M2 Electric Circuit 1 LECTURE 7 INTRODUCTION TO ELECTRIC CIRCUIT Outline 2 Introduction Circuit elements Circuit terminologies Basic laws Time response Responses: sinusoidal vs. non-sinusoidal excitations Complex impedance and frequency response Phasors and AC powers Three-phase systems 1 Electricity: How they work? 3 Electric Circuit 4 • The battery, places a net positive charge at one terminal and a net negative charge on the other • The free electrons (of negative charge) will drift toward the positive terminal • The negative terminal is a “supply” of electrons R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 2 Circuit Elements Active Elements Independent sources Passive Elements 5 • A dependent p source is an active element in which the source quantity is controlled by another voltage or current. • There are four different types: VCVS, CCVS, VCCS, CCCS Dependent sources C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill A Voltage Source 6 R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 3 A Current Source 7 http://www.olympusmicro.com/primer/java/solarcell/ A Power Supply 8 http://www.glentestco.com/product/product_pwrsupply01.htm 4 Resistors 9 http://www.macnn.com/articles/12/05/24/well.designed.adapter.protects.phone.from.damage.malfunction/ http://www.resistorguide.com/metal-film-resistor/ http://www.colourbox.com/image/the-printed-circuit-board-with-computer-chips-resistors-and-condensers-image-2350532 Inductors & Capacitors 10 http://www.splung.com/content/sid/3/page/capacitors http://www.area51esg.com/inductors-coils-chokes.html A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 5 Circuit Terminologies 11 • A branch represents a single element such as a voltage source or a resistor • A node is the point of connection between two or more branches • A loop is a closed path (same beginning and end nodes) with no node passed more than once • A mesh is a loop which does not contain any other loops within it C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill The Almighty Laws: Ohm’s Law 12 • George Simon Ohm • Ge German a (Erlangen, ( a ge , Co Cologne) og e) ((1789–1854) 789 854) • Physicist and Mathematician • Professor of Physics, • University of Cologne http://www-history.mcs.st-and.ac.uk/ Mathematicians/Ohm.html • v-i relationship of a resistor Note: the negative current and voltage result in the graph extended in the 3rd quadrant C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill 6 Kirchhoff’s Laws: KCL 13 • Kirchhoff’s current law http://www.biografiasy vidas.com/biografia/k/ kirchhoff.htm • German (Königsberg, (Königsberg Berlin) (1824-87) • Physicist • Professor of Physics, • University of Heidelberg R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall Kirchhoff’s Laws: KVL 14 Kirchhoff’s voltage law (KVL): the algebraic sum of the potential rises and drops p p around a closed loop p (or path) is zero. These laws will be important bases of circuit theorems and analysis techniques R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 7 Time Response: Resistor 15 There is no limitation on the rate of change imposed on the resistor voltage and current Purely resistive circuit A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning Time Response: R-L 16 A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 8 An Inductor and a Fluorescent Lamp 17 http://www.youtube.com/watch?v=z55566ep0Hg Breaking an Inductive Circuit 18 When the inductor current is interrupted the field begins to collapse causing a large induced voltage across the coil. A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 9 Breaking an Inductive Circuit 19 http://www.youtube.com/watch?v=INbS-71KSz0 Charging a Capacitor 20 http://www.youtube.com/watch?v=IvFVu7Jxa2I 10 Discharging a Capacitor 21 http://www.youtube.com/watch?v=5D2cLj28Pc8 Time Response: RC 22 A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 11 Time Response: RC 23 A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning A Sinusoidal Waveform 24 R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 12 Periodic Functions 25 Squarewave signal Sawtooth signal Full-wave signal Triangular signal R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall https://www.projectrhea.org/rhea/index.php/HW1.4_Ben_Laskowski_-_Periodic_and_Non-Periodic_Functions_ECE301Fall2008mboutin Fourier Series 26 http://www2.math.umd. edu/~dlevy/photos2/ph otos/mathematical_line age/jeanbaptiste_fourier.html French (Auxerre, Grenoble, Paris) (1768–1830) Mathematician, Egyptologist, and Administrator y q Professor of Mathematics,, École Polytechnique R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 13 27 R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall Phasor 28 A phasor is a rotating line whose projection on a vertical axis can be used torepresent sinusoidally varying quantities A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 14 Phasor Illustration 29 http://www.ceb.cam.ac.uk/pages/impedance-analysis-basics.html A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning Resistance and Sinusoidal Excitation • Response in time domain 30 • Phasor (frequency) domain A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 15 Inductance and Sinusoidal Excitation • Response in time domain 31 • Phasor domain A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning Capacitance and Sinusoidal Excitation • Response in time domain 32 • Phasor domain A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 16 Resonance 33 Resonant condition R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall Resonance 34 Practical implication: Capacitor and inductor voltages can be much larger than the supplied voltage R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 17 An Application of a Resonant Circuit 35 • Induction heating f = 15 kHz R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall One-Port vs. Two-Port Networks 36 Two-port network One-port network R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 18 37 Power 38 • Instantaneous power A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 19 Power 39 • Inductor • Observation 1) Average power is zero 2) The power alternately flows into and out of the inductor (also known as reactive power: Q) A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning Power 40 • Capacitor • Observation (similar to the inductor) 1) Average power is zero 2) The power alternately flows into and out of the inductor (also known as reactive power: Q) A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 20 Complex Power 41 S V I V I θ v θ i S V I cos (θ v θ i ) j V I sin (θ v θ i ) S = P + j Q • Power triangle C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill Why Rated VA? 42 • Using only active power • Reactive power is in the picture A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning 21 Three-Phase Systems 43 http://www.ece.umn.edu/users/riaz/animations/alternator.html Three-Phase System 44 Wye connection Delta connection R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall 22