lecture notes in electrical and electronics engineering

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LECTURE NOTES ON ELECTRICAL AND ELECTRONICS ENGINEERING II B. Tech I semester (JNTUH-R15) A. Sathish kumar Assistant Professor CIVIL ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING (AUTONOMOUS) DUNDIGAL, HYDERABAD - 500 043 SYLLABUS ELECTRICAL AND ELECTRONICS ENGINEERING OBJECTIVE: This course introduces the concepts of electrical DC and AC circuits, basic law’s of electricity, instruments to measure the electrical quantities, different methods to solve the electrical networks, construction operational features of energy conversion devices i.e. DC and AC machines, transformers. It also emphasis on basics of electronics, semiconductor devices and their characteristics and operational features UNIT-I: Electrical Circuits: Basic definitions, Types of elements, Ohm’s Law, Resistive networks, Kirchhoff’s Laws, Inductive networks, capacitive networks, Series, Parallel circuits and Star- delta and delta-star transformations. Instruments: Basic Principle of indicating instruments – permanent magnet moving coil and moving iron instruments. UNIT-II: DC Machines: Principle of operation of DC Generator – EMF equation - types – DC motor types –torque equation – applications – three point starter. UNIT-III: Transformers: Principle of operation of single phase transformers –EMF equation – losses – efficiency and regulation. AC Machines: Principle of operation of alternators – regulation by synchronous impedance method – Principle of operation of induction motor – slip – torque characteristics – applications. UNIT–IV: Diodes: P-n junction diode, symbol, V-I Characteristics, Diode Applications, and Rectifiers – Half wave, Full wave and Bridge rectifiers (simple Problems). Transistors: PNP and NPN Junction transistor, Transistor as an amplifier, SCR characteristics and applications. UNIT-V: Cathode Ray Oscilloscope: Principles of CRT (Cathode Ray Tube), Deflection, Sensitivity, Electrostatic and Magnetic deflection, Applications of CRO - Voltage, Current and frequency measurements. EEE: TEXT BOOKS: 1. Basic concepts of Electrical Engineering, PS Subramanyam, BS Publications. 2. Basic Electrical Engineering, S.N. Singh, PHI. EEE: REFERENCE BOOKS: 1. Basic Electrical Engineering, Abhijit Chakrabarthi, Sudipta nath, Chandrakumar Chanda, Tata-McGraw-Hill. 2. Principles of Electrical Engineering, V.K Mehta, Rohit Mehta, S.Chand Publications. 3. Basic Electrical Engineering, T.K.Nagasarkar and M.S. Sukhija, Oxford University Press. 4. Fundamentals of Electrical Engineering, RajendraPrasad, PHI. 5. Basic Electrical Engineering by D.P.Kothari , I.J. Nagrath, McGraw-Hill. ECE: TEXT BOOKS: 1. Electronic Devices and Circuits, S.Salivahanan, N.Suresh Kumar, A.Vallavaraj,Tata McGraw-Hillcompanies.. 2. Electronic Devices and Circuits, K. Lal Kishore,BS Publications. ECE: REFERENCE BOOKS: 1. Millman’s Electronic Devices and Circuits,J. Millman, C.C.Halkias, and Satyabrata Jit, TataMcGraw-Hill companies. 2. Electronic Devices and Circuits, R.L. Boylestad and Louis Nashelsky,PEI/PHI. 3. Introduction to Electronic Devices and Circuits, Rober T. Paynter,PE. 4. Integrated Electronics, J. Millman and Christos C. Halkias, Tata McGraw-Hill companies. 5. Electronic Devices and Circuits, Anil K. Maini, Varsha Agarwal,Wiley India Pvt. Ltd. OUTCOME: After going through this course the student gets a thorough knowledge on basic electrical circuits, parameters, and operation of the transformers in the energy conversion process, electromechanical energy conversion, construction operation characteristics of DC and AC machines and the constructional features and operation of measuring instruments like voltmeter, ammeter, wattmeter etc...and different semiconductor devices, their voltage- current characteristics, operation of diodes, transistors, realization of various electronic circuits with the various semiconductor devices, and cathode ray oscilloscope, With whichhe/she can able to apply the above conceptual things to real-world electrical and electronics problems and applications. UNIT – I ELECTRICAL CIRCUITS & INSTRUMENTS 1.1 INTRODUCTION Given an electrical network, the network analysis involves various methods. The process of finding the network variables namely the voltage and currents in various parts of the circuit is known as network analysis. Before we carry out actual analysis it is very much essential to thoroughly understand the various terms associated with the network. In this chapter we shall begin with the definition and understanding in detail some of the commonly used terms. The basic laws such as Ohm’s law, KCL and KVL, those can be used to analyse a given network Analysis becomes easier if we can simplify the given network. We will be discussing various techniques, which involve combining series and parallel connections of R, L and C elements andStar-Delta conversion.We are also discussing the basic instruments which are used to measure the voltage and current such as permanent magnet moving coil and moving iron instruments. 1.2 SYSTEMS OF UNITS As engineers, we deal with measurable quantities. Our measurement must be communicated in standard language that virtually all professionals can understand irrespective of the country. Such an international measurement language is the International System of Units (SI). In this system, there are six principal units from which the units of all other physical quantities can be derived. Quantity Basic Unit Symbol Length Meter M Mass kilogram kg Time second s Electric Current ampere A Temperature kelvin K Luminous intensity candela Cd One great advantage of SI unit is that it uses prefixes based on the power of 10 to relate larger and smaller units to the basic unit. Multiplier Prefix Symbol 12 10 Tera T 9 10 giga G 6 10 mega M 3 10 kilo K -3 10 milli m -6 10 micro -9 10 nano n -12 10 pico p 1.3 BASIC CONCEPTS AND DEFINITIONS 1.3.1 CHARGE The most basic quantity in an electric circuit is the electric charge. We all experience the effect of electric charge when we try to remove our wool sweater and have it stick to our body or walk across a carpet and receive a shock. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). Charge, positive or negative, is denoted by the letter q or Q. We know from elementary physics that all matter is made of fundamental building blocks known as atoms and that each atom consists of electrons, protons, and neutrons. We also -19 know that the charge ‘e’ on an electron is negative and equal in magnitude to 1.602x10 C, while a proton carries a positive charge of the same magnitude as the electron and the neutron has no charge. The presence of equal numbers of protons and electrons leaves an atom neutrally charged. 1.3.2 CURRENT Current can be defined as the motion of charge through a conducting material, measured in Ampere (A). Electric current, is denoted by the letter i or I. The unit of current is the ampere abbreviated as (A) and corresponds to the quantity of total charge that passes through an arbitrary cross section of a conducting material per unit second. Mathematically, Where is the symbol of charge measured in Coulombs (C), I is the current in amperes (A) and t is the time in second (s). The current can also be defined as the rate of charge passing through a point in an electric circuit. Mathematically, The charge transferred between time t and t is obtained as 1 2 A constant current (also known as a direct current or DC) is denoted by symbol I whereas a time-varying current (also known as alternating current or AC) is represented by the symbol or ( ). Figure 1.1 shows direct current and alternating current. Current is always measured through a circuit element as shown in Fig. 1.1 Fig. 1.1 Current through Resistor (R) Two types of currents: 1) A direct current (DC) is a current that remains constant with time. 2) An alternating current (AC) is a current that varies with time. Fig. 1.2Two common types of current: (a) direct current (DC), (b) alternative current (AC) Example 1.1 Determine the current in a circuit if a charge of 80 coulombs passes a given point in 20 seconds (s). Solution: Example 1.2 How much charge is represented by 4,600 electrons? Solution: -19 Each electron has - 1.602x10 C. Hence 4,600 electrons will have: -19 -16 -1.602x10 x4600 = -7.369x10 C Example 1.3 The total charge entering a terminal is given by =5 sin4 . Calculate the current at =0.5 . Solution: At =0.5 . = 31.42 Example 1.4 Determine the total charge entering a terminal between =1 and =2 if the current passing 2 the terminal is = (3 − ) . Solution: 1.3.3 VOLTAGE (or)POTENTIAL DIFFERENCE To move the electron in a conductor in a particular direction requires some work or energy transfer. This work is performed by an external electromotive force (emf), typically represented by the battery in Fig. 1.3. This emf is also known as voltage or potential difference. The voltage between two points aand b in an electric circuit is the energy (or ab work) needed to move a unit charge from a to b. Fig. 1.3(a) Electric Current in a conductor, (b)Polarity of voltage ab Voltage (or potential difference) is the energy required to move charge from one point to the other, measured in volts (V). Voltage is denoted by the letter v or V. Mathematically, where w is energy in joules (J) and q is charge in coulombs (C). The voltage or simply V ab is measured in volts (V). 1 volt = 1 joule/coulomb = 1 newton-meter/coulomb Fig. 1.3 shows the voltage across an element (represented by a rectangular block) connected to points a and b. The plus (+) and minus (-) signs are used to define reference direction or voltage polarity. The can be interpreted in two ways: (1) point a is at a potential of ab ab volts higher than point b, or (2) the potential at point a with respect to point b is . It ab follows logically that in general Voltage is always measured across a circuit element as shown in Fig. 1.4 Fig. 1.4 Voltage across Resistor (R) Example 1.5 An energy source forces a constant current of 2 A for 10 s to flow through a lightbulb. If 2.3 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb. Solution: Total charge dq= idt = 210 = 20 C The voltage drop is 1.3. 4 POWER Power is the time rate of expending or absorbing energy, measured in watts (W). Power, is denoted by the letter p or P. Mathematically, Where p is power in watts (W), w is energy in joules (J), and t is time in seconds (s). From voltage and current equations, it follows that; Thus, ifthe magnitude of current I and voltage are given, then power can be evaluated as the product of the two quantities and is measured in watts (W). Sign of power: Plus sign: Power is absorbed by the element. (Resistor, Inductor) Minus sign: Power is supplied by the element. (Battery, Generator) Passive sign convention: If the current enters through the positive polarity of the voltage, p = +vi If the current enters through the negative polarity of the voltage, p = – vi Fig 1.5 Polarities for Power using passive sign convention (a) Absorbing Power (b) Supplying Power 1.3.5 ENERGY Energy is the capacity to do work, and is measured in joules (J). The energy absorbed or supplied by an element from time 0 to t is given by, The electric power utility companies measure energy in watt-hours (WH) or Kilo watt-hours (KWH) 1 WH = 3600 J Example 1.6 A source e.m.f. of 5 V supplies a current of 3A for 10 minutes. How much energy is provided in this time? Solution: = = 5 × 3 × 10 × 60 = 9 Example 1.7 An electric heater consumes 1.8Mj when connected to a 250 V supply for 30 minutes. Find the power rating of the heater and the current taken from the supply. Solution: 6 = / = (1.8×10 )/ (30×60) = 1000 Power rating of heater = 1kW = Thus = / =1000/250=4 Hence the current taken from the supply is 4A. Example 1.7 Find the power delivered to an element at =3 if the current entering its positive terminals is =5cos60 and the voltage is: (a) =3 , (b) =3didt. Solution: (a) The voltage is =3 =15cos60 ; hence, the power is: = =75cos260 At =3 , −3 =75cos260 ×3×10 =53.48 (b) We find the voltage and the power as =3 =3 −60 5sin60 =−900 sin60 = =−4500 sin60 cos60 At =3 , =−4500 sin0.18 cos0.18 =−6.396 1.4 OHM’S LAW Georg Simon Ohm (1787–1854), a German physicist, is credited with finding the relationship between current and voltage for a resistor. This relationship is known as Ohm’s law. Ohm’s law states that at constant temperature, the voltage (V) across a conducting material is directly proportional to the current (I) flowing through the material. Mathematically, V I V=RI Wherethe constant of proportionality R is called the resistance of the material. The V-I relation for resistor according to Ohm’s law is depicted in Fig.1.6 Fig. 1.6 V-I Characteristics for resistor Limitations of Ohm’s Law: 1. Ohm’s law is not applicable to non-linear elements like diode, transistor etc. 2. Ohm’s law is not applicable for non-metallic conductors like silicon carbide. 1.5 CIRCUIT ELEMENTS An element is the basic building block of a circuit. An electric circuit is simply an interconnection of the elements. Circuit analysis is the process of determining voltages across (or the currents through) the elements of the circuit. There are 2 types of elements found in electrical circuits. a) Active elements (Energy sources): The elements which are capable of generating or delivering the energy are called active elements. E.g., Generators, Batteries b) Passive element (Loads): The elements which are capable of receiving the energy are called passive elements. E.g., Resistors, Capacitors and Inductors 1.5.1 ACTIVE ELEMENTS (ENERGY SOURCES) The energy sources which are having the capacity of generating the energy are called active elements.The most important active elements are voltage or current sources that generally deliver power/energy to the circuit connected to them. There are two kinds of sources a) Independent sources b) Dependent sources INDEPENDENT SOURCES: An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit elements. Ideal Independent Voltage Source: An ideal independent voltage source is an active element that gives a constant voltage across its terminals irrespective of the current drawn through its terminals. In other words, an ideal independent voltage source delivers to the circuit whatever current is necessary to maintain its terminal voltage. The symbol of idea independent voltage source and its V-I characteristics are shown in Fig. 1.7 Fig. 1.7 Ideal Independent Voltage Source Practical Independent Voltage Source: Practically, every voltage source has some series resistance across its terminals known as internal resistance, and is represented by Rse. For ideal voltage source Rse = 0. But in practical voltage source Rse is not zero but may have small value. Because of this Rse voltage across the terminals decreases with increase in current as shown in Fig. 1.8. Terminal voltage of practical voltage source is given by V = V - I Rse L S L Fig. 1.8 Practical Independent Voltage Source Ideal Independent Current Source: An ideal independent Current source is an active element that gives a constant current through its terminals irrespective of the voltage appearing across its terminals. That is, the current source delivers to the circuit whatever voltage is necessary to maintain the designated current. The symbol of idea independent current source and its V-I characteristics are shown in Fig. 1.9 Fig. 1.9 Ideal Independent Current Source Practical Independent Current Source: Practically, every current source has some parallel/shunt resistance across its terminals known as internal resistance, and is represented by Rsh. For ideal current source Rsh = ∞ (infinity). But in practical voltage source Rsh is not infinity but may have a large value. Because of this Rsh current through the terminals slightly decreases with increase in voltage across its terminals as shown in Fig. 1.10. Terminal current of practical current source is given by I = Is -Ish L Fig. 1.10 Practical Independent Current Source DEPENDENT (CONTROLLED) SOURCES An ideal dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current. Dependent sources are usually designated by diamond-shaped symbols, as shown in Fig. 1.11. Since the control of the dependent source is achieved by a voltage or current of some other element in the circuit, and the source can be voltage or current, it follows that there are four possible types of dependent sources, namely: 1. A voltage-controlled voltage source (VCVS) 2. A current-controlled voltage source (CCVS) 3. A voltage-controlled current source (VCCS) 4. A current-controlled current source (CCCS) Fig. 1.11 Symbols for Dependent voltage source and Dependent current source Dependent sources are useful in modeling elements such as transistors, operational amplifiers, and integrated circuits. An example of a current-controlled voltage source is shown on the right-hand side of Fig. 1.12, where the voltage 10i of the voltage source depends on the current i through element C. Students might be surprised that the value of the dependent voltage source is 10i V (and not 10i A) because it is a voltage source. The key idea to keep in mind is that a voltage source comes with polarities (+ -) in its symbol, while a current source comes with an arrow, irrespective of what it depends on. Fig. 1.12 The source in right hand side is current-controlled voltage source 1.5.2 PASSIVE ELEMENTS (LOADS) Passive elements are those elements which are capable of receiving the energy. Some passive elements like inductors and capacitors are capable of storing a finite amount of energy, and return it later to an external element. More specifically, a passive element is defined as one that cannot supply average power that is greater than zero over a infinite time interval. Resistors, capacitors, Inductors fall in this category. RESISTOR Materials in general have a characteristic behavior of resisting the flow of electric charge. This physical property, or ability to resist the flow of current, is known as resistance and is represented by the symbol R.The Resistance is measured in ohms ( ). The circuit element used to model the current-resisting behavior of a material is called the resistor. Fig. 1.13 (a) Typical Resistor, (b) Circuit Symbol for Resistor The resistance of a resistor depends on the material of which the conductor is made and geometrical shape of the conductor. The resistance of a conductor is proportional to the its length ( and inversely proportional to its cross sectional area (A). Therefore the resistance of a conductor can be written as, The proportionality constant is called the specific resistance o resistivity of the conductor and its value depends on the material of which the conductor is made. The inverse of the resistance is called the conductance and inverse of resistivity is called specific conductance or conductivity. The symbol used to represent the conductance is G and conductivity is . Thus conductivity and its units are siemens per meter By using Ohm’s Law, The power dissipated in a resistor can be expressed in terms of R as below The power dissipated by a resistor may also be expressed in terms of G as The energy lost in the resistor from time 0 to t is expressed as Or Where V is in volts, I is in amperes, R is in ohms, and energy W is in joules Example 1.8 In the circuit shown in Fig. below, calculate the current i, the conductance G, the power p and energy lost in the resistor W in 2hours. Solution: The voltage across the resistor is the same as the source voltage (30 V) because the resistor and the voltage source are connected to the same pair of terminals. Hence, the current is The conductance is We can calculate the power in various ways or or Energy lost in the resistor is INDUCTOR Fig. 1.14 (a) Typical Inductor, (b) Circuit symbol of Inductor A wire of certain length, when twisted into a coil becomes a basic inductor. The symbol for inductor is shown in Fig.1.14(b). If current is made to pass through an inductor, an electromagnetic field is formed. A change in the magnitude of the current changes the electromagnetic field. Increase in current expands the fields, and decrease in current reduces it. Therefore, a change in current produces change in the electromagnetic field, which induces a voltage across the coil according to Faraday's law of electromagnetic induction. i.e., the voltage across the inductor is directly proportional to the time rate of change of current. Mathematically, Where L is the constant of proportionality called the inductance of an inductor. The unit of inductance is henry (H).we can rewrite the above equation as Integrating both sides from time 0 to t, we get From the above equation we note that the current in an inductor is dependent upon the integral of the voltage across its terminal and the initial current in the coil . The power absorbed by the inductor is The energy stored by the inductor is From the above discussion, we can conclude the following. 1. The induced voltage across an inductor is zero if the current through it is constant. That means an inductor acts as short circuit to DC. 2. A small change in current within zero time through an inductor gives an infinite voltage across the inductor, which is physically impossible. In a fixed inductor the current cannot change abruptly i.e., the inductor opposes the sudden changes in currents. 3. The inductor can store finite amount of energy. Even if the voltage across the inductor is zero 4. A pure inductor never dissipates energy, only stores it. That is why it is also called a non- dissipative passive element. However, physical inductors dissipate power due to internal resistance. Example 1.9 Find the current through a 5-H inductor if the voltage across it is Also, find the energy stored at t = 5 s. assume initial conditions to be zero. Solution: The power Then the energy stored is CAPACITOR Fig. 1.15 (a) Typical Capacitor, (b) Capacitor connected to a voltage source, (c) Circuit Symbol of capacitor Any two conducting surfaces separated by an insulating medium exhibit the property of a capacitor. The conducting surfaces are called electrodes, and the insulating medium is called dielectric. A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two electrodes. The electric field is represented by lines of force between the positive and negative charges, and is concentrated within the dielectric. When a voltage source v is connected to the capacitor, as in Fig 1.15 (c), the source deposits a positive charge q on one plate and a negative charge — q on the other. The capacitor is said to store the electric charge. The amount of charge stored, represented by q, is directly pro- proportional to the applied voltage v so that Where C, the constant of proportionality, is known as the capacitance of the capacitor. The unit of capacitance is the farad (F). Although the capacitance C of a capacitor is the ratio of the charge q per plate to the applied voltage v, it does not depend on q or v. It depends on the physical dimensions of the capacitor. For example, for the parallel-plate capacitor shown in Fig.1.15 (a), the capacitance is given by Where A is the surface area of each plate, d is the distance between the plates, and is the permittivity of the dielectric material between the plates. The current flowing through the capacitor is given by We can rewrite the above equation as Integrating both sides from time 0 to t, we get From the above equation we note that the voltage across the terminals of a capacitor is dependent upon the integral of the current through it and the initial voltage . The power absorbed by the capacitor is The energy stored by the capacitor is From the above discussion we can conclude the following, 1. The current in a capacitor is zero if the voltage across it is constant; that means, the capacitor acts as an open circuit to DC. 2. A small change in voltage across a capacitance within zero time gives an infinite current through the capacitor, which is physically impossible. In a fixed capacitance the voltage cannot change abruptly. i.e., A capacitor will oppose the sudden changes in voltages. 3. The capacitor can store a finite amount of energy, even if the current through it is zero. 4. A pure capacitor never dissipates energy, but only stores it; that is why it is called non- dissipative passive element. However, physical capacitors dissipate power due to internal resistance. Example 1.10 Determine the current through a 200 capacitor whose voltage is shown in Fig. below Solution: The voltage waveform can be described mathematically as Since we take the derivative of to obtain the i Hence, the current wave form is as shown in the fig. below 1.6 NETWORK/CIRCUIT TERMINOLOGY In the following section various definitions and terminologies frequently used in electrical circuit analysis are outlined.  Network Elements: The individual components such as a resistor, inductor, capacitor, diode, voltage source, current source etc. that are used in circuit are known as network elements.  Network:The interconnection of network elements is called a network.  Circuit: A network with at least one closed path is called a circuit. So, all the circuits are networks but all networks are not circuits.  Branch: A branch is an element of a network having only two terminals.  Node: A node is the point of connection between two or more branches. It is usually indicated by a dot in a circuit.  Loop: A loop is any closed path in a circuit. A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more than once.  Mesh or Independent Loop: Mesh is a loop which does not contain any other loops in it. 1.7 KIRCHHOFF’S LAWS The most common and useful set of laws for solving electric circuits are the Kirchhoff’s voltage and current laws. Several other useful relationships can be derived based on these laws. These laws are formally known as Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). 1.7.1 KIRCHHOFF’S CURRENT LAW (KCL) This is also called as Kirchhoff's first law or Kirchhoff’s nodal law. Kirchhoff’s first law is based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change. Statement: Algebraic sum of the currents meeting at any junction or node is zero. The term 'algebraic' means the value of the quantity along with its sign, positive or negative. Mathematically, KCL implies that Where N is the number of branches connected to the node and is the nth current entering (or leaving) the node. By this law, currents entering a node may be regarded as positive, while currents leaving the node may be taken as negative or vice versa. Alternate Statement: Sum of the currents flowing towards a junction is equal to the sum of the currents flowing away from the junction. Fig 1.16 Currents meeting in a junction

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