of 230V and a frequency of 50Hz,
calculate the instantaneous values of voltage
at the following points:
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2mS
5mS
11mS
356mS

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AC Waveform: Answers to Exercises
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Step 1: Find VMax
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Step 2: Find Periodic Time

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(2mS) θ = 360E

Step 4: Calculate instantaneous voltage
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t = 0.02 sec OR 20mS

Step 3: Convert instantaneous time to Electrical
Degrees
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VMax = 325.3V

(2mS) v = +191.2V

Now repeat steps 3 and 4 for the other
instantaneous times.

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AC Waveform: Answers to Exercises
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Part 2
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Part 3
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(5mS) θ = 900E
(5mS) v = +325.3V
(11mS) θ = 1980E
(11mS) v = -100.5V

Part 4
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(356mS) θ = 64080E
(356mS) v = -309.4V

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