MET 487 Instrumentation and Automatic Control. Lecture 3
|
|
- Joel Gibbs
- 5 years ago
- Views:
Transcription
1 MET 487 Instrumentation and Automatic Control Lecture 3 Electrical Circuits and Components Lecture 2 - By P. Lin 1 Electrical Circuits and Components Basic Electrical Elements Resistor, Capacitor, Inductor Kirchhoff s s Laws KVL, KCL Series Circuits, Parallel Circuits Circuit Analysis Voltage and Current Sources and Meters Input and Output Impedance Alternating Current Circuit AC Circuit Analysis Impedance Matching Grounding and Electrical Interference Electrical Safety August 30, 2005 Lecture 2 - By P. Lin 2
2 Basic Electrical Elements Resistor Ohm s s Law: V = I*R, I = V/R, R = V/I Wire Resistance L R = ρ A Example: find the resistance of a copper wire: 1.0 mm in diameter, 10 m long Solution: ρ = 1.7x10-8 Ωm, D = m, r = D/2, L = 10m A = π r 2 = π (D 2 /4) = 7.8 x 10-7 m 2 R = ρ L/A = 0.22 Ω August 30, 2005 Lecture 2 - By P. Lin 3 Color Coded Resistor Lecture 2 - By P. Lin 4
3 Color Coded Resistor - Examples August 30, 2005 Lecture 2 - By P. Lin 5 Series Resistors Rt = R1 + R2 sum of resistance (ohms) Rt = = 220 Ω Two resistors plus wire resistance in series Rt = R1 + R2 + R3 Rt = = Ω Lecture 2 - By P. Lin 6
4 I Parallel Resistors A Vs I1 + I2 + - R1 R2 - I = Vs/R1 + Vs/R2 = Vs/(1/R1 + 1/R2) = Vs/ [(R1 *R2)/(R1 + R2)] = Vs/Rt Rt = (Product OVER Sum) If Vs = 12V, R1 = 10kΩ,, R2 = 10kΩ, Rt = 10k*10k/(10k+10k) = 5k I = 12/5k = 2.4 ma,, I1 = I2 = 1.2 ma V1 = V2 = Vs = 12 v Lecture 2 - By P. Lin 7 MATLAB Examples MATLAB Sum Calculator: enter the following lines at the MATLAB command window: >> ans = 220 >> Rt = Rt = 220 >> R1 = 100; >> R2 = 120; >> R1 + R ans = August 30, 2005 Lecture 2 - By P. Lin 8
5 Voltage Divider (Resistors in Series) IF R1 = 10K, VR2 = 12*10K/(10K+10K) = 6V IF R1 = 5K, VR2 = 12*10K/(5K+10K) = 12*2/3 = 8 V IF R1 = 2K, VR2 = 12*10K/(2K+10K) = 12*10/12 = 10 V Lecture 2 - By P. Lin 9 Electric Power Example: Electric Power Calculation, for R = 15 ohms, voltage = 120 volts: P = V^2 /R (watts). MATLAB Solution: >>R = 15.0; >>V = 120; >>P = V^2 / R P = 960 August 30, 2005 Lecture 2 - By P. Lin 10
6 Prefix and Power Some Prefixes for SI Units (International Standard) Power Prefix yocto zepto atto femto pico 10-9 nano 10-6 micro Abbrevi ation y z a f p n μ August 30, 2005 Lecture 2 - By P. Lin 11 Prefix and Power Some Prefixes for SI Units (International Standard) Power Prefix 10-3 milli 10-2 centi 10-1 deci 10 1 deka 10 3 kilo 10 6 mega 10 9 giga Abbrevi ation m c d da k M G Source: August 30, 2005 Lecture 2 - By P. Lin 12
7 Prefix and Power Some Prefixes for SI Units (International Standard) Power Prefix 10 tera 10 peta 10 exa 10 Zetta 10 Yotta Abbreviation T P E Z Y August 30, 2005 Lecture 2 - By P. Lin 13 Capacitor Capacitor q( t) 1 V ( t) = = I d C C ( τ ) τ I( t) = C dv dt Capacitors in Series Ceq = C1*C2/(C1 + C2) t 0 Capacitor in Parallel Ceq = C1 + C2 Ceq C1 C2 August 30, 2005 Lecture 2 - By P. Lin 14
8 Inductor Inductor dλ dφ V ( t) = L = L dt dt λ = LI, φ = LI di V ( t) = L dt 1 I( t) = L t 0 V ( τ ) dτ Inductors in Series Leq = L1 + L2 August 30, 2005 Lecture 2 - By P. Lin 15 Inductor Inductors in Parallel Leq = (L1* L2)/(L1 + L2) August 30, 2005 Lecture 2 - By P. Lin 16
9 Kirchhoff Voltage Law I2 + R2 - - V2 + I3 I1 R1 V1 + + I V3 R3 - E = 12V V4 - R4 + I4 August 30, 2005 Lecture 2 - By P. Lin 17 Kirchhoff Current Law I1 I3 I2 R1 V1 R2 V2 R3 V3 + + E = 12V E = 5V August 30, 2005 Lecture 2 - By P. Lin 18
10 Alternating Current AC Signal (voltage) V(t) ) = V m sin(ωt t + Φ) ) = V m sin(2πft + Φ) V(t) ) = Vdc + Vm sin(ωt t + Φ) --- with DC offset V m -- Amplitude (volt) V rms -- Root-Mean Square, or Effective value f -- Frequency (Hz) ω= = 2 π f t -- Radian frequency (rad( rad/sec) Φ = ωδt -- Phase Angle, leading or lagging T = 1/f -- Period (second) Example f = 60 Hz, T = 1/f = 16.7 ms, ω = 2πft 2 = t V rms = 120 V m = V rms = 169.7v, Φ = 45º = π/4 = radian V(t) ) = V m sin(2πft + Φ) ) = sin(377.7 t ) Volt August 30, 2005 Lecture 2 - By P. Lin 19 Alternating Current Click -> Debug -> Run August 30, 2005 Lecture 2 - By P. Lin 20
11 Alternating Current AC Signal (voltage) - Time domain equation V(t) ) = V m sin(ωt t + Φ) ) = Vm sin(2πft + Φ) Euler s s Formula e j(ωt+ t+φ) = cos(ωt t + Φ) ) +j sin(ωt t +Φ) + j= -1, also called 90 degree operator Polar Form Vrms = 120 v, Φ = 45º,, f = 60 Hz, ω = rad/sec V = V m e j(ωt+ t+φ) => V m /Φ = 120 /45/ 45º MATLAB Example: >> V = 169.7*exp(j*pi/4) V = i August 30, 2005 Lecture 2 - By P. Lin 21 Alternating Current Rectangular form V = Vm*cos cos(φ) ) + j Vm sin(φ) = * cos(45º) ) + j * sin (45º) = * cos(π/4) + j *sin(π/4) MATLAB Example >> V = *cos(pi/4)+j*169.7*sin(pi/4) V = i August 30, 2005 Lecture 2 - By P. Lin 22
12 AC Circuit Analysis A RLC circuit is shown on this slide, find a) Total impedance Z b) Voltage and current across each components Lecture 2 - By P. Lin 23 AC Circuit Analysis(continue) Analysis: Domain knowledge XL = 2πfL, where L is the inductance in Henry, f is the frequency of ac source XC = 1/(2 πfc), where C is the capacitance in Farard Z = R + j(xl XC) -- total impedance, where j shows the imaginary component of a complex number I = E/Z, total current VR = I*R, voltage drop across resistor VL = I*XL, voltage drop across the inductor VC = I*XC voltage drop across the capacitor Lecture 2 - By P. Lin 24
13 AC Circuit Analysis (continue) MATLAB Program %RLC_1.m f = 60; R = 8; % Peak value of the sine wave e = 10; XL = j*6; XC = -j*2; Z = R + (XL+XC) theta = angle(z) % pi % 180 pi % = ---- % theta_degree theta theta_degree = (180*theta)/pi % degree = pi mag_z = abs(z) Phasor Representation of Impedance Z = 8 + j*4 Lecture 2 - By P. Lin 25 AC Circuit Analysis (continue) MATLAB Program (cont.) %RLC_1.m % I = e/z I_thea_degree = angle(i) * (180)/pi I_mag = abs(i) VR = I*R VL = I*XL VC = I*XC KVL = e (VR + (VL + VC)) I = i I_theta_deg = I_mag = VR = i VL = i VC = i KVL = 0 Lecture 2 - By P. Lin 26
14 Power in Electrical Circuits Power: P = W/T = dw/dt Instantaneous Power in Resistive Circuits P = VI = I 2 R = V 2 /R Average Power Pavg = 0.5*(V m *I m )*cos cos(θ) V m = 2 2 * V rms ; I m = 2* 2*I rms Pavg = V rms *I rms *cos(θ) Average Power Consumed by a Resistor Pavg = V rms *I rms = RI 2 rms = V 2 rms /R August 30, 2005 Lecture 2 - By P. Lin 27 Power in Electrical Circuits Average Power Consumed by an AC Network Pavg = V rms *I rms *cos(θ) = I 2 rms Z * cos(θ) = (V 2 rms / Z ) * cos(θ) Power Factor (PF) PF = cos(θ): 0.75, 0.8, 0.85, 0.9, Lecture 23 - By P. Lin 28
REACTANCE. By: Enzo Paterno Date: 03/2013
REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or
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 informationCircuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18
Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)
More informationELECTRONICS E # 1 FUNDAMENTALS 2/2/2011
FE Review 1 ELECTRONICS E # 1 FUNDAMENTALS Electric Charge 2 In an electric circuit it there is a conservation of charge. The net electric charge is constant. There are positive and negative charges. Like
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques
More informationEE-0001 PEEE Refresher Course. Week 1: Engineering Fundamentals
EE-000 PEEE efresher Course Week : Engineering Fundamentals Engineering Fundamentals Bentley Chapters & Camara Chapters,, & 3 Electrical Quantities Energy (work), power, charge, current Electrostatic pressure,
More informationSinusoids and Phasors
CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying
More information2. Basic Components and Electrical Circuits
1 2. Basic Components and Electrical Circuits 2.1 Units and Scales The International System of Units (SI) defines 6 principal units from which the units of all other physical quantities can be derived
More informationINDUSTRIAL ELECTRICITY
INDUSTRIAL ELECTRICITY TODAY S TOPICS: Introduction (cont) Scientific Notation DUE Mon 1/13 11:00am HOMEWORK 1 Reading quizzes 1 & 2 Worksheet 1 QUESTIONS?? Scantron Use for reading quizzes only Don t
More informationSinusoidal Response of RLC Circuits
Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit R-L Series Circuit R-L Series Circuit R-L Series Circuit Instantaneous
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 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 informationChapter 10: Sinusoids and Phasors
Chapter 10: Sinusoids and Phasors 1. Motivation 2. Sinusoid Features 3. Phasors 4. Phasor Relationships for Circuit Elements 5. Impedance and Admittance 6. Kirchhoff s Laws in the Frequency Domain 7. Impedance
More informationPHY Tables & Formulas. You may refer to this handout on quizzes & exams. Do not add additional information. m
PHY 132 - Tables & Formulas You may refer to this handout on quizzes & exams. Do not add additional information. m Things you should know from PHY 131 and other prerequisites. (If you don t, learn them
More informationChapter 9 Objectives
Chapter 9 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 9 Objectives Understand the concept of a phasor; Be able to transform a circuit with a sinusoidal source into the frequency domain using phasor
More informationECE 241L Fundamentals of Electrical Engineering. Experiment 6 AC Circuits
ECE 241L Fundamentals of Electrical Engineering Experiment 6 AC Circuits A. Objectives: Objectives: I. Calculate amplitude and phase angles of a-c voltages and impedances II. Calculate the reactance and
More information04-Electric Power. ECEGR 452 Renewable Energy Systems
04-Electric Power ECEGR 452 Renewable Energy Systems Overview Review of Electric Circuits Phasor Representation Electrical Power Power Factor Dr. Louie 2 Introduction Majority of the electrical energy
More informationBasic Electrical Circuits Analysis ECE 221
Basic Electrical Circuits Analysis ECE 221 PhD. Khodr Saaifan http://trsys.faculty.jacobs-university.de k.saaifan@jacobs-university.de 1 2 Reference: Electric Circuits, 8th Edition James W. Nilsson, and
More informationLINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09
LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09 ENGR. M. MANSOOR ASHRAF INTRODUCTION Thus far our analysis has been restricted for the most part to dc circuits: those circuits excited by constant or time-invariant
More informationLesson 1.1 MEASUREMENT, UNITS, SCIENTIFIC NOTATION, AND PRECISION
Lesson 1.1 MEASUREMENT, UNITS, SCIENTIFIC NOTATION, AND PRECISION I. Measurements Measurements can be either Qualitative or Quantitative Qualitiative Quality, like a color or smell, are simple observations
More informationLearnabout Electronics - AC Theory
Learnabout Electronics - AC Theory Facts & Formulae for AC Theory www.learnabout-electronics.org Contents AC Wave Values... 2 Capacitance... 2 Charge on a Capacitor... 2 Total Capacitance... 2 Inductance...
More informationFE Review 2/2/2011. Electric Charge. Electric Energy ELECTRONICS # 1 FUNDAMENTALS
FE eview ELECONICS # FUNDAMENALS Electric Charge 2 In an electric circuit there is a conservation of charge. he net electric charge is constant. here are positive and negative charges. Like charges repel
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 informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis
More information15-884/484 Electric Power Systems 1: DC and AC Circuits
15-884/484 Electric Power Systems 1: DC and AC Circuits J. Zico Kolter October 8, 2013 1 Hydro Estimated U.S. Energy Use in 2010: ~98.0 Quads Lawrence Livermore National Laboratory Solar 0.11 0.01 8.44
More information11. AC Circuit Power Analysis
. AC Circuit Power Analysis Often an integral part of circuit analysis is the determination of either power delivered or power absorbed (or both). In this chapter First, we begin by considering instantaneous
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 informationChapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson
Chapter 2 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 2 Objectives Understand symbols and behavior of the following circuit elements: Independent voltage and current sources; Dependent voltage and
More informationa + b Time Domain i(τ)dτ.
R, C, and L Elements and their v and i relationships We deal with three essential elements in circuit analysis: Resistance R Capacitance C Inductance L Their v and i relationships are summarized below.
More information1.1 - Scientific Theory
1.1 - Scientific Theory Babylonians/Egyptians Observation for the practical Religious Agriculture Pseudosciences (science + nonscience) Alchemy Astrology, etc. Greeks Good Theoreticians (knowledge for
More informationHarold s AP Physics Cheat Sheet 23 February Electricity / Magnetism
Harold s AP Physics Cheat Sheet 23 February 206 Kinematics Position (m) (rad) Translation Horizontal: x = x 0 + v x0 t + 2 at2 Vertical: y = y 0 + v y0 t 2 gt2 x = x 0 + vt s = rθ x = v / Rotational Motion
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 informationEXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection
OBJECT: To examine the power distribution on (R, L, C) series circuit. APPARATUS 1-signal function generator 2- Oscilloscope, A.V.O meter 3- Resisters & inductor &capacitor THEORY the following form for
More informationElectrical Engineering Fundamentals for Non-Electrical Engineers
Electrical Engineering Fundamentals for Non-Electrical Engineers by Brad Meyer, PE Contents Introduction... 3 Definitions... 3 Power Sources... 4 Series vs. Parallel... 9 Current Behavior at a Node...
More informationNote 11: Alternating Current (AC) Circuits
Note 11: Alternating Current (AC) Circuits V R No phase difference between the voltage difference and the current and max For alternating voltage Vmax sin t, the resistor current is ir sin t. the instantaneous
More informationELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT
Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the
More informationRefresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas
Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas A specifically designed programme for Da Afghanistan Breshna Sherkat (DABS) Afghanistan 1 Areas Covered Under this Module
More informationElectricity. From the word Elektron Greek for amber
Electricity From the word Elektron Greek for amber Electrical systems have two main objectives: To gather, store, process, transport information & Energy To distribute and convert energy Electrical Engineering
More informationAlternating Current Circuits
Alternating Current Circuits AC Circuit An AC circuit consists of a combination of circuit elements and an AC generator or source. The output of an AC generator is sinusoidal and varies with time according
More informationElectric Circuit Theory
Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1
More information09/29/2009 Reading: Hambley Chapter 5 and Appendix A
EE40 Lec 10 Complex Numbers and Phasors Prof. Nathan Cheung 09/29/2009 Reading: Hambley Chapter 5 and Appendix A Slide 1 OUTLINE Phasors as notation for Sinusoids Arithmetic with Complex Numbers Complex
More informationConsider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current.
AC power Consider a simple RC circuit We might like to know how much power is being supplied by the source We probably need to find the current R 10! R 10! is VS Vmcosωt Vm 10 V f 60 Hz V m 10 V C 150
More information8/17/2016. Summary. Summary. Summary. Chapter 1 Quantities and Units. Passive Components. SI Fundamental Units. Some Important Electrical Units
Passive Components Chapter 1 Quantities and Units Welcome to the Principles of Electric Circuits. You will study important ideas that are used in electronics. You may already be familiar with a few of
More informationSI base units. SI : Système International d'unités (International System of Units)
2 Units SI base units SI : Système International d'unités (International System of Units) Unite name (symbol) Definition established mass kilogram (kg) The mass of the International Prototype of the Kilogram
More informationLecture 11 - AC Power
- AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits
More informationSI units are divided into 2 classes: base units (7) and derived units. Athens Programme Course CTU 1 - Metrology of Electrical Quantities.
Athens Programme Course CTU 1 - Metrology of Electrical Quantities The 11th CGPM (1960) adopted the name Système International d'unités (International System of Units, abbreviation SI), for the recommended
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 informationSinusoidal Steady-State Analysis
Chapter 4 Sinusoidal Steady-State 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 information12. Introduction and Chapter Objectives
Real Analog - Circuits 1 Chapter 1: Steady-State 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 informationAdditional Formula Sheet for Final Exam
Additional Formula Sheet for Final Exam eading and thoroughly familiarizing yourself with this formula sheet is an important part of, but it is not a substitute for, proper exam preparation. The latter
More informationElectrical Circuit & Network
Electrical Circuit & Network January 1 2017 Website: www.electricaledu.com Electrical Engg.(MCQ) Question and Answer for the students of SSC(JE), PSC(JE), BSNL(JE), WBSEDCL, WBSETCL, WBPDCL, CPWD and State
More informationChapter 1. Chapter 1
Chapter 1 Scientific and Engineering Notation Very large and very small numbers are represented with scientific and engineering notation. 47,000,000 = 4.7 x 10 7 (Scientific Notation) = 47 x 10 6 (Engineering
More informationPrecision, Accuracy Measurements, Units, Scientific Notation
Precision, Accuracy Measurements, Units, Scientific Notation DIMENSIONAL ANALYSIS It is a technique used in chemistry to give precise and accurate values. I. Accuracy and Precision Accuracy how close a
More informationHandout 11: AC circuit. AC generator
Handout : AC circuit AC generator Figure compares the voltage across the directcurrent (DC) generator and that across the alternatingcurrent (AC) generator For DC generator, the voltage is constant For
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 informationEE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.
Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts]
More informationPhysics 1B Spring 2010: Final Version A 1 COMMENTS AND REMINDERS:
Physics 1B Spring 2010: Final Version A 1 COMMENTS AND REMINDERS: Closed book. No work needs to be shown for multiple-choice questions. 1. Four charges are at the corners of a square, with B and C on opposite
More informationAnnouncements: Today: more AC circuits
Announcements: Today: more AC circuits I 0 I rms Current through a light bulb I 0 I rms I t = I 0 cos ωt I 0 Current through a LED I t = I 0 cos ωt Θ(cos ωt ) Theta function (is zero for a negative argument)
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 informationELECTRONICS. EE 42/100 Lecture 2: Charge, Current, Voltage, and Circuits. Revised 1/18/2012 (9:04PM) Prof. Ali M. Niknejad
A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 2 p. 1/26 EE 42/100 Lecture 2: Charge, Current, Voltage, and Circuits ELECTRONICS Revised 1/18/2012 (9:04PM) Prof. Ali M. Niknejad
More informationProf. Anyes Taffard. Physics 120/220. Voltage Divider Capacitor RC circuits
Prof. Anyes Taffard Physics 120/220 Voltage Divider Capacitor RC circuits Voltage Divider The figure is called a voltage divider. It s one of the most useful and important circuit elements we will encounter.
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 informationmywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel
esson 6 Solution of urrent in Parallel and Seriesparallel ircuits n the last lesson, the following points were described:. How to compute the total impedance/admittance in series/parallel circuits?. How
More informationUnit 1. ET Unit 1. Quantities, Units, and Electrical Safety. Electronics Fundamentals Circuits, Devices and Applications - Floyd
ET 115 - Unit 1 Quantities, Units, and Electrical Safety Scientific and Engineering Notation Very large and very small numbers are represented with scientific and engineering notation. 47,000,000 = 4.7
More informationELEC ELE TRO TR MAGNETIC INDUCTION
ELECTRO MAGNETIC INDUCTION Faraday Henry 1791-1867 1797 1878 Laws:- Faraday s Laws :- 1) When ever there is a change in magnetic flux linked with a coil, a current is generated in the coil. The current
More informationChapter 31: AC Circuits
hapter 31: A ircuits A urrents and Voltages In this chapter, we discuss the behior of circuits driven by a source of A. Recall that A means, literally, alternating current. An alternating current is a
More informationCourse 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/phys272-spr10/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 informationLecture notes on * Measurement and Error * Least Square Fitting
Lecture notes on * Measurement and Error * Least Square Fitting Department of Optical Engineering University of Gaziantep Oct 2016 Sayfa 1 PART I Measurement and Error Sayfa 2 System of Units Physics is
More informationEM Oscillations. David J. Starling Penn State Hazleton PHYS 212
I ve got an oscillating fan at my house. The fan goes back and forth. It looks like the fan is saying No. So I like to ask it questions that a fan would say no to. Do you keep my hair in place? Do you
More informationLecture January, 2011
Lecture 2 31 January, 2011 Announcements (1/31/11) 401B and 501B: Laboratory Meeting Tues Feb 1, 4 00-7 00 pm Electricity Test in 2 weeks (Feb 14) Today s lecture 3 00-4 00, 5 00-6 00 3x5 Cards Foundations:
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 informationGen. Phys. II Exam 2 - Chs. 21,22,23 - Circuits, Magnetism, EM Induction Mar. 5, 2018
Gen. Phys. II Exam 2 - Chs. 21,22,23 - Circuits, Magnetism, EM Induction Mar. 5, 2018 Rec. Time Name For full credit, make your work clear. Show formulas used, essential steps, and results with correct
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 informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 20 121101 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Chapters 1-3 Circuit Analysis Techniques Chapter 10 Diodes Ideal Model
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 10 6/12/2007 Electricity and Magnetism Induced voltages and induction Self-Inductance RL Circuits Energy in magnetic fields AC circuits and EM waves Resistors, capacitors
More informationSINUSOIDAL STEADY STATE CIRCUIT ANALYSIS
SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS 1. Introduction A sinusoidal current has the following form: where I m is the amplitude value; ω=2 πf is the angular frequency; φ is the phase shift. i (t )=I m.sin
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 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 Post-test. You are required to attend one of the lectures on Thursday, Dec.
More informationELECTRO MAGNETIC INDUCTION
ELECTRO MAGNETIC INDUCTION 1) A Circular coil is placed near a current carrying conductor. The induced current is anti clock wise when the coil is, 1. Stationary 2. Moved away from the conductor 3. Moved
More informationSingle Phase Parallel AC Circuits
Single Phase Parallel AC Circuits 1 Single Phase Parallel A.C. Circuits (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) n parallel a.c. circuits similar
More informationSinusoidal Steady-State Analysis
Sinusoidal Steady-State 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 informationSinusoidal Steady-State Analysis
Sinusoidal Steady-State Analysis Mauro Forti October 27, 2018 Constitutive Relations in the Frequency Domain Consider a network with independent voltage and current sources at the same angular frequency
More informationSI UNITS AND SOME CONVERSION FACTORS. A. Woldai, B. Makkawi, and D. Al-Gobaisi International Center for Water and Energy Systems, Abu Dhabi, UAE
SI UNITS AND SOME CONVERSION FACTORS A. Woldai, B. Makkawi, and D. Al-Gobaisi International Center for Water and Energy Systems, Abu Dhabi, UAE Keywords : SI units, Dynamic viscosity, Surface tension,
More informationPower and Energy Measurement
Power and Energy Measurement ENE 240 Electrical and Electronic Measurement Class 11, February 4, 2009 werapon.chi@kmutt.ac.th 1 Work, Energy and Power Work is an activity of force and movement in the direction
More informationPhysics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33
Session 33 Physics 115 General Physics II AC: RL vs RC circuits Phase relationships RLC circuits R. J. Wilkes Email: phy115a@u.washington.edu Home page: http://courses.washington.edu/phy115a/ 6/2/14 1
More informationSome Important Electrical Units
Some Important Electrical Units Quantity Unit Symbol Current Charge Voltage Resistance Power Ampere Coulomb Volt Ohm Watt A C V W W These derived units are based on fundamental units from the meterkilogram-second
More informationName: Lab: M8 M2 W8 Th8 Th11 Th2 F8. cos( θ) = cos(θ) sin( θ) = sin(θ) sin(θ) = cos. θ (radians) θ (degrees) cos θ sin θ π/6 30
Name: Lab: M8 M2 W8 Th8 Th11 Th2 F8 Trigonometric Identities cos(θ) = cos(θ) sin(θ) = sin(θ) sin(θ) = cos Cosines and Sines of common angles Euler s Formula θ (radians) θ (degrees) cos θ sin θ 0 0 1 0
More informationChapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively
Chapter 3 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively In the LC circuit the charge, current, and potential difference vary sinusoidally (with period T and angular
More information2. The following diagram illustrates that voltage represents what physical dimension?
BioE 1310 - Exam 1 2/20/2018 Answer Sheet - Correct answer is A for all questions 1. A particular voltage divider with 10 V across it consists of two resistors in series. One resistor is 7 KΩ and the other
More informationModule 4. Single-phase AC Circuits
Module 4 Single-phase AC Circuits Lesson 14 Solution of Current in R-L-C Series Circuits In the last lesson, two points were described: 1. How to represent a sinusoidal (ac) quantity, i.e. voltage/current
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 informationSCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self-paced Course
SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING Self-paced Course MODULE 26 APPLICATIONS TO ELECTRICAL CIRCUITS Module Topics 1. Complex numbers and alternating currents 2. Complex impedance 3.
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 informationChapter 1: The Science of Physics. Physics 1-2 Mr. Chumbley
Chapter 1: The Science of Physics Physics 1-2 Mr. Chumbley The Topics of Physics The origin of the word physics comes from the ancient Greek word phusika meaning natural things The types of fields of
More informationBASIC NETWORK ANALYSIS
SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding Series-Parallel dc Network Analysis......................... 1.1 Branch-Current Analysis of a dc Network......................
More informationCLUSTER LEVEL WORK SHOP
CLUSTER LEVEL WORK SHOP SUBJECT PHYSICS QUESTION BANK (ALTERNATING CURRENT ) DATE: 0/08/06 What is the phase difference between the voltage across the inductance and capacitor in series AC circuit? Ans.
More informationA capacitor is a device that stores electric charge (memory devices). A capacitor is a device that stores energy E = Q2 2C = CV 2
Capacitance: Lecture 2: Resistors and Capacitors Capacitance (C) is defined as the ratio of charge (Q) to voltage (V) on an object: C = Q/V = Coulombs/Volt = Farad Capacitance of an object depends on geometry
More informationIntroduction to Digital Logic Missouri S&T University CPE 2210 Number Systems
Introduction to Digital Logic Missouri S&T University CPE 2210 Number Systems Egemen K. Çetinkaya Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science and
More informationIntroduction to Electrical and Computer Engineering. International System of Units (SI)
Introduction to Electrical and Computer Engineering Basic Circuits and Simulation Basic Circuits and Simulation (1 of 22) International System of Units (SI) Length: meter (m) Mass: kilogram (kg) Time:
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 information