circuit theory basic slides, Exercises of Electrical Engineering

Download circuit theory basic slides and more Exercises Electrical Engineering in PDF only on Docsity! 1 1SM EECE 251, Set 1 EECE251 Circuit Analysis I Set 1: Basic Concepts and Resistive Circuits Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca 2SM Course Material • Lecture notes (http://www.ece.ubc.ca/~shahriar/eece251.html) • Textbook: Basic Engineering Circuit Analysis, 10th edition by J. David Irwin and R. Mark Nelms, John Wiley & Sons, 2011. • Must purchase WileyPlus edition: - Binder Ready version from UBC Bookstore includes access to electronic version online. • Link to our section on WileyPlus: http://edugen.wileyplus.com/edugen/class/cls295775/ • Another good reference: – Fundamentals of Electric Circuits, 4th Edition by Charles Alexander and Matthew Sadiku, McGraw Hill, 2009 EECE 251, Set 1 2 3SM Evaluation • Assignments 10% • Midterms 40% • Final Exam 50% EECE 251, Set 1 4SM Motivation EECE 251, Set 1 Electrical circuits seem to be everywhere! 5 9SM EECE 251, Set 1 A More Complicated Circuit A Radio Receiver 10SM System of Units The International System of Units, or Système International des Unités (SI), also known as metric system uses 7 mutually independent base units. All other units are derived units. SI Base Units 6 11SM SI Prefixes 12SM EECE 251, Set 1 Review of Basic Circuit Concepts • Electric Charge is the basis for describing all electrical phenomena . • Charge is an electrical property of the atomic particles of which matter consists and is measured in coulombs (Charles Augustin de Coulomb (1736-1806) a French Scientist) • Inside an atom, there is negative charge on electrons, positive charge on protons and no charge on neutrons. • The charge of an electron is equal to that of an proton and is: e =1.602 × 10 -19 C 7 13SM EECE 251, Set 1 Charge • Note that in 1C of charge there are: 1/ 1.602 × 10 -19 = 6.24 × 10 18 electrons • Laboratory values of charges are more likely to be a fraction of a Coulumb (e.g., pC, nC, µC, or mC). • Law of conservation of charge: charge can neither be created nor destroyed, only transferred. (This is a law in classical physics and may not be true in some odd cases!. We are not dealing with those cases anyway.) • Electrical effects are attributed to both separation of charges and/or charges in motion! 14SM EECE 251, Set 1 A Material Classification • Conductor: a material in which charges can move to neighboring atoms with relative ease. – One measure of this relative ease of charge movement is the electric resistance of the material – Example conductor material: metals and carbon – In metals the only charged particles that can move are electrons • Insulator: a material that opposes the charge movement (ideally infinite opposition, i.e., no charge movement) – Example insulators: Dry air and glass • Semi-conductor: a material whose conductive properties are somewhat in between those of conductor and insulator – Example semi-conductor material: Silicon with some added impurities 10 19SM Magnitude of Some Typical Currents EECE 251, Set 1 20SM EECE 251, Set 1 Voltage (Separation of Charge) • Voltage (electromotive force, or potential) is the energy required to move a unit charge through a circuit element, and is measured in Volts (Alessandro Antonio Volta (1745-1827) an Italian Physicist). • Similar to electric current, there are two important types of voltage: DC and AC dq dW v = 11 21SM Typical Voltage Magnitudes EECE 251, Set 1 22SM Voltage • “Voltage between two points in a circuit is the difference in energy level of a unit charge located at each of the two points. • Voltage is very similar to a gravitational force. • Some examples: EECE 251, Set 1 12 23SM EECE 251, Set 1 Voltage Polarity • The plus (+) and minus (-) sign are used to define voltage polarity. • The assumption is that the potential of the terminal with (+) polarity is higher than the potential of the terminal with (-) polarity by the amount of voltage drop. • The polarity assignment is somewhat arbitrary! Is this a scientific statement?!! What do you mean by arbitrary?!!! 24SM EECE 251, Set 1 Voltage Polarity • Figures (a) and (b) are two equivalent representation of the same voltage: • Both show that the potential of terminal a is 9V higher than the potential of terminal b. 15 29SM EECE 251, Set 1 Passive Sign Convention • Calculate the power absorbed or supplied by each of the following elements: 30SM Example • Given the two diagrams shown below, determine whether the element is absorbing or supplying power and how much. EECE 251, Set 1 16 31SM Example • Determine the unknown voltage or current in the following figures: EECE 251, Set 1 32SM Example • Suppose that your car is not starting. To determine whether the battery is faulty, you turn on the light switch and find that the lights are very dim, indicating a weak battery. You borrow a friend's car and a set of jumper cables. However, how do you connect his car's battery to yours? What do you want his battery to do? EECE 251, Set 1 17 33SM EECE 251, Set 1 Energy Calculation • Instantaneous power: • Energy absorbed or supplied by an element from time t0 to time t>t0 )()()( titvtp = ∫ ∫=== t t t t divdpttWW 0 0 )()()(),( 0 τττττ Remainder of Circuit Circuit element consuming/generating power p(t) + - )(tv )(ti 34SM Circuit Elements • Circuit components can be broadly classified as being either active or passive. • An active element is capable of generating energy. – Example: current or voltage sources • A passive element is an element that does not generate energy, however, they can either consume or store energy. – Example: resistors, capacitors, and inductors EECE 251, Set 1 20 39SM EECE 251, Set 1 Ideal Dependent (Controlled) Source • An ideal dependent (controlled) source is an active element whose quantity is controlled by a voltage or current of another circuit element. • Dependent sources are usually presented by diamond-shaped symbols: 40SM EECE 251, Set 1 Dependent (Controlled) Source • There are four types of dependent sources: • Voltage-controlled voltage source (VCVS) • Current-controlled voltage source (CCVS) + - V s (t)= I(t) + - V(t) I(t) 21 41SM EECE 251, Set 1 Dependent (Controlled) Source • Voltage-controlled current source (VCCS) • Current-controlled current source (CCCS) I s (t)= V(t) + - V(t) I(t) 42SM EECE 251, Set 1 Example: Dependent Source • In the following circuits, identify the type of dependent sources: 22 43SM Example: Power Calculation • Compute the power absorbed or supplied by each component in the following circuit. EECE 251, Set 1 44SM Example • Use Tellegan’s theorem to find the current I0 in the following circuit: EECE 251, Set 1 25 49SM EECE 251, Set 1 Resistance • The constant of the proportionality is the resistivity of the material, i.e., ρ A l R ∝ A l R ρ= 50SM EECE 251, Set 1 Resistance • In honor of George Simon Ohm (1787-1854), a German physicist, the unit of resistance is named Ohm (Ω). • A conductor designed to have a specific resistance is called a resistor. 26 51SM EECE 251, Set 1 Ohm’s Law • The voltage v across a resistor is directly proportional to the current i flowing through the resistor. The proportionality constant is the resistance of the resistor, i.e., • One can also write: • Instantaneous power dissipated in a resistor )()( tRitv = )()()( 1 )( tGvtitv R ti =⇒= )( )( )()()( 2 2 tRi R tv titvtp === 52SM EECE 251, Set 1 Linear and Nonlinear Resistors • Linear resistor Nonlinear resistor • In this course, we assume that all the elements that are designated as resistors are linear (unless mentioned otherwise) 27 53SM EECE 251, Set 1 Resistors (Fixed and Variable) • Fixed resistors have a resistance that remains constants. • Two common type of fixed resistors are: (a) wirewound (b) composition (carbon film type) 54SM Fixed Resistors • Inside the resistor • A common type of resistor that you will work with in your labs: • It has 4 color-coded bands (3 for value and one for tolerance) – How to read the value of the resistor? EECE 251, Set 1 30 59SM Example • Given the following network, find R and VS. EECE 251, Set 1 60SM Example • Given the following circuit, find the value of the voltage source and the power absorbed by the resistance. EECE 251, Set 1 31 61SM Wheatstone Bridge • A Wheatstone Bridge circuit is an accurate device for measuring resistance. The circuit, shown below, is used to measure the unknown resistor Rx. The center leg of the circuit contains a galvanometer (a very sensitive device used to measure current). When the unknown resistor is connected to the bridge, R3 is adjusted until the current in the galvanometer is zero, at which point the bridge is balanced. EECE 251, Set 1 62SM Wheatstone Bridge • In the balanced condition: That is: • Invented by Samuel Hunter Christie (1784–1865), a British scientist and mathematician. • Improved and popularized by Sir Charles Wheatstone FRS (1802–1875), an English scientist and inventor EECE 251, Set 1 xR R R R 2 3 1 = 3 1 2 R R R Rx       = 32 63SM Wheatstone Bridge • Engineers use the Wheatstone bridge circuit to measure strain in solid material. For example, in a system used to determine the weight of a truck (shown below). The platform is supported by cylinders on which strain gauges are mounted. The strain gauges, which measure strain when the cylinder deflects under load, are connected to a Wheatstone bridge. EECE 251, Set 1 64SM Wheatstone Bridge • Typically, the strain gauge has a resistance of 120Ω under no-load conditions and changes value under load. The variable resistor in the bridge is a calibrated precision device. EECE 251, Set 1 35 69SM Loop • A “loop” is any closed path in the circuit that does not cross any true node but once. • A “window pane loop” is a loop that does not contain any other loops inside it. • An “independent loop” is a loop that contains at least one branch that is not part of any other independent loop. EECE 251, Set 1 70SM EECE 251, Set 1 Example • In the following circuit, find the number of branches, nodes, and window pane loops. Are the window pane loops independent? 36 71SM EECE 251, Set 1 Series and Parallel Connections • Two or more elements are connected “in series” when they belong to the same branch.(even if they are separated by other elements). • In general, circuit elements are in series when they are sequentially connected end-to-end and only share binary nodes among them. • Elements that are in series carry the same current. 72SM EECE 251, Set 1 Series and Parallel Circuits • Two or more circuit elements are “in parallel” if they are connected between the same two “true nodes”. • Consequently, parallel elements have the same voltage 37 73SM EECE 251, Set 1 Kirchhoff’s Current Law (KCL) • Gustav Robert Kirchhoff (1824-1887), a German physicist, stated two basic laws concerning the relationship between the currents and voltages in an electrical circuit. • KCL: The algebraic sum of the currents entering a node (or a closed boundary) is zero. • The current entering a node may be regarded as positive while the currents leaving the node may be taken as negative or vice versa. 74SM EECE 251, Set 1 KCL • KCL is based on the law of conservation of charge. • Example: Write the KCL for the node A inside this black box circuit: i4 i3 i2 i1 Black box circuit A 40 79SM EECE 251, Set 1 KCL Example • Draw an appropriate closed boundary to find I in the following graphical circuit representation. 2A 3A I 80SM Example • In the following circuit, use a closed surface to find I4. EECE 251, Set 1 41 81SM EECE 251, Set 1 Kirchhoff’s Voltage Law (KVL) • KVL: The algebraic sum of the voltage drops around any closed path (or loop) is zero at any instance of time. • Write KVL for the above circuit. Sum of voltage drops=Sum of voltage rises 82SM EECE 251, Set 1 KVL Example • Find VAC and VCH in the following circuit. -2V A B C D E G F H + + + - - - - 2V 1V + 4V 42 83SM EECE 251, Set 1 Example • In the following circuit, find vo and i. 84SM Example • In the following circuit, assume VR1=26V and VR2=14V. Find VR3. EECE 251, Set 1 45 89SM EECE 251, Set 1 Voltage Division • In a series combination of n resistors, the voltage drop across the resistor Rj for j=1,2, …, n is: • What is the formula for two series resistors?! )()( 21 tv RRR R tv in n j j +++ = L 90SM EECE 251, Set 1 Parallel Resistors • The equivalent conductance of resistors connected in parallel is the sum of their individual conductances: • Why? neq neq RRRR GGGG 1111 21 21 +++=+++= LL or 46 91SM EECE 251, Set 1 Current Division • In a parallel combination of n resistors, the current through the resistor Rj for j=1,2, …, n is: • Why? )()( 21 ti GGG G ti in n j j +++ = L 92SM EECE 251, Set 1 Parallel Resistors and Current Division Example • For the special case of two parallel resistors • Why? )()(),()(, 21 1 2 21 2 1 21 21 ti RR R titi RR R ti RR RR Req + = + = + = and 47 93SM EECE 251, Set 1 Example • In the following circuit find Req: 94SM Example • In the following circuit find the resistance seen between the two terminal s A and B, i.e., RAB • EECE 251, Set 1 50 99SM Example • Given the network shown in Fig. 2.31: (a) find the required value for the resistor R; (b) use Table 2.1 to select a standard 10% tolerance resistor for R; (c) using the resistor selected in (b), determine the voltage across the 3.9-kΩ resistor; (d) calculate the percent error in the voltage V1, if the standard resistor selected in (b) is used; and (e) determine the power rating for this standard component. EECE 251, Set 1 100SM Board Notes EECE 251, Set 1 51 101SM EECE 251, Set 1 Wye-Delta Transformations • In some circuits the resistors are neither in series nor in parallel. • For example consider the following bridge circuit: how can we combine the resistors R1 through R6? 102SM EECE 251, Set 1 Wye and Delta Networks • A useful technique that can be used to simply many such circuits is transformation from wye (Y) to delta (∆) network. • A wye (Y) or tee (T) network is a three-terminal network with the following general form: 52 103SM EECE 251, Set 1 Wye and Delta Networks • The delta (∆) or pi (Π) network has the following general form: 104SM EECE 251, Set 1 Delta-Wye Conversion • In some cases it is more convenient to work with a Y network in place of a ∆ network. • Let’s superimpose a wye network on the existing delta network and try to find the equivalent resistances in the wye network