Fundamentals of alternating current technology

Transcription

1 Fundamentals of alternating current technology Workbook With CD-ROM Y 1 Y 2 I I R I C I L φ P 90 G U R C L S QL QC Festo Didactic EN

2 Order No.: Edition: 10/2010 Author: Christine Löffler Graphics: Thomas Ocker, Doris Schwarzenberger Layout: 03/2011, Susanne Durz Festo Didactic GmbH & Co. KG, Denkendorf, Germany, 2013 Internet: The purchaser shall receive a single right of use which is non-exclusive, non-time-limited and limited geographically to use at the purchaser's site/location as follows. The purchaser shall be entitled to use the work to train his/her staff at the purchaser's site/location and shall also be entitled to use parts of the copyright material as the basis for the production of his/her own training documentation for the training of his/her staff at the purchaser's site/location with acknowledgement of source and to make copies for this purpose. In the case of schools/technical colleges and training centres, the right of use shall also include use by school and college students and trainees at the purchaser's site/location for teaching purposes. The right of use shall in all cases exclude the right to publish the copyright material or to make this available for use on intranet, Internet and LMS platforms and databases such as Moodle, which allow access by a wide variety of users, including those outside of the purchaser's site/location. Entitlement to other rights relating to reproductions, copies, adaptations, translations, microfilming and transfer to and storage and processing in electronic systems, no matter whether in whole or in part, shall require the prior consent of Festo Didactic GmbH & Co. KG.

3 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 1 Exercise 2: Investigating the behaviour of a capacitor 19 Exercise 3: Selecting a suitable capacitance for a high-pass filter 39 Exercise 4: Reducing voltage peaks when switching a solenoid coil 51 Exercise 5: Determining the inductance of a coil 65 Exercise 6: Investigating RC elements by measurement 77 Exercise 7: Tracing the frequency response of a high-pass and low-pass filter 89 Exercise 8: Compensating the reactive power for an electric motor 101 Exercise 9: Selecting a three-phase circuit for connecting a storage heater 113 Exercise 10: Generating different output stages for a heater 127 Exercises and worksheets 1 Exercise 2: Investigating the behaviour of a capacitor 19 Exercise 3: Selecting a suitable capacitance for a high-pass filter 39 Exercise 4: Reducing voltage peaks when switching a solenoid coil 51 Exercise 5: Determining the inductance of a coil 65 Exercise 6: Investigating RC elements by measurement 77 Exercise 7: Tracing the frequency response of a high-pass and low-pass filter 89 Exercise 8: Compensating the reactive power for an electric motor 101 Exercise 9: Selecting a three-phase circuit for connecting a storage heater 113 Exercise 10: Generating different output stages for a heater 127 Festo Didactic GmbH & Co. KG III

4 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

5 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 V

6 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 at: did@de.festo.com The authors and Festo Didactic look forward to your comments. VI Festo Didactic GmbH & Co. KG

7 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 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 VII

8 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

9 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 Book of tables Workbooks Digital learning programs Technical expertise for electrical professions Electrical engineering Electrical engineering/electronics Fundamentals of direct current technology Fundamentals of alternating current technology Fundamentals of semiconductors Basic electronic circuits 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 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 IX

10 Learning objectives Fundamentals of alternating current technology 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. X Festo Didactic GmbH & Co. KG

11 Allocation of learning objectives and exercises Fundamentals of AC technology Learning objective 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 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 XI

12 Exercise 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

13 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 Component Order no. Quantity Basic power supply unit EduTrainer Universal patch panel EduTrainer Component set for electrical engineering/electronics Jumper plug set, 19 mm, grey-black Overview of the component set for electrical engineering/electronics, order no Component Quantity Resistor, 10 /2 W 1 Resistor, 22 /2 W 2 Resistor, 33 /2 W 1 Resistor, 100 /2 W 2 Resistor, 220 /2 W 1 Resistor, 330 /2 W 1 Resistor, 470 /2 W 2 Resistor, 680 /2 W 1 Resistor, 1 k /2 W 3 Resistor, 2.2 k /2 W 2 Resistor, 4.7 k /2 W 2 Resistor, 10 k /2 W 3 Resistor, 22 k /2 W 3 Resistor, 47 k /2 W 2 Resistor, 100 k /2 W 2 Resistor, 1 M /2 W 1 Festo Didactic GmbH & Co. KG XIII

14 Component Quantity Potentiometer, 1 k /0.5 W 1 Potentiometer, 10 k /0.5 W 1 Resistor, temperature-dependent (NTC), 4.7 k /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, 1N Zener diode, ZPD 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 = Transformer coil, N = 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 XIV Festo Didactic GmbH & Co. KG

15 Graphical symbols for the equipment set Component Graphical symbol Component Graphical symbol Resistor Zener diode Potentiometer DIAC Resistor, temperaturedependent (NTC) NPN transistor Resistor, light-dependent (LDR) PNP transistor Resistor, voltage-dependent (VDR) P-channel JFET transistor U Capacitor N-channel JFET transistor Capacitor, polarised UNIJUNCTION transistor Coil P-channel MOSFET transistor Diode Thyristor Festo Didactic GmbH & Co. KG XV

16 Component Graphical symbol Component Graphical symbol TRIAC Blue LED Transformer coil Red or green LED Indicator light Changeover switch XVI Festo Didactic GmbH & Co. KG

17 Allocation of components and exercises Fundamentals of alternating current technology Exercise Component Resistor, 100 /2 W 1 Resistor, 470 /2 W 1 1 Resistor, 1 k /2 W Resistor, 4.7 k /2 W 1 Resistor, 10 k /2 W 1 Resistor, 22 k /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 1 Capacitor, 47 nf/100 V 1 Capacitor, 0.1 μf/100 V 1 Capacitor, 0.22 μf/100 V Capacitor, 0.47 μf/100 V 1 Capacitor, 1.0 μf/100 V 1 Coil, 100 mh/50 ma Transformer coil, N = Transformer coil, N = Digital multimeter Oscilloscope, 2-channel Basic power supply unit EduTrainer Festo Didactic GmbH & Co. KG XVII

18 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 Standards The following standards are applied in this workbook: EN to EN Graphical symbols for circuit diagrams EN Industrial systems, installations and equipment and industrial products; structuring principles and reference designations IEC Low-voltage electrical installations Fundamental principles, assessment of general characteristics, definitions IEC 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

19 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 Letters are assigned as appropriate to each component. Multiple components of the same type within a circuit are numbered. Resistors: R, R1, R2, etc. Capacitors: C, C1, C2, etc. Coils: L, L1, L2, etc. Signalling devices: 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 XIX

20 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

21 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 R L AC circuit with oscilloscope Festo Didactic GmbH & Co. KG

22 Project assignments 1. Describe what AC voltage is. 2. Answer the questions on phasor and linear representation of alternating variables. 3. Explain the main characteristics used in connection with alternating current. 4. Familiarise yourself with the operation of the oscilloscope and answer the questions. 5. Perform the initial measurements using the oscilloscope. 6. 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

23 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 u T 2 T t Square-wave waveform Typical electrical signal shapes Festo Didactic GmbH & Co. KG

24 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 U P. u U P U P α u α π 2 π 3π 2 2π α, t -U P Phasor representation and linear representation of a sinusoidal AC voltage Specify the formula for calculating the momentary voltage value u. The formula is: Opposite side u sin Hypotenuse U P The momentary value u is therefore: u U P sin 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 sin( t) P 4 Festo Didactic GmbH & Co. KG

25 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 U P U P Highest or lowest AC voltage value, also called amplitude or peak value. Peak current I P I P Highest or lowest alternating current value. Peak-to-peak voltage U PP PP P U 2 U Difference between the positive and negative peak value. With sinusoidal voltage: U PP is twice the amplitude. Effective voltage U eff U U P eff 2 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. Effective current I eff I eff I P 2 The effective value is the alternating current that will give the same power at an ohmic resistor as a direct current with this value. Periodic duration T in s T 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 1 f T Angular frequency in 1 s Number of periods per second. 2 f Angle covered per time unit in radians. Momentary value u u U P sin( t) Time-dependent momentary value of a sinusoidal AC voltage. Momentary value i i I P sin( t) Time-dependent momentary value of a sinusoidal alternating current. Characteristics used in AC technology Festo Didactic GmbH & Co. KG

26 Add some of the characteristics to the representation of the sinusoidal AC voltage. To do this, match the characteristics with the numbers. u t 4 Sinusoidal AC voltage Number Designation 1 Peak value U P 2 Peak-to-peak value U PP 3 Effective voltage U eff 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 MEASURE ACQUIRE HELP AUTOSET REF MENU UTILITY CURSOR DISPLAY DEFAULT SETUP SINGLE SEQ RUN/ STOP SAVE PRINT VERTICAL POSITION HORIZONTAL POSITION TRIGGER LEVEL CH1 MENU MATH MENU CH2 MENU HORIZ MENU SET TO ZERO TRIG MENU SET TO 50% VOLT/DIV SEC/DIV FORCE TRIG TRIG VIEW CH1 CH2 EXT.TRIG. USB Flash Drive Example of an oscilloscope 6 Festo Didactic GmbH & Co. KG

27 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 Switch 0/I Rotary knob POSITION CH1 Rotary knob VOLTS/DIV (CH1) Button CH1 MENU Rotary knob POSITION Rotary knob SEC/DIV Brief description Mains switch Positions the signal from channel 1 (CH1) vertically. Sets the sensitivity of the CH1 input signal vertically. Switches the display of channel 1 on or off. Positions all signals horizontally. Sets the time-base sweep for the signals. Button CH1 MENU -> Probe Probe setting for channel 1. Button CH1 MENU -> Coupling Button CH1 MENU -> Invert Button TRIG MENU Button TRIG MENU -> Edge Input connector EXT. TRIG. Sets the following for channel 1: DC, AC, Ground. Ground means: switches the channel to ground. Inverts the signal from channel CH1. Trigger settings Sets Edge as the trigger type. 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

28 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: U PP 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 U PP and the periodic duration T. Peak-to-peak voltage U PP : U PP corresponds to 4 scale divisions (DIV). V UPP 4DIV 2 8V DIV Periodic duration T: T corresponds to 6 scale divisions. ms T 6DIV ms. DIV 8 Festo Didactic GmbH & Co. KG

29 Performing a measurement using the oscilloscope Investigate the temporal waveform of an AC voltage using the oscilloscope display. Build the circuit. G U Y 1 Circuit for tracing a sinusoidal AC voltage using an oscilloscope Identifier Designation Values Oscilloscope 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

30 Settings on the oscilloscope Channel 1: Y 1 = 1 V/DIV Time-base sweep: 0(Y) 1 X = 0.1 ms/div Oscilloscope graph for the AC voltage to be investigated Measure the peak-to-peak voltage U PP and the periodic duration T. Peak-to-peak voltage U PP : V UPP 6DIV 1 6V DIV Periodic duration T: ms T 10 DIV ms DIV Determine the peak voltage U P, the effective voltage U eff and the frequency f from the measured values mathematically. Peak voltage U P : UPP 6V UP 3V 2 2 Effective voltage U eff : UP 3V U eff 212V. 2 2 Frequency f: f 110 1kHz T 1ms s 10 Festo Didactic GmbH & Co. KG

31 Measure the effective value U eff using the digital multimeter. Compare the measured effective value and the mathematically determined effective value. Measured U eff : U eff = 2.01 V Calculated U eff : U eff = 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 R M must be added to the electrical circuit. The voltage drop U RM 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

32 Specify the formula for calculating the current I at the active resistance R. I U R Voltage and current at the active resistor Y 1 R L U RL G UP = 6.6 V (sinusoidal) f = 1 khz R M U RM Y 2 Resistance circuit with R L = 1 k, R M = 100, U P = 6.6 V, f = 1 khz Identifier Designation Values R L Resistor 1 k /2W R M Resistor 100 /2 W Oscilloscope 2-channel Basic power supply unit EduTrainer Equipment list Note To enable the voltages U RL and U RM 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 U RM 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

33 Build the circuit. Connect the function generator. Set a sinusoidal voltage U P = 6.6 V with the frequency f = 1 khz. Make the necessary settings for the measurements on the oscilloscope. Measure the sinusoidal voltage U RL at the resistor R L using the oscilloscope. Transfer the voltage waveform to the oscilloscope graph. Measure the voltage U RM at the measuring resistor R L using the oscilloscope. Transfer this voltage waveform to the oscilloscope graph too. Y 1 Settings on the oscilloscope Y 2 0(Y), 1 (Y 2) Channel 1: Y 1 = 2 V/DIV Channel 2: Y 2 = 0.5 V/DIV (invert) Time-base sweep: X = 0.1 ms/div Centre zero lines of channel 1 and channel 2 Trigger: Y 1 Oscilloscope graph for u RL and u RM Determine the momentary values u RL and u RM 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

34 Time t (ms) Voltage u RL (V) Voltage u RM (V) Current i (ma) Effective power p (mw) Measurement log mw ma V Power p 30 Current i 15 Voltage u 6 u p i ms Time t Voltage, current and power waveform at the ohmic resistor R L 14 Festo Didactic GmbH & Co. KG

35 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 Ueff Ieff Ohm's law gives two further formulae for calculating the power: eff 2 eff P R I or P eff U 2 eff R Specify the effective value of the power for the resistance circuit. UP IP 6V 6mA Peff Ueff I eff 18 mw Festo Didactic GmbH & Co. KG

36 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 R L = 1 k 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 U P = 6 V has the effective value: U P 6V U eff 424V. 2 2 A DC voltage of U = 4.24 V gives the same power at an ohmic resistor as the effective value U eff = 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 R L U RL Resistance circuit with R L = 1 k, U = 4.24 V Identifier Designation Values R L Resistor 1 k /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

37 Calculate the electrical power at the ohmic resistor in the DC circuit from the measured values. P U I 424V. 419mA=17.8mW. Enter the waveform of the measured electrical variables and the calculated electrical power in the corresponding graph. DC circuit AC circuit U = 4.24 V G R L U RL U P =6V R L U RL Current I ma Voltage U V U I ms 1.0 Time t Current i ma Voltage u V u i ms 1.0 Time t Power P mw P Power p mw p ms ms 1.0 Time t Time t Comparison: Power in the DC circuit and AC circuit for R L = 1 k Festo Didactic GmbH & Co. KG

38 Describe the relationship between the two power curves. 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. 18 Festo Didactic GmbH & Co. KG

39 Contents Exercises and worksheets 1 Exercise 2: Investigating the behaviour of a capacitor 19 Exercise 3: Selecting a suitable capacitance for a high-pass filter 39 Exercise 4: Reducing voltage peaks when switching a solenoid coil 51 Exercise 5: Determining the inductance of a coil 65 Exercise 6: Investigating RC elements by measurement 77 Exercise 7: Tracing the frequency response of a high-pass and low-pass filter 89 Exercise 8: Compensating the reactive power for an electric motor 101 Exercise 9: Selecting a three-phase circuit for connecting a storage heater 113 Exercise 10: Generating different output stages for a heater 127 Festo Didactic GmbH & Co. KG I

40 II Festo Didactic GmbH & Co. KG

41 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 R L AC circuit with oscilloscope Festo Didactic GmbH & Co. KG

42 Project assignments 1. Describe what AC voltage is. 2. Answer the questions on phasor and linear representation of alternating variables. 3. Explain the main characteristics used in connection with alternating current. 4. Familiarise yourself with the operation of the oscilloscope and answer the questions. 5. Perform the initial measurements using the oscilloscope. 6. 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

43 Describing AC voltage Describe what AC voltage is. 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 u T 2 T t u T 2 T t Typical electrical signal shapes Festo Didactic GmbH & Co. KG

44 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 U P. u U P U P α u α α, t -U P Phasor representation and linear representation of a sinusoidal AC voltage Specify the formula for calculating the momentary voltage value u. 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: 4 Festo Didactic GmbH & Co. KG

45 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 U P U P Peak current I P I P Peak-to-peak voltage U PP Effective voltage U eff Effective current I eff Periodic duration T in s T Frequency f in Hz Angular frequency ω in 1 s Momentary value u Momentary value i Characteristics used in AC technology Festo Didactic GmbH & Co. KG

46 Add some of the characteristics to the representation of the sinusoidal AC voltage. To do this, match the characteristics with the numbers. u t 4 Sinusoidal AC voltage Number Designation 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 MEASURE ACQUIRE HELP AUTOSET REF MENU UTILITY CURSOR DISPLAY DEFAULT SETUP SINGLE SEQ RUN/ STOP SAVE PRINT VERTICAL POSITION HORIZONTAL POSITION TRIGGER LEVEL CH1 MENU MATH MENU CH2 MENU HORIZ MENU SET TO ZERO TRIG MENU SET TO 50% VOLT/DIV SEC/DIV FORCE TRIG TRIG VIEW CH1 CH2 EXT.TRIG. USB Flash Drive Example of an oscilloscope 6 Festo Didactic GmbH & Co. KG

47 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 Mains switch Positions the signal from channel 1 (CH1) vertically. Sets the sensitivity of the CH1 input signal vertically. Switches the display of channel 1 on or off. Positions all signals horizontally. Sets the time-base sweep for the signals. Probe setting for channel 1. Sets the following for channel 1: DC, AC, Ground. Ground means: switches the channel to ground. Inverts the signal from channel CH1. Trigger settings Sets Edge as the trigger type. Input connector for an external trigger source. Measurement channel 1 Measurement channel 2 Basic oscilloscope functions Describe the effect of the trigger function on oscilloscope traces. Festo Didactic GmbH & Co. KG