Electrical Fundamentals for Aircraft Maintenance Licence PDF

Maintenance Training Organisation Part -147 MODULE 03 Electrical Fundamentals for Aircraft Maintenance Licence...

Maintenance Training Organisation Part -147 MODULE 03 Electrical Fundamentals for Aircraft Maintenance Licence Category B1 www.aviotraceswiss.com  Cat. B1 - Table of Contents Table of Contents 3.1 Electron Theory....................................................................................................................... 7 3.1.1 Structure and distribution of electrical charges in atoms, molecules, ions and compounds................................................................................................................................ 7 3.1.2 Molecular structure of conductors, semiconductors and insulators............................. 15 3.2 Static electricity and conduction........................................................................................... 17 3.2.1 Static electricity and distribution of electrostatic charges............................................ 17 3.2.2 Electrostatic laws of attraction and repulsion............................................................... 26 3.2.3 Units of charge and Coulomb’s law................................................................................ 27 3.2.4 Conduction of electricity in solids, liquids, gases and vacuum...................................... 29 3.3 Electrical terminology........................................................................................................... 31 3.3.1 Terms, units and factor affecting them.......................................................................... 31 3.4 Generation of electricity....................................................................................................... 35 3.4.1 Production of electricity by the following methods: light, heat, friction, pressure, chemical action, magnetism and motion................................................................................ 35 3.5 DC sources of electricity........................................................................................................ 43 3.5.1 Construction and basic chemical action of: primary cells, secondary cells, lead acid cells, nickel cadmium cells, other alkaline cells...................................................................... 43 3.5.2 Cells connected in series and parallel............................................................................ 54 3.5.3 Internal resistance and its effect on a battery............................................................... 58 3.5.4 Construction, materials and operation of thermocouples............................................ 60 3.5.5 Operation of photo-cells................................................................................................ 65 3.6 DC circuits.............................................................................................................................. 67 3.6.1 Ohm’s law, Kirchhoff's voltage and current laws........................................................... 67 3.6.2 Calculations using the above laws to find resistance, voltage and current................... 71  Cat. B1 - Table of Contents 3.6.3 Significance of the internal resistance of a supply......................................................... 76 3.7 Resistance/resistor................................................................................................................ 79 3.7.A.1 Resistance and affecting factors................................................................................. 79 3.7.A.2 Specific resistance....................................................................................................... 81 3.7.A.3 Resistor color code, values and tolerances, preferred values, wattage ratings......... 82 3.7.A.4 Resistors in series and parallel.................................................................................... 89 3.7.A.5 Calculation of total resistance using series, parallel and series-parallel combinations 93 3.7.A.6 Operation and use of potentiometers and rheostats................................................. 97 3.7.A.7 Operation of Wheatstone Bridge.............................................................................. 102 3.7.B.1 Positive and negative temperature coefficient conductance................................... 104 3.7.B.2 Fixed resistors, stability, tolerance and limitations, methods of construction......... 107 3.7.B.3 Variable resistors, thermistors, voltage dependent resistors................................... 109 3.7.B.4 Construction of potentiometers and rheostats........................................................ 111 3.7.B.5 Construction of Wheatstone Bridge......................................................................... 111 3.8 Power.................................................................................................................................. 113 3.8.1 Power, work and energy (kinetic and potential).......................................................... 113 3.8.2 Dissipation of power by a resistor................................................................................ 114 3.8.3 Power formula.............................................................................................................. 115 3.8.4 Calculations involving power, work and energy.......................................................... 116 3.9 Capacitance/capacitor......................................................................................................... 119 3.9.1 Operation and function of a capacitor......................................................................... 119 3.9.2 Factors affecting capacitance area of plates, distance between plates, number of plates, dielectric and dielectric constant, working voltage, voltage rating.......................... 121 3.9.3 Capacitor types, construction and function................................................................. 123 3.9.4 Capacitor color coding.................................................................................................. 127 3.9.5 Calculations of capacitance and voltage in series and parallel circuits....................... 129 3.9.6 Exponential charge and discharge of a capacitor, time constants............................... 131 3.9.7 Testing of capacitors.................................................................................................... 133 3.10 Magnetism........................................................................................................................ 135  Cat. B1 - Table of Contents 3.10.A.1 Theory of magnetism.............................................................................................. 135 3.10.A.2 Properties of a magnet........................................................................................... 136 3.10.A.3 Action of a magnet suspended in the Earth's magnetic field................................. 139 3.10.A.4 Magnetization and demagnetization...................................................................... 140 3.10.A.5 Magnetic shielding.................................................................................................. 142 3.10.A.6 Various types of magnetic material........................................................................ 143 3.10.A.7 Electromagnets construction and principles of operation..................................... 144 3.10.A.8 Hand clasp rules to determine magnetic field around current carrying conductor 146 3.10.B.1 Magneto-motive force, field strength, magnetic flux density, permeability, hysteresis loop, retentivity, coercive force reluctance, saturation point, eddy currents..... 149 3.10.B.2 Precautions for care and storage of magnets......................................................... 157 3.11 Inductance/Inductor......................................................................................................... 159 3.11.1 Faraday's law.............................................................................................................. 159 3.11.2 Lenz's law and polarity determining rules................................................................. 161 3.11.3 Action of inducing a voltage in a conductor moving in a magnetic field; induction principles; effects of the magnetic field strength................................................................. 162 3.11.4 Back EMF, self induction............................................................................................ 163 3.11.5 Effects of the following on the magnitude of an induced voltage: rate of change of flux, number of conductor turns........................................................................................... 164 3.11.6 Mutual induction and effect of change rate of primary current and mutual inductance on induced voltage................................................................................................................ 164 3.11.7 Factors affecting mutual inductance: number of turns in coil, physical size of coil, permeability of coil, position of coils with respect to each other........................................ 165 3.11.8 Exponential curve of inductor current and saturation point..................................... 165 3.11.9 Inductors in series and in parallel and principle uses of inductors............................ 168 3.12 DC Motor/Generator Theory............................................................................................ 171 3.12.1 Basic motor and generator theory............................................................................. 171 3.12.2 Construction and purpose of components in DC generator...................................... 175 3.12.3 Operation and factors affecting output and direction of current flow in DC generators 182 3.12.4 Operation and factors affecting output power, torque, speed and direction of rotation of DC motors........................................................................................................... 186  Cat. B1 - Table of Contents 3.12.5 Series wound, shunt wound and compound motors................................................. 188 3.12.6 Starter Generator construction.................................................................................. 190 3.13 AC Theory.......................................................................................................................... 191 3.13.1 Sinusoidal waveform: phase, period, frequency, cycle.............................................. 191 3.13.2 Instantaneous, average, root mean square, peak, peak to peak current values and calculations of these values, in relation to voltage, current and power............................... 193 3.13.3 Triangular/Square waves........................................................................................... 195 3.13.4 Single and 3 phase principles..................................................................................... 197 3.14 Resistive (R), Capacitive (C) and Inductive (L) Circuits...................................................... 201 3.14.1 Phase relationship of voltage and current in L, C and R circuits, parallel, series and series parallel........................................................................................................................ 201 3.14.2 Power dissipation in L, C and R circuits...................................................................... 207 3.14.3 Impedance, phase angle, power factor and current calculations.............................. 208 3.14.4 True power, apparent power and reactive power calculations................................. 209 3.15 Transformers..................................................................................................................... 211 3.15.1 Transformer construction principles and operation.................................................. 211 3.15.2 Transformer losses and methods for overcoming them............................................ 216 3.15.3 Transformer action under load and no-load conditions............................................ 221 3.15.4 Primary and Secondary current, voltage, turns ratio, power, efficiency................... 222 3.15.5 Calculation of line and phase voltages and currents in a three phase system.......... 224 3.15.6 Auto transformers and other type of transformers................................................... 227 3.16 Filters................................................................................................................................. 229 3.16.1 Operation, application and uses of the following filters: low pass, high pass, band pass, band stop..................................................................................................................... 229 3.17 AC generators.................................................................................................................... 241 3.17.1 Rotation of loop in a magnetic field and waveform produced.................................. 241 3.17.2 Operation and construction of revolving armature and revolving field type AC generators............................................................................................................................. 243 3.17.3 Single phase, two phase and three phase alternators............................................... 247 3.17.4 Three phase star and delta connections advantages and uses.................................. 251 3.17.5 Permanent Magnet Generators................................................................................. 252  Cat. B1 - Table of Contents 3.18 AC motors.......................................................................................................................... 255 3.18.1 Construction, principles of operation and characteristics of: AC synchronous and induction motors both single and polyphase........................................................................ 255 3.18.2 Methods of speed control and direction of rotation................................................. 265 3.18.3 Methods of producing a rotating field: capacitor, inductor, shaded or split pole..... 266  Cat. B1 - Table of Contents PAGE INTENTIONALLY LEFT BLANK  Cat. B1 - 3.1 Electron Theory 3.1 Electron Theory 3.1.1 Structure and distribution of electrical charges in atoms, molecules, ions and compounds Matter and Elements We can define as matter everything that occupies space and has a weight. Examples of matter are the air we breathe, water, clothes but also animals and our body. Generally matter can be found in one of the following states: solid, liquid, gaseous. Basically, an element is a substance that can't be reduced to a simpler form. For example: gold, silver, oxygen or iron. There are more than 100 known elements and every compound we come in contact with in our everyday life is made of one or more of them. When one or more elements are chemically combined a compound is originated. Common examples of compounds are: salt, made of sodium and chlorine, and water, made of hydrogen and oxygen. The atom can be simply defined as the smallest particle that encloses all these characteristics. However remember that, despite the previous definition, atoms of one element are different from atoms of another element. As a result, each element presents its own specific characteristics. This means that since in nature there are more than 100 different known elements, as a consequence there are more than 100 different atoms. A doubt that might arise is certainly related to the diversity and the multiplicity of the matter that surrounds us. How can 100 simple elements form all solid, liquid and gaseous substances existing in nature? The answer is simple and complex at the same time. If we consider the letters of the alphabet, by correctly combining these letters we can create various words and sentences. The answer is clear but the way to implement it can be complex. Atoms or elements duly combine themselves in order to create all the different forms of matter that surround us. Structure of the Atom Each atom consists of electrons, protons and, in some cases, neutrons (Fig.1.1). Electrons, protons and neutrons are generally defined as sub-atomic particles. We can state that sub-atomic particles of a generic atom are identical to sub-atomic particles of any other atom. What distinguishes one atom from another is the different number of sub-atomic particles and their different position.  Cat. B1 - 3.1 Electron Theory Different tests allowed measuring the mass and the size of sub-atomic particles. The result was that protons have positive charge, while electrons have same but opposite charge, hence negative. They are also very different in terms of mass. Protons have a mass 1800 times bigger than electrons mass. Neutrons instead have a mass which is approximately the same as the one of protons but they do not have any electrical charge. Protons and neutrons form the nucleus of the atom, while several electrons orbit around the nucleus. Fig. 1.1 - Subatomic particles and atomic structure The 100 known elements are classified basing on the complexity of their atoms and according to the number of protons that compose the nucleus. The number of protons is defined as Atomic Number. For example, hydrogen has atomic number 1, while helium has atomic number 2.  Cat. B1 - 3.1 Electron Theory Fig. 1.2 – Mass number and atomic number Remember that atoms of the same element are identical, and at neutral state they have the same number of protons and electrons. This means that each atom has charge equal to zero, since the electrical charge of the electrons is compensated by the electrical charge of protons. Molecules If we take in consideration any substance, water for example, and we subdivide it into smaller and smaller portions, we will get to a point where water loses its chemical properties and it will not be considered as water anymore. This minimum substance unit is called molecule. Molecules are made up of two or more atoms. The elements consist of molecules made up of two or more atoms of the same kind. For example a molecule of oxygen consists of two atoms of oxygen. (Fig.1.3)  Cat. B1 - 3.1 Electron Theory Fig. 1.3 – Representation of an oxygen molecule Fig. 1.4 – Schematic representation of chemical bonds of an oxygen molecule  Cat. B1 - 3.1 Electron Theory Compounds are made up of different types of atoms, for example a molecule of water consists of one atom of oxygen and two of hydrogen (Fig.1.5). Fig. 1.5 - Molecule of water Energy levels Electrons move around the nucleus following particular orbits. These orbits are contained into concentric spaces named “shells”. In general terms, shells correspond to determined and pre- fixed energy levels. Under normal conditions, an electron occupies the nearest shell the nucleus, compatibly with the presence of other electrons. If an electron receives energy from outside, for example by crashing against a photon or another particle, it will be forced to jump onto a more external shell, having acquired more potential energy. However this phenomenon is temporary. In fact after a second split it spontaneously goes back to the original shell, releasing outside the energy surplus. Therefore each shell corresponds to a different energy level. The generic electron will move on to the next level only if the energy received from the outside is sufficient to fill the energy gap between the two levels. The first external shell an electron can access, for example, will have a radius four times bigger than the original; the second shell will have a radius nine times bigger than the original, and so on. The shells are identified with letters K, L, M, N, O, P, Q.  Cat. B1 - 3.1 Electron Theory Each shell can contain a maximum number of electrons, amounting to the double square of the shell number, starting to count from the most internal shell. In the formula, N is number of electrons and n is the shell number. For example, the most internal shell will have two by one squared equal to two electrons; the second shell will have two by two squared equal to eight; the third will have two by square three equal to eighteen; the fourth will have thirty two and so on (Fig.1.6). Fig. 1.6 – Atomic shells The shells are subdivided into sub-shells; also the sub-shells are identified by letters. The sub- shells can contain a maximum number of electrons (Fig.1.7).  Cat. B1 - 3.1 Electron Theory Fig. 1.7 – Shell and energy levels Under normal conditions, the number of electrons inside an atom is the same as the number of protons, but they can transfer or acquire electrons according to a process called ionization. An atom with a number of electrons different from the number of protons is defined as ionized, and it is a negative ion if, having acquired too many electrons, it has a negative charge, while it will be a positive ion if, having lost electrons, it has more protons than electrons and therefore it has a positive charge. The tendency of an atom to lose or gain electrons determines its chemical and electrical characteristics. This tendency depends on the so-called valence of an atom. The valence of an atom is the number of electrons that the atom has in the outer shell. The outer shell of an atom is also called valence shell, while the electrons located on it are called valence electrons (Fig.1.8).  Cat. B1 - 3.1 Electron Theory Fig. 1.8 – Valence electrons Atoms spontaneously tend to reach stability by keeping the most external shell complete. For example, an atom which is only missing one or two electrons, in order to complete the valence shell will tend to acquire electrons and to become a negative ion. Instead, an atom which is missing many electrons will more easily tend to give its electrons away, losing a whole shell. Therefore its valence shell will be its internal shell, previously completed.  Cat. B1 - 3.1 Electron Theory 3.1.2 Molecular structure of conductors, semiconductors and insulators The tendency of an atom to transfer electrons determines its characteristics as electrical conductor. The electrical flow is similar to a chain displacement of electrons. This concept can be explained with a simple comparison. Let’s imagine a can of sweets, with both sides open. If we introduce a sweet from one of the two sides, it will push the other sweets which are immediately near it. They will then push the other sweets forward and so on, until one of the sweets is pushed outside the other side. If we replace the can with a generic conductor and the sweets with electrons, we can see how power passes through. Fig. 1.9 – Conventional and real flow of electric current All materials can be divided into three categories:  Conductors: these are the materials whose atoms easily give their electrons away. Therefore they conduct electricity very well. Generally they consist of atoms with valence one, two or three.  Insulators: these are materials whose atoms do not give their electrons away easily, and therefore they offer resistance to the electricity flow. Usually they consist of atoms with valence 5 or higher.  Cat. B1 - 3.1 Electron Theory  Semiconductors: these are materials that, under normal conditions, cannot be classified as conductors or insulators. Usually they consist of atoms with valence 4. Conductors: usually metals are good conductors of electricity. Some metals are better conductors than others, for example gold and silver are excellent conductors although, due to their cost, copper and aluminum are more used. In particular since aluminum is lighter, it is used when weight is a relevant factor. Insulators: typical examples of insulators are rubber, plastic and air. Semiconductors: examples of popular semiconductors are germanium and silicon. Semiconductors are materials that, at room temperature, are not good conductors or good insulators. It is possible to change their characteristics according to the temperature or by adding impurities. An intrinsic semiconductor, for example a pure silicon crystal, increases its conduction capacity when the temperature increases. Extrinsic semiconductors instead, are produced by introducing impurities into crystals of pure semiconductors. This process is called “doping”.  Cat. B1 - 3.2 Static electricity and conduction 3.2 Static electricity and conduction 3.2.1 Static electricity and distribution of electrostatic charges There are two main aspects related to electricity, current and static electricity. With regard to electricity in the form of current, the electrons move along the circuit and they do their job through the magnetic field created by their own movement or through heat generated by their forced passage into a resistance. From this point of view, static electricity is not useful, since most of the times static electricity is considered as a drawback and not as a form of electric energy that can be used. Static electricity must be taken into serious consideration during the fuel supply of an aircraft. An example will help clarify this concept: during the flight of a plane, the friction between the air and the surface of the plane develops an electrostatic charge. When the aircraft finally lands, the electrostatic charge does not discharge rapidly, because the tires isolate the aircraft from the land. If the first thing that comes into contact with the electrostatic charged aircraft is the fuel gun, when this is introduced into the tank, the discharge that takes place will be able to set fire to the fuel vapors, causing severe consequences. In order to avoid this inconvenience, it is always necessary to ground the aircraft before fuelling. Usually this is done by electrically connecting the aircraft to the tanker, which is also earthed to the ground. Generation of electrostatic charge In the ancient times, one or more forms of static electricity were known. For example, the Greeks observed that by rubbing a piece of cloth on amber, the latter became able to attract small bits of wood or fabric, which, after touching amber, flew away once again. Today it is well-known that the reason for this behavior is the fact that the contact between the fabric and amber is sufficient to transfer a certain number of electrons from the fabric into amber. Since both fabric and amber initially have the same number of negative electrons and positive protons in their related substances, the transfer of a certain number of electrons into amber results as negative charge, therefore amber will have a higher number of negative charge carriers, while as a result there will be a lack of electrons on the fabric, which will have the same charge but positive.  Cat. B1 - 3.2 Static electricity and conduction Fig. 2.1 – Example of electrons migration due to contact Now, we wonder how a piece of charged amber can electrically influence other objects that are electrically neutral and that are quite distant from amber itself. This is due to the fact that an electrical charge changes the characteristics of the surrounding space and sets up an electrical field. This change in the characteristics of the space that surrounds a charged body is the reason for the origin of the forces that apply on other bodies that are located near the charged one. Fig. 2.2 – Electric field around a charged body  Cat. B1 - 3.2 Static electricity and conduction Lines of force The electrical field can be graphically represented through the Faraday’s scheme. Faraday’s method consists of drawing a set of lines, which represent the lines of the electrical field around a charged body, arranged in such a way as to represent the direction of the force exercised by the electrical field on a small test charge, located in different spots around the charged body. This method allows us to represent the direction and the shape of electrical fields, also complex ones, generated by several charges or charged bodies, located all around (Fig.2.3). no interaction b/n line of forces perpendicular to the filed Fig. 2.3 – Lines of force between two opposite charges A further improvement of Faraday’s method consists in changing the number of lines of force which are drawn in a certain portion of the electric field, in such a way as to offer an indication of the intensity of the force exercised on the test charge located in the related part of the electric field. On the representations of the electric field, the areas of the field with more intensity are characterized by the concentration of the lines of force, while the areas where the electric field is weak are characterized by a higher distance from the lines of force (Fig.2.4). check property of electrical field  Cat. B1 - 3.2 Static electricity and conduction Fig. 2.4 – Faraday’s representation of three different field intensities The direction of the arrows added on the lines of force, represents the third quantity shown through this method. The arrows show the direction towards which the test body moves, with positive charge, when it enters the electric field (Fig.2.5). Fig. 2.5 – Faraday’s convention for the verse of the arrows  Cat. B1 - 3.2 Static electricity and conduction By using the lines of force, it is possible to represent the electric field around one charged sphere, or between two spheres with opposite charge, or between two spheres with the same charge. It is necessary to specify that, although the representations are two-dimensional due to practical reasons, the electric field is three-dimensional. Fig. 2.6 – Examples of electric field representation Resulting electric fields Let’s now see how it is possible to draw an electric field near several charged bodies. Fortunately it is possible to mathematically determine the intensity and the direction of an electric field in a determined point. This is possible thanks to two electric phenomena: the first is that the charge of any body is positioned fully on its external surface, the second is that the direction and the intensity of the electric field in any point equals the sum of all the fields generated by all the charged bodies that are positioned around that point. As a consequence, if you want to know the intensity and the direction of the electric field near the different charged bodies, it will be necessary to calculate the intensity and the direction generated separately by each charged body, then sum up all their effects, making sure that you respect the direction of each effect. This type of sum is a vector sum of the vectors that correspond to the related electric fields, which are characterized by their related intensity and direction.  Cat. B1 - 3.2 Static electricity and conduction Fig. 2.7 – Vectorial composition of two electric fields In order to better clarify the concept of vector sum let us suppose we are in two points in a space characterized by two charged bodies where the direction and the intensity of electric forces generated by the two charges is known. They can be represented as two vectors, one directed horizontally and towards the right and the other one directed vertically and towards the top. The resulting vector, the sum of the two vectors, can be calculated as the diagonal of the parallelogram built with the projection of the two vectors (Fig.2.8).  Cat. B1 - 3.2 Static electricity and conduction Fig. 2.8 – Vectorial sum In the examined case the vector is oriented at 45 degrees and towards the north-east. Obviously its intensity will depend on the intensity of its components. Fig. 2.9 - How to find the total field generated by two positive charges  Cat. B1 - 3.2 Static electricity and conduction Distribution of electric charges When a body, with a blunt or a uniform surface gets electrically charged, the charge distributes uniformly on its entire surface. If the surface is wrinkled or of irregular shape, the charge will concentrate on the spots or areas where the curve is sharper (Fig.2.10). Fig. 2.10 – Example of point of maximum charge concentration (the lightning rod) This explains how static dischargers, used on the aerodynamic surface of many aircrafts, work. As already said, when a plane flies in the air, the friction with the air determines an accumulation of static charge on the surface of the aircraft. In order to avoid accumulating too much charge, the static wicks or the null field discharger is installed on many aircrafts. These devices are fixed on the aircraft control surface and create spots where static electricity can concentrate and therefore discharge in the air (Fig.2.11).  Cat. B1 - 3.2 Static electricity and conduction Fig. 2.11 – Static wicks These control surfaces are connected to the fuselage structure by hinges, which do not provide a good route for static electricity towards the static dischargers. In order to avoid this inconvenience, many aircraft are provided with bus bars or bonding straps, which ensure the conductive route between the two structures.  Cat. B1 - 3.2 Static electricity and conduction 3.2.2 Electrostatic laws of attraction and repulsion Work and electric field Since a piece of amber or rubbed plastic is able to exercise a force and lift small objects, we can conclude that an electric field can do something useful. For this reason, it is very similar to the gravitational field that surrounds the earth. By lifting a weight above the ground, the system composed by the earth, weight and the gravitational field, acquires something that it did not have before. It is energy, the ability to perform a task: in fact the weight can be connected to a rope that makes a tree turn while the weight is going back to the ground, or it can be connected to a pulley system which is able to lift another weight. In this case we can say that the weight has a certain quantity of potential energy. The quantity of potential energy owned by a body depends on the relation between the body and the gravitational field. This can be explained by the fact that it is necessary to spend a certain quantity of work in order to lift a weight, winning against the force of gravity. If we do not consider the loss due to friction or the poor performance of the lifting mechanism, the quantity of work required in order to lift the weight at a certain height, is exactly the same as the potential energy owned by the weight at that height. The electric field that surrounds a charged body presents effects that are similar to the gravitational field that surrounds the earth. In fact, in the previous example replace the weight with a test charge and the gravitational field with the electric field. Similarly to the gravitational field also the electric field exercises a force able to displace the test charge. However this electric field is further complicated by the fact that a charged body, in the presence of an electric field, can be attracted or rejected, while the forces that exist in the gravitational field are only forces of attraction. We can conclude that between two charges exist attraction or repulsion force and it always stays on the straight line between two charges. If two charges have same sign, the force will be a force of repulsion. If two charges have opposite sign, the force will be a force of attraction.  Cat. B1 - 3.2 Static electricity and conduction 3.2.3 Units of charge and Coulomb’s law The first person who studied the forces involved in the electric field was the French physicist Charles Coulomb. Coulomb defined the fundamental unit of electric charge in terms of quantities that can be directly measured, such as force and distance. After performing a set of tests, Coulomb concluded that the effects of the electric field decreases with the square of the distance between the two charged bodies. By using torsion balance and two small permanent magnets, Coulomb was able to show that the forces produced by the existing magnetic field between the two magnets also decrease with the square of the distance between them. In mathematical terms: the force F, which is exercised on both bodies due to the field that interacts between the bodies, is inversely proportional to the square of the distance between the bodies. Expressed with a formula: In the formula, d is the distance between the bodies. The forces exercised by the field on the two bodies, do not depend only on the distance between the two bodies, but also on the quantity of charge, which has generated the electric field between the two bodies. Coulomb’s discovery can be expressed as follows: Where:  qA and qB are quantity of charge of bodies A and B  K is Coulomb’s constant  ± depend from charge of bodies A and B. The measurement unit of the quantity of charge is the Coulomb C. This unit is multiple of the electron charge; in fact 1C is equal to 6.24x1018 times the charge of one electron. Then the fundamental electric charge is the charge of electron, ±e = 1.6 * 10-19 C, while other charges are multiple of that. Potential energy and electric potential There is an analogy between gravitational field and electric field. A weight suspended above the earth surface owns a certain quantity of potential energy due to the force exercised on the body by the gravitational field. This means that the body is able to perform a task. Similarly, a  Cat. B1 - 3.2 Static electricity and conduction charged body located in an electric field generated by one or more charged bodies, is also able to perform a task. Potential energy is defined as the application of a force along a distance: If we recall Coulomb’s expression of force: and we replace the previous expression we obtain: This represents the potential energy or the difference in electric potential. If we assume that qB is equal to the unitary test charge, the previous equation gets simplified and gives the expression of the potential V, which is the potential energy for each test charge in the field generated by charge qA: K depends on the means in which the electric field is located: Where:  ε0 = dielectric constant of vacuum = 8.85 * 10-12 C/(N*m^2)  εr = dielectric constant of environment means (dielectric constant of solid and liquid is bigger than 1, dielectric constant of water is 80). K is not constant since it depend on the environment et  Cat. B1 - 3.2 Static electricity and conduction 3.2.4 Conduction of electricity in solids, liquids, gases and vacuum Solids, liquids and gases propagate electric current in different ways, with different laws. In solids the conduction of electricity is due to movement of free electrons. In fact inside the electric field there is an electric potential and the charges go to a higher level of electric potential then the level they come from. The direction of flow of negative charges has the same flow intensity of positive charges, which have opposite direction. Conventionally we define positive direction the direction of positive charges. The electric conductivity in solid matter respects Ohm’s laws and we can divide material in three categories:  Conductors  Semiconductors  Insulators. In liquids and gases, in fluid materials, the current flow is not only caused by electrons motion, but it also depends on atoms and ionized molecules too; so in fluid materials the conduction of electricity is a phenomenon more complicated than in solid materials. In vacuum environmental, where there is no kind of material, there isn’t conduction, but electrons, atoms or ions can cross it.  Cat. B1 - 3.2 Static electricity and conduction PAGE INTENTIONALLY LEFT BLANK  Cat. B1 - 3.3 Electrical terminology 3.3 Electrical terminology 3.3.1 Terms, units and factor affecting them Electric charge Electric charge refers to the number of electrons which are present in an object. Nevertheless the number of electrons contained in commonly used objects, also the smallest objects, is so high that, if the electron was used as a unit of measurement, we would have very high numbers poorly useful for calculations. For this reason a specific unit of measurement, the Coulomb, is used, due to the fact that it is a multiple of the electron. One coulomb is 6.24 by 10 raised to the eighteenth power electrons: When two poles of a circuit have opposite charges, the excess of electrons in the negative pole tend to flow towards the positive pole, until filling the gap. This flow of electrons is called electric current. Potential difference and electromotive force When between two poles of a circuit there is a difference of electric charge, the result is a potential difference. It is possible to quantify the potential difference as work performed by the attraction-repulsion force generated by the electric field, which is used to move the charges from one point to another. The attraction-repulsion force can be calculated by Coulomb’s law: “The force of attraction between two poles is the product of the charge of the first pole multiplied by the charge of the second pole, divided by the square of the distance between the two poles”. The field of electromagnetic force between the two poles attracts the electrons excess from the negative pole towards the positive pole. This force of attraction is called electromotive force or voltage. Electromotive force is indicated as EMF.  Cat. B1 - 3.3 Electrical terminology The unit of measurement of potential difference is the volt. The volt is also used as the unit of measurement of electromotive force. Electric current When there is potential difference between the two poles, the electrons in excess in the negative pole are attracted to the positive pole. The flow of electrons from one pole to the other is called electric current. Electric current is measured as the variation in the charge quantity during the time unit. Its intensity is indicated as “i”. The unit of measurement of current intensity is the ampere. Electrons flow from the negative to the positive pole. However, the first people who studied electric phenomena were not able to see the movement of electrons and, although they realized that electric current was a flow, they misunderstood its direction and they thought that electricity flew from the positive pole to the negative pole, the opposite of what happens in reality. Since this misunderstanding does not lead to any difference in calculations, the traditional conception was kept over time. Therefore conventionally electric flow is represented with a direction that is opposite to the real flow of electrons (Fig.3.1). Fig. 3.1 - Conventional and real flow of electric current  Cat. B1 - 3.3 Electrical terminology In commonly-used electric circuits it is possible to find two types of electric flow:  Direct Current flow is the normal flow where electrons continuously flow from the negative to the positive pole  Alternating Current flow is produced by periodically reversing the polarity of the circuit in such a way that the electrons are pushed first in one direction and than in the other. Resistance and Conductance When the electrons flow inside a conductor, they meet a set of obstacles due to the physical structure of the conductor itself. This obstacle against the flow of electrons is called resistance of the conductor and it is indicated with the letter R. In particular, the resistance of a conductor is influenced by:  The quantity of free electrons are present in the conductor: more electrons are free to move in the conductor, more easily electric current will go through the conductor  The section of the conductor: we can compare the conductor with a pipe where electrons pass through, if the pipe widens the electrons will move along it more easily and rapidly then along a narrow pipe  The length of the conductor: we can compare the resistance of the conductor with a sort of friction against electrons flow, if the conductor is longer, friction, which affects the current when it passes through, will be higher  The temperature of the conductor: in fact when it changes, also resistance of conductor will change, some conductors increase their resistance when temperature increases and others instead, reduce it. Therefore each conductor has a temperature coefficient, which can be either positive or negative, and that quantifies how much the resistance depends on temperature. Another characteristic often associated to conductors is conductance, which indicates how easily a conduct lets the electric energy pass through. Conductance simply is the opposite of resistance, therefore for a conductor, conductance is: Where G is the conductance and R is the resistance. The unit of measurement of the resistance is the ohm Ω and the unit of measurement of conductance is the siemens S:  Cat. B1 - 3.4 Generation of electricity Units of measurement Let’s now have a look at the main units of measurement that are used in electric circuits and their definitions. The coulomb, indicated as “C”, is the unit of measurement of electric charge and it has been defined as “a number of electrons equal to 6.24 multiplied by 10 raised to the 18th power” The ampere, indicated as “A”, is the measure which indicates the intensity of electric current; through several experiments and mathematical calculations, the ampere has been defined as “the quantity of current that, if let go through two conductors of endless length, zero section at a distance of one meter from the other, it would cause a force of attraction between the two conductors amounting to 2 by 10 raised to the seventh, newtons per meter” = The volt, indicated as “V”, is the unit of measurement of potential difference and it is also used to measure electromotive force. The volt has been defined as “the potential difference between two points, on a cable, with a current of one ampere, which dissipates one watt of power in the conductor” The ohm, indicated with the Greek letter “Ω”, is the unit of measurement of the resistance of conductors. The ohm has been defined as “the resistance of one conductor where, if you apply a potential resistance of one volt on one of the two ends, the current produced inside that conductor has intensity of one ampere”  Cat. B1 - 3.4 Generation of electricity 3.4 Generation of electricity 3.4.1 Production of electricity by the following methods: light, heat, friction, pressure, chemical action, magnetism and motion Voltage generators When there is potential difference between two poles, the excess electrons in the negative pole tend to flow towards the positive pole, eliminating the initial potential difference. However, in order to use the flow of electric energy in a practical way, the flow has to be continuous over time. As a consequence, it is necessary to set up a device which constantly restore the electrons of the negative pole, or which keeps on taking electrons away from the positive pole. In this way the potential difference remains constant. This device is called voltage generator. There are five ways to generate voltage:  Using light  Using heat  Using the properties of some materials  Using certain chemical reactions  Using electromagnetic phenomena. Photoelectric generators Light is made up of photons, which have double properties: undulating and corpuscular. In fact they are simultaneously waves, because they have a certain frequency, and particles, because they have a certain mass.  Cat. B1 - 3.4 Generation of electricity Fig. 4.1 – Wave motion of the photons In general, the phenomenon we perceive as light intensity depends on the quantity of photons which create the beam of light. Since each photon is a wave, it has a frequency. This phenomenon is perceived by the human eye, in the visible light field, as a difference in the light color. Each photon has a different quantity of energy, in function of its frequency. Higher the frequency is, more energy has the photon. When a beam of light goes over an object, the single photons of the beam can interact with the electrons of the atomic structure of the object. If a photon bumps into an electron and has enough energy, that means an enough high frequency, it forces the atom to give the electron. This phenomenon occurs only if the energy associated to the photon is such to overpass the force, which keeps the electron bound to its orbital. In other words, it is required a minimum threshold value, which depends on the material characteristics. If the beam of light has a frequency enough high, at light intensity increase, the number of given electrons increases. If, on the contrary, the beam of light has a frequency which doesn't reach the minimum threshold value, increasing the intensity there will be no emission phenomenon. A material subjected to a beam of light with constant intensity and opportune frequency, it emits continuously electrons, obtaining and keeping a positive charge. That is called photoelectric phenomenon.  Cat. B1 - 3.4 Generation of electricity Fig. 4.2 – Photovoltaic cell Materials giving more easily electrons are metals. Materials more commonly used are silver oxide and copper oxide. A voltage generator exploiting photoelectric effects is named photovoltaic cell. Generators that use heat When a metal is heated on one end, electrons inside it tend to move. In most of metals, copper for example, the electrons move from the warmest side to the coldest side. Nevertheless in some metals, such as iron, the electrons move to the opposite direction, from the coldest side to the warmest one. By putting in touch a metal of the first type with a metal of the second type, and warming them up in their point of connection, a flow of electrons is created, from the coldest side of the second-type metal, to the coldest side of the first-type metal. This type of generator is called thermocouple.  Cat. B1 - 3.4 Generation of electricity Fig. 4-3 - Thermocouple Thermocouples generate little potential difference, if we compare them with other types of generators, so usually they are not used to develop electric energy, but rather as a system to measure temperature. Piezoelectric generators Piezoelectricity is the ability of some materials, usually crystals, to generate a potential difference when they are subject to mechanical stress. Examples of piezoelectric materials are:  Quartz  Tourmaline  Rochelle salt, which is sodium and potassium tartrate. The molecules composing piezoelectric crystals are usually arranged according to a specific geometrical scheme. By deforming crystal, this structure partially deforms. As result, electric internal forces are not balanced anymore and electrons move inside the crystal, polarizing the crystal in one direction, in case of compression, or in the opposite direction, in case of traction. By periodically applying pressure and traction, an alternating voltage generator is obtained. This effect is generally used for small voltage generators used in sound reproduction field, for microphones, oscillators, and so on A H R S.  Cat. B1 - 3.4 Generation of electricity Fig. 4.4 – Piezoelectric effect It is also possible to do the opposite, and apply an alternating voltage to the piezoelectric crystal, which compresses and expands, as a reply to the voltage, with a frequency that depends on the nature of the crystal, on its shape, and its size. Generators that use chemical reactions A primary cell is a system made up of two different metals, called electrodes, dipped into a liquid, called electrolyte, with which they have an ionization reaction, and connected between two of them by a conductor.  Cat. B1 - 3.4 Generation of electricity Electrolyte Fig. 4.5 – Example of primary cell The two metals ionize at a different speed and, in this way, they get a different electric charge, by generating a potential difference. The electrons flow through the conductor, from the electrode with more negative charge to the electrode with more positive charge. The quantity of electromotive force mainly depends on the electrochemical characteristics of the two metals. A battery is a set of primary cells connected in series. Fig. 4.6 – Lead acid battery Generators that use electromagnetic effects  Cat. B1 - 3.4 Generation of electricity The most common method to generate electricity is the one that transforms kinetic energy into electric energy, by exploiting the principle of electromagnetic induction. In accordance with this principle, if a conductor is moved inside a magnetic field or if a magnetic field is moved around a conductor, the conductor itself will be polarized. Fig. 4.7 – Electromagnetic induction By building a mechanism, which moves a conductor inside the magnetic field in a cyclic way, using as a source of movement for example a water-activated turbine, like in hydroelectric plants, or by steam or simply by human movement, like in a bicycle dynamo, and connecting the two poles of the conductor to the ends of an electric circuit, it is possible to generate a flow of current inside the circuit. Friction Although the friction is not used to create electric current, the electrostatic energy is a kind of electro-motive force that we can’t ignore. The air, for example, flowing on the skin of the airplane, creates an accumulation of electrons, and then thanks to the friction between itself and the piloting surfaces of the airplane it is able to generate electrostatic energy. This phenomenon is more evident on the piloting surfaces because these surfaces are not in contact with the rest of the aircraft due to the presence of pivots. In this case, we don’t consider the static electricity as an electric current but as the cause of the trouble on the board receivers. For this reason we try to remove it from the aircraft structure using the static wicks.  Cat. B1 - 3.4 Generation of electricity PAGE INTENTIONALLY LEFT BLANK  Cat. B1 - 3.5 DC sources of electricity 3.5 DC sources of electricity 3.5.1 Construction and basic chemical action of: primary cells, secondary cells, lead acid cells, nickel cadmium cells, other alkaline cells Batteries and cells Batteries are widely-spread generators of direct current. A battery is made up of a set of cells, assembled in series or in parallel. In a cell, electrodes have chemical reactions with the electrolyte, and generate or acquire positive or negative ions, due to the chemical energy of the reaction. Due to the different intensity or different sign of the reaction, the electrodes develop a potential difference, by transforming the chemical energy of the reaction into electric energy. The electrolyte is an acid solution, alkaline or saline, liquid in the first cell models, semi-liquid in the models currently used. The cells can be subdivided into two categories:  Primary cells, which are cells exploiting an irreversible chemical reaction, a chemical reaction that, once it has occurred, cannot be brought back to its initial stage; primary cells keep on generating potential difference until they are depleted; in this type of cells, one of the electrodes, generally the negative one, is corroded by the reaction with the electrolyte, which - in turn - loses its chemical properties.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.1 – Example primary cell  Secondary cells use a reversible chemical reaction, so they can be recharged by absorbing electric energy, and storing it as chemical energy; in this type of cells, by applying potential difference to the two electrodes, in the opposite direction as compared to the direction of the potential difference usually provided by the cell, it is possible to force the electrodes and the electrolyte to go back to their original chemical state.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.2 – Lead acid battery The voltage developed by a cell depends on the chemical properties of the materials composing it and on the resistance of the circuit it is applied to, including the internal resistance of the cell. Chemistry of primary cells An example of primary cell is the zinc-carbon cell. The zinc-carbon cell is made up of:  a zinc electrode, which acts as anode  a graphite cathode, connected one to the other by a conductor, and dipped into a paste made of ammonium chloride  Manganese dioxide, and granular carbon, which acts as electrolyte.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.3 – Zinc – Carbon primary cell The electrolyte corrodes the zinc, and forms zinc chloride, leaving excess electrons on the zinc bar, and free positive ions of ammonium on the electrolyte. These excess electrons flow from the zinc anode to the graphite cathode through the conductor, charging the graphite negatively. The ammonium ions, present in the electrolyte, are attracted by the graphite electrode, due to its negative charge, and - when they reach it - they re-acquire electrons and become neutralized. In this way the circuit is closed, they separate into hydrogen gas and Ammonia gas, which are then absorbed by the manganese dioxide mix. The process continues until the zinc electrode is fully corroded. Primary cells of common use The most-commonly used primary cells are:  The zinc-carbon battery: it generates a voltage of 1.5 Volt, regardless of the size of the battery.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.4 - Zinc – Carbon pile  The alkaline battery: it is the evolution of the zinc-carbon battery. Differently from the zinc-carbon battery, the alkaline battery uses a paste of Potassium hydroxide and generates a voltage of 1.5 Volt.  Cat. B1 - 3.5 DC sources of electricity  Mercury battery: it consists of a zinc anode and a steel cathode, while an alkaline paste of potassium hydroxide is used as electrolyte, mercury batteries are comparatively smaller than zinc-carbon batteries, and they also last longer. It generates a voltage of 1.3 V. Mercury batteries, due to their characteristics, are applied on small devices, like watches and pocket calculators. Fig. 5.5 - Mercury battery Secondary cells and accumulators Secondary cells are different from primary cells because the chemical reaction, that takes place in secondary cells, is reversible. In other words, by applying a potential difference to the electrodes, opposite to the potential difference generated by the cell, it is possible to generate the reverse chemical reaction which brings the electrodes and the electrolyte back to the original chemical state. Therefore secondary cells are rechargeable. Secondary cells are usually used in batteries, which are generally called: accumulators. The most common example of accumulator is the lead battery. Lead battery (structure) Commonly-used lead batteries consist of 6 or 12 cells, each one developing a voltage of around 2.1 V. Lead batteries are made up of the following parts: a rigid case of shockproof plastic, built to resist to the chemical action of the electrolyte, to mechanical shocks that the battery could be subject to and to extreme temperatures. Inside the case there are:  a block of plates, composing the anodes of each cell  a second block of plates, composing all the cathodes of each cell  a set of porous spacers that mark the boundary of each cell.  Cat. B1 - 3.5 DC sources of electricity Each cell then consists of:  an anode of lead powder, with spongy texture, mixed with expanded material, which prevents its dissipation.  a cathode of lead dioxide.  an electrolyte composed of a solution of sulfuric acid e and water. The block of cathodes is connected to a terminal representing the positive pole of the battery, usually marked with the plus symbol, often indicated in red. The block of anodes is connected to a terminal that represents the negative pole of the battery, usually marked with the minus symbol. On the cover of the case there is a set of holes, with safety valves in order to prevent the electrolyte leak, and locked with screw caps. The holes are used to charge up the battery and check it. Fig. 5.6 - Representation of a lead acid battery  Cat. B1 - 3.5 DC sources of electricity Fig. 5.7 - Exploded view of a lead acid battery Lead battery (discharged) Fig. 5.8 – Lead acid battery: discharge reaction  Cat. B1 - 3.5 DC sources of electricity When a charged Lead battery is connected to a circuit, the following reactions take place: The lead anode acquires sulfates from the electrolyte, transforming into Lead sulfate, which is retained inside the anode by the expanded material. During this process it gives electrons away, which move towards the cathode through the circuit, and it leaves the electrolyte charged with hydrogen positive ions. The cathode of Lead dioxide acquires electrons and gives away negative ions of oxygen, which combine with Hydrogen ions present in the electrolyte to form water molecules (H2O). At this stage, the lead now charged positively attracts also sulfates from the electrolyte, converting into identical lead sulfate. At the end of the process, both the anode and the cathode are made of identical lead sulfate, while the electrolyte, having lost all its sulfates, is fully made of water and the battery is completely discharged. Lead battery (charged) Fig. 5.9 - Lead acid battery: charge reaction In order to charge a discharged battery, it is necessary to apply electric voltage to the poles, in opposite direction as compared to the voltage generated by the battery. The lead sulfate,  Cat. B1 - 3.5 DC sources of electricity which is present in the anode, obtains electrons from the circuit, releasing negative sulfate into water. At the end of this process, the anode is again made of Lead powder. The Lead sulfate in the cathode loses electrons towards the circuit, and it simultaneously gives sulfate ions to the water that composes the electrolyte. There it obtains negative oxygen ions from the water. At the end of this process, the cathode is again composed of Lead dioxide. The negative ions of oxygen that go away from the electrolyte leave it full of positive ions of Hydrogen. Inside the electrolyte, positive ions of hydrogen combine with the negative sulfates, in order to recreate sulfuric acid, H2SO4. At the end of this process, the electrolyte goes back to its initial composition of water and sulfuric acid. The Lead cell goes back to its initial chemical state, and it is charged again. Assessment of charge level It is possible to measure the level of charge of a Lead battery, through the analysis of the electrolyte density, which results to be:  more acid, and therefore thicker when the battery is charged  more aqueous, and therefore less thick when the battery is discharged. The density of the electrolyte can be measured with a densimeter, a tool that measures the density of the electrolyte, by using the specific weight difference between the acid, which is heavier, and water, which is less heavy. Fig. 5.10 - Densimeter  Cat. B1 - 3.5 DC sources of electricity The densimeter is made up of a straw, inside which there is a calibrated drip riser. One part of the electrolyte is sucked inside the straw; at this stage the drip riser is floating on the electrolyte, with its floating level depending on its specific weight, and on the density of the electrolyte. On the stem of the floating device, there is a graduated scale, which measures its floating level, in terms of electrolyte density. When the electrolyte density goes below 1.15 kg per cubic meter, the battery is considered discharged. The measurement must be done at a standard temperature of 27 centigrade degrees. The measurement should be performed at a different temperature and a correction has to be added to the result. Fig. 5.11 – Table of correction points  Cat. B1 - 3.5 DC sources of electricity Nickel-cadmium batteries As well as Lead batteries, also nickel-cadmium batteries are commonly used. Their anodes are made of Nickel hydroxide, their cathodes of cadmium hydroxide and their electrolyte of potassium hydroxide. Differently from Lead batteries, each cell has its own separate block. The main differences as compared to lead batteries are that:  they can develop a current of higher intensity.  they can be recharged several times.  they resist more to excessive charge.  they are comparatively heavier.  they must be fully discharged before being charged again, otherwise they grow the so-called memory effect. Due to the memory effect, if one battery with capacity of 100% is discharged by 75%, and then recharged, the remaining 25% of energy will never be used again due to chemical changes that occur during the recharging process. Thanks to their ability to develop high intensity current, they are typically used as starter batteries or deep cycle batteries. 3.5.2 Cells connected in series and parallel Batteries in series and parallel In a battery, the cells can be connected between them in different ways, with different results in terms of voltage and intensity of final current. The first way to connect cells is by connecting them in series: the cells are connected in series when the anode of cell A is connected to the cathode of cell B, the anode of cell B is connected to the cathode of cell C, and so on, with the cathode of the first cell and the anode of the last cell connected to the circuit of the user mechanisms; the voltage generated by each cell is summed up in order to determine the voltage generated by the whole battery.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.12 – Cell connected in series For example: if a battery is composed of four cells arranged in series and each cell releases 1.5 V, the voltage of battery will be: 1.5[V] * 4 = 6[V]. The second way to connect cells is in parallel: the cells are connected in parallel when all the anodes are connected between them, all the cathodes are connected between them and the group of anodes and the group of cathodes are connected to the user’s circuit; the intensity generated by the cells is summed up to determine the intensity generated by the battery.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.13 - Cell connected in parallel For example: if a battery is composed of four cells arranged in parallel and each cell releases 0.125A, the amperage of battery will be: 0.125[A] * 4 = 0.5[A]. Finally, the battery cells can be connected between them also in series and in parallel. This special solution is used when it's necessary to obtain both high intensity and high voltage. First the groups of cells are assembled in series then these groups of cells are assembled in parallel.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.14 – Series and parallel connection For example: in order to obtain a battery of 6V and 0.5A, with cells of 1.5V and 0.125A, 16 cells are needed, divided into 4 groups, the cells of each group are assembled in series, therefore forming 4 batteries of 6V and 0.125A each. Then the four batteries are assembled in parallel, in order to obtain one battery of 0.5 Ampere and 6 Volt. Capacity of a battery The capacity of a battery is measured in Ampere-hour [AH] and represents the intensity of current generated multiplied by the duration of a battery in hour. For example: a battery, able to develop 20A for 5 hours of time, will have a capacity of: 20[A] * 5[h] = 100[AH]; and a battery, which is able to develop 25A, for 4 hours of time, will have a capacity of: 25[A] * 4[h] = 100[AH]. The Ampere hour, as a matter of fact, is a unit of measure of the electric charge and is equivalent to 3,600 Coulomb. The standard discharge speed represents the intensity discharged by a battery, supposing it is discharged completely over a standard time. The reference time usually is 20 hours, but in some cases different reference time is used, like 5 or - commonly in the aeronautical field - 1 hour. For example, a battery, with capacity of 100[A*h], will have a standard discharge speed according to the reference time:  For a reference time of 20 hours  100[A*h] : 20[h] = 5[A].  For a reference time of 5 hours  100[A*h] : 5[h] = 20[A].  For a reference time of 1 hour  100[A*h] : 1[h] = 100[A].  Cat. B1 - 3.5 DC sources of electricity 3.5.3 Internal resistance and its effect on a battery Internal resistance Batteries and cells have an internal resistance, which has an impact on the performance of the battery in the circuit. The internal resistance of a cell depends on:  The size of the electrodes  The distance between the two electrodes, more distance there is between two electrodes and higher will be the resistance  The resistance of the electrolyte. The resistance of a battery depends on:  The resistance of the cell composing it  The way in which the cells are connected: o in case the cells are connected in series, the resistance of the battery amounts to the sum of the resistance of the individual cells, for example, a battery, composed of 5 cells connect in series, with a resistance of 4[Ω] each, will have a total resistance of 4[Ω] * 5 = 20[Ω]; o in case the cells are connected in parallel, the resistance of the battery is equal to the resistance of the single cell divided by the number of cells, for example, a battery, composed of 5 cells in parallel, with a resistance of 4[Ω] each, will have a total resistance of 4[Ω] : 5 = 0.8[Ω]. Recharging batteries Commonly-used batteries are usually rechargeable, and they can be recharged in specific locations. There are two main ways to recharge batteries:  First method is based on Constant Current: o a current of constant recharge is sent to the battery, the value of the recharging current is usually specified on the battery, this value should not be specified, it will not be possible to go over 7 percent of the capacity of the battery in ampere hour; when the battery charge increases, the voltage generated by the battery increases, so it is necessary to constantly change the recharge voltage, in order to keep the current constant.  Second method based on Constant Voltage: o a recharge voltage is sent to the battery, with voltage constant over time slightly higher than the battery voltage, in order to be higher than its internal resistance, for example, if a battery has a voltage of 24[V], it will be necessary to have a voltage of 25 or 26[V] in order to recharge it;  Cat. B1 - 3.5 DC sources of electricity when the battery charge increases, the battery voltage increases, therefore the recharge current that goes through will decrease, when the constant voltage method is used, it is necessary to verify that, at the beginning of the process, when the recharge speed is very high, the battery is not overheated. Batteries: maintenance and safety procedures In order to keep a battery in good conditions, it is necessary to perform periodically the following checks:  Make sure that the terminals of the battery are clean and in good conditions visual  Make sure that the case of the battery is cleaned, undamaged and has no leakage  Make sure that the level of the electrolyte is not too low and, in that case, add distilled water, in order to bring it back to an acceptable level  Check that the electrolyte has a sufficient density of active ingredient, either tools acid or alkaline, with the use of a densimeter. When you handle a battery, it is necessary to comply with the following safety procedures:  Do not connect the two terminals of a battery directly, if you connect the two terminals directly, you will obtain a short circuit and, in some batteries, this could lead to the explosion of the battery  Always wear protective clothes, if you have to move a battery, always grip it from the handles  Never get in close proximity of sparks, or free flames such as a cigarette, with a battery under recharge  Do not let the electrolyte go out of the battery and, should this happen, immediately dilute it with abundant water and the appropriate neutralizing substances  If the electrolyte gets in contact with the skin, rinse it immediately with a good don't use soap quantity of water for at least 15 minutes  Should the electrolyte get in contact with the eyes, rinse it immediately with a good quantity of water for at least 15 minutes, and make sure that the eyelids are well open, so that the water can wash the whole eye, at the same time call urgently a doctor.  Cat. B1 - 3.5 DC sources of electricity 3.5.4 Construction, materials and operation of thermocouples Thermocouples In order to measure the temperature inside the motor, probes are usually used, made up of a set of thermocouples. A thermocouple works thanks to the interaction of two different metals, welded on the two ends, called junctions. If the two metals are connected in a circuit, and if they are heated in their two points of contact, an electromotive force is generated in the circuit, which is proportional to the temperature difference between the two junctions. Fig. 5.15 – Thermocouple junctions The heated junction is called hot junction, while the other is called cold junction. By measuring the electromotive force near the cold junction, it is possible to calculate the temperature of the hot junction. Thermocouples are installed in a ceramic insulator and encapsulated in a protection metallic sheath. This is the probe. The hot junction of the system stretches out in a space inside the probe. There are some crossing holes, in order to let the gas flow through the junction. The position of the holes depends on the thermocouple, which can be of two types: stagnation or rapid response thermocouple.  Cat. B1 - 3.5 DC sources of electricity Stagnation thermocouple In stagnation thermocouples, the gases enter the probe through an opening directed towards the jet, and, after touching the hot junction, they go out from a hole which is not in line with the entrance hole, on the opposite side. Fig. 5.16 - Stagnation thermocouples This characteristic allows reducing the effect of high speed to a minimum, and to obtain precise temperature measurements, also in presence of high speed flows. Stagnation thermocouples are typically used in turbine motors, for the measurement of the temperature of exhaust gases, or E G T. Rapid response thermocouple Rapid response thermocouples are designed to be used in low-speed discharge ducts like, for example, turboprop engines. The probe has two identical crossing holes, aligned on the two sides, so that the gases can touch the hot junction with minimum stagnation. Rapid response thermocouples are characterized by a very low reaction time usually included between 0.5 seconds and 1 second.  Cat. B1 - 3.5 DC sources of electricity RAPID RESPONSE 0.5 seconds - 1.0 seconds Fig. 5.17 - Rapid response thermocouples Installation of thermocouples In order to obtain a correct indication of temperature, on turbine motors the measurement of temperature in a specific position is taken by using several probes, arranged radially around the area where the measurement is taken. Moreover, this multiple installation guarantees the correct operation of the indication system, in case of thermocouple breaks.  Cat. B1 - 3.5 DC sources of electricity Fig. 5.18 – Installation of thermocouples In this configuration, the electric outputs of the different thermocouples are connected among them, and they form a circuit in parallel. The cables of thermocouple probes form a common cabling, which ends in a junction box also representing the junction point for the cable connected to the temperature indicator. Moreover, probes in contact to the outside are usually installed, near the air inlets, in order to compensate the temperature variations of the incoming air flow. The conductors that connect the junction box to the indication system are usually made of Alumel, an alloy of nickel and aluminum, or Chromel, an alloy of nickel and chromium. If these conductors are made of the same materials as thermocouples, they are called ex-voltage conductors. Instead, if the conductors are not made of the same material as thermocouples, they are defined as compensation conductors. Temperature compensation on a cold junction The various combinations of materials required for thermocouples used on aircrafts comply with standard ratios of temperature and electromotive force. Therefore the indicators are calibrated by the manufacturer in compliance with standards. The relation between g and electromotive force is calculated, for each thermocouple, on a reference standard temperature for cold junction. It is necessary to consider that cold junction will not always be  Cat. B1 - 3.5 DC sources of electricity at the reference temperature for which the thermocouple has been calibrated. As a consequence, any temperature change as compared to the reference temperature on the cold junction will generate a slight electromotive force, causing errors on the indicator. There are methods to compensate these temperature variations, in order to ensure a correct reading of the indicator. One of the most common methods to perform this type of compensation is the use of a bimetallic blade, sensitive to temperature variations, during the rotary winding of the indicator, which gets longer or shorter when the temperature of the cold junction changes. In this way, it corrects the tool. Fig. 5.19 - Temperature compensation system is used to correct the data read from the cold junction Other methods are based on the use of compensatory electric circuits, based on the use of a Wheatstone bridge, connected to a resistor which is sensitive to room temperature. Compensation due to resistance variation during rotary winding Temperature changes also have an influence on the resistance of the rotary winding, including the indicator tool. In fact, if the temperature increases, also the winding resistance increases, causing a current drop. As a consequence of this, a lower indication than the real one will appear on the tool indicator. A way to avoid this problem is to connect a thermistor in series with the indicator winding. In fact the thermistor is characterized by a negative temperature  Cat. B1 - 3.5 DC sources of electricity coefficient, and therefore its resistance diminishes when temperature increases. If the temperature increases, and the resistance of winding increases, the resistance of the thermistor diminishes. The total resistance will remain unchanged. In this way, the current and the indication will be consistent, and the value read on the tool will be correct. 3.5.5 Operation of photo-cells Photocells are a tool made up of a surface of photosensitive material, which releases electrons when it is hit by a ray of light of a certain frequency, which acts as a cathode, an anode that collects the electrons released by the cathode and a circuit that connects them. When a light of a certain frequency hits the cathode, the latter releases electrons which, being collected by the anode, create potential difference in the circuit; instead, when the cathode is not hit by the light, the circuit is inert. For example, some photocells are made up of a cathode consisting of a curved surface, and an anode located in the focal point of the cathode. When the light hits the cathode, the latter releases electrons are taken on by the anode. Then the electrons flow into the circuit, and they go back to the cathode. Another type of common photocell consists of a three-layer structure. The lower layer is a plate of copper. Fig. 5.20 – Schematic representation of a photo-cell  Cat. B1 - 3.5 DC sources of electricity Above the plate of copper there is a layer of photosensitive copper oxide, which acts as a cathode. The third layer consists of a very thin metal sheet, which lets the light go through and collects the electrons released by the copper oxide, acting as an anode. A circuit connects the metal sheet to the copper oxide, so that the electrons taken on by the anode can go back to the cathode. The photocells generate a low potential difference, but they react with extreme speed and precision both to the impact of light and the frequency of light. They are usually used as sensors for motion or color, for example for printers or scanners. The most commonly used materials for cathodes are: Silver oxide, copper oxide, silicon, germanium, selenium.  Cat. B1 - 3.6 DC circuits 3.6 DC circuits 3.6.1 Ohm’s law, Kirchhoff's voltage and current laws Ohm’s law Ohm’s law is a fundamental relationship that explains the behavior of current flowing in a circuit, in function of voltage and resistance. By observing how the electron moves through a material with a certain resistance, it is easy to notice that with a constant value of resistance, higher is the voltage, and then the electro- motive force, greater is the current intensity. In the same way, if the electro-motive force remains constant, the higher the resistance the lower the current intensity. Ohm’s law resumes in a formula the observation just explained. This means that the electric current that flows in a conductor is directly proportional to the voltage across it and inversely proportional to its resistance value. The same formula can be written in two different ways: Using these formulas we can find resistance, voltage or current intensity by knowing the value of two of them. Kirchhoff’s current law To understand Kirchhoff’s current law we must compare the current flow with a fluid flowing in a tube. In fact this law is equal to the law of conservation of fluid flow which says that the amount of fluid that comes into a node must be the same to the amount of fluid that comes out. In the same way the Kirchhoff’s current law says that “The amount of current that comes in a circuital node must be equal to the amount of current that comes out from the same node. In  Cat. B1 - 3.6 DC circuits other words, the algebraic sum of the currents which flow through that circuital node must be null.” To apply this law we must consider that the convention says that the input currents must be taken with a positive sign, instead, the output currents must be taken with a negative sign. Therefore the Kirchhoff’s current law can be written as follows: Kirchhoff’s voltage law Kirchhoff’s voltage law is a sort of law of conservation of energy. In fact, this law says that all the energy supplied by the DC sources (for example the batteries) must be equal to the energy used by all the loads of the circuit (for example electric motors, resistors, inductors, capacitor, etc…). Observe the following circuit. total 180v b/c series 60 OHM Fig. 6.1 – Closed mesh Kirchhoff’s voltage law says that “In a closed mesh the sum of the electro-motive forces must be equal to the sum of the voltage drops across the loads. In other words, the algebraic sum of the voltages in a closed mesh must be null.”  Cat. B1 - 3.6 DC circuits To apply this law we must consider that in generators the voltage has the same direction of the current; instead in user devices the voltage has the opposite direction with respect to the current. Fig. 6.2 - Current and tension convention  Cat. B1 - 3.6 DC circuits Fig. 6.3 – Application of Kirchhoff’s voltage law Therefore, by observing the mesh clockwise or anti-clockwise, if the voltage direction is the same that we have taken to check the mesh, we can consider the voltage as positive. In the opposite case we must consider the voltage as negative. We can write, therefore, as follows:  Cat. B1 - 3.6 DC circuits 3.6.2 Calculations using the above laws to find resistance, voltage and current Now let’s consider some application of the laws just explained. Consider the following circuit: V=R*I Fig. 6.4 – Example of resistance calculation As we can see, we know the value of the voltage across the load and the current intensity flowing through it. The only unknown value is the resistance. To find it we have to apply Ohm’s law written in this way: Therefore, by applying this law we find the value of resistance that is 3Ω. If we know the value of the voltage and the value of the resistance we can use the following formula:  Cat. B1 - 3.6 DC circuits For example, let’s consider the following circuit: Fig. 6.5 - Example of current calculation In this example, by applying the previous formula we find that the current is equal to 2A. Instead if we consider a circuit like this: Fig. 6.6 - Example of voltage calculation  Cat. B1 - 3.6 DC circuits we have to use the following formula: Therefore, the voltage value is 30V. Fig. 6.7 – Application of the Kirchhoff’s current law The figure above represents a circuital node in which there are two input currents whose value is known and two output currents and one of these is unknown. To find it we have to apply Kirchhoff’s current law: In this case the number of currents is four: two positives, and two negatives.  Cat. B1 - 3.6 DC circuits Fig. 6.8 – Convention of the nodal currents Therefore, indicating the unknown current with x, we can write: Now let’s consider the following circuit: Fig. 6.9 - Exercise  Cat. B1 - 3.6 DC circuits To find the unknown current we have to apply Kirchhoff’s voltage law. First of all, we have to sign the correct verse of the voltage in the closed mesh. Obviously, for the two batteries E1 and E2 the voltage has the same direction of the current because they are generator devices, instead for the resistors R1 and R2 the voltage drop has the opposite direction. Therefore, we can write Kirchhoff’s voltage law following the circuit clockwise. Fig. 6.10 - Kirchhoff’s voltage law Using the formula: we can write:  Cat. B1 - 3.6 DC circuits Since we know Ohm’s law, we can substitute VR1 and VR2 with the product between the current and the respective resistances. Therefore the previous equation becomes: Therefore i = 2A. 3.6.3 Significance of the internal resistance of a supply As we said before, batteries and cells have an internal resistance, which has an impact on the performance of the battery in the circuit. The internal resistance of a cell depends on:  The size of the electrodes  The distance between the two electrodes, more distance there is between two electrodes higher will be the resistance  The resistance of the electrolyte. In fact if we connect for example a multimeter to a battery of 12 V, when it isn’t connected to the circuit, we will probably read a voltage of 12,30 V, where 0,30 V is the value of the internal voltage drop that occurs when we connect the battery to the load. For this reason, when we study a circuit we have to consider this resistance and the voltage drop across it. Let’s consider, for example, the following circuit.  Cat. B1 - 3.6 DC circuits Fig. 6.11 – Internal resistance of a battery As we can see the voltage across the battery is 13 V that is exactly equal to the sum of the voltage drops across all the resistors of the circuit. If we want to find the voltage rating of the battery when it isn’t connected to the circuit we have to find the Es value that will not be 13 V because we must consider also the internal resistance of 1 Ω. Therefore, by applying Kirchhoff’s voltage law we can write: It means that, in this case, the internal voltage drop is 2 V.  Cat. B1 - 3.6 DC circuits PAGE INTENTIONALLY LEFT BLANK  Cat. B1 - 3.7 Resistance/resistor 3.7 Resistance/resistor 3.7.A.1 Resistance and affecting factors When a current flow passes through a conductor, electrons collide with the atoms of the conductor along the way, thus undergoing a sort of friction. Such phenomenon is called electrical resistance. Each conductor is therefore characterized by its own resistance. The resistance of a conductor depends on the characteristics of the conductor itself and it influences the intensity of the current passing through the conductor, by applying a certain voltage to its extremes, according to Ohm’s laws: Intensity of current is the voltage applied divided by the resistance of the conductor. By inverting the equation, we can define resistance as voltage divided by intensity: We have just said that the electrical resistance may be thought of as an interference with the free flow of electrons. Therefore the physical structure and type of material has direct influence on its resistance. Then, a conductor that has obstructions or barriers within it to the free flow or electrons will have resistance and the longer the wire the more obstacles there are, and so its resistance increase with length. This makes we understand that the conductor’s resistance is directly proportional to its length. If we take a wire with a certain length and we add to it another one of exactly the same length putting it in parallel with the first one, it will increase the overall cross-sectional area of conductor available to the passage of electrons. Then, as the cross-sectional area is increased the resistance will decrease. This characteristic behavior is not linear. It means that the resistance is also inversely proportional to the cross-sectional area:  Cat. B1 - 3.7 Resistance/resistor The third factor that affects resistance is the type of material used in its construction. All materials have their own characteristic properties and one is their ability to conduct electrical current. This property is known as resistivity. Obviously the resistance value results to be directly proportional to the material resistivity: Fig. 7.1 – Cross sectional area and length of a conductor Summarizing what we have just said, the resistance of a conductor depends on three fu