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    Stem: Science, Technology, Engineering and Maths Principles V11
    Stem: Science, Technology, Engineering and Maths Principles V11
    Stem: Science, Technology, Engineering and Maths Principles V11
    Ebook1,373 pages8 hours

    Stem: Science, Technology, Engineering and Maths Principles V11

    By Clive W. Humphris

    ()

    Read preview

    About this ebook

    An enhanced eBook published in full colour. With EXTENSIVE FREE page and STEM online INTERACTIVE CONTENT enabled with your eBook receipt, explored by inserting any values that could occur in a real situation into hundreds of menu driven topics thereby bringing the topic or any other textbook examples to life.

    Full colour graphics that are redrawn for every input change will make your learning experience more enjoyable and effective as it encourages experimentation of real world situations where almost any practical value is accepted.

    Interactive Technology when used in the classroom can motivate passive students by encouraging their active participation where STEM subjects are ideally suited to mobile interactive technology on their digital devices.

    Students who struggle to be fully engaged in normal classroom activity can often achieve the unexpected once sat in front of a digital screen where they can learn without the embarrassment of full class exposure.

    For each topic group students can TEST THEIR UNDERSTANDING by considering an open question whereby their ease of answering will provide an indication of personal progress.

    LanguageEnglish
    PublisherClive W. Humphris
    Release dateJun 18, 2014
    ISBN9781311626264
    Stem: Science, Technology, Engineering and Maths Principles V11
    Author

    Clive W. Humphris

    Clive W. Humphris M0DXJ: Ex Technology Teacher. Software Developer, Author and Director of eptsoft limited. Married with two children and four grandchildren.Apprentice Instrument Maker at Marconi’s with Senor Technical Management roles in Radio Rentals and Alcatel Business Systems before starting eptsoft providing educational software to schools colleges and universities worldwide since 1992.Interests outside of developing digital products for eptsoft, include Running, Walking and Reading.

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      Book preview

      Stem - Clive W. Humphris

      STEMPrinciples600

      Table of Contents

      Introduction

      Basic Electronics

      Conductor and Insulator

      Resistor Value Test

      Simple Dc Circuits

      Types of Switching

      Variable Voltages

      Ohm's Law

      DC Voltage

      DC Current

      Series and Parallel Resistors

      AC Measurement.

      AC Voltage and Current

      AC Theory.

      RCL Series

      RCL Parallel

      Capacitance

      Capacitors

      Inductance

      Inductors

      Impedance

      Radio and Communication

      Tuned Circuits

      Attenuators

      Passive Filters

      Active Filters

      Oscillators

      Circuit Theorems

      Complex Numbers

      DC Power

      AC Power

      Silicon Controlled Rectifier

      Power Supply

      Voltage Regulation

      Magnetism

      Electrical Machines

      Transformers

      Three Phase Systems

      Energy Transfer and Cost

      Atomic Structures

      Diode Theory

      Diode Applications

      Transistor Theory

      Bipolar Transistors

      Transistor Configurations

      Active Transistor Circuits

      Field Effect Transistors

      Basic Operational Amplifier

      Op-Amp Theory

      Op-Amp Applications

      Sum and Difference Amplifiers

      Analogue Multi-Meter

      Measurement

      Component Testing

      PIC Introduction

      PIC Architecture

      PIC A to D

      Pic Byte Instructions

      Pic Bit Instructions

      Pic Literal Instructions

      Area

      Surface Area and Symmetry

      Volume

      Compound Measures

      Geometry

      Motion

      Machines

      Optics

      Computer Hardware

      Data Structures

      Data Files

      Computer Systems

      Data Handling

      System Development

      Computer Coding

      Data Analysis

      Binary Numbers

      Binary Arithmetic

      Logic Gates 1

      Logic Gates 2

      Logic Families

      Flop Flops

      Combinational Logic

      Counters

      Counting

      Shift Registers

      Timers

      Logic Interfacing

      Boolean Algebra

      Micro-Computers

      Data Address Bus

      Memory Addressing

      Arithmetic and Logic Unit

      Microprocessor Timing

      Instructions and Control

      Memory Cells

      Microprocessor Memory

      Addressing Modes

      Instruction Set 1

      Instruction Set 2

      Instruction Set 3

      Number Systems

      Number Conversion

      Number Types

      Roots

      Angles and Parallels

      Triangle Ratios

      Triangle Angles

      Percentages

      Ratios

      Fractions

      Vectors

      Circle Angles

      Laws

      Algebra 0

      Algebra 1

      Algebra 2

      Mathematical Rules

      Powers and Indices

      Simplifying

      Linear Equations

      Graphing

      Slope and Translation

      Curves and Angle Conversion

      7 40 2012-02-27T15:21:00Z 2012-04-07T12:28:00Z 2 280 1600 eptsoft 13 3 1964 9.3821 Normal 1

      STEM: Science, Technology, Engineering and Maths Principles V11

      by Clive W. Humphris

      Portable Learning, Reference and Revision Tools.

      Copyright by eptsoft limited 2018

      All rights reserved.

      Acknowledgement.

      Our thanks and appreciation goes to John D. Ransley MIEE from Whitbourne in Worcestershire for all his help and expert guidance in developing this software title.

      Introduction.

      A combined eBook title containing all eptsoft STEM topics available in one place. 

      First published in 1992 has been used extensively in schools & colleges worldwide and continually updated.

      Now available as a mobile reference containing colourful images and calculations for over nine-hundred topics is ideally suited to tablet or phone digital devices.

      Topic groups are selected from an extensive Table of Contents.

      Technical descriptions are written in note form thereby avoiding large amounts of text and wherever possible images include additional notes highlighting relevant points.

      All images are drawn using program code which insures the size and shape displayed reflects the actual default values for that topic i.e. angles and lengths.  Program code enables us to utilise all available screen colours making diagrams attractive and easy to understand.

      Values shown in calculations are produced by running the calculations in code from the default values before displaying.

      Enhanced eBooks: Here calculations can be also tested against any standard subject textbook to compare the results.

      Interactive Technology when used in the classroom can motivate passive students by encouraging their active participation where STEM subjects are ideally suited to Mobile Interactive Technology.

      Students are more likely to be comfortable with technology they understand i.e. their phone and can interact with, often preferring 'Learning-by-Doing' over traditional pencil and paper methods.

      Full colour graphics that are redrawn for every input change will make the learning experience more enjoyable and effective as it encourages experimentation of real world situations as almost any practical values are accepted.

      Students who struggle to be fully engaged in normal classroom activity can often achieve the unexpected once sat in front of a digital screen where they can learn without the embarrassment of full class exposure.

      Mobile Interactive Technology can bring any STEM textbook to life by inserting printed values from the book into their mobile device and comparing the results.

      Colourful visual presentation assists the learning process as students will more likely remember, thereby increasing their personal confidence as they believe they are learning more as a result. Knowing the content is on their phone encourages them to dip-in in a spare moment more than open a traditional textbook.

      Conclusion: Students will spend more time engaged with the Mobile Interactive Technology than with a traditional textbook.

      For each topic group students can TEST THEIR UNDERSTANDING by considering an open question whereby their ease of answering will provide an indication of personal progress.

      BASIC ELECTRONICS: Finding Circuit Voltages.

      Interactive Content!

      When calculating a voltage, in this case a DC we are determining the potential difference (PD) developed across an electrical device due to the current flowing through it. This will be explained further when we come to explore Ohm's Law. In this instance we are finding the voltages developed across the resistor and the lamp.

      The components shown are in what is called a series circuit, the resistor is in series with the lamp as the electron current flow is through one followed by the other. Remove either the resistor or the lamp and the circuit ceases to function, what's known as an open-circuit.

      This simple circuit provides the opportunity to introduce some electronics mathematics which for the moment its sufficient to say that if we want to find how much current is being drawn from the battery when the lamp is lit, we can calculate it. Found by dividing the sum of the voltages across the resistor and lamp by the total circuit resistance. When the individual potential differences are added they will always equal the supply potential of the battery. This is known as Kirchhoff's Voltage Law.

      Note: the polarity of the voltage. This is important when it comes to connecting your Voltage Test Meter where the black lead is applied to the more negative part of the circuit and the red lead to the more positive.

      BASIC ELECTRONICS: Measuring Voltage and Current.

      The electric current which flows through a circuit is a measure of the rate of flow of electric charge (electron movement) past any given point.

      An ammeter is used to measure current flow, but before we can do this, it is first necessary to insert the meter into the current path within the circuit. Note voltages appear across electrical devices (shown by the voltmeter connections) which posses resistance, whereas current flows through them.

      The current can also be calculated using the formula for Ohm's Law. The ammeter can be placed at any point in the circuit and will always give the same current reading, which is determined by the battery potential voltage divided by the resistor value added to the lamp resistance or the total circuit resistance.

      As the value of R1 is increased then the current is limited around the circuit and in a practical situation the lamp would glow less brightly. As the resistance of the lamp is fixed the voltage developed across the filament will also fall in direct proportion to the current I.

      BASIC ELECTRONICS: Variable Resistance.

      A variable resistor (known as a potentiometer) is a fixed value resistor onto which a slider is attached to tap off the resistance at any given point across a carbon track. VR1 is connected to form a potential divider circuit, the output voltage depending upon the slider position. Move the slider towards point [a] and the output voltage increases, towards [c] and it decreases. Is there a linear relationship between voltage output and slider position i.e. do you get half the voltage output at the control mid point?

      The answer should be yes, but only because the output is open circuit. As soon as a load resistance is connected across the output this smooth linear voltage variation from one end of the control to the other will be upset and will be explained when we come to voltage dividers.

      Variable resistors are commonly found in modern audio amplifiers where the variable DC voltage is used to adjust the level of volume, bass and treble within an integrated circuit amplifier using a DC controlled attenuator. Variable resistors can also be found in AC circuits where the signal attenuation can be adjusted from maximum to zero by varying the slider position.

      There are two types of potentiometer, linear, where the resistance across the track increases evenly from one end to the other and logarithmic where there is a greater change of resistance to angle of rotation at one end than the other. The latter are less common now, but can upset measurements if the wrong type is used. Where higher currents are involved potentiometers are available with a wire wound track and printed circuit boards demand sub-miniature horizontal and vertical mounting types. Finally for greater precision multiple turn resistors should be used.

      BASIC ELECTRONICS: Adding Positive Values.

      When the numbers to be added are all positive the total will be the cumulative addition of each new value.

      An example is when adding resistor values in series, as each resistor is connected the total resistance becomes larger.

      Voltages and currents, as we shall see later, can only be added directly when they have the same phase angle or direction.

      BASIC ELECTRONICS: Adding Negative Values.

      A negative current is simply a way of mathematically defining a current flowing in the opposite direction to a positive one.

      When -I1, -I2 and -I3 are added together at point X to become -I total.

      Normally its good practice to include brackets ( ) around a negative number. It avoids confusion of + and - operators appearing next to one another.

      It's useful to remember that a minus added to a minus is just a bigger minus.

      BASIC ELECTRONICS: Adding Signed Values.

      Positive and negative voltages developed across a circuit will cancel each other when added together, the resultant or total taking the sign of the greater quantity. Voltages and currents normally represent peak or RMS values or any other instantaneous measurement, any can be used so long as the same method is applied throughout.

      Adding positive and negative numbers is common in AC circuits, the (+) and (-) signs indicating voltages or currents in phase opposition.

      During the first half of the waveform the resultant will be in one phase, then reversed during the following half cycle.

      BASIC ELECTRONICS: Algebraic Addition of Currents.

      Currents can be made to flow in both directions through a conductor, or as in this example a resistor.

      Some electrons moving from left to right will be cancelled out by those moving right to left, the sign just represents one or other direction.

      The resultant current being I1 - I2 or I2 - I1. This is the same as adding a positive current (flowing in one direction) to a negative current (in the opposite direction).

      You will note the sign is not included for the final result as the answer just represents an amount of current flowing in the circuit, the direction is usually unimportant for further calculations and could complicate the result of say, Ohm's Law by showing a negative voltage.

      BASIC ELECTRONICS: Subtracting Signed Voltages.

      As an example of subtracting a negative value from a positive.

      Consider a series resistor network, which measures 20V at one end and -11V at the other. What is the potential difference between the two ends?

      The rule for subtracting a negative value from a positive is, change the sign of the negative (-n2) and add.

      When calculating the voltage or potential difference, ignore the sign of the final answer.

      BASIC ELECTRONICS: Subtracting Negative Currents.

      Calculations in electronics often involve negative numbers.

      Remember that a negative value is usually a current or voltage with the opposite phase to that of a similar amount or value which is positive.

      This calculation can be made easier by changing the sign of n2 and adding.

      4 3 2012-01-09T14:39:00Z 2012-03-28T15:02:00Z 2 884 5043 eptsoft 42 10 6193 9.3821

      CONDUCTOR AND INSULATOR: Conductor.

      Interactive Content!

      For an electric current to flow there has to be a source of electrons, i.e. a battery. Closing the switch completes the circuit. This electron flow causes the lamp to light. If the switch is opened the electron movement ceases and the lamp is therefore turned off.

      Electrons are released from the negative battery terminal (-), and attracted by the positive terminal (+) through the circuit. The amount of electron movement being limited by the resistance of the lamp, the filament of which is made of tungsten. Filament resistance causes more work (power) in moving the electrons and heat is generated, up to as much as 1000°C which is white hot and emits visible light.

      The direction of current flow can be considered in two ways, either as conventional current when the flow is from positive (+) to negative (-) or as electron flow, where electrons are released from the negative battery terminal and attracted by positive terminal.

      Both are valid. In simple DC circuits conventional current is appropriate. However, to explain the operation of a semiconductor, which is a transistor or diode, then electron flow must be considered as we are then primarily interested in the combination of negative electrons and positive holes.

      4 3 2012-01-09T14:39:00Z 2012-03-28T15:02:00Z 2 884 5043 eptsoft 42 10 6193 9.3821

      CONDUCTOR AND INSULATOR: Insulator.

      An insulator placed within the conducting path will prevent current flow, the electric current cannot pass through the insulating material as there are no free electrons to enable current to flow.

      The air space between the open contacts of a switch is a typical insulator. Insulating materials are chosen because they have very few free electrons with which to form an electron flow. Closing the switch in this instance therefore has no effect.

      Within any material there is always some electron movement (even insulators) this can be caused by external events, heat for example, especially in good conductors such as copper which have very loosely coupled electrons in their outer shell and easily dislodged.

      Relative to normal current flow this activity is minute and as the electron movement is random in all directions it cancels out. However, remove the insulator and close the switch and these random electrons are pulled towards the positive potential of the battery. Contributing to current flow as others are released. The negative terminal of the battery provides a supply of electrons to balance those attracted away by the positive potential.

      4 3 2012-01-09T14:39:00Z 2012-03-28T15:02:00Z 2 884 5043 eptsoft 42 10 6193 9.3821

      CONDUCTOR AND INSULATOR: Measuring an Electric Current.

      The amount of current flowing in a circuit is dependent upon two factors, the circuit resistance R and the applied voltage or electromotive force (EMF). EMF is electrical force and is required to move electrons (current flow) in a conductor.

      Electrons don't actually travel around a conducting path. Each is pulled away from its parent atom by the attraction of a positively charged atom (+ION) close by. This in turn leaves a positive charge behind to attract an electron from an adjacent neutral atom further down the line; the effect is the negatively charged stream of electrons move in the direction of the positive potential. Millions and millions of them in an instant.

      It is important to understand that if the EMF is increased the current or electron movement also increases in direct proportion. Double the voltage and the current doubles. The value of R will remain fixed. We will explore this further with the calculations for Ohm's Law.

      For the moment its sufficient to just have an appreciation for what is happening within a simple electric circuit. It's this intuitive feel for what is actually going on which helps in the understanding of circuits, you get to know what to expect in any given situation, which only comes from spending time playing with electronics. Remember you can't see voltage and current only the effect of it, but you can feel it!

      4 3 2012-01-09T14:39:00Z 2012-03-28T15:02:00Z 2 884 5043 eptsoft 42 10 6193 9.3821

      CONDUCTOR AND INSULATOR: Conductor Resistance.

      This topic is simply a voltage supply, feeding a reel of cable with a load resistance connected to the end. However, all conductors contain resistance and for long lengths of cable carrying large currents this can result in a significant loss of voltage across the load. This difference between the supply voltage and the load voltage is called a 'voltage drop'. Voltage starvation across an electric motor can cause it to run slow, or lamps will be dimmed, or heating becomes inefficient.

      When calculating the volts drop on a length of cable, it should be remembered that it consists of two parallel conductors and so the cable resistance-per-metre must be doubled for the length of cable on the drum. Cable should always be unwound from the drum before use, as it acts as a large inductor and can cause the core to melt due to the heat generated by stray eddy currents.

      The equivalent circuit shows the cable and load resistances as a series resistive circuit where the calculations are for a voltage divider, these will all be investigated later and you can come back to them.

      Inadequate cable diameters for a given load will also cause the cable to run hot, eventually resulting in failure. This is the exact principle of a fuse. Fortunately there is a solution to voltage drop. Just use a thicker cable, where the resistance-per-meter will be less for your particular load requirements.

      RESISTOR VALUE TEST: Select Random Value.

      Interactive Content!

      Resistor values can be determined using the Resistor Colour Code. For the 4-band type, the first two bands are numerical values the third is the multiplier or number of noughts.

      For example 3.9kOhms = orange(3), white(9), red(2) = 3900ohms or 3.9kOhms. For values below 10ohms the third band is coloured gold which is a multiplier of 0.1. The fourth band indicates tolerance.

      Resistor values are also available as 5-band types. You can select a routine to determine the value of both types Resistor Colour Codes in the Toolbox menu along with another selection for Preferred Resistor Values. Resistors are available in a number of ranges, the most common being the E12(10%) and E24(5%) series, the latter having a closer tolerance, therefore more values are required to ensure every likely value is covered.

      The Toolbox also contains a routine for finding preferred types. Calculations will often produce odd resistor values and in some cases very close tolerance high stability types may be required. For this purpose the E48(2%), E96(1%) and E192(0.5%) ranges are available, obviously this closer precision is reflected in their cost.

      SIMPLE DC CIRCUITS: Three Resistors in Series.

      Interactive Content!

      In a practical circuit consisting of just three resistors, connected in series across a battery, four circuit parameters can be measured using a simple multi-meter. Firstly the current I flowing which is determined by inserting an ammeter in series with the resistors and then the three voltage drops across the individual resistors.

      The current is a result of the applied voltage divided by the total series circuit resistance. Apply the formula for series resistance to determine the total resistance R.

      Individual resistor voltage drops are each found by applying Ohm's Law. Resistance R1, R2 or R3 multiplied by the series circuit current. Adding the individual voltage drops together will always equal the applied battery voltage.

      SIMPLE DC CIRCUITS: Two Parallel Resistors.

      Shown are three components connected together forming a circuit. A battery or source of electric current and two resistors. From this diagram a number of circuit parameters may be found. Some are known others need to be calculated.

      Considering the current as being 'conventional' where it flows from the battery positive terminal and divides into two branches. The amount of current in each branch will be inversely proportional to the resistor value, i.e. the larger resistor value the less current flows.

      Firstly we need to find the total current I, but before we can do this we require the equivalent circuit resistance from the formula. We know the applied battery voltage. However each individual branch current could just as easily be calculated by applying Ohm's Law and the two current values added together which will equal I. Current is never lost (Kirchhoff's Law) the sum of individual currents will always equal the total current.

      As you can see there are several ways of solving this problem. If you were given the total current and the resistor values, could you have found the battery voltage?

      SIMPLE DC CIRCUITS: Potential Divider.

      A simple potential divider is just two resistors connected in series across a battery. So long as we don't have large variations in load current the voltage at the resistor junction will be remain fixed.

      The voltage dropped across the lower resistor provides the output voltage, determined by the relationship between Ra and Rb. The calculations will demonstrate this in more detail. What is the output voltage if the lower resistor is made a quarter of the resistance of the upper value?

      The simple voltage divider circuit is commonly used to make a transistor base biasing network where the base current requirements are small.

      However, there are further considerations when the current requirements increase or are subject to large variations.

      SIMPLE DC CIRCUITS: Loading a Potential Divider.

      Loading the voltage divider connects the resistance of the load in parallel with the lower resistance Rb. We will call this parallel combination Rx. Note the shorthand for resistors in parallel. To determine the total current, first calculate the value of Rx, then divide the battery or supply voltage by the addition of Ra + Rx.

      Load current Iout is simply the resistor junction voltage over the load resistance RL.

      In practice the value of Rb is chosen to be about one tenth of the value of the load. This ensures that any fluctuations in load current have a limited effect on the divided output voltage.

      Experiment with the values of Rb relative to RL and note the changes on the Ra, Rb junction voltage.

      SIMPLE DC CIRCUITS: Pull Up, Down Resistors.

      The use of pull up and pull down resistors is a common feature in electronics. Closing S1 in the left hand diagram pulls down the voltage at the lower end of Ra by shorting it to the zero line. Current flowing in Ra will then depend solely upon the resistor value and the supply voltage.

      In the diagram to the right, the voltage at the top of Rb is pulled up to the supply voltage by closing S2. With equal value resistors will the current flowing be the same in both circuits when the switches are closed?

      S1 and S2 could be replaced by transistors acting as switches which effectively become short circuited between the collector and emitter terminals when made to conduct heavily. Resistor Ra is a collector load and Rb an emitter resistor.

      When a transistor is biased OFF, i.e. no base volts the transistor is open circuit. For T1 the collector voltage would be high, no collector current flowing and for T2 the emitter voltage would be zero, with no emitter current flowing. Biasing ON T1 and its collector output voltage is pulled down and for T2 the emitter voltage is pulled up.

      TYPES OF SWITCHING: Push Switch.

      Interactive Content!

      Switch contacts when open provide an interruption of the current flow within a circuit and when closed completes the conducting path. Shown is one of the simplest of schematic diagrams that consists of just three components, indicated by appropriate symbols. Clearly shown are the component connections and the effect of what happens when the switch button is pushed. One of the simplest types of switch has to be the push-to-make, i.e. for a doorbell, here is a push-to-break.

      Within the pages of a components catalogue you can find dozens of different combinations of switch types. When selecting a switch there are two main considerations, current rating and the maximum working voltage. Using a switch that is under-rated can be unreliable and dangerous because of arcing of the contacts or physically expose the user to an electric shock because of a voltage breakdown of the insulation.

      In this diagram the battery can represent any number of cells connected in series which increase the supply voltage (potential difference) as each cell is added. Battery cells are usually in multiples of 1.5V, and those of the rechargeable type are lower at 1.2V.

      To calculate the current I flowing in this simple circuit we can use Ohm's Law by applying the formula shown. Try changing the battery supply voltage and note the changing current. In a practical circuit the more current that flows the brighter the lamp would glow. Increasing the voltage and thereby the current, above that permitted by the bulb and the filament acts like a fuse.

      TYPES OF SWITCHING: Change-over Switch.

      Switches are available in many different types. Here is an example of a changeover switch that redirects the battery connection to either the lamp or the buzzer. This is a break-before-make switch.

      Others are make-before-break, where power is connected to both parts of the circuit during changeover. Switches are used as relay contacts, rotary selectors, slider contacts etc.

      Here we have given the two devices a different working resistance. This demonstrates that the current drawn from the battery changes as the switch is thrown. As the battery has what is called 'internal resistance' this can cause a reduction in the potential difference PD between the battery terminals as the load resistance increases.

      Electronic buzzers have no moving contacts and therefore do not generate RF interference, but produce a clear penetrating sound. Typical uses are in internal burglar alarm sounders. The output frequency is around 400Hz with impedance of a few hundred ohms, consuming approximately 35mA when a voltage between four to twenty volts is applied.

      TYPES OF SWITCHING: Stair-case Switch.

      The staircase switch arrangement derives its name from its purpose in domestic house wiring, where it is often necessary to be able to switch a single lamp from any number of different places. There are two types of switch used, A and D are normal changeover types. The others B and C are called intermediate switches (of which there can be any number) are crossover types.

      What happens is the intermediate switches changeover the central pair of conductors.

      There is no need for a clever logic diagram to explain or carry out this action, its simply the bulb lights or extinguishes for every switch action. Follow the lamp current path for yourself for all the available switch states.

      TYPES OF SWITCHING: Relay Switch.

      A relay is a device, which is an electrically operated switch. It works by energising an electromagnet that pulls or releases switch contacts that are make (shorted out) or break (open circuit) depending upon whether the relay coil is energised. Close S1 and a current is made to flow in the relay coil. This causes a magnetic field to develop which pulls the central switch contact [b] to the left, making the circuit with [a] for the bulb to light.

      Release S1 and the magnetic field collapses and the contact [b] returns to its rest position, against the right hand contact [c], causing the buzzer to sound. In use a reverse biased diode should be connected across the energising coil for protection as the high back-EMF that is generated when the current is switched off can easily damage any associated circuitry.

      Relays are available in both single-pole and double-pole switch actions. Typical switch contact resistance is measured as 50mOhms (milli-Ohms) with operating times of around a couple of milliseconds. Maximum switching currents can exceed 10Amps, but for most applications, a much smaller and less expensive device would suffice.

      A relay has a mechanical switching operation, not electronic, as is the case of a thyristor semiconductor device. The electromagnetic coil resistance is between 80 and 1kOhms depending on the type when designed for an operating voltage of around 5Volts to 30Volts. The life of the contacts can exceed 100,000 operations but this depends largely on the amount of current being switched and if it is AC or DC as the former tends to maintain cleaner switch contacts due to its uni-polar direction.

      TYPES OF SWITCHING: Three-level Switch.

      Most switches found in component catalogues are fairly standard, where only the method of mounting or presentation differs. However, there will be times when a specialist action is called for. Typical examples are found in electric cookers and washing machines. As the latter can be very complicated we will concentrate on the former to switch the heating elements in an oven or cooker hot plate.

      The example shown consists of three switch positions, plus an ON/OFF, which also forms part of the thermostat. The thermostat will be bi-metal strip, which bends and makes or breaks a pair of switch contacts to complete the circuit depending upon the temperature setting. But it's the switching action, which is of interest here.

      The two elements Re1 and Re2 are resistances which are designed to make use of their dissipated heat which is normally wasted. They could be considered as underrated wire wound types, which become hot due to excessive current owing to their low value. In the 'Low Heat' setting they are connected in series, as their combined resistance increases across the (L) - (N) terminals the current flow and therefore heat dissipated will be relatively low. 'Medium Heat' and just one element is connected and for 'High Heat' both are switched ON, which for purposes of calculations are in connected in parallel.

      Note the supply voltage is AC, but we use the RMS value, because it has the same energy content as an equivalent DC voltage. Select for more details of the calculations. As both Re1 and Re2 are always the same we can use a simplified method of finding the equivalent series and parallel values.

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      VARIABLE VOLTAGES: DC Voltage.

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      DC voltages are constant over time. The voltage range is determined by the battery, which could equally be some form of regulated DC power supply.

      In practice the lamp would glow brighter as the battery voltage is increased, but it will always remain at the same level whilst the voltage is constant.

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      VARIABLE VOLTAGES: Switching a DC Voltage.

      A switch causes the lamp to light when the contacts are closed, by placing a voltage across the bulb filament. Operating the switch makes the lamp to go ON and OFF as the applied voltage is first present and current flows and which then falls to zero as the voltage is removed.

      In a practical circuit the ON-OFF periods would not necessarily be constant as shown here, but would vary with the on-off time.

      The output has what is commonly called a square-wave-form. The ON period is referred to as the mark and the OFF as the space. We will explore this effect later when we look at timing circuits.

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      VARIABLE VOLTAGES: Variable DC Voltage.

      By introducing a variable resistor across our battery, some interesting changes can be observed over time, i.e. the output voltage will vary. The output is changed slowly, not switched, so between slider positions the voltage will be made to increase or decrease gradually.

      You will probably by now see the variable resistor as a voltage divider circuit. The output voltage will depend upon the slider position, which effectively splits the variable resistor track into two quite separate resistor sections. Changing the variable resistor component value will increase or decrease the current drawn from the battery and can be calculated using Ohm's Law.

      Variable resistors can be linear as in this case, when the track has the same relationship between slider position and resistor value or logarithmic, having very small changes in resistance to slider position at one end and very large changes at the other.

      Logarithmic resistors are less common now and were mostly used as volume controls, and now with the introduction of IC's these components have been largely replaced with DC controlled circuits.

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      VARIABLE VOLTAGES: Alternating DC Voltage.

      Again a variable resistor is used to simulate an AC waveform. That is one that goes above and below the zero volt line. The battery potentials provide the maximum and minimum voltage swings.

      Note the polarity of the batteries at their junction and the variable resistor slider, then observe the output voltage. What would be the effect if the batteries had unequal voltages?

      OHM'S LAW: Current.

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      A simple DC circuit consists of a current source (the battery) connected across a resistor. Electrons are propelled by the electromotive force (voltage) of the battery. Expelled from the negative terminal (-) and attracted by the positive (+) terminal.

      Using Ohm's Law the circuit voltage, current or resistance can be found. An easy way of remembering each of the formulae is to draw a triangle as shown. Covering the result variable in the triangle leaves the required formula.

      The graph shows a linear relationship between V, I and R, i.e. an increase in the voltage across the resistor causes a proportional increase in the current through the resistor.

      The plot Window shows an accurate representation for your chosen values.

      OHM'S LAW: Voltage.

      A simple DC circuit consists of a current source (the battery) connected across a resistor. Electrons are propelled by the electromotive force (voltage) of the battery. Expelled from the negative terminal (-) and attracted by the positive (+) terminal.

      Using Ohm's Law the circuit voltage, current or resistance can be found. An easy way of remembering each of the formulae is to draw a triangle as shown. Covering the result variable in the triangle leaves the required formula.

      The graph shows a linear relationship between V, I and R, i.e. an increase in the voltage across the resistor causes a proportional increase in the current through the resistor.

      The plot Window shows an accurate representation for your chosen values.

      OHM'S LAW: Resistance.

      A simple DC circuit consists of a current source (the battery) connected across a resistor. Electrons are propelled by the electromotive force (voltage) of the battery. Expelled from the negative terminal (-) and attracted by the positive (+) terminal.

      Using Ohm's Law the circuit voltage, current or resistance can be found. An easy way of remembering each of the formulae is to draw a triangle as shown. Covering the result variable in the triangle leaves the required formula.

      The graph shows a linear relationship between V, I and R, i.e. an increase in the voltage across the resistor causes a proportional increase in the current through the resistor.

      The plot Window shows an accurate representation for your chosen values.

      OHM'S LAW: Formula Transformation.

      The subject of the equation is the variable we are attempting to find. In the first example its V, and R in the second. Note: that the expression is in algebraic form. Formulae transformations should be made before inserting the final values and not as in the case of the calculations Window where the process is shown using actual values.

      Manipulation of the variables is across the equals sign (shorthand L.H.S left hand side and R.H.S for right hand side) also above and below the division line. Variables with the same sign above and below the line can be cancelled.

      The formulae shown are used in electronics to determine the voltage, current and resistance in a simple DC circuit. By transposing the formula the value of the third variable can always be found, providing the other two are known.

      Practically all electronics formulae are derived from Ohm's Law and so a grasp of these transformation principles is essential to aid your understanding of more complex calculations.

      DC VOLTAGE: Voltage Divider.

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      A simple voltage divider circuit can be constructed as shown, using just two resistors connected across a voltage supply.

      Current I will flow through R1 and R2 determined by their combined value. The lower voltage (Vout) across R2 is found by Ohm's Law I × R2.

      Circuits connected to the Vout junction are referred to as the Load. Load current will flow through R1 in addition to R2 current and effectively pull down the voltage at this junction due to the increased voltage drop across R1.

      DC VOLTAGE: Loading a Voltage Divider.

      A voltage divider produces a fixed voltage reference. If the current drawn from the junction of R1 and R2 is small relative to the current through R1 then the loading effect can be ignored. However, increased loading current can pull down this junction voltage, thereby removing any voltage stabilisation.

      Basically, if the load conditions are fixed by a steady current then the voltage divider is ideal and the circuit voltages can be calculated as shown. Where the load current varies considerably then the use of a series voltage regulator would be a better approach.

      Vout is determined by the ratio of R2 : (R1 + R2). Connecting a load across R2 increases the total current through R1 causing a greater voltage drop across R1, which lowers the junction output voltage.

      To stabilise the output voltage against load current changes, a practical rule of thumb is to choose the values of R1 and R2 in the correct ratio so that the divider current is 10 times greater than the load current.

      DC CURRENT: Current Divider.

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      Connecting resistors in parallel divides the total circuit current into n branches. I equals the sum of the individual branch currents.

      Total circuit current I can also be found using Ohm's Law, by dividing the applied battery voltage by the equivalent circuit resistance.

      Note: there is an inverse relationship between each branch current and that branch resistance.

      DC CURRENT: Further Current Dividing.

      A current will flow in R1, R2 and R3 which is inversely proportional to their values. The total current will always equal the combined branch currents.

      Individual branch currents can be found by multiplying total current I by the ratio of the branch resistance to the total circuit resistance.

      DC CURRENT: Kirchhoff's Current Law.

      Kirchhoff's current law states that the current flowing into a node (circuit joining point) will always equal the current flowing out. Nodes are identified in this diagram as the small magenta circles.

      The current at any of these points will be measured as equal to I. Similarly individual parallel section branch currents between the nodes when added will equal the total current.

      To find the individual branch currents, calculate the equivalent parallel resistance for each section and using Ohm's Law find the voltage between the nodes.

      The current flowing in R1 for example will be the parallel resistor section (R1, R2, and R3) voltage (potential difference) divided by the value of R1. Each of the other branch currents can be found in the same way.

      DC CURRENT: Further Current Law.

      The current flowing into a node or junction will always equal the current flowing out. Here voltage source Va causes Ia to flow via R3 and R1 and Vb causes a current Ib to flow in R3 and R2. The total current into the node via R3 consists of Ia + Ib, where it divides and flows out of the junction back to Va and Vb to complete each loop.

      There are more accurate ways of making these calculations by applying the various circuit theorems which we shall explore later.

      SERIES AND PARALLEL RESISTORS: Series Resistors.

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      The total circuit resistance of n resistors connected in series can be found by adding the values together.

      Current (electron flow) is common for all values of R1, R2 and R3.

      As the current makes its way through the circuit each resistor will develop a voltage across it which can be calculated using Ohm's Law. The individual resistor voltage drops when added will equal the applied (battery) voltage.

      SERIES AND PARALLEL RESISTORS: Two Resistors in Parallel.

      When resistors are connected in parallel their combined resistance will always be lower than the smallest value. The equivalent for two equal value resistors will be half either value.

      The simple formula shown can be applied in this instance.

      SERIES AND PARALLEL RESISTORS: Three or more Resistors in Parallel.

      Connecting three or more resistors in parallel involves a slightly more complex approach. As for two resistors their combined total will always be lower than the smallest value.

      The reciprocal of resistance is called Conductance this is the ease by which current can flow. To calculate, first find the conductance of each value and add them together, the reciprocal of the total is the equivalent resistance.

      SERIES AND PARALLEL RESISTORS: Series Parallel Resistors.

      When resistors are connected in series/parallel or any other combination the total circuit current will be dependent upon their combined resistance.

      Here the equivalent value of R2 and R3 is found first and then added to the value of R1.

      Circuit current flows through R1 before dividing into I1 and I2 branches, when added together these branch currents will equal the circuit current. R1 × I is another way of stating 'voltage across R1' using Ohm's Law.

      SERIES AND PARALLEL RESISTORS: Further Series Parallel Resistors.

      To calculate the total resistance you will need to determine the equivalent values of each parallel section first. Then simply add the equivalent and actual values as for series resistors, where R = R1 || R2 + R3 + R4 || R5. '||' being shorthand for in parallel.

      Combining resistors in this way can be useful to obtain a non-preferred value.

      SERIES AND PARALLEL RESISTORS: Triangle Method.

      For a practical electronics application of trigonometry a method of graphically finding the value of the equivalent resistance Requ for a parallel circuit is shown. R1 or R2 can also be found when only one is known along with the equivalent circuit resistance. Position the pointers on the R1 and R2 scales. The equivalent resistor value can be read off on the middle scale. Alternatively, place R1 or R2 and fit the line to read Requ. The second resistor value can then be determined.

      Scales must represent equal value ranges, i.e. Ohms, kOhms or Mohms.

      This method employs the right angle triangle with a 60, 30°

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