Fundamentals of
alternating current technology
Workbook
With CD-ROM
Y1
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Festo Didactic
567217 EN
Order No.:
Edition:
Author:
Graphics:
Layout:
567217
10/2010
Christine Löffler
Thomas Ocker, Doris Schwarzenberger
03/2011, Susanne Durz
© Festo Didactic GmbH & Co. KG, 73770 Denkendorf, Germany, 2011
Internet: www.festo-didactic.com
e-mail: did@de.festo.com
The copying, distribution and utilization of this document as well as the communication of its contents to
others without expressed authorization is prohibited. Offenders will be held liable for the payment of
damages. All rights reserved, in particular the right to carry out patent, utility model or ornamental design
registration.
Contents
Use for intended purpose __________________________________________________________________ IV
Preface
______________________________________________________________________________ V
Introduction ____________________________________________________________________________ VII
Work and safety instructions ______________________________________________________________ VIII
Training package Fundamentals of alternating current technology (TP 1011) _______________________ IX
Learning objectives – Fundamentals of alternating current technology _______________________________X
Allocation of learning objectives and exercises – Fundamentals of AC technology _____________________ XI
Equipment set __________________________________________________________________________ XIII
Allocation of components and exercises – Fundamentals of alternating current technology ___________ XVII
Notes for the teacher/trainer______________________________________________________________ XVIII
Structure of the exercises _________________________________________________________________ XIX
Component designations __________________________________________________________________ XIX
CD-ROM contents ________________________________________________________________________ XX
Exercises and solutions
Exercise 1:
Exercise 2:
Exercise 3:
Exercise 4:
Exercise 5:
Exercise 6:
Exercise 7:
Exercise 8:
Exercise 9:
Exercise 10:
Recording and representing characteristics used in AC technology _______________________1
Investigating the behaviour of a capacitor _________________________________________ 19
Selecting a suitable capacitance for a high-pass filter ________________________________ 39
Reducing voltage peaks when switching a solenoid coil ______________________________ 51
Determining the inductance of a coil ______________________________________________ 65
Investigating RC elements by measurement ________________________________________ 77
Tracing the frequency response of a high-pass and low-pass filter ______________________ 89
Compensating the reactive power for an electric motor ______________________________ 101
Selecting a three-phase circuit for connecting a storage heater _______________________ 113
Generating different output stages for a heater ____________________________________ 127
Exercises and worksheets
Exercise 1:
Exercise 2:
Exercise 3:
Exercise 4:
Exercise 5:
Exercise 6:
Exercise 7:
Exercise 8:
Exercise 9:
Exercise 10:
Recording and representing characteristics used in AC technology _______________________1
Investigating the behaviour of a capacitor _________________________________________ 19
Selecting a suitable capacitance for a high-pass filter ________________________________ 39
Reducing voltage peaks when switching a solenoid coil ______________________________ 51
Determining the inductance of a coil ______________________________________________ 65
Investigating RC elements by measurement ________________________________________ 77
Tracing the frequency response of a high-pass and low-pass filter ______________________ 89
Compensating the reactive power for an electric motor ______________________________ 101
Selecting a three-phase circuit for connecting a storage heater _______________________ 113
Generating different output stages for a heater ____________________________________ 127
© Festo Didactic GmbH & Co. KG 567217
III
Use for intended purpose
The training package Fundamentals of electrical engineering/electronics may only be used:
• For its intended purpose in teaching and training applications
• When its safety functions are in flawless condition
The components included in the training package are designed in accordance with the latest technology
as well as recognised safety rules. However, life and limb of the user and third parties may be endangered,
and the components may be impaired if they are used incorrectly.
The learning system from Festo Didactic has been developed and produced exclusively for training
and further education in the fields of automation and technology. The training companies and/or
trainers must ensure that all trainees observe the safety instructions described in this workbook.
Festo Didactic hereby excludes any and all liability for damages suffered by trainees, the training
company and/or any third parties, which occur during use of the equipment sets in situations which
serve any purpose other than training and/or vocational education, unless such damages have been
caused by Festo Didactic due to malicious intent or gross negligence.
IV
© Festo Didactic GmbH & Co. KG 567217
Preface
Festo Didactic's learning system for automation and technology is geared towards various educational
backgrounds and vocational requirements. The learning system is therefore broken down as follows:
• Technology-oriented training packages
• Mechatronics and factory automation
• Process automation and control technology
• Mobile robotics
• Hybrid learning factories
The learning system for automation and technology will be updated and extended in parallel
with developments in the area of training and professional practice.
The technology packages deal with various technologies including pneumatics, electropneumatics,
hydraulics, electrohydraulics, proportional hydraulics, programmable logic controllers, sensors,
electrical engineering, electronics and electric drives.
The modular design of the learning system allows for applications which go above and beyond
the limitations of the individual training packages. For example, PLC actuation of pneumatic,
hydraulic and electric drives is possible.
© Festo Didactic GmbH & Co. KG 567217
V
All training packages feature the following components:
• Hardware
• Media
• Seminars
Hardware
The hardware in the training packages consists of industrial components and systems that are
specially designed for training purposes. The components contained in the training packages
are specifically designed and selected for the projects in the accompanying media.
Media
The media provided for the individual topics consist of a mixture of teachware and software.
The teachware includes:
• Technical books and textbooks (standard works for teaching basic knowledge)
• Workbooks (practical exercises with supplementary instructions and sample solutions)
• Glossaries, manuals and technical books (providing more in-depth information on the various topics)
• Sets of transparencies and videos (for clear and dynamic instruction)
• Posters (for clear-cut illustration of facts)
Within the software, the following programs are available:
• Digital training programs (learning content specifically prepared for the purpose of virtual training)
• Simulation software
• Visualisation software
• Software for acquiring measurement data
• Project engineering and design engineering software
• Programming software for programmable logic controllers
The teaching and learning media are available in several languages. They are intended for use in classroom
instruction, but are also suitable for self-study.
Seminars
A wide range of seminars covering the contents of the training packages round off the system for training
and vocational education.
If you have any suggestions or feedback about this manual,
please send us an e-mail at: did@de.festo.com
The authors and Festo Didactic look forward to your comments.
VI
© Festo Didactic GmbH & Co. KG 567217
Introduction
This workbook is part of the learning system for automation and technology by Festo Didactic
GmbH & Co. KG. The system provides a solid basis for practice-oriented basic and further training. The
training package Fundamentals of electrical engineering/electronics TP 1011 covers the following topics:
• Fundamentals of direct current technology
• Fundamentals of alternating current technology
• Fundamentals of semiconductors
• Basic electronic circuits
The workbook Fundamentals of alternating current technology continues on from the introduction
to electrical engineering/electronics. It focuses primarily on teaching about the behaviour of resistors,
capacitors and coils in an AC circuit. In addition, it also focuses on circuits with capacitor and coil is phase
shifting of current and voltage in AC circuits. The representation and evaluation of phase shifts is dealt
with in detail in hybrid circuits. The electrical variables of active power, reactive power and apparent
power are also investigated. Finally, it looks at power in the context of star and delta circuits in
three-phase AC voltage systems.
A laboratory workstation equipped with a protected power supply, two digital multimeters,
a storage oscilloscope and safety laboratory cables is needed to build and evaluate the circuits.
All circuits for the 10 exercises in Fundamentals of alternating current technology are built using
the equipment set TP 1011. The basic theoretical principles needed to understand these exercises
are covered by technical textbooks.
Technical data for the individual components (linear and non-linear resistors, capacitors, coils,
light emitting diodes, measuring equipment, etc.) is also available.
© Festo Didactic GmbH & Co. KG 567217
VII
Work and safety instructions
General information
• Trainees should only work with the circuits under the supervision of a trainer.
• Observe the specifications included in the technical data for the individual components
and in particular all safety instructions!
• Faults which may impair safety must not be generated in the training environment and must
be eliminated immediately.
Electrical components
•
Risk of fatal injury from interrupted protective earth conductor
– The protective earth conductor (yellow/green) must not be interrupted either outside or inside
the device.
– The insulation of the protective earth conductor must not be damaged or removed.
• In industrial facilities, the regulations BGV A3 "Electrical systems and equipment" of the German
institute for health and safety must be observed.
• In schools and training facilities, the operation of power supply units must be responsibly monitored
by trained personnel.
• Caution!
The capacitors in the device can still be charged even if the device has been disconnected
from all power sources.
• When replacing fuses: only use specified fuses with the correct rated current.
• Never switch on the power supply unit immediately after it has been moved from a cold room
to a warm one. The condensate that forms can, under unfavourable conditions, damage your
device. Leave the device switched off until it has reached room temperature.
• Only use voltages of max. 60 V DC and 25 V AC as the operating voltage for the circuits in the individual
exercises. Note also the information on the maximum operating voltage of the components used.
• The power must be disconnected before establishing electrical connections.
• The power must be disconnected before breaking electrical connections.
• Only use connecting cables with safety plugs for electrical connections.
• Only pull the safety plugs when disconnecting connecting cables – never pull the cable.
• Always connect the storage oscilloscope to the power supply using an isolating transformer.
VIII
© Festo Didactic GmbH & Co. KG 567217
Training package Fundamentals of alternating current technology
(TP 1011)
The training package TP 1011 consists of a multitude of individual training materials. This part
of the training package TP 1011 deals with the fundamentals of alternating current technology.
Individual components included in the training package TP 1011 can also be included in other packages.
Important components of TP 1011
• Permanent workstation with EduTrainer® universal patch panel
• Component set for electrical engineering/electronics with jumper plugs and safety laboratory cables
• Basic power supply unit EduTrainer®
• Complete set of laboratory equipment
Media
The teachware for the training package TP 1011 consists of technical textbooks, books of tables and workbooks.
The textbooks clearly communicate the fundamentals of alternating current technology. The workbooks
contain the worksheets for each of the exercises, the solutions to each individual worksheet and a CD-ROM.
A set of ready-to-use exercise sheets and worksheets for each exercise is supplied with each workbook.
Technical data for the hardware components is made available along with the training package
and on the CD-ROM.
Media
Textbooks
Technical expertise for electrical professions
Electrical engineering
Book of tables
Electrical engineering/electronics
Workbooks
Fundamentals of direct current technology
Fundamentals of alternating current technology
Fundamentals of semiconductors
Basic electronic circuits
Digital learning programs
WBT Electrical engineering 1 – Fundamentals of electrical engineering
WBT Electrical engineering 2 – Direct and alternating current circuits
WBT Electronics 1 – Fundamentals of semiconductor technology
WBT Electronics 2 – Integrated circuits
WBT Electrical protective measures
Overview of media for the training package TP 1011
The digital learning programs Electrical engineering 1, Electrical engineering 2, Electronics 1, Electronics 2
and Electrical protective measures are available as software for the training package TP 1011. These
learning programs deal in detail with the fundamentals of electrical engineering/electronics. The learning
content is conveyed both by descriptions of the topics and by application using practical case studies.
The media are offered in numerous languages. You'll find further training materials in our catalogue
and on the Internet.
© Festo Didactic GmbH & Co. KG 567217
IX
Learning objectives – Fundamentals of alternating current technology
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X
You will be able to describe the characteristics used in AC technology and perform calculations using
these characteristics.
You will be familiar with the different representations used for variables associated with alternating current.
You will be able to record characteristics used in connection with alternating current by using an
oscilloscope and evaluate them.
You will be familiar with how an ohmic resistor behaves in an AC circuit.
You will be able to describe the behaviour of a capacitor in an AC circuit.
You will be able to determine and calculate the capacitive reactance of a capacitor.
You will be able to determine the phase shift of current and voltage at the capacitor in the AC circuit
by measurement and evaluate it.
You will be able to determine and calculate the capacitive reactive power.
You will be able to calculate the capacitance of capacitors connected in series and in parallel.
You will be able to investigate capacitors connected in series and in parallel by measurement and
extrapolate laws.
You will be familiar with the structure, application and characteristics of a coil.
You will be able to analyse the switch-on and switch-off behaviour of a coil by measurement.
You will know what effect the self-induction of a coil has on its behaviour.
You will be able to describe the behaviour of a coil in an AC circuit.
You will be able to determine the inductance and inductive reactance of a coil.
You will be able to determine the phase shift of current and voltage at the coil in the AC circuit
by measurement and evaluate it.
You will be able to use phasor and linear diagrams to add alternating variables in RC circuits.
You will be familiar with RC elements as frequency-dependent voltage dividers.
You will be able to use RC elements as high-pass and low-pass filters.
You will be familiar with the importance of reactive power in the public electricity supply system.
You will be able to measure and apply the power factor cos φ.
You will be able to calculate and apply the RLC parallel circuit as a compensating circuit for
reactive power.
You will be familiar with the relationship between effective power, reactive power and apparent
power and how they are represented.
You will be able to use phasor and linear diagrams to add alternating variables in hybrid circuits.
You will be familiar with the principle of generation of three-phase AC voltage.
You will be familiar with the basic circuits (star circuit and delta circuit) in three-phase current
systems and be able to build them.
You will be able to measure and calculate the power in star and delta circuits.
You will be able to selectively use individual phases in a three-phase current system to generate power.
You will know what effect the failure of a phase will have on the power of a consuming device
in a star circuit.
© Festo Didactic GmbH & Co. KG 567217
Allocation of learning objectives and exercises – Fundamentals
of AC technology
Exercise
1
2
3
4
5
6
7
8
9
10
Learning objective
You will be able to describe the characteristics used in AC
technology and perform calculations using these characteristics.
•
You will be familiar with the different representations used
for variables associated with alternating current.
•
You will be able to record characteristics used in connection with
alternating current by using an oscilloscope and evaluate them.
You will be familiar with how an ohmic resistor behaves in
an AC circuit.
You will be able to describe the behaviour of a capacitor
in an AC circuit.
You will be able to determine and calculate the capacitive
reactance of a capacitor.
•
•
•
•
•
You will be able to determine the phase shift of current
and voltage at the capacitor in the AC circuit by measurement
and evaluate it.
You will be able to determine and calculate the capacitive
reactive power.
You will be able to calculate the capacitance of capacitors
connected in series and in parallel.
You will be able to investigate capacitors connected in series and
in parallel by measurement and extrapolate laws.
You will be familiar with the structure, application and
characteristics of a coil.
You will be able to analyse the switch-on and switchoff behaviour of a coil by measurement.
You will know what effect the self-induction of a coil has
on its behaviour.
© Festo Didactic GmbH & Co. KG 567217
•
•
•
•
•
•
•
XI
Exercise
1
2
3
4
5
6
7
•
•
8
9
10
Learning objective
You will be able to describe the behaviour of a coil in an AC circuit.
•
You will be able to determine the inductance and inductive
reactance of a coil.
•
You will be able to determine the phase shift of current and voltage
at the coil in the AC circuit by measurement and evaluate it.
You will be able to use phasor and linear diagrams to add
alternating variables in RC circuits.
You will be familiar with RC elements as frequency-dependent
voltage dividers.
You will be able to use RC elements as high-pass and
low pass filters.
•
•
You will be familiar with the importance of reactive power in the
public electricity supply system.
•
You will be able to measure and apply the power factor cos φ.
•
You will be able to calculate and apply the RLC parallel circuit as
a compensating circuit for reactive power.
•
You will be familiar with the relationship between effective power,
reactive power and apparent power and how they are represented.
•
You will be able to use phasor and linear diagrams to add
alternating variables in hybrid circuits.
•
You will be familiar with the principle of generation of three-phase
AC voltage.
•
You will be familiar with the basic circuits (star circuit and delta
circuit) in three-phase current systems and be able to build them.
•
You will be able to measure and calculate the power in star and
delta circuits.
•
You will be able to selectively use individual phases in a threephase current system to generate power.
You will know what effect the failure of a phase will have on the
power of a consuming device in a star circuit.
XII
•
•
•
© Festo Didactic GmbH & Co. KG 567217
Equipment set
The workbook Fundamentals of alternating current technology covers the structure and function
of capacitors and coils as well as the behaviour of these components in basic circuits and simple
application circuits.
The equipment set Fundamentals of electrical engineering/electronics TP 1011 contains all the
components required to achieve the specified learning objectives. Two digital multimeters and
safety laboratory cables are also needed for building and evaluating functioning circuits.
Equipment set Fundamentals of electrical engineering/electronics, order no. 571780
Component
Order no.
Quantity
Basic power supply unit EduTrainer®
567321
1
Universal patch panel EduTrainer®
567322
1
Component set for electrical engineering/electronics
567306
1
Jumper plug set, 19 mm, grey-black
571809
1
Overview of the component set for electrical engineering/electronics, order no. 567306
Component
Quantity
Resistor, 10 Ω/2 W
1
Resistor, 22 Ω/2 W
2
Resistor, 33 Ω/2 W
1
Resistor, 100 Ω/2 W
2
Resistor, 220 Ω/2 W
1
Resistor, 330 Ω/2 W
1
Resistor, 470 Ω/2 W
2
Resistor, 680 Ω/2 W
1
Resistor, 1 kΩ/2 W
3
Resistor, 2.2 kΩ/2 W
2
Resistor, 4.7 kΩ/2 W
2
Resistor, 10 kΩ/2 W
3
Resistor, 22 kΩ/2 W
3
Resistor, 47 kΩ/2 W
2
Resistor, 100 kΩ/2 W
2
Resistor, 1 MΩ/2 W
1
© Festo Didactic GmbH & Co. KG 567217
XIII
XIV
Component
Quantity
Potentiometer, 1 kΩ/0.5 W
1
Potentiometer, 10 kΩ/0.5 W
1
Resistor, temperature-dependent (NTC), 4.7 kΩ/0.45 W
1
Resistor, light-dependent (LDR), 100 V/0.2 W
1
Resistor, voltage-dependent (VDR), 14 V/0.05 W
1
Capacitor, 100 pF/100 V
1
Capacitor, 10 nF/100 V
2
Capacitor, 47 nF/100 V
1
Capacitor, 0.1 μF/100 V
2
Capacitor, 0.22 μF/100 V
1
Capacitor, 0.47 μF/100 V
2
Capacitor, 1.0 μF/100 V
2
Capacitor, 10 μF/250 V, polarised
2
Capacitor, 100 μF/63 V, polarised
1
Capacitor, 470 μF/50 V, polarised
1
Coil, 100 mH/50 mA
1
Diode, AA118
1
Diode, 1N4007
6
Zener diode, ZPD 3.3
1
Zener diode, ZPD 10
1
DIAC, 33 V/1 mA
1
NPN transistor, BC140, 40 V/1 A
2
NPN transistor, BC547, 50 V/100 mA
1
PNP transistor, BC160, 40 V/1 A
1
P-channel JFET transistor, 2N3820, 20 V/10 mA
1
N-channel JFET transistor, 2N3819, 25 V/50 mA
1
UNIJUNCTION transistor, 2N2647, 35 V/50 mA
1
P channel MOSFET transistor, BS250, 60 V/180 mA
1
Thyristor, TIC 106, 400 V/5 A
1
TRIAC, TIC206, 400 V/4 A
1
Transformer coil, N = 200
1
Transformer coil, N = 600
2
Transformer iron core with holder
1
Indicator light, 12 V/62 mA
1
Light emitting diode (LED), 20 mA, blue
1
Light emitting diode (LED), 20 mA, red or green
1
Changeover switch
1
© Festo Didactic GmbH & Co. KG 567217
Graphical symbols for the equipment set
Component
Graphical symbol
Component
Resistor
Zener diode
Potentiometer
DIAC
Resistor, temperaturedependent (NTC)
NPN transistor
Resistor, light-dependent
(LDR)
PNP transistor
Resistor, voltage-dependent
P-channel JFET transistor
Graphical symbol
(VDR)
U
Capacitor
N-channel JFET transistor
Capacitor, polarised
UNIJUNCTION transistor
Coil
P-channel MOSFET transistor
Diode
Thyristor
© Festo Didactic GmbH & Co. KG 567217
XV
Component
XVI
Graphical symbol
Component
TRIAC
Blue LED
Transformer coil
Red or green LED
Indicator light
Changeover switch
Graphical symbol
© Festo Didactic GmbH & Co. KG 567217
Allocation of components and exercises – Fundamentals of alternating
current technology
Exercise
1
2
3
4
5
6
7
8
9
10
3
3
1
1
Component
Resistor, 100 Ω/2 W
1
Resistor, 470 Ω/2 W
1
Resistor, 1 kΩ/2 W
1
Resistor, 4.7 kΩ/2 W
1
1
1
1
1
1
1
Resistor, 10 kΩ/2 W
1
Resistor, 22 kΩ/2 W
1
Resistor, voltage-dependent (VDR), 14 V/0.05 W
1
Capacitor, 100 pF/100 V
1
Capacitor, 10 nF/100 V
1
Capacitor, 47 nF/100 V
1
Capacitor, 0.1 μF/100 V
1
Capacitor, 0.22 μF/100 V
1
1
1
Capacitor, 0.47 μF/100 V
1
Capacitor, 1.0 μF/100 V
1
1
Coil, 100 mH/50 mA
1
Transformer coil, N = 200
1
Transformer coil, N = 600
1
Digital multimeter
1
Oscilloscope, 2-channel
®
Basic power supply unit EduTrainer
© Festo Didactic GmbH & Co. KG 567217
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
XVII
Notes for the teacher/trainer
Learning objectives
The main objective of this workbook is to explain how to analyse and evaluate simple AC circuits
with a resistor, capacitor and coil. It does this through a combination of theoretical questions and
practical exercises where the students are required to build the circuits and measure electrical variables.
The combination of both theory and practice ensures faster progress and longer-lasting learning. The more
specific learning objectives are documented in the matrix. Concrete, individual learning objectives are
assigned to each exercise.
Required time
The time required for working through the exercises depends on the student’s previous knowledge
of the subject matter. Each exercise should take approx. 1 to 1.5 hours.
Equipment set components
The workbook, set of exercises and equipment match each other. All 10 exercises can be completed using
components from one equipment set TP 1011.
Standards
The following standards are applied in this workbook:
EN 60617-2 to EN 60617-8
Graphical symbols for circuit diagrams
EN 81346-2
Industrial systems, installations and equipment and industrial products;
structuring principles and reference designations
IEC 60364-1
Low-voltage electrical installations – Fundamental principles,
assessment of general characteristics, definitions
IEC 60364-4-41
Low-voltage electrical installations – Protective measures –
Protection against electric shock
Classifications in the workbook
Solutions and supplements in graphics or diagrams are in red.
Exception: Information and evaluations relating to current are always in red, information and evaluations
relating to voltage are always in blue.
Classifications in the set of exercises
Texts which require completion are identified with a grid or grey table cells.
Graphics which require completion include a grid.
Notes for the lesson
These provide additional information about the training approach, method or about the components.
These notes are not included in the set of exercises.
XVIII
© Festo Didactic GmbH & Co. KG 567217
Solutions
The solutions specified in this workbook are the results of test measurements. The results of your
measurements can deviate from these data.
Learning topics
The training subject "Fundamentals of direct current technology" is part of the learning topics in technical
colleges for electronic engineering.
Structure of the exercises
All 10 exercises have the same structure and are broken down into:
• Title
• Learning objectives
• Problem description
• Circuit or positional sketch
• Project assignment
• Work aids
• Worksheets
The workbook contains the solutions for each worksheet in the set of exercises.
Component designations
The components in the circuit diagrams are identified in accordance with DIN EN 81346-2. Letters are
assigned as appropriate to each component. Multiple components of the same type within a circuit are
numbered.
Resistors:
Capacitors:
Coils:
Signalling devices:
R, R1, R2, etc.
C, C1, C2, etc.
L, L1, L2, etc.
P, P1, P2, etc.
Note
If resistors, capacitors or coils are being interpreted as physical variables, the letter identifying them
is shown in italics (symbols). If numbers are required for numbering, these are treated like indices and
subscript is used.
© Festo Didactic GmbH & Co. KG 567217
XIX
CD-ROM contents
The workbook is included on the CD-ROM as a PDF file. The CD-ROM also provides you with
additional media.
The CD-ROM contains the following folders:
• Operating instructions
• Images
• Product information
Operating instructions
Contains operating instructions for various components in the training package. These instructions
are helpful when using and commissioning the components.
Images
Contains photos and graphics of components and industrial applications. These can be used
to illustrate individual tasks or to supplement project presentations.
Product information
Contains the manufacturer's product information for selected components. The representations
and descriptions of the components in this format are intended to demonstrate how they are presented
in an industrial catalogue. Additional information regarding the components is also included.
XX
© Festo Didactic GmbH & Co. KG 567217
Exercise 1
Recording and representing characteristics used in AC technology
Learning objectives
After completing this exercise:
• You will be able to describe the characteristics used in AC technology and perform calculations using
these characteristics.
• You will be familiar with the different representations used for variables associated with alternating current.
• You will be able to record characteristics used in connection with alternating current using the
oscilloscope and evaluate them.
• You will be familiar with how an ohmic resistor behaves in an AC circuit.
Problem description
You are to start work in the Quality Assurance department, where you will be testing faulty
electronic circuits.
In preparation, you will perform measurements on simple AC circuits.
Circuit
G
U
RL
AC circuit with oscilloscope
© Festo Didactic GmbH & Co. KG 567217
1
Exercise 1: Recording and representing characteristics used in AC technology
1.
2.
3.
4.
5.
6.
Project assignments
Describe what AC voltage is.
Answer the questions on phasor and linear representation of alternating variables.
Explain the main characteristics used in connection with alternating current.
Familiarise yourself with the operation of the oscilloscope and answer the questions.
Perform the initial measurements using the oscilloscope.
Investigate the current, voltage and power waveform in a simple resistance circuit.
•
•
•
•
Work aids
Textbooks, books of tables
Data sheets
WBT Electrical engineering 1
Internet
Note
Do not switch on the electrical power supply until you have made and checked all the connections. Once
you have completed the exercise, switch off the power supply again before dismantling the components.
2
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
Describing AC voltage
–
Describe what AC voltage is.
AC voltage is a voltage that periodically changes its polarity (direction) and value.
The illustration shows three frequent temporal waveforms of alternating variables.
–
Enter the name of the waveform in the table.
Signal waveform
Designation
u
T
2
T
t
Sinusoidal waveform
u
Triangular waveform
T
2
T
t
T
2
T
t
u
Square-wave waveform
Typical electrical signal shapes
© Festo Didactic GmbH & Co. KG 567217
3
Exercise 1: Recording and representing characteristics used in AC technology
Explaining phasor and linear representation of alternating current
The sinusoidal line for the AC voltage can be constructed from the rotating phasor in the circle.
The radius of the circle corresponds to the amplitude of the sinusoidal oscillation and is called UP.
u
UP
UP
α
u
α
90°
180°
270°
360°
π
2
π
3π
2
2π
α, t
-UP
Phasor representation and linear representation of a sinusoidal AC voltage
–
Specify the formula for calculating the momentary voltage value u.
The formula is:
sin α =
Opposite side
u
=
Hypotenuse U P
The momentary value u is therefore:
u = U P ⋅ sin α
The higher the frequency of the sinusoidal oscillation, the shorter the periodic duration and the faster
the rotation of the associated phasor. The angular frequency ω is used as a measure for the speed
of the phasor movement.
–
–
Specify the formula for calculating the momentary value u as a function of ω.
To do this, also add the sinusoidal curve to the graph. Under the angle value in degrees, enter
the corresponding value in radians.
Formula for calculating the momentary value u:
u = U P ⋅ sin ( ω t )
4
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
Describing the characteristics used in connection with alternating current
To work in the field of AC technology, you will need to be familiar with the characteristics used in connection
with alternating current.
–
Briefly describe the main characteristics used in connection with AC technology. To do this, complete
the corresponding fields in the table.
Characteristic
Symbol or formula
Description
Peak voltage UP
UP
Highest or lowest AC voltage value, also called amplitude or peak value.
Peak current IP
IP
Highest or lowest alternating current value.
Peak-to-peak voltage UPP
U PP = 2 ⋅ U P
Difference between the positive and negative peak value.
Effective voltage Ueff
U eff =
Effective current Ieff
I eff =
Periodic duration T in s
UP
2
IP
2
T
With sinusoidal voltage: UPP is twice the amplitude.
The effective value is the AC voltage value that will give the same power
at an ohmic resistor as a DC voltage with this value.
The effective value is the alternating current that will give the same power
at an ohmic resistor as a direct current with this value.
A period (full wave with positive and negative half-wave) lasts a certain
amount of time. This time is called the periodic duration T.
Frequency f in Hz
f =
1
T
Number of periods per second.
ω = 2⋅π⋅ f
Angle covered per time unit in radians.
Momentary value u
u = U P ⋅ sin ( ω t )
Time-dependent momentary value of a sinusoidal AC voltage.
Momentary value i
i = I P ⋅ sin( ω t )
Time-dependent momentary value of a sinusoidal alternating current.
Angular frequency ω in
1
s
Characteristics used in AC technology
© Festo Didactic GmbH & Co. KG 567217
5
Exercise 1: Recording and representing characteristics used in AC technology
–
Add some of the characteristics to the representation of the sinusoidal AC voltage. To do this, match
the characteristics with the numbers.
u
3
1
2
0
t
4
Sinusoidal AC voltage
Number
Designation
1
Peak value UP
2
Peak-to-peak value UPP
3
Effective voltage Ueff
4
Periodic duration T
Describing the basic functions of an oscilloscope
Oscilloscopes offer many adjustment and connection options, which differ depending on the design
and model. Certain basic settings, however, are common to all oscilloscopes.
AUTORANGE SAVE/RECALL
UTILITY
MEASURE
ACQUIRE
HELP
CURSOR
DISPLAY
DEFAULT SETUP
VERTICAL
POSITION
SAVE
CH1
MENU
RUN/
STOP
SINGLE
SEQ
REF
MENU
PRINT
AUTOSET
MATH
MENU
HORIZONTAL
POSITION
CH2
MENU
VOLT/DIV
TRIGGER
LEVEL
HORIZ
MENU
TRIG
MENU
SET TO
ZERO
SET TO
50%
SEC/DIV
FORCE
TRIG
TRIG
VIEW
CH1
CH2
EXT.TRIG.
USB
Flash Drive
Example of an oscilloscope
6
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
–
–
Find out how the oscilloscope that you will be using for your measurements works.
Complete the table with the names of the controls that trigger the described functions.
Control
Brief description
Switch 0/I
Mains switch
Rotary knob POSITION CH1
Positions the signal from channel 1 (CH1) vertically.
Rotary knob VOLTS/DIV (CH1)
Sets the sensitivity of the CH1 input signal vertically.
Button CH1 MENU
Switches the display of channel 1 on or off.
Rotary knob POSITION
Positions all signals horizontally.
Rotary knob SEC/DIV
Sets the time-base sweep for the signals.
Button CH1 MENU -> Probe
Probe setting for channel 1.
Button CH1 MENU -> Coupling
Sets the following for channel 1: DC, AC, Ground.
Ground means: switches the channel to ground.
Button CH1 MENU -> Invert
Inverts the signal from channel CH1.
Button TRIG MENU
Trigger settings
Button TRIG MENU -> Edge
Sets Edge as the trigger type.
Input connector EXT. TRIG.
Input connector for an external trigger source.
CH1
Measurement channel 1
CH2
Measurement channel 2
Basic oscilloscope functions
Note for the lesson
The basic functions and controls are illustrated using the 2-channel digital storage oscilloscope
Tektronix TDS 1002B as an example.
–
Describe the effect of the trigger function on oscilloscope traces.
The trigger function can be used with periodic signals to set the start time of the beam
on the oscilloscope's display to the same amplitude value as for the previous signal.
This produces a seemingly stationary image.
© Festo Didactic GmbH & Co. KG 567217
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Exercise 1: Recording and representing characteristics used in AC technology
Proceed as follows when creating an oscilloscope trace:
• Make sure that the X and Y deflections are calibrated.
• Make sure that the zero line is where you want it.
• If you are setting a frequency on the function generator, measure the frequency using the
oscilloscope to make sure it matches.
• Always portray at least one period when performing a trace.
• Always enter the zero line in the trace.
• Always enter the time-base sweep in the trace.
• Always enter the voltage sweep of each channel used (CH1 and CH2) in the trace.
• Pay attention to the reciprocal time references of the signals when tracing.
• Always use the slowest signal as the trigger.
Settings on the oscilloscope:
UPP
T
Y = 2 V/DIV
X = 0.1 ms/DIV
Measurement example for the oscilloscope
–
Evaluate the measurement results of the oscilloscope trace. Determine the peak-to-peak voltage
UPP and the periodic duration T.
Peak-to-peak voltage UPP:
UPP corresponds to 4 scale divisions (DIV).
U PP = 4 DIV ⋅ 2
V
=8V
DIV
Periodic duration T:
T corresponds to 6 scale divisions.
T = 6 DIV ⋅ 0.1
8
ms
= 0.6 ms
DIV
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
Performing a measurement using the oscilloscope
Investigate the temporal waveform of an AC voltage using the oscilloscope display.
–
Build the circuit.
G
Y1
U
Circuit for tracing a sinusoidal AC voltage using an oscilloscope
Identifier
Designation
–
Oscilloscope
Values
2-channel
®
–
Basic power supply unit EduTrainer
–
Equipment list
–
–
–
Connect the function generator.
Make the settings for the measuring ranges on the oscilloscope as specified.
Set the frequency and voltage on the function generator to get a voltage waveform similar to that in the
oscilloscope graph shown below.
© Festo Didactic GmbH & Co. KG 567217
9
Exercise 1: Recording and representing characteristics used in AC technology
Settings on the oscilloscope
Channel 1:
Y1 = 1 V/DIV
Time-base sweep:
0 (Y1)
X = 0.1 ms/DIV
Oscilloscope graph for the AC voltage to be investigated
–
Measure the peak-to-peak voltage UPP and the periodic duration T.
Peak-to-peak voltage UPP:
U PP = 6 DIV ⋅ 1
V
=6V
DIV
Periodic duration T:
T = 10 DIV ⋅ 0.1
–
ms
= 1 ms
DIV
Determine the peak voltage UP, the effective voltage Ueff and the frequency f from the measured values
mathematically.
Peak voltage UP:
UP =
U PP 6 V
=
=3V
2
2
Effective voltage Ueff:
U eff =
UP
2
=
3V
2
= 2.12 V
Frequency f:
f =
10
1
1
1
=
= 1 ⋅ 103 = 1 kHz
T 1 ms
s
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
–
–
Measure the effective value Ueff using the digital multimeter.
Compare the measured effective value and the mathematically determined effective value.
Measured Ueff:
Ueff = 2.01 V
Calculated Ueff:
Ueff = 2.12 V
Slight deviations between the measured values and the calculated values are due to measuring errors
and component tolerances.
Measuring voltage, current and power at the ohmic resistor
Represent the temporal waveform of AC voltage and alternating current at an ohmic resistor. Construct the
power curve for the resistor from the momentary values for current and voltage. Compare this power curve
with the power curve at a comparable DC voltage.
–
Describe how to represent the waveform of currents using the oscilloscope.
To be able to measure the current, a current measurement resistor RM must be added to
the electrical circuit. The voltage drop URM at the current measurement resistor is determined
using the oscilloscope and used as a basis for calculating the current flowing through the circuit.
–
Describe what is meant by an active resistor.
In AC technology, an ohmic resistor is called an active resistor. The active resistor has the same
effect in the AC circuit as in the DC circuit. It acts on the electrical energy and converts it into heat,
light or mechanical energy. The power converted at the active resistor is also called effective power.
© Festo Didactic GmbH & Co. KG 567217
11
Exercise 1: Recording and representing characteristics used in AC technology
Specify the formula for calculating the current I at the active resistance R.
–
U
R
I=
Voltage and current at the active resistor
Y1
G
RL
URL
RM
URM
UP = 6.6 V
(sinusoidal)
f = 1 kHz
Y2
Resistance circuit with RL = 1 kΩ, RM = 100 Ω, UP = 6.6 V, f = 1 kHz
Identifier
Designation
Values
RL
Resistor
1 kΩ/2W
RM
Resistor
100 Ω/2 W
–
Oscilloscope
–
2-channel
®
Basic power supply unit EduTrainer
–
Equipment list
Note
To enable the voltages URL and URM to be represented simultaneously on the oscilloscope, the reference
point of the two voltages is placed between the two resistances. As a result, the voltage signal URM
must be inverted.
Make sure that no ground loops occur across the protective earth conductors when the two measurement
channels are connected to the oscilloscope. Connect an isolating transformer to prevent this.
12
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
–
–
–
–
–
–
–
–
Build the circuit.
Connect the function generator.
Set a sinusoidal voltage UP = 6.6 V with the frequency f = 1 kHz.
Make the necessary settings for the measurements on the oscilloscope.
Measure the sinusoidal voltage URL at the resistor RL using the oscilloscope.
Transfer the voltage waveform to the oscilloscope graph.
Measure the voltage URM at the measuring resistor RL using the oscilloscope.
Transfer this voltage waveform to the oscilloscope graph too.
Settings on the oscilloscope
Y1
Channel 1:
Y1 = 2 V/DIV
Channel 2:
Y2 = 0.5 V/DIV
(invert)
Y2
0 (Y1), (Y2)
Time-base sweep:
X = 0.1 ms/DIV
Centre zero lines of channel 1
and channel 2
Trigger: Y1
Oscilloscope graph for uRL and uRM
–
–
Determine the momentary values uRL and uRM for the times specified in the measurement log.
Enter the momentary values in the measurement log.
Calculate the current i and the effective power p for the times specified in the measurement log.
Enter these values too. Also specify the formula for calculating p.
Formula for calculating the momentary values for power:
p =u ⋅i
–
Represent the current values i, the voltage values u and the power waveform p in the prepared graph.
© Festo Didactic GmbH & Co. KG 567217
13
Exercise 1: Recording and representing characteristics used in AC technology
Time t (ms)
Voltage uRL (V)
Voltage uRM (V)
Current i (mA)
Effective power p (mW)
0
0
0
0
0
0.1
3.8
0.38
3.8
14.4
0.15
5.0
0.5
5.0
25.0
0.25
6.0
0.6
6.0
36.0
0.35
5.0
0.5
5.0
25.0
0.4
3.8
0.38
3.8
14.4
0.5
0
0
0
0
0.6
-3.8
-0.38
-3.8
14.4
0.65
-5.0
-0.5
-5.0
25.0
0.75
-6.0
-0.6
-6.0
36.0
0.85
-5.0
-0.5
-5.0
25.0
0.9
-3.8
-0.38
-3.8
14.4
1.0
0
0
0
0
25
10
mW
mA
V
30
15
Voltage u
50
Current i
Power p
Measurement log
p
6
20
10
4
10
5
2
0
0
0
u
i
0.1
-10
-5
-2
-20
-10
-4
-30
-15
-6
-40
-20
-8
-50
-25
-10
0.2
0.3
0.4
0.5
0.6
0.7
0.8
ms
1.0
Time t
Voltage, current and power waveform at the ohmic resistor RL
14
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
–
Describe the waveform of the current and voltage curve.
Current and voltage are in phase. They reach their zero crossovers and peak values at the same time.
–
Describe the waveform of the power curve.
The waveform of the power curve is also sinusoidal, but has no negative components. The frequency
is twice that of the voltage and current waveform.
The waveform of the effective power at the ohmic resistor can be replaced with a constant mean value.
It is the effective value of the power.
–
Specify the formula for calculating the effective value of the power P.
Peff = U eff ⋅ I eff
Ohm's law gives two further formulae for calculating the power:
2
Peff = R ⋅ I eff
–
Peff =
or
2
U eff
R
Specify the effective value of the power for the resistance circuit.
Peff = U eff ⋅ I eff =
UP
2
⋅
IP
2
=
6 V 6 mA
⋅
= 18 mW
2
2
© Festo Didactic GmbH & Co. KG 567217
15
Exercise 1: Recording and representing characteristics used in AC technology
Power in the DC and AC circuit
To be able to compare the power in the DC and AC circuit, determine the power output at the ohmic resistor
RL = 1 kΩ at a DC voltage of U = 4.24 V.
–
Explain why the comparison measurement for direct current is performed at a DC voltage of U = 4.24 V.
The sinusoidal AC voltage with UP = 6 V has the effective value:
U eff =
UP
2
=
6V
2
= 4.24 V
A DC voltage of U = 4.24 V gives the same power at an ohmic resistor as the effective value
Ueff = 4.24 V of an AC voltage.
–
Measure the power of the illustrated circuit in the DC circuit using the indirect method and write
down the measured values.
U = 4.24 V
RL
URL
Resistance circuit with RL = 1 kΩ, U = 4.24 V
Identifier
Designation
Values
RL
Resistor
1 kΩ/2W
–
Digital multimeter
–
–
Basic power supply unit EduTrainer®
–
Equipment list for the resistance circuit connected to direct current
Measured values of the electrical variables for calculating power:
U = 4.24 V
I = 4.19 mA
16
© Festo Didactic GmbH & Co. KG 567217
Exercise 1: Recording and representing characteristics used in AC technology
–
Calculate the electrical power at the ohmic resistor in the DC circuit from the measured values.
& mW
P = U ⋅ I = 4.24 V ⋅ 4.19 mA =17.8
Enter the waveform of the measured electrical variables and the calculated electrical power
in the corresponding graph.
DC circuit
AC circuit
5
0
V
I
2
0
-5
-2
-10
-4
-15
-20
mA
U
4
G
URL
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms 1.0
10
5
0
UP = 6 V
V
-2
-10
-4
-6
-15
-6
-8
-20
-8
Time t
50
mW
mW
Power P
50
30
20
P
10
0
30
URL
i
2
0
RL
u
4
-5
Power p
10
RL
Current i
Current I
mA
Voltage U
U = 4.24 V
Voltage u
–
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms 1.0
Time t
p
20
10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms 1.0
Time t
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ms 1.0
Time t
Comparison: Power in the DC circuit and AC circuit for RL = 1 kΩ
© Festo Didactic GmbH & Co. KG 567217
17
Exercise 1: Recording and representing characteristics used in AC technology
–
Describe the relationship between the two power curves.
•
•
•
18
A constant, invariable power is output in the DC circuit.
The power output fluctuates greatly in the AC circuit.
With a sinusoidal AC voltage, both sources output the same power on average if the maximum
value of the power output for the AC voltage is exactly twice the temporally constant power
of the DC voltage source.
© Festo Didactic GmbH & Co. KG 567217
Exercise 2
Investigating the behaviour of a capacitor
Learning objectives
After completing this exercise:
• You will be able to describe the behaviour of a capacitor in an AC circuit.
• You will be able to determine and calculate the capacitive reactance of a capacitor.
• You will be able to determine the phase shift of current and voltage at the capacitor by measurement
and evaluate it.
• You will be able to determine and calculate the capacitive reactive power.
Problem description
A series resistor is needed in an AC circuit for an LED. The series resistor should release as little
electrical energy as possible in the form of heat. At your disposal are ohmic resistors and capacitors.
Investigate the behaviour of the capacitor connected to AC voltage and examine whether the capacitor
can be used as a loss-free series resistor.
Positional sketch
L1
L1
L2
L2
L3
L3
EMERGENCY
STOP
N
N
PE
PE
Power supply unit for three-phase alternating current with LED indicator
© Festo Didactic GmbH & Co. KG 567217
19
Exercise 2: Investigating the behaviour of a capacitor
5.
Work assignments
Compare the behaviour of the capacitor connected to AC and DC voltage.
Investigate the behaviour of the capacitor in the AC circuit by measuring the charging and
discharging process.
Examine the current and voltage waveform at the capacitor in the AC circuit.
Investigate the frequency dependence of a capacitor's capacitive reactance. To do this, trace
the resistance curve.
Trace the capacitor's power curve and decide whether the capacitor can be used as a series resistor.
•
•
•
•
Work aids
Textbooks, books of tables
Data sheets
WBT Electrical engineering 2
Internet
1.
2.
3.
4.
Note for the lesson
There are two ways of completing the exercise:
•
First, research the basic behaviour of the capacitor in the AC circuit,
•
then check the results through an experiment
or vice versa.
If the decision about the order is left to the student, he can take his individual needs into consideration.
Note
Do not switch on the electrical power supply until you have made and checked all the connections. Once
you have completed the exercise, switch off the power supply again before dismantling the components.
20
© Festo Didactic GmbH & Co. KG 567217