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Electronic Control & Digital Electronics
Electronic Control &
Digital Electronics
Electronic Control &
Digital Electronics
NQF Level 4
NQF Level 4
Student’s Book
Elect control-digi elec 4 (s).indd 1
Jowaheer Consulting and Technologies, RBJ van Heerden, R Jonker & MWH Smit
STUDENT’S BOOK
TVET FIRST
2015/02/25 8:35 AM
Electronic Control & Digital
Electronics
NQF Level 4
Student’s Book
Jowaheer Consulting and Technologies, RBJ van Heerden,
R Jonker & MWH Smit
Electronic Control & Digital Electronics NQF Level 4
Student’s Book
© Jowaheer Consulting and Technologies, RBJ van Heerden, R Jonker & MWH Smit, 2014
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
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First published in 2014 by
Troupant Publishers [Pty] Ltd
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Distributed by Macmillan South Africa [Pty] Ltd
ISBN: 978-1-4308-0322-5
Web PDF ISBN: 978-1-4308-0391-1
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Acknowledgements
Microsoft product screenshots used with permission from Microsoft. The publisher also
acknowledges the following companies, whose product screenshots appear in Module 14:
Apple Inc., LogicCircuit and AVAST.
While every effort has been made to ensure the information published in this work is
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Contents
Topic 1: Alternating current theory .........................................................1
Module 1: RC circuits ...................................................................................................... 2
Unit 1.1: RC series circuits...................................................................................................................................................... 2
Unit 1.2: RC parallel circuits ................................................................................................................................................ 12
Module 2: RL circuits ..................................................................................................... 17
Unit 2.1: RL series circuits .................................................................................................................................................... 17
Unit 2.2: RL parallel circuits................................................................................................................................................. 25
Module 3: RLC circuits and resonance ............................................................................. 30
Unit 3.1: RLC series circuits ................................................................................................................................................. 30
Unit 3.2: RLC parallel circuits .............................................................................................................................................. 40
Topic 2: Fundamentals of electronics ....................................................53
Module 4: Sinusoidal oscillators ...................................................................................... 54
Unit 4.1: Basic principles of oscillators............................................................................................................................... 55
Unit 4.2: Types of oscillators ................................................................................................................................................ 59
Module 5: Non-sinusoidal oscillators................................................................................ 68
Unit 5.1: Multivibrators ........................................................................................................................................................ 68
Unit 5.2: 555 timers ............................................................................................................................................................... 72
Module 6: Power supplies .............................................................................................. 77
Unit 6.1: Inverting power supply ....................................................................................................................................... 77
Unit 6.2: Switched-mode power supply ............................................................................................................................ 80
Module 7: Bipolar junction transistor (BJT) biasing and amplifiers ...................................... 83
Unit 7.1: Biasing, operating points and DC load line of a transistor ............................................................................. 84
Unit 7.2: Coupling methods used in amplifiers ................................................................................................................ 93
Unit 7.3: Transistor and feedback amplifiers..................................................................................................................... 96
Module 8: Silicon-controlled rectifiers (SCRs) and triacs .................................................. 107
Unit 8.1: Silicon-controlled rectifiers (SCRs) ................................................................................................................... 108
Unit 8.2: Triacs ..................................................................................................................................................................... 114
Topic 3: Basic design procedures .......................................................119
Module 9: Reading and interpreting semiconductor manuals ............................................ 120
Unit 9.1: Finding and interpreting the operational limits of semiconductor devices by using
technical manuals................................................................................................................................................................ 120
Unit 9.2: Looking up replacement parts in technical manuals ..................................................................................... 128
Module 10: Designing, constructing, testing, fault-finding and repairing basic
electronic circuits ........................................................................................................ 132
Unit 10.1: Designing, constructing and testing basic electronic circuits ..................................................................... 132
Unit 10.2: Fault-finding and repairing basic electronic circuits.................................................................................... 157
Topic 4: Binary decoding and loading software onto a computer ............171
Module 11: Boolean algebra ......................................................................................... 172
Unit 11.1: Logic gates and Boolean expressions ............................................................................................................. 172
Unit 11.2: Rules of Boolean algebra and De Morgan’s theorems ................................................................................. 179
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Module 12: Binary code ............................................................................................... 188
Unit 12.1: Binary code......................................................................................................................................................... 188
Module 13: Encoders, decoders and shift registers.......................................................... 200
Unit 13.1: Encoders and decoders..................................................................................................................................... 200
Unit 13.2: Registers and shift registers ............................................................................................................................. 203
Module 14: Loading software onto a computer ............................................................... 210
Unit 14.1: Loading software onto a computer ................................................................................................................ 210
Unit 14.2: Causes of software malfunctioning ................................................................................................................ 221
Unit 14.3: Preventing software problems ........................................................................................................................ 225
Topic 5: Operating PLCs ....................................................................231
Module 15: Designing and fault-finding PLC circuits ....................................................... 232
Unit 15.1: Introduction to PLCs ........................................................................................................................................ 233
Unit 15.2: Simple ladder logic diagrams.......................................................................................................................... 246
Unit 15.3: Basic fault-finding in PLCs .............................................................................................................................. 259
Glossary ..........................................................................................267
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Topic 1:
Alternating current
theory
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Module 1:
RC circuits
Introduction
Working with electricity does not only involve direct current (DC)
circuits. Alternating current (AC) circuits are as just important. When
components such as resistors, inductors and capacitors are connected
in a circuit, either in series or in parallel combination, they behave
differently and you need a good understanding of their characteristics
under different conditions. In this topic you will learn more about the
characteristics of resistors, capacitors and inductors in series or parallel
and the concept of resonance.
Overview
At the end of this module, you will be able to:
• Describe the relationship between current and voltage in a resistancecapacitor (RC) circuit.
• Determine the impedance and phase angle (ø) in an RC circuit.
• Explain the frequency selectivity characteristic of RC series circuits
(low- and high-pass circuits).
• Explain the effects of faulty components in RC circuits.
Units in this module
Did you know?
A resistor-capacitor (RC)
circuit can be used as a
filter for electrical signals
or noise. This is because
they can block certain
frequencies and allow
other frequencies to get
though. RC circuits are
also used as a type of
timer switch because
they charge to the source
voltage and then discharge
at a constant and specific
rate. For example, the
windscreen wipers on a car
are controlled using an RC
circuit.
Unit 1.1: RC series circuits
Unit 1.2: RC parallel circuits
Unit 1.1: RC series circuits
Resistance only
Figure 1.1 shows a circuit with
a resistance of R ohms that is
connected across the terminal of
an AC supply.
R
IR
VR
Figure 1.1: Circuit diagram with
resistance only
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VR
As you know,
VR +
Note
Ohm’s law
states that the
The two phasors are drawn
slightly apart so that they can
magnitude of a
IR
be distinguished from each
current is directly
IR
other.
proportional to
0
t
the magnitude
of the voltage
and inversely
proportional to
–
the value of the
Figure 1.2: Voltage and current waveforms
resistance. This
IR
also applies to the instantaneous values of current
and voltage in an AC circuit. At any instant when
the voltage is zero, the current is also zero. When
the voltage is at its maximum, the current is also
VR
at its maximum since the resistance is constant.
Figure 1.3: Phasor diagram for a resistive circuit
See Figure 1.2.
In a purely resistive AC circuit, the current (IR) and the applied voltage
(VR) are in phase. Phase is used to indicate the time relationship between
alternating voltage and current. The phasors representing the voltage and
current in a resistive circuit are shown in the phasor diagram in Figure 1.3.
A leading waveform is
defined as a waveform
that is ahead of the other
waveform. A lagging
waveform is a waveform
that is behind the other
waveform. In Figure
1.4 the phase shift is
90°. Waveform A leads
waveform B and waveform
B lags waveform A.
Capacitance only
Waveform and phasor
diagram
C
Figure 1.5 shows a circuit
consisting of a capacitor with
capacitance C connected across
an AC supply. In a purely
capacitive AC circuit, the
current (IC) leads the supply
voltage (VC) by 90º. See
Figure 1.6. The phasor diagram
for a purely capacitive circuit
is shown in Figure 1.7.
In a purely
capacitive circuit
containing a
capacitor, the
opposition to the
flow of alternating
current is called the
capacitive reactance
(XC) and is measured
in ohms:
XC = 1
2πfC
IC
VC
Figure 1.5: Circuit diagram with capacitance only
Capacitive reactance
VC +
Did you know?
Figure 1.4: Waveform
A leads waveform B
and waveform B lags
waveform A
VC
Note
IC
IC
0
t
The voltage-current phase
relationship in a capacitive
circuit is the opposite of that in
an inductive circuit.
–
Figure 1.6: Voltage and current waveforms for a purely
capacitive circuit
Module 1: RC circuits
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where:
XC = capacitive reactance in ohms (Ω)
f = frequency of the supply in hertz (Hz)
C = capacitance in farads (F)
IC
and
VC = IC × XC
XC
(Ω)
where:
VC = voltage across the capacitor in volts (V)
IC = current through capacitor in amperes (A)
The capacitive reactance is inversely
proportional to the frequency. See
Figure 1.9. The current produced by
a given voltage is proportional to the
frequency.
VC
Figure 1.7: Phasor diagram for a
purely capacitive circuit
0
f (Hz)
Figure 1.9: Graph of capacitive
reactance (XC) against frequency (f)
Did you know?
Example 1.1
A 10 μF capacitor is connected across a 240 V, 50 Hz supply.
Calculate the current flowing through the capacitor.
Figure 1.8 shows a Leyden
jar which is a device that
‘stores’ static electricity
between two electrodes on
the inside and outside of a
glass jar. It was the original
form of the capacitor.
Given: C = 10 μF; VC = 240 V; f = 50 Hz
Solution
XC = 1
2πfC
=
1
2π × 50 × 10 × 10–6
= 318,31 Ω
XC =
VC
IC
= 240
318,31
Figure 1.8: The Leyden
jar
= 0,754 A
C
R
I
VC
VR
RC series circuit
Figure 1.10 shows an RC series circuit consisting of
resistance (R) and capacitance (C). The combination
is connected across a supply voltage (V) volts with a
frequency of (f) hertz. I represents the current flowing
through the circuit. The current is the same in all parts
of the circuit.
V
Figure 1.10: RC series circuit
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Phasor diagram for RC series circuit
The phasor diagram is shown in Figure 1.12. The current (I) leads the
supply voltage (V) by an angle between 0º and 90º. Add the voltages using
a voltage triangle as shown in Figure 1.13. Using Pythagoras’ theorem:
V2 = VR2 + VC2
Therefore:
V = VR2 + VC2
VR
VR
I
VR = IR
ɸ
ɸ
V
V = IZ
Figure 1.12: Phasor diagram of an
RC series circuit
Capacitors are used
with resistors in timing
circuits. They are also
used to smooth varying
DC supplies and in filter
circuits because capacitors
pass AC signals easily
but block DC signals.
Figure 1.11 shows some
electrolytic capacitors.
VC
Figure 1.11: Electrolytic
capacitors
V
VC
Did you know?
VC = IXC
Figure 1.13: Voltage triangle
Impedance in an RC series circuit
The total opposition to the current flow in any AC circuit is called
impedance (Z). Both resistance and reactance in an AC circuit oppose
current flow. The impedance (Z) of an AC circuit is derived using the
impedance triangle as shown in Figure 1.14.
In an AC circuit, the impedance (Z) is the ratio of the supply voltage to the
current:
Z =V
I
As can be seen from Figure 1.14:
Z2 = R2 + XC2
R
R
ɸ
XC
Z
Z
CC
Figure 1.14: The impedance
triangle
Therefore:
if Z = R2 + XC2
then tan ø =
XC
X
, sin ø = C and cos ø = R
R
Z
Z
Relationship between current and voltage in an RC series circuit
As you already know:
• In a purely resistive AC circuit, the current (IR) and the applied voltage
(VR) are in phase.
• In a purely capacitive AC circuit, the current (IC) leads the supply
voltage (VC) by 90º.
• When there is a combination of resistance and capacitive reactance in an
AC series circuit, the current (I) leads the supply voltage (V) by an angle
between 0º and 90º depending on the values of resistance and capacitive
reactance.
Did you know?
Early capacitors were also
known as condensers,
a term that is still
occasionally used today.
Alessandro Volta first used
the term for this purpose
in 1782 with reference to
the device’s ability to store
a higher density of electric
charge than a normal
isolated conductor.
Module 1: RC circuits
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Example 1.2
A resistor of 10 Ω is connected in series with a capacitor of 45 μF. The
supply voltage is 240 V, 50 Hz. Calculate:
1. The capacitive reactance.
2. The impedance.
3. The current flowing through the circuit.
4. The phase angle.
5. The voltage across the resistor.
6. The voltage across the capacitor.
Given: R = 10 Ω; C = 45 μF = 45 × 10–6 F; V = 240 V; f = 50 Hz
Solution
1.
Capacitive reactance XC
XC = 1
2πfC
=
1
2π × 50 × 45 × 10–6
= 70,736 Ω
2.
Impedance Z
Z = R2 + XC2
Z = 102 + 70,7362
= 71,439 Ω
3.
Current I
V
I =
Z
= 240
71,439
= 3,360 A
4.
Phase angle ø
X
tan ø = C
R
70,736
tan ø =
10
ø = tan–1 7,074
ø = 81,953° (leading)
5.
6.
6
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Voltage across resistor VR
VR = I × R
= 3,360 × 10
= 33,600 V
Voltage across capacitor VC
VC = I × XC
= 3,360 × 70,736
= 237,673 V
Module 1: RC circuits
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Assessment activity 1.1
Work in groups of five.
1. Copy and complete the following sentences with the missing
words:
1.1 In a purely resistive AC circuit, the current (IR) and the applied
voltage (VR) are in _____.
1.2 In a purely capacitive AC circuit, the current (IC) _____ the
supply voltage (VC) by 90º.
1.3 When there is a combination of resistance and capacitive
reactance in an AC series circuit, the current (I) _____ the
supply voltage (V) by an angle between 0º and _____º
depending on the values of resistance and capacitive reactance.
2. A resistor of 10 Ω is connected in series with a capacitor of 350 μF.
The supply voltage is 230 V, 50 Hz. Calculate:
2.1 The capacitive reactance.
2.2 The impedance.
2.3 The current flowing through the circuit.
2.4 The phase angle.
2.5 The voltage across the resistor.
2.6 The voltage across the capacitor.
Frequency selectivity characteristic of an RC series
circuit (low- and high-pass circuits)
Frequency selectivity is the ability of a circuit to select a specific frequency
and reject all other frequencies. The two types of frequency selectivity
characteristics of an RC series circuit are the low-pass filter and the highpass filter.
Low-pass filter
Figure 1.15 shows a low-pass
filter with the output across
the capacitor. The capacitive
reactance (XC) decreases as the
frequency increases. Therefore,
the output voltage is less than
the input voltage. Figure 1.16
shows the frequency response
curve. This is a graph showing
the magnitude of the output
voltage of the filter as a function
of the frequency. It is generally
used to characterise the range
of frequencies in which the filter
is designed to operate.
Words &
Terms
frequency selectiv
ity: the
ability of a circuit
to select a
specific frequency
and reject
all other frequencie
s
R
C
Vout
Vin
Figure 1.15: A low-pass filter
frequency respon
se curve: a
graph showing th
e magnitude
of the output volta
ge of the
filter as a function
of the
frequency; genera
lly used
to characterise th
e range of
frequencies in wh
ich the filter
is designed to opera
te
output
voltage
frequency
Figure 1.16: Frequency response curve for a
low-pass RC circuit
Module 1: RC circuits
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High-pass filter
C
Figure 1.17 shows a high-pass
filter with the output across
the resistor. The capacitive
reactance (XC) decreases as the
frequency increases. Therefore,
the magnitude of the output
voltage increases. The output
voltage is greater at higher
frequencies but is reduced as
the frequency decreases.
Figure 1.18 shows the
frequency response curve.
Vin
cut-off frequency
(f ): the
frequency at which c
the
capacitive reactanc
e equals
the resistance in
a low-pass
or high-pass RC cir
cuit
bandwidth (BW):
the range
of frequencies that
pass from
the input to the ou
tput of a
circuit
The cut-off frequency (fc) is
the frequency at which the
capacitive reactance equals
the resistance in a low-pass
or high-pass RC circuit. It is
calculated as follows:
R = 1
2πfcC
fc
= 1
2πRC
At fc , the output voltage of
the RC circuit is 70,7 % or 1
2
of its maximum value.
The bandwidth (BW) is the
range of frequencies that pass
from the input to the output
of a circuit. See Figure 1.19.
Vout
Figure 1.17: A high-pass filter
Cut-off frequency and
bandwidth of an RC circuit
Words &
Terms
R
output
voltage
frequency
Figure 1.18: Frequency response curve for a
high-pass RC circuit
output
voltage
70,7%
of Vmax
bandwidth
fc
frequency
Figure 1.19: Cut-off frequency and bandwidth
Example 1.3
Calculate the cut-off frequency for the circuit shown in Figure 1.20.
R 10 kΩ
C 15,9 nF
Vin
Vout
Figure 1.20: A low-pass filter circuit
Given: R = 10 kΩ; C = 15,9 nF
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Solution
fc = 1
2πRC
=
1
2π × 10 × 103 × 15,9 × 10–9
≈ 1 kHz
Example 1.4
Figure 1.21 shows a typical response curve for a low-pass RC circuit.
Determine the bandwidth of the low-pass RC circuit.
output
voltage (V)
4,5
4
3,6
3,18
3
2
1
1
2
frequency (kHz)
10
20
40
5 560
Figure 1.21: Typical response curve for a low-pass RC circuit
Solution
70,7% of 4,5 V = 3,18 V. On Figure 1.21, 3,18 V represents a
bandwidth of 20 kHz.
In the workplace
RC circuits are used with operational amplifiers to create active
electrical noise filters which are more effective than passive RC circuits.
This is because passive RC filters always have a signal output which is
lower than the input.
Effects of faulty components on RC series circuits
The following are the effects of faulty components on RC series circuits:
• Open resistor: An open resistor results in no current flow. Therefore,
the voltage across the capacitor is 0 V and the total input voltage will
appear across the open resistor.
• Open capacitor: An open capacitor results in no current flow. Therefore,
the voltage across the resistor is 0 V and the total input voltage will
appear across the open capacitor.
Module 1: RC circuits
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• Shorted capacitor: A shorted capacitor results in no current flow.
Therefore, the voltage across the capacitor is 0 V and the total input
voltage will appear across the resistor.
• Leaky capacitor: A leaky capacitor will affect the response of the circuit.
Assessment activity 1.2
Work in pairs.
1. A resistor of 20 Ω is connected in series with a capacitor of 20 μF. If
the voltage across both components is 230 V AC:
1.1 Calculate the impedance and phase angle for each of the
following frequencies:
a) 1 kHz.
b) 10 kHz.
c) 20 kHz.
d) 40 kHz.
1.2 From the above calculations, what is your conclusion with
respect to the impedance and phase angle when the frequency
increases?
Assessment activity 1.3
Work in pairs.
Task 1 RC series circuit
Your lecturer will supply you with the necessary components and
equipment to perform the following experiment.
What to do
1. Connect the components R and C as shown in the circuit diagram
in Figure 1.22.
2. Adjust the power supply.
3. Take the readings for the voltages for VR, VC and VS.
4. Note the reading of the ammeter A1.
5. Repeat Step 3 by varying
VR
VC
the supply voltage (VS)
and record the readings
in an observation table
R
C
like the one below.
A1
VS
Figure 1.22: Series circuit
Component
Component rating
Resistor
Capacitor
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Observation table
VS
VR
VC
Ammeter reading A1
Circuit impedance
Circuit resistance
Task 2 RC series circuit
Your lecturer will supply you with the necessary components and
equipment to perform the following experiment using the same circuit
as shown in Figure 1.22.
Component
Component rating
Resistor
Capacitor
What to do
1. Connect the components
R and C as shown in
the circuit diagram in
Figure 1.22.
2. Adjust the power supply.
3. Take the readings for VR,
VC and A1.
4. Disconnect the resistor R
in the circuit to simulate
an open circuit as shown
in Figure 1.23.
5. Take the readings for VR,
VC and A1.
6. Reconnect the resistor
R in the circuit and
disconnect C in the
circuit to simulate an
open circuit as shown in
Figure 1.24.
7. Take the readings for VR,
VC and A1.
8. With the capacitor
disconnected, short out
the terminals as shown
in Figure 1.25 to simulate
a short circuit.
9. Take the readings for VR
and A1.
VR
VC
C
VS
A1
Figure 1.23: Resistor R disconnected
VR
VC
R
A1
VS
Figure 1.24: Capacitor C disconnected
VR
R
short
VS
A1
Figure 1.25: Shorting out the capacitor to
simulate a short circuit
Module 1: RC circuits
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Unit 1.2: RC parallel circuits
There is one major difference between a series circuit and a parallel circuit:
current is the same in all parts of a series circuit while voltage is the same
across all branches of a parallel circuit. Therefore, in parallel AC circuits,
the voltage vector is the reference vector.
RC parallel circuit
IR
Figure 1.26 shows a resistor (R) and a capacitor (C) connected in parallel
across an AC supply voltage (V).
R
C
IC
Phasor diagram for RC parallel circuit
I
V
Figure 1.26: Parallel RC circuit
IC
As can be seen from the circuit, the current (IR) flowing through the
resistor is in phase with the supply voltage (V) and the current (IC) flowing
in the capacitor leads the supply voltage by 90º. Figure 1.27 shows the
phasor diagram.
From the phasor diagram it can be seen that
I
I = IR2 + IC2
Current through resistor IR =
V
R
Current through capacitor IC =
ø
V
IR
Figure 1.27: Phasor diagram
The phase angle is:
I
tan ø = C
IR
I
sin ø = C
I
IR
cos ø =
I
V
XC
Impedance in an RC parallel circuit
The impedance of the circuit is given by Z =
V
I
Example 1.5
A capacitor of 50 μF is connected in parallel with a 40 Ω resistor across
a 223 V, 50 Hz supply. Calculate:
1. The current in each branch.
2. The supply current.
3. The phase angle.
4. The circuit impedance.
Given: C = 50 μF; R = 40 Ω; V = 223 V; f = 50 Hz
Solution
1. Current through resistor IR
V
IR =
R
= 223
40
= 5,575 A
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Current through capacitor IC
V
IC =
XC
V
=
½πfC
= 2πfCV
= 2 × π × 50 × 50 × 10–6 × 223
= 3,503 A
2.
Supply current I
I = IR2 + IC2
= (5,575)2 + (3,503)2
Did you know?
When the power factor of a
parallel AC circuit is unity,
in other words when the
voltage and total current
are in phase at a particular
frequency, then the parallel
circuit is said to be at
resonance.
= 31,081 + 12,271
= 43,352
= 6,584 A
3.
Phase angle ø
I
tan ø = C
IR
I
ø = tan–1 C
IR
ø = tan–1 3,503
5,575
ø = tan–1 0,628
= 32,143° (leading)
4.
Impedance Z
V
Z =
I
= 223
6,584
= 33,870 Ω
Assessment activity 1.4
Work on your own.
1. A capacitor of 25 μF is connected in parallel with a 40 Ω resistor
across a 12 V AC supply.
1.1 Calculate the impedance and phase angle when the frequency
is set to:
a) 20 Hz.
b) 50 Hz.
c) 1 kHz.
1.2 From the above calculations, what is your conclusion with
respect to the impedance and phase angle when the frequency
increases?
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Effects of faulty components on an RC parallel circuit
The following are the effects of faulty components on an RC parallel circuit:
• Open resistor: An open resistor results in no current flow through the
resistor, but the supply current will flow through the capacitor. Total
input voltage will appear across the open resistor and capacitor as they
are in parallel.
• Open capacitor: An open capacitor results in no current flow through
the capacitor, but the supply current will flow through the resistor. The
total input voltage will appear across the open capacitor and resistor as
they are connected in parallel.
• Shorted capacitor: A shorted capacitor will cause current to flow
through the capacitor and can cause circuit damage.
• Leaky capacitor: A leaky capacitor will affect the response of the circuit.
Assessment activity 1.5
Work in pairs.
Task 1 RC parallel circuit
Your lecturer will supply you with the necessary components and
equipment to perform the following experiment.
What to do
1. Connect the components R and C as shown in the circuit diagram
in Figure 1.28.
2. Adjust the power supply.
3. Take the readings for VR, VC and VS.
4. Note the readings of ammeters A1, A2 and A3.
5. Repeat Step 3 by varying the supply voltage and record the
readings in an observation table like the one below.
A1
A3
A2
VS
VR
R
C
VC
Figure 1.28: RC parallel circuit
Component
Component rating
Resistor
Capacitor
Observation table
VS
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VR
VC
Ammeter readings
A1, A2 and A3
Circuit impedance
Circuit resistance
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Summary
• In a purely resistive AC circuit, the current (IR) and the applied voltage
(VR) are in phase.
• In a purely capacitive AC circuit, the current (IC) leads the supply
voltage (VC) by 90º.
• In a purely capacitive circuit containing a capacitor, the opposition to
the flow of alternating current is called the capacitive reactance (XC) and
is measured in ohms.
• The total opposition to the current flow in any AC circuit is called
impedance (Z). Both resistance and reactance in an AC circuit oppose
current flow. The impedance (Z) of an AC circuit is derived using the
impedance triangle.
• In an RC series circuit the current (I) leads the supply voltage (V) by an
angle between 0º and 90º.
• In an RC parallel circuit, the current flowing through the resistor (IR)
is in phase with the supply voltage (V) and the current flowing in the
capacitor (IC) leads the supply voltage by 90º.
• Frequency selectivity is the ability of a circuit to select a specific
frequency and reject all other frequencies. The two types of frequency
selectivity characteristics of an RC series circuit are the low-pass filter
and the high-pass filter.
• With a low-pass filter, the output is across the capacitor. The capacitive
reactance (XC) decreases as frequency increases. Therefore, the output
voltage is less than the input voltage.
• With a high-pass filter, the output is across the resistor. The capacitive
reactance (XC) decreases as frequency increases. Therefore, the
magnitude of the output voltage increases. The output voltage is greater
at higher frequencies but is reduced as the frequency decreases.
• The frequency at which the capacitive reactance equals the resistance
in low-pass or high-pass RC circuits is called the cut-off frequency
and is designated by (fc = 1 ).
2πRC
• The following are the effects of faulty components on RC series circuits:
− Open resistor: An open resistor results in no current flow. Therefore,
the voltage across the capacitor is 0 V and the total input voltage
will appear across the open resistor.
− Open capacitor: An open capacitor results in no current flow.
Therefore, the voltage across the resistor is 0 V and the total input
voltage will appear across the open capacitor.
− Shorted capacitor: A shorted capacitor results in no current flow.
Therefore, the voltage across the capacitor is 0 V and the total input
voltage will appear across the resistor.
− Leaky capacitor: A leaky capacitor will affect the response of the circuit.
• The following are the effects of faulty components on RC parallel circuits:
− Open resistor: An open resistor results in no current flow through
the resistor, but the supply current will flow through the capacitor.
Total input voltage will appear across the open resistor and capacitor
as they are in parallel.
− Open capacitor: An open capacitor results in no current flow through
the capacitor, but the supply current will flow through the resistor.
The total input voltage will appear across the open capacitor and
resistor as they are connected in parallel.
− Shorted capacitor: A shorted capacitor will cause current to flow
through the capacitor and can cause circuit damage.
− Leaky capacitor: A leaky capacitor will affect the response of the circuit.
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Summative assessment
1.
2.
3.
Are the following statements true or false?
1.1 In a purely resistive AC circuit, the current (IR) and the applied voltage (VR) are in phase.
1.2 In a purely capacitive circuit containing a capacitor, the opposition to the flow of alternating
current is called the capacitive reactance (XC) and is measured in farads.
1.3 An RC series circuit consists of resistance (R) and capacitance (C). When the combination is
connected across an AC supply voltage (V) volts, I represents the current flowing through
the circuit. The current is different in all parts of the circuit.
1.4 Capacitive reactance is inversely proportional to frequency.
1.5 There is one major difference between a series circuit and a parallel circuit: the current is
the same in all parts of a series circuit whereas voltage is the same across all branches of a
parallel circuit and therefore, the voltage vector is the reference vector.
1.6 If the supply voltage to an RC series circuit is 12 V and if the resistor is open-circuit, then the
voltage across the resistor is 0 V.
1.7 If the value of R = 1,2 kΩ and C = 25 µF in an RC series circuit, the cut-off frequency is 10 kHz.
1.8 In a low-pass filter, the capacitive reactance (XC) decreases as frequency increases. Therefore,
the output voltage is less than the input voltage.
A 25 μF capacitor is connected across a 110 V, 60 Hz supply. Calculate the current flowing
through the capacitor.
Figure 1.29 shows the response curve for a low-pass filter RC circuit. Determine the bandwidth
of the circuit.
output
voltage
2
1,5
1,414
1
0,5
1
2
10 20
40
38
50
frequency (kHz)
Figure 1.29: Response curve for a low-pass RC circuit
4.
5.
C 100 μF
Study Figure 1.30 and answer the following questions:
R 1,2 k Ω
4.1 Calculate:
a) The capacitive reactance.
b) The phase angle.
VR
VC
10 V
c) The impedance.
f 2 kHz
4.2 If the resistor R is open-circuit, what are the
readings for VR and VC?
4.3 If the capacitor C is open-circuit, what are the
Figure 1.30: RC series circuit
readings for VR and VC?
A capacitor of 1 μF is connected in parallel with a 100 Ω resistor across a 24 V, 1 kHz supply.
Calculate:
5.1 The current in each branch.
5.2 The supply current.
5.3 The phase angle.
5.4 The circuit impedance.
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