L L, R, C. Kirchhoff s rules applied to AC circuits. C Examples: Resonant circuits: series and parallel LRC. Filters: narrowband,


 Derrick Adams
 1 years ago
 Views:
Transcription
1 Today in Physics 1: A circuits Solving circuit problems one frequency at a time. omplex impedance of,,. Kirchhoff s rules applied to A circuits. it V in Examples: esonant circuits: i series and parallel. Filters: narrowband, lowpass, highpass V out November 1 Physics 1, Fall 1 1
2 By the book, not. Note that we are not following the techniques introduced in the book, in A circuits. it In the book, A circuit problems are solved by the phasor approach, in which the currents in circuit components are determined by a form of vector addition. In the judgment of your professors, this is a poor choice for introducing an important topic. It is much easier to solve A circuit problems by using the algebra of complex numbers. All but a few have seen complex numbers before, and we can bring the others up to speed quickly. eal engineers and scientists solve A circuit problems with complex numbers, not phasors. November 1 Physics 1, Fall 1
3 One frequency at a time The different timedependent behavior of,, and makes for circuit problems that are superficially difficult. For example: What is the current, I(t), in the circuit at right, for a voltage V(t) which is a general function of time? Vt We can use the second Kirchhoff rule to generate an equation to solve for I = dq/dt: Q di Vt I dt I t dq dq 1 Q V t dt dt November 1 Physics 1, Fall 1 3
4 One frequency at a time (continued) That looks hard to solve, and indeed it is. an t be integrated directly, like all the other differential equations we ve met. But it turns out, as you will find in MTH 81 or ME 1, that any function V(t) can be represented td as a sum of sines and cosines; for example, 1 V t V costd Fourier s theorem where is an angular frequency. Suppose we deal with one frequency at a time. Vt I t November 1 Physics 1, Fall 1 4
5 One frequency at a time (continued) For one frequency component, dq dq 1 Q V cost dt dt and we solve for I dq dt. Q() and I() will still depend on t.? V cost Virtue: Q, and I, will also vary sinusoidally how could they not? apart from a delay resulting from a compromise between the delays between V and I for and : I Q Q cos t sin I I sin t November 1 Physics 1, Fall 1 5
6 One frequency at a time (continued) Even easier, in the algebra and calculus sense, is to use imaginary numbers: it V V e V cos t iv sin t under the agreement that we always take the real part at the end of the problem, as there are no imaginary voltages and currents in nature. In these terms, 1 i t Fourier s V t V e d theorem (again) and we use i only to simplify the math. i t? eve e I November 1 Physics 1, Fall 1 6
7 eminders about imaginary and complex numbers i i 1 i 1 e i e Im A i i i A A e A cos ia sin A e A Im A arctan Im A e 1 Phasor Im A representations of A e A i 1 i complex numbers e A A Electrical engineers usually refer to i as j, for perverse reasons best known to themselves. November 1 Physics 1, Fall 1 7
8 One frequency at a time (continued) et s prove that Q Q e is the solution to the differential equation above: i t dq dq Q V e dt dt Q e i 1 it iq e i t i t 1 Q e i t i t V e i t? eve Qe 1 i V e I November 1 Physics 1, Fall 1 8
9 One frequency at a time (continued) The term in brackets can be written as u1 i u e u euim u 1 i arctan 1 i V i so Qe e, whence u 1 Q V 1, and 1 i t? eve e I November 1 Physics 1, Fall 1 9
10 One frequency at a time (continued) arctan 1 arctan, 1 q.e.d. Furthermore, i t? eve dq it it I iq e Qe dt e I Q cos t Q sin t e I with Q and as given above. November 1 Physics 1, Fall 1 1
11 eactance and impedance eturn for a moment to the differential equation we solved: dq dq Q V e dt dt 1 i t and insert the solution. In the first and third terms we get i t? eve d i t d i t Q e i Q e i I dt dt 1 it 1 d i t Qe Qe 1 I i dt i e I November 1 Physics 1, Fall 1 11
12 eactance and impedance (continued) Thus we can rewrite the differential equation for Q a loop equation, remember as i I I 1 I i t V e i Apparently, at a given frequency, and have a property rather like resistance which relates their current and voltage. We call it reactance, X: Im X 1 e X i X i e V = IX: thus V lags I Phasor X 1 i e g by / for, and leads by / for. representation of the reactances November 1 Physics 1, Fall 1 1
13 eactance and impedance (continued) And thus the series A circuit looks just like a series of resistors in D circuits, the only change being a complex version of Ohm s law: it 1 V V e Ii IZ i Here Z is the impedance of the series combination. So what have we done? 1. By taking one frequency at a time, we have swapped a complicated calculus problem for a simple algebra problem. That s always a good trade. Im X 1 Z e X In phasorspeak, speak Z is the vector sum of the resistances and reactances. November 1 Physics 1, Fall 1 13
14 eactance and impedance (continued). To find currents and voltages in A circuits, inductors and capacitors can be treated with the Kirchhoff rules precisely as resistors are, using the reactances X and X. For example, the current in the series circuit again: 1 1 i V it Z i i Z e I e i Z 1 where Z Z 1 and arctan Im Z e Z arctan Three lines, instead of three pages. November 1 Physics 1, Fall 1 14
15 Parallel circuit Problem 393 in the book, except for a 9 phase shift: Determine the current through each component in this parallel circuit, and the total current leaving the voltage source. V cost November 1 Physics 1, Fall 1 15
16 Parallel circuit (continued) V cost I Individual currents, I I I it I V e X: V i t V i t i t I e I e I i V e i i V V e i t e or, as they would be measured, V V I sin t I cos t I V sin t t November 1 Physics 1, Fall 1 16
17 Parallel circuit (continued) V cost I I I In the second part of the problem we could just add the currents, but it will be useful to compare to the series if we work out the impedance of the parallel combination: i i Z i I Z November 1 Physics 1, Fall 1 17
18 Parallel circuit (continued) V cost I I I 1 arctan Im 1 Z e 1 Z arctan i So the impedance is Z Z e, with Z and as given above, and 1 V V 1 it it I 1 e I e Z I of which the real part gets measured: November 1 Physics 1, Fall 1 18 e I I cos t.
19 Parallel circuit (continued) V cost I I I I 11 4 The circuit draws a lot of current except for angular I frequencies near 1 ; 1 V the resonance in this case is a maximum of impedance. (See 1 below.) November 1 Physics 1, Fall 1 19
20 Parallel circuit (continued) ompare the impedance of the series and parallel circuits at the resonance frequency, 1 : 1 1 Z,series Z,parallel 1 For the series the impedance reaches its minimum at this frequency; for the parallel one, its maximum. November 1 Physics 1, Fall 1
21 Narrowband filter (continued) V in V cos t Vout This suggests the use of circuits as narrowband or notch th filters. For example, series as narrowband: V it V out I e Z Amplitude: V Z,series 1 V 1 V 1 Zseries,series out November 1 Physics 1, Fall 1 1
22 Narrowband filter (continued) g Vout V From this we define the voltage gain, and plot: g ) 1.5 For this plot, component values are chosen such that / = 3., This is a useful building block for signalprocessing circuits: only voltages with frequencies near the resonance frequency are transmitted from the input to the output. November 1 Physics 1, Fall 1
23 owpass filter Many other useful signalprocessing gizmos make good A circuit examples, like this one. Problem 313 in the book: Find the voltage gain, V out V in, in this circuit, and discuss the behavior of the gain when f and f. V in V cos t Vout Note: f = / is the frequency of oscillation, in cycles per unit time. November 1 Physics 1, Fall 1 3
24 owpass filter (continued) V in V cos t Vout As before, we compute the impedance and current: 1 i Z X X i i t V in V e i V i e i t I Z i i 1 V V IX it 1 i e out November 1 Physics 1, Fall 1 4 1
25 owpass filter (continued) V in V cos t Vout i Express in the form Ae : it Ve V out 1 e 1 V 1 e iarctan i tarctan Again, recall that t only the real part is measured. November 1 Physics 1, Fall 1 5
26 owpass filter (continued) V in V cos t Vout The voltage gain is the ratio of the input and output voltages: V g e out 1 cos arctan i t Ve 1 If tan ab, then cos b a b. November 1 Physics 1, Fall 1 6
27 owpass filter (continued) Note the limits of low and high frequency: 1 g 1 g g 1 g 1 1 lim g The circuit efficiently transmits angular frequencies below 1/, and attenuates those above this value; hence its name November 1 Physics 1, Fall 1 7
28 Singlepole lowpass and highpass filters owpass Highpass V in V out V in V out Vin V out V in Vout November 1 Physics 1, Fall 1 8
Course Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits
ourse Updates http://www.phys.hawaii.edu/~varner/phys272spr10/physics272.html eminders: 1) Assignment #10 due Today 2) Quiz # 5 Friday (hap 29, 30) 3) Start A ircuits Alternating urrents (hap 31) In this
More informationI. Impedance of an RL circuit.
I. Impedance of an RL circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the RL circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC
More information1 Phasors and Alternating Currents
Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential
More information12 Chapter Driven RLC Circuits
hapter Driven ircuits. A Sources... . A ircuits with a Source and One ircuit Element... 3.. Purely esistive oad... 3.. Purely Inductive oad... 6..3 Purely apacitive oad... 8.3 The Series ircuit...
More informationChapter 33. Alternating Current Circuits
Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation  Lower case
More informationPhysics 2112 Unit 20. Outline: Driven AC Circuits Phase of V and I Conceputally Mathematically With phasors
Physics 2112 Unit 20 Outline: Driven A ircuits Phase of V and I onceputally Mathematically With phasors Electricity & Magnetism ecture 20, Slide 1 Your omments it just got real this stuff is confusing
More informationAC Circuits Homework Set
Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.
More informationLearnabout Electronics  AC Theory
Learnabout Electronics  AC Theory Facts & Formulae for AC Theory www.learnaboutelectronics.org Contents AC Wave Values... 2 Capacitance... 2 Charge on a Capacitor... 2 Total Capacitance... 2 Inductance...
More informationChapter 32A AC Circuits. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 32A AC Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should be able to: Describe
More informationLectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011
Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits Nov. 7 & 9, 2011 Material from Textbook by Alexander & Sadiku and Electrical Engineering: Principles & Applications,
More informationLecture 24. Impedance of AC Circuits.
Lecture 4. Impedance of AC Circuits. Don t forget to complete course evaluations: https://sakai.rutgers.edu/portal/site/sirs Posttest. You are required to attend one of the lectures on Thursday, Dec.
More informationPart 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is
1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field
More informationz = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1)
11 Complex numbers Read: Boas Ch. Represent an arb. complex number z C in one of two ways: z = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1) Here i is 1, engineers call
More informationRLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is
RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge
More informationLecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1
Physics 1 ecture 1 esonance and power in A circuits Physics 1 ecture 1, Slide 1 I max X X = w I max X w e max I max X X = 1/w I max I max I max X e max = I max Z I max I max (X X ) f X X Physics 1 ecture
More information8.1 Alternating Voltage and Alternating Current ( A. C. )
8  ALTENATING UENT Page 8. Alternating Voltage and Alternating urrent ( A.. ) The following figure shows N turns of a coil of conducting wire PQS rotating with a uniform angular speed ω with respect to
More informationRLC Circuits. 1 Introduction. 1.1 Undriven Systems. 1.2 Driven Systems
RLC Circuits Equipment: Capstone, 850 interface, RLC circuit board, 4 leads (91 cm), 3 voltage sensors, Fluke mulitmeter, and BNC connector on one end and banana plugs on the other Reading: Review AC circuits
More informationPhysics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current
Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current People of mediocre ability sometimes achieve outstanding success because they don't know when to quit. Most men succeed because
More informationPhysics272 Lecture 20. AC Power Resonant Circuits Phasors (2dim vectors, amplitude and phase)
Physics7 ecture 0 A Power esonant ircuits Phasors (dim vectors, amplitude and phase) What is reactance? You can think of it as a frequencydependent resistance. 1 ω For high ω, χ ~0  apacitor looks
More information12. Introduction and Chapter Objectives
Real Analog  Circuits 1 Chapter 1: SteadyState Sinusoidal Power 1. Introduction and Chapter Objectives In this chapter we will address the issue of power transmission via sinusoidal or AC) signals. This
More informationKirchhoff's Laws and Circuit Analysis (EC 2)
Kirchhoff's Laws and Circuit Analysis (EC ) Circuit analysis: solving for I and V at each element Linear circuits: involve resistors, capacitors, inductors Initial analysis uses only resistors Power sources,
More informationAlternating Current Circuits. Home Work Solutions
Chapter 21 Alternating Current Circuits. Home Work s 21.1 Problem 21.11 What is the time constant of the circuit in Figure (21.19). 10 Ω 10 Ω 5.0 Ω 2.0µF 2.0µF 2.0µF 3.0µF Figure 21.19: Given: The circuit
More informationRLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:
RLC Series Circuit In this exercise you will investigate the effects of changing inductance, capacitance, resistance, and frequency on an RLC series AC circuit. We can define effective resistances for
More informationAlternating Current. Chapter 31. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman
Chapter 31 Alternating Current PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 8_8_2008 Topics for Chapter 31
More informationLCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module. What you'll learn in Module 9. Module 9 Introduction
Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing
More informationPHYS 3900 Homework Set #02
PHYS 3900 Homework Set #02 Part = HWP 2.0, 2.02, 2.03. Due: Mon. Jan. 22, 208, 4:00pm Part 2 = HWP 2.04, 2.05, 2.06. Due: Fri. Jan. 26, 208, 4:00pm All textbook problems assigned, unless otherwise stated,
More informationEIT Review 1. FE/EIT Review. Circuits. John A. Camara, Electrical Engineering Reference Manual, 6 th edition, Professional Publications, Inc, 2002.
FE/EIT eview Circuits Instructor: uss Tatro eferences John A. Camara, Electrical Engineering eference Manual, 6 th edition, Professional Publications, Inc, 00. John A. Camara, Practice Problems for the
More informationSolutions For the problem setup, please refer to the student worksheet that follows this section.
1 TASK 3.3.3: SHOCKING NUMBERS Solutions For the problem setup, please refer to the student worksheet that follows this section. 1. The impedance in part 1 of an AC circuit is Z 1 = 2 + j8 ohms, and the
More informationChapter 28: Alternating Current
hapter 8: Alternating urrent Phasors and Alternating urrents Alternating current (A current) urrent which varies sinusoidally in tie is called alternating current (A) as opposed to direct current (D).
More informationAC Circuit Analysis and Measurement Lab Assignment 8
Electric Circuit Lab Assignments elcirc_lab87.fm  1 AC Circuit Analysis and Measurement Lab Assignment 8 Introduction When analyzing an electric circuit that contains reactive components, inductors and
More informationAC Circuits. The Capacitor
The Capacitor Two conductors in close proximity (and electrically isolated from one another) form a capacitor. An electric field is produced by charge differences between the conductors. The capacitance
More informationRLC Circuits and Resonant Circuits
P517/617 Lec4, P1 RLC Circuits and Resonant Circuits Consider the following RLC series circuit What's R? Simplest way to solve for is to use voltage divider equation in complex notation. X L X C in 0
More informationGeneral Physics (PHY 2140)
General Physics (PHY 40) eminder: Exam this Wednesday 6/3 ecture 04 4 questions. Electricity and Magnetism nduced voltages and induction Selfnductance Circuits Energy in magnetic fields AC circuits and
More informationReview of Linear TimeInvariant Network Analysis
D1 APPENDIX D Review of Linear TimeInvariant Network Analysis Consider a network with input x(t) and output y(t) as shown in Figure D1. If an input x 1 (t) produces an output y 1 (t), and an input x
More informationSinusoidal SteadyState Analysis
Chapter 4 Sinusoidal SteadyState Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.
More informationDriven RLC Circuits Challenge Problem Solutions
Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs
More informationPhasors: Impedance and Circuit Anlysis. Phasors
Phasors: Impedance and Circuit Anlysis Lecture 6, 0/07/05 OUTLINE Phasor ReCap Capacitor/Inductor Example Arithmetic with Complex Numbers Complex Impedance Circuit Analysis with Complex Impedance Phasor
More informationThe RC Circuit: An Approach with Fourier Transforms
The RC Circuit: An Approach with Fourier Transforms In this article we shall mathematically analyse the Resistor Capacitor RC) circuit with the help of Fourier transforms FT). This very general technique
More information11. The Series RLC Resonance Circuit
Electronicsab.nb. The Series RC Resonance Circuit Introduction Thus far we have studied a circuit involving a () series resistor R and capacitor C circuit as well as a () series resistor R and inductor
More informationChapter 31: RLC Circuits. PHY2049: Chapter 31 1
hapter 31: RL ircuits PHY049: hapter 31 1 L Oscillations onservation of energy Topics Damped oscillations in RL circuits Energy loss A current RMS quantities Forced oscillations Resistance, reactance,
More informationChapter 21: RLC Circuits. PHY2054: Chapter 21 1
Chapter 21: RC Circuits PHY2054: Chapter 21 1 Voltage and Current in RC Circuits AC emf source: driving frequency f ε = ε sinωt ω = 2π f m If circuit contains only R + emf source, current is simple ε ε
More informationInductance, RL Circuits, LC Circuits, RLC Circuits
Inductance, R Circuits, C Circuits, RC Circuits Inductance What happens when we close the switch? The current flows What does the current look like as a function of time? Does it look like this? I t Inductance
More informationCIRCUIT ANALYSIS II. (AC Circuits)
Will Moore MT & MT CIRCUIT ANALYSIS II (AC Circuits) Syllabus Complex impedance, power factor, frequency response of AC networks including Bode diagrams, secondorder and resonant circuits, damping and
More informationYell if you have any questions
Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored
More informationEXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection
OBJECT: To examine the power distribution on (R, L, C) series circuit. APPARATUS 1signal function generator 2 Oscilloscope, A.V.O meter 3 Resisters & inductor &capacitor THEORY the following form for
More informationLecture 05 Power in AC circuit
CA2627 Building Science Lecture 05 Power in AC circuit Instructor: Jiayu Chen Ph.D. Announcement 1. Makeup Midterm 2. Midterm grade Grade 25 20 15 10 5 0 10 15 20 25 30 35 40 Grade Jiayu Chen, Ph.D. 2
More informationNetwork Graphs and Tellegen s Theorem
Networ Graphs and Tellegen s Theorem The concepts of a graph Cut sets and Kirchhoff s current laws Loops and Kirchhoff s voltage laws Tellegen s Theorem The concepts of a graph The analysis of a complex
More informationNETWORK ANALYSIS WITH APPLICATIONS
NETWORK ANALYSIS WITH APPLICATIONS Third Edition William D. Stanley Old Dominion University Prentice Hall Upper Saddle River, New Jersey I Columbus, Ohio CONTENTS 1 BASIC CIRCUIT LAWS 1 11 General Plan
More informationElectricity & Magnetism Lecture 20
Electricity & Magnetism Lecture 20 Today s Concept: AC Circuits Maximum currents & voltages Phasors: A Simple Tool Electricity & Magne?sm Lecture 20, Slide 1 Other videos: Prof. W. Lewin, MIT Open Courseware
More informationModule 4. Singlephase AC Circuits. Version 2 EE IIT, Kharagpur 1
Module 4 Singlephase A ircuits ersion EE IIT, Kharagpur esson 4 Solution of urrent in  Series ircuits ersion EE IIT, Kharagpur In the last lesson, two points were described:. How to represent a sinusoidal
More informationECE145A/218A Course Notes
ECE145A/218A Course Notes Last note set: Introduction to transmission lines 1. Transmission lines are a linear system  superposition can be used 2. Wave equation permits forward and reverse wave propagation
More informationIn Chapter 15, you learned how to analyze a few simple ac circuits in the time
In Chapter 15, you learned how to analyze a few simple ac circuits in the time domain using voltages and currents expressed as functions of time. However, this is not a very practical approach. A more
More information1 2 U CV. K dq I dt J nqv d J V IR P VI
o 5 o T C T F 3 9 T K T o C 73.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC L pv nrt 3 Ktr nrt 3 CV R ideal monatomic gas 5 CV R ideal diatomic gas w/o vibration V W pdv V U Q W W Q e Q Q e Carnot
More informationEXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA
EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA DISCUSSION The capacitor is a element which stores electric energy by charging the charge on it. Bear in mind that the charge on a capacitor
More informationPhysics 294H. lectures will be posted frequently, mostly! every day if I can remember to do so
Physics 294H l Professor: Joey Huston l email:huston@msu.edu l office: BPS3230 l Homework will be with Mastering Physics (and an average of 1 handwritten problem per week) Helproom hours: 12:402:40
More informationThe simplest type of alternating current is one which varies with time simple harmonically. It is represented by
ALTERNATING CURRENTS. Alternating Current and Alternating EMF An alternating current is one whose magnitude changes continuously with time between zero and a maximum value and whose direction reverses
More information20. Alternating Currents
University of hode sland DigitalCommons@U PHY 204: Elementary Physics Physics Course Materials 2015 20. lternating Currents Gerhard Müller University of hode sland, gmuller@uri.edu Creative Commons License
More informationInductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits
Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Selfinductance A timevarying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying
More informationExam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field
Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,
More informationAC Source and RLC Circuits
X X L C = 2π fl = 1/2π fc 2 AC Source and RLC Circuits ( ) 2 Inductive reactance Capacitive reactance Z = R + X X Total impedance L C εmax Imax = Z XL XC tanφ = R Maximum current Phase angle PHY2054: Chapter
More informationThe Basic Elements and Phasors
4 The Basic Elements and Phasors 4. INTRODUCTION The response of the basic R, L, and C elements to a sinusoidal voltage and current will be examined in this chapter, with special note of how frequency
More informationCM2202: Scientific Computing and Multimedia Applications General Maths: 3. Complex Numbers
CM2202: Scientific Computing and Multimedia Applications General Maths: 3. Complex Numbers Prof. David Marshall School of Computer Science & Informatics A problem when solving some equations There are
More informationLow Pass Filters, Sinusoidal Input, and Steady State Output
Low Pass Filters, Sinusoidal Input, and Steady State Output Jaimie Stephens and Michael Bruce 524 Abstract Discussion of applications and behaviors of low pass filters when presented with a steadystate
More informationNotes on Electric Circuits (Dr. Ramakant Srivastava)
Notes on Electric ircuits (Dr. Ramakant Srivastava) Passive Sign onvention (PS) Passive sign convention deals with the designation of the polarity of the voltage and the direction of the current arrow
More informationRC, RL, and LCR Circuits
RC, RL, and LCR Circuits EK307 Lab Note: This is a two week lab. Most students complete part A in week one and part B in week two. Introduction: Inductors and capacitors are energy storage devices. They
More informationRevision of Basic A.C. Theory
Revision of Basic A.C. Theory 1 Revision of Basic AC Theory (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) Electricity is generated in power stations
More informationSinusoidal SteadyState Analysis
Sinusoidal SteadyState Analysis Almost all electrical systems, whether signal or power, operate with alternating currents and voltages. We have seen that when any circuit is disturbed (switched on or
More informationPHYSICS NOTES ALTERNATING CURRENT
LESSON 7 ALENAING CUEN Alternating current As we have seen earlier a rotating coil in a magnetic field, induces an alternating emf and hence an alternating current. Since the emf induced in the coil varies
More informationSinusoidal Steady State Circuit Analysis
Sinusoidal Steady State Circuit Analysis 9. INTRODUCTION This chapter will concentrate on the steadystate response of circuits driven by sinusoidal sources. The response will also be sinusoidal. For
More informationLecture 9 Time Domain vs. Frequency Domain
. Topics covered Lecture 9 Time Domain vs. Frequency Domain (a) AC power in the time domain (b) AC power in the frequency domain (c) Reactive power (d) Maximum power transfer in AC circuits (e) Frequency
More informationDynamic circuits: Frequency domain analysis
Electronic Circuits 1 Dynamic circuits: Contents Free oscillation and natural frequency Transfer functions Frequency response Bode plots 1 System behaviour: overview 2 System behaviour : review solution
More information02 Operations with Complex Numbers
Simplify. 1. i 10 2. i 2 + i 8 3. i 3 + i 20 4. i 100 5. i 77 esolutions Manual  Powered by Cognero Page 1 6. i 4 + i 12 7. i 5 + i 9 8. i 18 Simplify. 9. (3 + 2i) + ( 4 + 6i) 10. (7 4i) + (2 3i) 11.
More informationGabriel Kron's biography here.
Gabriel Kron, Electric Circuit Model of the Schrödinger Equation, 1945  Component of :... Page 1 of 12 {This website: Please note: The following article is complete; it has been put into ASCII due to
More information1 of 7 8/2/ :10 PM
{This website: Please note: The following article is complete; it has been put into ASCII due to a) space requirement reduction and b) for having thus the possibility to enlarge the fairly small figures.
More informationInductance, RL and RLC Circuits
Inductance, RL and RLC Circuits Inductance Temporarily storage of energy by the magnetic field When the switch is closed, the current does not immediately reach its maximum value. Faraday s law of electromagnetic
More informationChapter 10. Experiment 8: Electromagnetic Resonance Introduction V L V C V R
Chapter 10 Experiment 8: Electromagnetic esonance 10.1 Introduction If a pendulum whose angular frequency is ω 0 for swinging freely is subjected to a small applied force F(t) = F 0 cos ωt oscillating
More informationElectrical Engineering Fundamentals for NonElectrical Engineers
Electrical Engineering Fundamentals for NonElectrical Engineers by Brad Meyer, PE Contents Introduction... 3 Definitions... 3 Power Sources... 4 Series vs. Parallel... 9 Current Behavior at a Node...
More informationPES 1120 Spring 2014, Spendier Lecture 36/Page 1
PES 0 Spring 04, Spenier ecture 36/Page Toay: chapter 3  R circuits: Dampe Oscillation  Driven series R circuit  HW 9 ue Wenesay  FQs Wenesay ast time you stuie the circuit (no resistance) The total
More informationINDUCTORS AND AC CIRCUITS
INDUCTOS AND AC CICUITS We begin by introducing the new circuit element provided by Faraday s aw the inductor. Consider a current loop carrying a current I. The current will produce a magnetic flux in
More informationPHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA.
PHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationElectricity & Magnetism Lecture 21
Electricity & Magnetism Lecture 21 Uncertainties DC Meters! Digital error of at least ±1 digit in the rightmost digit.! Analog 'calibra:on' error is specified by a percentage of the reading, o?en about
More informationCORRESPONDENCE BETWEEN PHASOR TRANSFORMS AND FREQUENCY RESPONSE FUNCTION IN RLC CIRCUITS
CORRESPONDENCE BETWEEN PHASOR TRANSFORMS AND FREQUENCY RESPONSE FUNCTION IN RLC CIRCUITS Hassan Mohamed Abdelalim Abdalla Polytechnic Department of Engineering and Architecture, University of Studies of
More informationELEC 202 Electric Circuit Analysis II Lecture 10(a) Complex Arithmetic and Rectangular/Polar Forms
Dr. Gregory J. Mazzaro Spring 2016 ELEC 202 Electric Circuit Analysis II Lecture 10(a) Complex Arithmetic and Rectangular/Polar Forms THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street,
More informationLecture #3. Review: Power
Lecture #3 OUTLINE Power calculations Circuit elements Voltage and current sources Electrical resistance (Ohm s law) Kirchhoff s laws Reading Chapter 2 Lecture 3, Slide 1 Review: Power If an element is
More informationReview of DC Electric Circuit. DC Electric Circuits Examples (source:
Review of DC Electric Circuit DC Electric Circuits Examples (source: http://hyperphysics.phyastr.gsu.edu/hbase/electric/dcex.html) 1 Review  DC Electric Circuit Multisim Circuit Simulation DC Circuit
More informationCapacitor and Inductor
Capacitor and Inductor Copyright (c) 2015 2017 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or
More informationElectrical measurements:
Electrical measurements: Last time we saw that we could define circuits though: current, voltage and impedance. Where the impedance of an element related the voltage to the current: This is Ohm s law.
More informationDesigning Information Devices and Systems II Spring 2016 Anant Sahai and Michel Maharbiz Midterm 2
EECS 16B Designing Information Devices and Systems II Spring 2016 Anant Sahai and Michel Maharbiz Midterm 2 Exam location: 145 Dwinelle (SIDs ending in 1 and 5) PRINT your student ID: PRINT AND SIGN your
More informationCalculus/Physics Schedule, Second Semester. Wednesday Calculus
/ Schedule, Second Semester Note to instructors: There are two key places where the calculus and physics are very intertwined and the scheduling is difficult: GaussÕ Law and the differential equation for
More informationFourier series. XE31EO2  Pavel Máša. Electrical Circuits 2 Lecture1. XE31EO2  Pavel Máša  Fourier Series
Fourier series Electrical Circuits Lecture  Fourier Series Filtr RLC defibrillator MOTIVATION WHAT WE CAN'T EXPLAIN YET Source voltage rectangular waveform Resistor voltage sinusoidal waveform  Fourier
More informationGet Discount Coupons for your Coaching institute and FREE Study Material at ELECTROMAGNETIC INDUCTION
ELECTROMAGNETIC INDUCTION 1. Magnetic Flux 2. Faraday s Experiments 3. Faraday s Laws of Electromagnetic Induction 4. Lenz s Law and Law of Conservation of Energy 5. Expression for Induced emf based on
More informationPhasor Diagram. Figure 1: Phasor Diagram. A φ. Leading Direction. θ B. Lagging Direction. Imag. Axis Complex Plane. Real Axis
1 16.202: PHASORS Consider sinusoidal source i(t) = Acos(ωt + φ) Using Eulers Notation: Acos(ωt + φ) = Re[Ae j(ωt+φ) ] Phasor Representation of i(t): = Ae jφ = A φ f v(t) = Bsin(ωt + ψ) First convert the
More informationAC Circuits and Electromagnetic Waves
AC Circuits and Electromagnetic Waves Physics 102 Lecture 5 7 March 2002 MIDTERM Wednesday, March 13, 7:309:00 pm, this room Material: through next week AC circuits Next week: no lecture, no labs, no
More informationPhasor mathematics. Resources and methods for learning about these subjects (list a few here, in preparation for your research):
Phasor mathematics This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationPhysics 2112 Unit 11
Physics 2112 Unit 11 Today s oncept: ircuits Unit 11, Slide 1 Stuff you asked about.. what happens when one resistor is in parallel and one is in series with the capacitor Differential equations are tough
More informationDifferential Equations and Linear Algebra Supplementary Notes. Simon J.A. Malham. Department of Mathematics, HeriotWatt University
Differential Equations and Linear Algebra Supplementary Notes Simon J.A. Malham Department of Mathematics, HeriotWatt University Contents Chapter 1. Linear algebraic equations 5 1.1. Gaussian elimination
More informationAlgebraic substitution for electric circuits
Algebraic substitution for electric circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationCapacitance, Resistance, DC Circuits
This test covers capacitance, electrical current, resistance, emf, electrical power, Ohm s Law, Kirchhoff s Rules, and RC Circuits, with some problems requiring a knowledge of basic calculus. Part I. Multiple
More informationReview of Basic Electrical and Magnetic Circuit Concepts EE
Review of Basic Electrical and Magnetic Circuit Concepts EE 442642 Sinusoidal Linear Circuits: Instantaneous voltage, current and power, rms values Average (real) power, reactive power, apparent power,
More informationExam 3 Solutions. The induced EMF (magnitude) is given by Faraday s Law d dt dt The current is given by
PHY049 Spring 008 Prof. Darin Acosta Prof. Selman Hershfield April 9, 008. A metal rod is forced to move with constant velocity of 60 cm/s [or 90 cm/s] along two parallel metal rails, which are connected
More information