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TVET FIRST NQF Level 4 The TVET First NC(V) Series helps students, colleges and lecturers to meet the challenges and opportunities presented by the National Certificate (Vocational) curricula. The Student’s Books: • cover all the Subject Outcomes of the subject • contain appropriate weighting of topics • provide clearly defined key concepts • provide comprehensive, current and easy-to-follow content, at the appropriate language level, in a logical sequence and at a suitable pace • present students with a wide variety of learning and assessment activities. Electronic Control & Digital Electronics Electronic Control & Digital Electronics Electronic Control & Digital Electronics NQF Level 4 NQF Level 4 Student’s Book Elect control-digi elec 4 (s).indd 1 Jowaheer Consulting and Technologies, RBJ van Heerden, R Jonker & MWH Smit STUDENT’S BOOK TVET FIRST 2015/02/25 8:35 AM Electronic Control & Digital Electronics NQF Level 4 Student’s Book Jowaheer Consulting and Technologies, RBJ van Heerden, R Jonker & MWH Smit Electronic Control & Digital Electronics NQF Level 4 Student’s Book © Jowaheer Consulting and Technologies, RBJ van Heerden, R Jonker & MWH Smit, 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, photocopying, recording, or otherwise, without the prior written permission of the copyright holder or in accordance with the provisions of the Copyright Act, 1978 [as amended]. Any person who does any unauthorised act in relation to this publication may be liable for criminal prosecution and civil claims for damages. First published in 2014 by Troupant Publishers [Pty] Ltd PO Box 4532 Northcliff 2115 Distributed by Macmillan South Africa [Pty] Ltd ISBN: 978-1-4308-0322-5 Web PDF ISBN: 978-1-4308-0391-1 It is illegal to photocopy any page of this book without written permission from the publisher. Acknowledgements Microsoft product screenshots used with permission from Microsoft. The publisher also acknowledges the following companies, whose product screenshots appear in Module 14: Apple Inc., LogicCircuit and AVAST. While every effort has been made to ensure the information published in this work is accurate, the authors, editors, publisher and printers take no responsibility for any loss or damage suffered by any person as a result of reliance upon the information contained herein. The publisher respectfully advises readers to obtain professional advice concerning the content. While every effort has been made to trace the copyright holders and obtain copyright permission from them, in some cases this has proved impossible due to logistic and time constraints. Any copyright holder who becomes aware of infringement on our side is invited to contact the publisher. Note: Any reference to Further Education and Training (FET) in this book should be taken to mean Technical and Vocational Education and Training (TVET). To order any of these books, contact Macmillan Customer Services at: Tel: (011) 731 3300 Fax: (011) 731 3535 E-mail: [email protected] Contents Topic 1: Alternating current theory .........................................................1 Module 1: RC circuits ...................................................................................................... 2 Unit 1.1: RC series circuits...................................................................................................................................................... 2 Unit 1.2: RC parallel circuits ................................................................................................................................................ 12 Module 2: RL circuits ..................................................................................................... 17 Unit 2.1: RL series circuits .................................................................................................................................................... 17 Unit 2.2: RL parallel circuits................................................................................................................................................. 25 Module 3: RLC circuits and resonance ............................................................................. 30 Unit 3.1: RLC series circuits ................................................................................................................................................. 30 Unit 3.2: RLC parallel circuits .............................................................................................................................................. 40 Topic 2: Fundamentals of electronics ....................................................53 Module 4: Sinusoidal oscillators ...................................................................................... 54 Unit 4.1: Basic principles of oscillators............................................................................................................................... 55 Unit 4.2: Types of oscillators ................................................................................................................................................ 59 Module 5: Non-sinusoidal oscillators................................................................................ 68 Unit 5.1: Multivibrators ........................................................................................................................................................ 68 Unit 5.2: 555 timers ............................................................................................................................................................... 72 Module 6: Power supplies .............................................................................................. 77 Unit 6.1: Inverting power supply ....................................................................................................................................... 77 Unit 6.2: Switched-mode power supply ............................................................................................................................ 80 Module 7: Bipolar junction transistor (BJT) biasing and amplifiers ...................................... 83 Unit 7.1: Biasing, operating points and DC load line of a transistor ............................................................................. 84 Unit 7.2: Coupling methods used in amplifiers ................................................................................................................ 93 Unit 7.3: Transistor and feedback amplifiers..................................................................................................................... 96 Module 8: Silicon-controlled rectifiers (SCRs) and triacs .................................................. 107 Unit 8.1: Silicon-controlled rectifiers (SCRs) ................................................................................................................... 108 Unit 8.2: Triacs ..................................................................................................................................................................... 114 Topic 3: Basic design procedures .......................................................119 Module 9: Reading and interpreting semiconductor manuals ............................................ 120 Unit 9.1: Finding and interpreting the operational limits of semiconductor devices by using technical manuals................................................................................................................................................................ 120 Unit 9.2: Looking up replacement parts in technical manuals ..................................................................................... 128 Module 10: Designing, constructing, testing, fault-finding and repairing basic electronic circuits ........................................................................................................ 132 Unit 10.1: Designing, constructing and testing basic electronic circuits ..................................................................... 132 Unit 10.2: Fault-finding and repairing basic electronic circuits.................................................................................... 157 Topic 4: Binary decoding and loading software onto a computer ............171 Module 11: Boolean algebra ......................................................................................... 172 Unit 11.1: Logic gates and Boolean expressions ............................................................................................................. 172 Unit 11.2: Rules of Boolean algebra and De Morgan’s theorems ................................................................................. 179 ECDE4.indb 3 2014/11/13 01:08:42 PM Module 12: Binary code ............................................................................................... 188 Unit 12.1: Binary code......................................................................................................................................................... 188 Module 13: Encoders, decoders and shift registers.......................................................... 200 Unit 13.1: Encoders and decoders..................................................................................................................................... 200 Unit 13.2: Registers and shift registers ............................................................................................................................. 203 Module 14: Loading software onto a computer ............................................................... 210 Unit 14.1: Loading software onto a computer ................................................................................................................ 210 Unit 14.2: Causes of software malfunctioning ................................................................................................................ 221 Unit 14.3: Preventing software problems ........................................................................................................................ 225 Topic 5: Operating PLCs ....................................................................231 Module 15: Designing and fault-finding PLC circuits ....................................................... 232 Unit 15.1: Introduction to PLCs ........................................................................................................................................ 233 Unit 15.2: Simple ladder logic diagrams.......................................................................................................................... 246 Unit 15.3: Basic fault-finding in PLCs .............................................................................................................................. 259 Glossary ..........................................................................................267 ECDE4.indb 4 2014/11/13 01:08:42 PM Topic 1: Alternating current theory ECDE4.indb 1 2014/11/13 01:08:43 PM Module 1: RC circuits Introduction Working with electricity does not only involve direct current (DC) circuits. Alternating current (AC) circuits are as just important. When components such as resistors, inductors and capacitors are connected in a circuit, either in series or in parallel combination, they behave differently and you need a good understanding of their characteristics under different conditions. In this topic you will learn more about the characteristics of resistors, capacitors and inductors in series or parallel and the concept of resonance. Overview At the end of this module, you will be able to: • Describe the relationship between current and voltage in a resistancecapacitor (RC) circuit. • Determine the impedance and phase angle (ø) in an RC circuit. • Explain the frequency selectivity characteristic of RC series circuits (low- and high-pass circuits). • Explain the effects of faulty components in RC circuits. Units in this module Did you know? A resistor-capacitor (RC) circuit can be used as a filter for electrical signals or noise. This is because they can block certain frequencies and allow other frequencies to get though. RC circuits are also used as a type of timer switch because they charge to the source voltage and then discharge at a constant and specific rate. For example, the windscreen wipers on a car are controlled using an RC circuit. Unit 1.1: RC series circuits Unit 1.2: RC parallel circuits Unit 1.1: RC series circuits Resistance only Figure 1.1 shows a circuit with a resistance of R ohms that is connected across the terminal of an AC supply. R IR VR Figure 1.1: Circuit diagram with resistance only 2 ECDE4.indb 2 Module 1: RC circuits 2014/11/13 01:08:43 PM VR As you know, VR + Note Ohm’s law states that the The two phasors are drawn slightly apart so that they can magnitude of a IR be distinguished from each current is directly IR other. proportional to 0 t the magnitude of the voltage and inversely proportional to – the value of the Figure 1.2: Voltage and current waveforms resistance. This IR also applies to the instantaneous values of current and voltage in an AC circuit. At any instant when the voltage is zero, the current is also zero. When the voltage is at its maximum, the current is also VR at its maximum since the resistance is constant. Figure 1.3: Phasor diagram for a resistive circuit See Figure 1.2. In a purely resistive AC circuit, the current (IR) and the applied voltage (VR) are in phase. Phase is used to indicate the time relationship between alternating voltage and current. The phasors representing the voltage and current in a resistive circuit are shown in the phasor diagram in Figure 1.3. A leading waveform is defined as a waveform that is ahead of the other waveform. A lagging waveform is a waveform that is behind the other waveform. In Figure 1.4 the phase shift is 90°. Waveform A leads waveform B and waveform B lags waveform A. Capacitance only Waveform and phasor diagram C Figure 1.5 shows a circuit consisting of a capacitor with capacitance C connected across an AC supply. In a purely capacitive AC circuit, the current (IC) leads the supply voltage (VC) by 90º. See Figure 1.6. The phasor diagram for a purely capacitive circuit is shown in Figure 1.7. In a purely capacitive circuit containing a capacitor, the opposition to the flow of alternating current is called the capacitive reactance (XC) and is measured in ohms: XC = 1 2πfC IC VC Figure 1.5: Circuit diagram with capacitance only Capacitive reactance VC + Did you know? Figure 1.4: Waveform A leads waveform B and waveform B lags waveform A VC Note IC IC 0 t The voltage-current phase relationship in a capacitive circuit is the opposite of that in an inductive circuit. – Figure 1.6: Voltage and current waveforms for a purely capacitive circuit Module 1: RC circuits ECDE4.indb 3 3 2014/11/13 01:08:43 PM where: XC = capacitive reactance in ohms (Ω) f = frequency of the supply in hertz (Hz) C = capacitance in farads (F) IC and VC = IC × XC XC (Ω) where: VC = voltage across the capacitor in volts (V) IC = current through capacitor in amperes (A) The capacitive reactance is inversely proportional to the frequency. See Figure 1.9. The current produced by a given voltage is proportional to the frequency. VC Figure 1.7: Phasor diagram for a purely capacitive circuit 0 f (Hz) Figure 1.9: Graph of capacitive reactance (XC) against frequency (f) Did you know? Example 1.1 A 10 μF capacitor is connected across a 240 V, 50 Hz supply. Calculate the current flowing through the capacitor. Figure 1.8 shows a Leyden jar which is a device that ‘stores’ static electricity between two electrodes on the inside and outside of a glass jar. It was the original form of the capacitor. Given: C = 10 μF; VC = 240 V; f = 50 Hz Solution XC = 1 2πfC = 1 2π × 50 × 10 × 10–6 = 318,31 Ω XC = VC IC = 240 318,31 Figure 1.8: The Leyden jar = 0,754 A C R I VC VR RC series circuit Figure 1.10 shows an RC series circuit consisting of resistance (R) and capacitance (C). The combination is connected across a supply voltage (V) volts with a frequency of (f) hertz. I represents the current flowing through the circuit. The current is the same in all parts of the circuit. V Figure 1.10: RC series circuit 4 ECDE4.indb 4 Module 1: RC circuits 2014/11/13 01:08:44 PM Phasor diagram for RC series circuit The phasor diagram is shown in Figure 1.12. The current (I) leads the supply voltage (V) by an angle between 0º and 90º. Add the voltages using a voltage triangle as shown in Figure 1.13. Using Pythagoras’ theorem: V2 = VR2 + VC2 Therefore: V = VR2 + VC2 VR VR I VR = IR ɸ ɸ V V = IZ Figure 1.12: Phasor diagram of an RC series circuit Capacitors are used with resistors in timing circuits. They are also used to smooth varying DC supplies and in filter circuits because capacitors pass AC signals easily but block DC signals. Figure 1.11 shows some electrolytic capacitors. VC Figure 1.11: Electrolytic capacitors V VC Did you know? VC = IXC Figure 1.13: Voltage triangle Impedance in an RC series circuit The total opposition to the current flow in any AC circuit is called impedance (Z). Both resistance and reactance in an AC circuit oppose current flow. The impedance (Z) of an AC circuit is derived using the impedance triangle as shown in Figure 1.14. In an AC circuit, the impedance (Z) is the ratio of the supply voltage to the current: Z =V I As can be seen from Figure 1.14: Z2 = R2 + XC2 R R ɸ XC Z Z CC Figure 1.14: The impedance triangle Therefore: if Z = R2 + XC2 then tan ø = XC X , sin ø = C and cos ø = R R Z Z Relationship between current and voltage in an RC series circuit As you already know: • In a purely resistive AC circuit, the current (IR) and the applied voltage (VR) are in phase. • In a purely capacitive AC circuit, the current (IC) leads the supply voltage (VC) by 90º. • When there is a combination of resistance and capacitive reactance in an AC series circuit, the current (I) leads the supply voltage (V) by an angle between 0º and 90º depending on the values of resistance and capacitive reactance. Did you know? Early capacitors were also known as condensers, a term that is still occasionally used today. Alessandro Volta first used the term for this purpose in 1782 with reference to the device’s ability to store a higher density of electric charge than a normal isolated conductor. Module 1: RC circuits ECDE4.indb 5 5 2014/11/13 01:08:44 PM Example 1.2 A resistor of 10 Ω is connected in series with a capacitor of 45 μF. The supply voltage is 240 V, 50 Hz. Calculate: 1. The capacitive reactance. 2. The impedance. 3. The current flowing through the circuit. 4. The phase angle. 5. The voltage across the resistor. 6. The voltage across the capacitor. Given: R = 10 Ω; C = 45 μF = 45 × 10–6 F; V = 240 V; f = 50 Hz Solution 1. Capacitive reactance XC XC = 1 2πfC = 1 2π × 50 × 45 × 10–6 = 70,736 Ω 2. Impedance Z Z = R2 + XC2 Z = 102 + 70,7362 = 71,439 Ω 3. Current I V I = Z = 240 71,439 = 3,360 A 4. Phase angle ø X tan ø = C R 70,736 tan ø = 10 ø = tan–1 7,074 ø = 81,953° (leading) 5. 6. 6 T1Mod1.indd 6 Voltage across resistor VR VR = I × R = 3,360 × 10 = 33,600 V Voltage across capacitor VC VC = I × XC = 3,360 × 70,736 = 237,673 V Module 1: RC circuits 2014/11/17 01:23:15 PM Assessment activity 1.1 Work in groups of five. 1. Copy and complete the following sentences with the missing words: 1.1 In a purely resistive AC circuit, the current (IR) and the applied voltage (VR) are in _____. 1.2 In a purely capacitive AC circuit, the current (IC) _____ the supply voltage (VC) by 90º. 1.3 When there is a combination of resistance and capacitive reactance in an AC series circuit, the current (I) _____ the supply voltage (V) by an angle between 0º and _____º depending on the values of resistance and capacitive reactance. 2. A resistor of 10 Ω is connected in series with a capacitor of 350 μF. The supply voltage is 230 V, 50 Hz. Calculate: 2.1 The capacitive reactance. 2.2 The impedance. 2.3 The current flowing through the circuit. 2.4 The phase angle. 2.5 The voltage across the resistor. 2.6 The voltage across the capacitor. Frequency selectivity characteristic of an RC series circuit (low- and high-pass circuits) Frequency selectivity is the ability of a circuit to select a specific frequency and reject all other frequencies. The two types of frequency selectivity characteristics of an RC series circuit are the low-pass filter and the highpass filter. Low-pass filter Figure 1.15 shows a low-pass filter with the output across the capacitor. The capacitive reactance (XC) decreases as the frequency increases. Therefore, the output voltage is less than the input voltage. Figure 1.16 shows the frequency response curve. This is a graph showing the magnitude of the output voltage of the filter as a function of the frequency. It is generally used to characterise the range of frequencies in which the filter is designed to operate. Words & Terms frequency selectiv ity: the ability of a circuit to select a specific frequency and reject all other frequencie s R C Vout Vin Figure 1.15: A low-pass filter frequency respon se curve: a graph showing th e magnitude of the output volta ge of the filter as a function of the frequency; genera lly used to characterise th e range of frequencies in wh ich the filter is designed to opera te output voltage frequency Figure 1.16: Frequency response curve for a low-pass RC circuit Module 1: RC circuits ECDE4.indb 7 7 2014/11/13 01:08:44 PM High-pass filter C Figure 1.17 shows a high-pass filter with the output across the resistor. The capacitive reactance (XC) decreases as the frequency increases. Therefore, the magnitude of the output voltage increases. The output voltage is greater at higher frequencies but is reduced as the frequency decreases. Figure 1.18 shows the frequency response curve. Vin cut-off frequency (f ): the frequency at which c the capacitive reactanc e equals the resistance in a low-pass or high-pass RC cir cuit bandwidth (BW): the range of frequencies that pass from the input to the ou tput of a circuit The cut-off frequency (fc) is the frequency at which the capacitive reactance equals the resistance in a low-pass or high-pass RC circuit. It is calculated as follows: R = 1 2πfcC fc = 1 2πRC At fc , the output voltage of the RC circuit is 70,7 % or 1 2 of its maximum value. The bandwidth (BW) is the range of frequencies that pass from the input to the output of a circuit. See Figure 1.19. Vout Figure 1.17: A high-pass filter Cut-off frequency and bandwidth of an RC circuit Words & Terms R output voltage frequency Figure 1.18: Frequency response curve for a high-pass RC circuit output voltage 70,7% of Vmax bandwidth fc frequency Figure 1.19: Cut-off frequency and bandwidth Example 1.3 Calculate the cut-off frequency for the circuit shown in Figure 1.20. R 10 kΩ C 15,9 nF Vin Vout Figure 1.20: A low-pass filter circuit Given: R = 10 kΩ; C = 15,9 nF 8 ECDE4.indb 8 Module 1: RC circuits 2014/11/13 01:08:45 PM Solution fc = 1 2πRC = 1 2π × 10 × 103 × 15,9 × 10–9 ≈ 1 kHz Example 1.4 Figure 1.21 shows a typical response curve for a low-pass RC circuit. Determine the bandwidth of the low-pass RC circuit. output voltage (V) 4,5 4 3,6 3,18 3 2 1 1 2 frequency (kHz) 10 20 40 5 560 Figure 1.21: Typical response curve for a low-pass RC circuit Solution 70,7% of 4,5 V = 3,18 V. On Figure 1.21, 3,18 V represents a bandwidth of 20 kHz. In the workplace RC circuits are used with operational amplifiers to create active electrical noise filters which are more effective than passive RC circuits. This is because passive RC filters always have a signal output which is lower than the input. Effects of faulty components on RC series circuits The following are the effects of faulty components on RC series circuits: • Open resistor: An open resistor results in no current flow. Therefore, the voltage across the capacitor is 0 V and the total input voltage will appear across the open resistor. • Open capacitor: An open capacitor results in no current flow. Therefore, the voltage across the resistor is 0 V and the total input voltage will appear across the open capacitor. Module 1: RC circuits ECDE4.indb 9 9 2014/11/13 01:08:45 PM • Shorted capacitor: A shorted capacitor results in no current flow. Therefore, the voltage across the capacitor is 0 V and the total input voltage will appear across the resistor. • Leaky capacitor: A leaky capacitor will affect the response of the circuit. Assessment activity 1.2 Work in pairs. 1. A resistor of 20 Ω is connected in series with a capacitor of 20 μF. If the voltage across both components is 230 V AC: 1.1 Calculate the impedance and phase angle for each of the following frequencies: a) 1 kHz. b) 10 kHz. c) 20 kHz. d) 40 kHz. 1.2 From the above calculations, what is your conclusion with respect to the impedance and phase angle when the frequency increases? Assessment activity 1.3 Work in pairs. Task 1 RC series circuit Your lecturer will supply you with the necessary components and equipment to perform the following experiment. What to do 1. Connect the components R and C as shown in the circuit diagram in Figure 1.22. 2. Adjust the power supply. 3. Take the readings for the voltages for VR, VC and VS. 4. Note the reading of the ammeter A1. 5. Repeat Step 3 by varying VR VC the supply voltage (VS) and record the readings in an observation table R C like the one below. A1 VS Figure 1.22: Series circuit Component Component rating Resistor Capacitor 10 ECDE4.indb 10 Module 1: RC circuits 2014/11/13 01:08:45 PM Observation table VS VR VC Ammeter reading A1 Circuit impedance Circuit resistance Task 2 RC series circuit Your lecturer will supply you with the necessary components and equipment to perform the following experiment using the same circuit as shown in Figure 1.22. Component Component rating Resistor Capacitor What to do 1. Connect the components R and C as shown in the circuit diagram in Figure 1.22. 2. Adjust the power supply. 3. Take the readings for VR, VC and A1. 4. Disconnect the resistor R in the circuit to simulate an open circuit as shown in Figure 1.23. 5. Take the readings for VR, VC and A1. 6. Reconnect the resistor R in the circuit and disconnect C in the circuit to simulate an open circuit as shown in Figure 1.24. 7. Take the readings for VR, VC and A1. 8. With the capacitor disconnected, short out the terminals as shown in Figure 1.25 to simulate a short circuit. 9. Take the readings for VR and A1. VR VC C VS A1 Figure 1.23: Resistor R disconnected VR VC R A1 VS Figure 1.24: Capacitor C disconnected VR R short VS A1 Figure 1.25: Shorting out the capacitor to simulate a short circuit Module 1: RC circuits ECDE4.indb 11 11 2014/11/13 01:08:45 PM Unit 1.2: RC parallel circuits There is one major difference between a series circuit and a parallel circuit: current is the same in all parts of a series circuit while voltage is the same across all branches of a parallel circuit. Therefore, in parallel AC circuits, the voltage vector is the reference vector. RC parallel circuit IR Figure 1.26 shows a resistor (R) and a capacitor (C) connected in parallel across an AC supply voltage (V). R C IC Phasor diagram for RC parallel circuit I V Figure 1.26: Parallel RC circuit IC As can be seen from the circuit, the current (IR) flowing through the resistor is in phase with the supply voltage (V) and the current (IC) flowing in the capacitor leads the supply voltage by 90º. Figure 1.27 shows the phasor diagram. From the phasor diagram it can be seen that I I = IR2 + IC2 Current through resistor IR = V R Current through capacitor IC = ø V IR Figure 1.27: Phasor diagram The phase angle is: I tan ø = C IR I sin ø = C I IR cos ø = I V XC Impedance in an RC parallel circuit The impedance of the circuit is given by Z = V I Example 1.5 A capacitor of 50 μF is connected in parallel with a 40 Ω resistor across a 223 V, 50 Hz supply. Calculate: 1. The current in each branch. 2. The supply current. 3. The phase angle. 4. The circuit impedance. Given: C = 50 μF; R = 40 Ω; V = 223 V; f = 50 Hz Solution 1. Current through resistor IR V IR = R = 223 40 = 5,575 A 12 ECDE4.indb 12 Module 1: RC circuits 2014/11/13 01:08:45 PM Current through capacitor IC V IC = XC V = ½πfC = 2πfCV = 2 × π × 50 × 50 × 10–6 × 223 = 3,503 A 2. Supply current I I = IR2 + IC2 = (5,575)2 + (3,503)2 Did you know? When the power factor of a parallel AC circuit is unity, in other words when the voltage and total current are in phase at a particular frequency, then the parallel circuit is said to be at resonance. = 31,081 + 12,271 = 43,352 = 6,584 A 3. Phase angle ø I tan ø = C IR I ø = tan–1 C IR ø = tan–1 3,503 5,575 ø = tan–1 0,628 = 32,143° (leading) 4. Impedance Z V Z = I = 223 6,584 = 33,870 Ω Assessment activity 1.4 Work on your own. 1. A capacitor of 25 μF is connected in parallel with a 40 Ω resistor across a 12 V AC supply. 1.1 Calculate the impedance and phase angle when the frequency is set to: a) 20 Hz. b) 50 Hz. c) 1 kHz. 1.2 From the above calculations, what is your conclusion with respect to the impedance and phase angle when the frequency increases? Module 1: RC circuits ECDE4.indb 13 13 2014/11/13 01:08:45 PM Effects of faulty components on an RC parallel circuit The following are the effects of faulty components on an RC parallel circuit: • Open resistor: An open resistor results in no current flow through the resistor, but the supply current will flow through the capacitor. Total input voltage will appear across the open resistor and capacitor as they are in parallel. • Open capacitor: An open capacitor results in no current flow through the capacitor, but the supply current will flow through the resistor. The total input voltage will appear across the open capacitor and resistor as they are connected in parallel. • Shorted capacitor: A shorted capacitor will cause current to flow through the capacitor and can cause circuit damage. • Leaky capacitor: A leaky capacitor will affect the response of the circuit. Assessment activity 1.5 Work in pairs. Task 1 RC parallel circuit Your lecturer will supply you with the necessary components and equipment to perform the following experiment. What to do 1. Connect the components R and C as shown in the circuit diagram in Figure 1.28. 2. Adjust the power supply. 3. Take the readings for VR, VC and VS. 4. Note the readings of ammeters A1, A2 and A3. 5. Repeat Step 3 by varying the supply voltage and record the readings in an observation table like the one below. A1 A3 A2 VS VR R C VC Figure 1.28: RC parallel circuit Component Component rating Resistor Capacitor Observation table VS 14 ECDE4.indb 14 VR VC Ammeter readings A1, A2 and A3 Circuit impedance Circuit resistance Module 1: RC circuits 2014/11/13 01:08:46 PM Summary • In a purely resistive AC circuit, the current (IR) and the applied voltage (VR) are in phase. • In a purely capacitive AC circuit, the current (IC) leads the supply voltage (VC) by 90º. • In a purely capacitive circuit containing a capacitor, the opposition to the flow of alternating current is called the capacitive reactance (XC) and is measured in ohms. • The total opposition to the current flow in any AC circuit is called impedance (Z). Both resistance and reactance in an AC circuit oppose current flow. The impedance (Z) of an AC circuit is derived using the impedance triangle. • In an RC series circuit the current (I) leads the supply voltage (V) by an angle between 0º and 90º. • In an RC parallel circuit, the current flowing through the resistor (IR) is in phase with the supply voltage (V) and the current flowing in the capacitor (IC) leads the supply voltage by 90º. • Frequency selectivity is the ability of a circuit to select a specific frequency and reject all other frequencies. The two types of frequency selectivity characteristics of an RC series circuit are the low-pass filter and the high-pass filter. • With a low-pass filter, the output is across the capacitor. The capacitive reactance (XC) decreases as frequency increases. Therefore, the output voltage is less than the input voltage. • With a high-pass filter, the output is across the resistor. The capacitive reactance (XC) decreases as frequency increases. Therefore, the magnitude of the output voltage increases. The output voltage is greater at higher frequencies but is reduced as the frequency decreases. • The frequency at which the capacitive reactance equals the resistance in low-pass or high-pass RC circuits is called the cut-off frequency and is designated by (fc = 1 ). 2πRC • The following are the effects of faulty components on RC series circuits: − Open resistor: An open resistor results in no current flow. Therefore, the voltage across the capacitor is 0 V and the total input voltage will appear across the open resistor. − Open capacitor: An open capacitor results in no current flow. Therefore, the voltage across the resistor is 0 V and the total input voltage will appear across the open capacitor. − Shorted capacitor: A shorted capacitor results in no current flow. Therefore, the voltage across the capacitor is 0 V and the total input voltage will appear across the resistor. − Leaky capacitor: A leaky capacitor will affect the response of the circuit. • The following are the effects of faulty components on RC parallel circuits: − Open resistor: An open resistor results in no current flow through the resistor, but the supply current will flow through the capacitor. Total input voltage will appear across the open resistor and capacitor as they are in parallel. − Open capacitor: An open capacitor results in no current flow through the capacitor, but the supply current will flow through the resistor. The total input voltage will appear across the open capacitor and resistor as they are connected in parallel. − Shorted capacitor: A shorted capacitor will cause current to flow through the capacitor and can cause circuit damage. − Leaky capacitor: A leaky capacitor will affect the response of the circuit. Module 1: RC circuits ECDE4.indb 15 15 2014/11/13 01:08:46 PM Summative assessment 1. 2. 3. Are the following statements true or false? 1.1 In a purely resistive AC circuit, the current (IR) and the applied voltage (VR) are in phase. 1.2 In a purely capacitive circuit containing a capacitor, the opposition to the flow of alternating current is called the capacitive reactance (XC) and is measured in farads. 1.3 An RC series circuit consists of resistance (R) and capacitance (C). When the combination is connected across an AC supply voltage (V) volts, I represents the current flowing through the circuit. The current is different in all parts of the circuit. 1.4 Capacitive reactance is inversely proportional to frequency. 1.5 There is one major difference between a series circuit and a parallel circuit: the current is the same in all parts of a series circuit whereas voltage is the same across all branches of a parallel circuit and therefore, the voltage vector is the reference vector. 1.6 If the supply voltage to an RC series circuit is 12 V and if the resistor is open-circuit, then the voltage across the resistor is 0 V. 1.7 If the value of R = 1,2 kΩ and C = 25 µF in an RC series circuit, the cut-off frequency is 10 kHz. 1.8 In a low-pass filter, the capacitive reactance (XC) decreases as frequency increases. Therefore, the output voltage is less than the input voltage. A 25 μF capacitor is connected across a 110 V, 60 Hz supply. Calculate the current flowing through the capacitor. Figure 1.29 shows the response curve for a low-pass filter RC circuit. Determine the bandwidth of the circuit. output voltage 2 1,5 1,414 1 0,5 1 2 10 20 40 38 50 frequency (kHz) Figure 1.29: Response curve for a low-pass RC circuit 4. 5. C 100 μF Study Figure 1.30 and answer the following questions: R 1,2 k Ω 4.1 Calculate: a) The capacitive reactance. b) The phase angle. VR VC 10 V c) The impedance. f 2 kHz 4.2 If the resistor R is open-circuit, what are the readings for VR and VC? 4.3 If the capacitor C is open-circuit, what are the Figure 1.30: RC series circuit readings for VR and VC? A capacitor of 1 μF is connected in parallel with a 100 Ω resistor across a 24 V, 1 kHz supply. Calculate: 5.1 The current in each branch. 5.2 The supply current. 5.3 The phase angle. 5.4 The circuit impedance. 16 ECDE4.indb 16 Module 1: RC circuits 2014/11/13 01:08:46 PM