EECKT130 Electrical Circuits 1 PDF

#1 Bachelor of Science in Electrical Engineering FLEX Course Material Introduce electric circuits and its importance. Introduce basic terms and concepts related to electricity and electric circu...

#1 Bachelor of Science in Electrical Engineering FLEX Course Material Introduce electric circuits and its importance. Introduce basic terms and concepts related to electricity and electric circuits. Understand the EECKT130 importance of electrical diagrams in analyzing electric circuits. Electrical Circuits 1 Electrical Parameters and Electrical Terms Christian L. Pao Faculty, BS Electrical Engineering College of Engineering  FOCAL POINTS In the field of electrical engineering, analyzing electric circuits is a must. Electrical parameters gives a hint on how does an electrical component behave. Using diagrams in an electric circuit eases the ability to analyze and troubleshoot a circuit. Lesson 1 Introduction to Electric Circuits ? Lesson 2 Electric Charge and Current Lesson 3 Voltage Lesson 4 Electrical Power and Energy INSIDE Lesson 5 Circuit Elements, Diagrams, and Symbols  #1 Understand the importance of electric circuits in the field of Introduction to Electric electrical engineering. Circuits 3 Introduction to Electric Circuits Electric circuit theory and electromagnetic theory are the two fundamental theories upon which all branches of electrical engineering are built. Many branches of electrical engineering, such as power, electric machines, control, electronics, communications, and instrumentation, are based on electric circuit theory. The basic electric circuit theory course is the most important course for an electrical engineering student, and always an excellent starting point for a beginning student in electrical engineering education. In electrical engineering, we are often interested in communicating or transferring energy from one point to another. To do this requires an interconnection of electrical devices. Such interconnection is referred to as an electric circuit, and each component of the circuit is known as an element. 4 Electric Circuits An electric circuit is an interconnection of electrical elements. A simple electric circuit is shown the figure below. It consists of three basic elements: a battery, a lamp, and connecting wires. Such a simple circuit can exist by itself; it has several applications, such as a flashlight, a search light, and so forth. Electric circuits may be a single loop, multiple loops, or a combination of multiple electric circuits. 5 Electric Circuits Electric circuits are used in numerous electrical systems to accomplish different tasks. The major concern of this course is to be able to analyze electric circuits. By the analysis of a circuit, we mean a study of the behavior of the circuit: How does it respond to a given input? How do the interconnected elements and devices in the circuit interact? To be able to do such, basic concepts must first be defined and be understood. These concepts include charge, current, voltage, circuit elements, power, and energy. 6  #2 Determine the behavior of charge and current. Determine types of Electric current. Formulate the equation of current Charge and Current 7 Electric Charge The concept of electric charge is the underlying principle for explaining all electrical phenomena. Also, the most basic quantity in an electric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). May also be defined as a physical property of matter that causes it to experience a force when placed in an electromagnetic field. 8 Important Notes on Electric Charge The coulomb is a large unit for charges. In 1 C of charge, there are 6.24 * 1018 electrons. Thus realistic or laboratory values of charges are on the order of pC, nC, or μC According to experimental observations, the only charges that occur in nature are integral multiples of the electronic charge: e = -1.602 * 10-19 coulomb. The law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus the algebraic sum of the electric charges in a system does not change. Properties of Charges: Unlike Charges attract and like charges repel. Electric Charge is conserved. Electric Charge is quantized. 9 Electric Current Consider the electric flow of electric charges. A unique feature of electric charge or electricity is the fact that it is mobile; that is, it can be transferred from one place to another, where it can be converted to another form of energy. Electric current is the time rate of change of charge, measured in amperes (A). Shown in the figure below is the behavior of electric current due to flow of electronic charge in a conductor. When a conducting wire is connected to a battery, the charges are compelled to move positive charges move in one direction. negative charges move in the opposite direction. It is conventional to take the current flow as the movement of positive charges. That is, opposite to the flow of negative charges. This convention was introduced by Benjamin Franklin (1706–1790), the American scientist and inventor. Although we now know that current in metallic conductors is due to negatively charged electrons, we will follow the universally accepted convention that current is the net flow of positive charges. Charge flows from positive to negative terminal (Conventional Flow) Charge flows from negative to positive terminal (Electron Flow) 10 Electric Charge and Current Mathematically, the relationship between current i, charge q, and time t is: Where: Current is measured in Amperes (A). 1 ampere = 1 coulomb/second The charge transferred between time t0 and t is obtained by integrating the given equation with respect to t. Thus: Electric charge will flow depending on how electricity is produced. There are several types of current; that is, charge can vary in multiple ways. Two common types of current are direct current and alternating current 11 Direct Current and Alternating Current Direct Current Alternating Current (DC) (AC) A current that remains constant A current that varies with time. (commonly sinusoidally) with “I” is used to represent constant time. current. “i” is used to represent varying current. Devices such as flashlight and Household appliances such as cellphone use this type of television and washing machine current. use this type of current. 12 Sample Problems 1 1. How much charge is represented by 5,200 electrons? 2. Calculate the amount of charge represented by three million protons. 3. The total charge entering a terminal is given by q = 5t sin 4πt mC. Calculate the current at t = 0.6 sec. 4. The total charge entering a terminal is given by q = (10 – 10e-2t) mC. Calculate the current at t = 0.4 sec. 5. Determine the total charge entering the terminal between t = 1 sec and t = 3 sec if the current passing the terminal is i = (4t3 – t) A. 13  #3 Determine the behavior of voltage. Voltage Understand the importance of voltage for the current to flow. Formulate the equation of voltage. 14 Voltage 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). This means that electric current will only be possible if there is a driving force for the charge to move. This EMF is also known as voltage or potential difference. Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V). The voltage between two points in an electric circuit is the energy (or work) needed to move a unit charge; mathematically: Where: Voltage is measured in Volts (V). 1 volt = 1 joule/coulomb 15 Current and Voltage Current and voltage are the two basic variables in electric circuits. The common term signal is used for an electric quantity such as a current or a voltage (or even electromagnetic wave) when it is used for conveying information. Like electric current, a constant voltage is called a DC voltage and is represented by “V”, whereas a sinusoidally time-varying voltage is called an AC voltage and is represented by “v”. A DC voltage is commonly produced by a battery. An AC voltage is produced by an electric generator. 16  #4 Relate the concept of power and energy to electricity Electrical Formulate the equation of electrical power and energy. Power and Energy 17 Power Although current and voltage are the two basic variables in an electric circuit, they are not sufficient by themselves. For practical purposes, we need to know how much power an electric device can handle. Power is the time rate of expending or absorbing energy, measured in watts (W). Mathematically: Where: 1 watt = 1 joule/sec Formula indicated is in time-varying quantities. 18 Electrical Power Following the equations for power, voltage, and current, a new set of formula can be derived as follows: From the given equation, power supplied or absorbed by an element can be defined as the product of the voltage across the element with the current flowing through it. 19 Electrical Power and Energy The law of conservation of energy must be obeyed in any electric circuit. For this reason, the algebraic sum of power in a circuit, at any instant of time, must be zero: The energy absorbed or supplied by an element from time t0 time t is: Energy is the capacity to do work, measured in joules (J). The electric power utility companies measure energy in watt-hours (Wh), where: 1 Wh = 3600 J 1 kWh = 1000 Wh 20 Sample Problems 2 1. An energy source forces a constant current of 3 A for 10 s to flow through a lightbulb. If 2.4 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb. 2. To move charge q from point a to point b requires -40 J. Find the voltage drop vab if: (a) q = 2 C, (b) -8 C. 3. Find the power delivered to an element at t = 4 msec if the current entering its positive terminal is i = 5 cos 60πt A and the voltage is: (a) v = 3i , (b) v = 3di/dt. 4. How much electrical energy does five 100-W electric bulbs consume in three hours? 5. A homeowner consumes 800 kWh in January. Determine the electricity bill for the month using the following residential rate schedule: a. Base monthly charge of $12.00. b. First 100 kWh per month at 16 cents/kWh. c. Next 200 kWh per month at 10 cents/kWh. d. Over 300 kWh per month at 6 cents/kWh. 21  #5 Identify different circuit elements. Circuit Elements, Diagrams, and Determine different types of diagrams used to interpret electric circuits. Read symbols used in electrical diagrams. Symbols 22 Circuit Elements 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 two types of elements found in electric circuits. Active Element - capable of generating energy. Examples are generators, batteries, and operational amplifiers. Passive Element – not capable of generating energy. Examples are resistors, capacitors, and inductors. The most important active elements are voltage or current sources that generally deliver power to the circuit connected to them. There are two kinds of sources: Ideal independent Ideal dependent (or controlled) an active element that provides a an active element in which the specified voltage or current that source quantity is controlled by is completely independent of another voltage or current. other circuit elements. 23 Electrical Diagrams In the field of electrical engineering, diagrams are used to simplify the image of a circuit. Electrical diagrams are illustrations showing how an electric circuit is connected. These diagrams also help to understand how to troubleshoot an electric circuit. There are several types of electrical diagrams that is being used depending on the application. Schematic Diagram Single-Line Diagram Ladder Diagram Wiring Diagram Block Diagram Electrical Plan 24 Electrical Diagrams Schematic Diagram shows the components and interconnections of the circuit using standardized symbolic representations. The presentation of the interconnections between circuit components does not necessarily correspond to the physical arrangements in the finished device. Single-Line Diagram (One-Line Diagram) A more simplified way to represent a electrical connections especially for three-phase power system. Does not show the exact electrical connections of the circuits. Uses a single line to represent all three phases. May show ratings and sizes of electrical equipment and circuit conductors as well as the protective devices. 25 Electrical Diagrams Ladder Diagram specialized schematics commonly used to document industrial control logic systems. called “ladder” diagrams because they resemble a ladder, with two vertical rails (supply power) and as many “rungs” (horizontal lines) as there are control circuits to represent. Wiring Diagram Used to show wiring connections in a simple, easy-to-follow way. Commonly used with home appliances and electrical systems of automobiles. 26 Electrical Diagrams Block Diagram Used to show the relationship between various component groups or stages in the operation of a circuit. Helps in analyzing the operation of a circuit with multiple stages. Electrical Plan A drawing to scale that shows walls and rooms with associated electrical items (Switches, lights, receptacles, etc.) Shown from an above view. Typical also includes a legend of the electrical symbols used in the plan. 27 Symbols used in Schematic Diagram Electrical and electronic symbols are a graphical representation of electrical and electronic components or devices. These symbols are used in circuits to recognize a component Each component has typical functionality according to its operational characteristics. Electrical and electronic symbols used in circuits are defined with various national and international standards. IEC standard, JIC standard, ANSI standard, IEEE standard, etc., Though electrical symbols are standardized, may vary from country to country, or engineering discipline, based on traditional conventions. This enables anyone to read a circuit or schematic diagram with ease and clarity. There is a symbol for each, and every electrical component or device used in a circuit such as passive components, active components, measuring instruments, logic gates etc. 28 Symbols used in Schematic Diagram 29  SUMMARY An electric circuit consists of electrical elements connected together. Current is the rate of charge flow. 𝑑𝑞 𝑖= 𝑑𝑡 Voltage is the energy required to move 1 C of charge through an element. 𝑑𝑤 𝑣= 𝑑𝑡 Power is the energy supplied or absorbed per unit time. It is also the product of voltage and current. 𝑑𝑤 𝑝= = 𝑣𝑖 𝑑𝑡 Voltage and current sources can be dependent or independent. A dependent source is one whose value depends on some other circuit variable. Electrical diagrams are illustrations showing how an electric circuit is connected. 30  ANSWER KEY Sample Problems Please refer to this section if you find trouble in answering the questions given. Sample Problem 1 1. - 8.33 * 10-16 C 2. + 4.806 * 10-13 C 3. 16.405 mA 4. 8.987 mA 5. 76 C Sample Problem 2 1. 80 V 2. (a) – 20 V, (b) + 5 V 3. (a) 39.855 W, (b) -7.055 kW 4. 1,500 Wh or 1.5 kWh 5. $ 78.00 31  REFERENCES Fundamentals of Electric Circuits 4th Ed. By: Alexander and Sadiku Basic Engineering Circuit Analysis 9th Ed. By: Irwin and Nelms Basic Engineering Circuit Analysis 10th Ed. By: Nillson and Riedel Electrical Technology By: B.L. Theraja and A.K. Theraja 32