Chapter 33. Alternating Current Circuits

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Chapter 33. Alternating Current Circuits"

Transcription

1 Chapter 33 Alternating Current Circuits 1

2 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt

3 AC power source The AC power source provides an alternative voltage, Notation - Lower case symbols will indicate instantaneous values - Capital letters will indicate fixed values The output of an AC power source is sinusoidal v = sin ωt v is the instantaneous voltage v(t) is the imum output voltage of the source ω is the angular frequency of the AC voltage 3

4 AC voltage The angular frequency is ω = πƒ = v = V ( ωt + φ) π T cos ƒ is the frequency of the source T is the period of the source The voltage is positive during one half of the cycle and negative during the other half The current in any circuit driven by an AC source is an alternating current that varies sinusoidally with time Commercial electric power plants in the US use a frequency of 60 Hz 4

5 Resistor in AC circuit Consider a circuit consisting of an AC source and a resistor The AC source is symbolized by v = v R = sin ωt v R is the instantaneous voltage across the resistor The instantaneous current in the resistor is vr ir = = sin ωt = I sin ωt R R 5

6 Resistor in AC circuit v = v = sin( ωt) R vr ir = = sin ωt = I sin ωt R R The current and the voltage are in phase Resistors behave essentially the same way in both DC and AC circuits 6

7 Resistor in AC circuit: Phasor diagram v = v = sin( ωt) R vr ir = = sin ωt = I sin ωt R R A phasor is a vector whose length is proportional to the imum value of the variable it represents The vector rotates at an angular speed equal to the angular frequency associated with the variable The projection of the phasor onto the vertical axis represents the instantaneous value of the quantity it represents 7

8 rms current and voltage ir = I sin ωt The average current in one cycle is zero rms stands for root mean square T 1/ T 1/ ir dt ( ωt) dt T Irms = = I sin T π 1/ I I sin () τ dτ I 0 1 = = = π Alternating voltages can also be discussed in terms of rms values Vrms = =

9 rms current and voltage: power The rate at which electrical energy is dissipated in the circuit is given by P = i R where i is the instantaneous current The average power delivered to a resistor that carries an alternating current is P av = I rms R 9

10 Inductors in AC circuit v + v L = 0, or di v L = 0 dt di v = L = sinωt dt L ωl il = sin ωt dt= cos ωt i L π = sin ωt I = ωl ωl This shows that the instantaneous current i L in the inductor and the instantaneous voltage v L across the inductor are out of phase by ( π / ) rad = 90 o. 10

11 Inductors in AC circuit v = ωt sin sin π i = L I ωt I = V ωl 11

12 Inductors in AC circuit v = ωt sin i = sin L I ωt π I = V ωl The phasors are at 90 o with respect to each other This represents the phase difference between the current and voltage Specifically, the current lags behind the voltage by 90 o 1

13 Inductors in AC circuit v = ωt sin i = sin L I ωt π I = V ωl The factor ωl has the same units as resistance and is related to current and voltage in the same way as resistance The factor is the inductive reactance and is given by: X L = ωl As the frequency increases, the inductive reactance increases I = X L 13

14 Capacitors in AC circuit v + v c = 0 and so v = v C = sin ωt v c is the instantaneous voltage across the capacitor The charge is q = C v C =C sin ωt The instantaneous current is given by dq ic = = ωccos ωt dt π ic = ωc Vsin ωt + The current is (π/) rad = 90 o out of phase with the voltage 14

15 Capacitors in AC circuit v = sin C V ωt = sin π ic ωc V ωt + 15

16 Capacitors in AC circuit v = sinωt C = sin π ic ωc V ωt + The phasor diagram shows that for a sinusoidally applied voltage, the current always leads the voltage across a capacitor by 90 o This is equivalent to saying the voltage lags the current 16

17 Capacitors in AC circuit v = sinωt C = sin π ic ωc V ωt + The imum current I = ωc V = (1/ ωc) The impeding effect of a capacitor on the current in an AC circuit is called the capacitive reactance and is given by 1 XC and I = ωc X C 17

18 v =sinωt i = I sinωt L I = V R v =sinωt π il = Isin ωt ωl I = = X L I v = sinωt C = sin π ic I ωt + = = (1/ ωc) XC 18

19 RLC series circuit The instantaneous voltage would be given by v = sin ωt The instantaneous current would be given by i = I sin (ωt - φ) φ is the phase angle between the current and the applied voltage Since the elements are in series, the current at all points in the circuit has the same amplitude and phase 19

20 RLC series circuit The instantaneous voltage across the resistor is in phase with the current The instantaneous voltage across the inductor leads the current by 90 The instantaneous voltage across the capacitor lags the current by 90 0

21 RLC series circuit The instantaneous voltage across each of the three circuit elements can be expressed as v = I R sin ωt = sin ωt R π vl = I XL sin ωt + = L cos ωt π vc = I XC sin ωt = C cos ωt R 1

22 RLC series circuit v = I R sin ωt = sin ωt R π vl = I XL sin ωt + = L cos ωt π vc = I XC sin ωt = C cos ωt R In series, voltages add and the instantaneous voltage across all three elements would be v = v R + v L + v C Easier to use the phasor diagrams

23 RLC series circuit i = I sin ωt v = I R sin ωt = sin ωt R π vl = I XL sin ωt + = L cos ωt π vc = I XC sin ωt = C cos ωt v = v + v + v = R L C = V sin ωt + cos ωt V cos ωt = R L C = V sin ( ωt + φ) R Easier to use the phasor diagrams 3

24 RLC series circuit The phasors for the individual elements: The individual phasor diagrams can be combined Here a single phasor I is used to represent the current in each element In series, the current is the same in each element 4

25 RLC series circuit Vector addition is used to combine the voltage phasors L and C are in opposite directions, so they can be combined Their resultant is perpendicular to R 5

26 RLC series circuit From the vector diagram, can be calculated ( ) ( I ) ( I I ) V = V + V = R + X X R L C L C ( ) V = I R + X X L C 6

27 RLC series circuit ( ) V = I R + X X L C The current in an RLC circuit is I = = R + ( XL XC) Z Z is called the impedance of the circuit and it plays the role of resistance in the circuit, where ( ) Z R + XL XC 7

28 RLC series circuit I = Z ( ) Z R + XL XC impedance triangle 8

29 RLC series circuit: impedance triangle ( ) Z R + XL XC The impedance triangle can also be used to find the phase angle, φ 1 XL XC φ = tan R The phase angle can be positive or negative and determines the nature of the circuit R Also, cos φ = Z i = I sin ωt v = V sin ( ωt + φ ) 9

30 RLC series circuit ( ) Z R + XL XC φ X X R 1 L C = tan 30

31 Power in AC circuit I = Z I rms I = The average power delivered by the generator is converted to internal energy in the resistor P av = ½ I cos φ = I rms rms cos φ cos φ is called the power factor of the circuit We can also find the average power in terms of R 1 1 V R Pav = Irms R = I R = R = Z R + X X ( ) L C 31

32 Resonances in AC circuit P av R R Z R + X X = = ( ) L C Resonance in P ( occurs at the frequency ω av ω ) o where the current has its imum value To achieve imum current, the impedance must have a minimum value This occurs when X L = X C or 1 XL = ω0l= XC = ω0c Solving for the frequency gives ω o = 1 LC The resonance frequency also corresponds to the natural frequency of oscillation of an LC circuit 3

33 Resonances in AC circuit P av R R R = = = 1 R + ωl ωc ω o Z R + ( XL XC) = 1 LC P av ( ω ) = 0 R Resonance occurs at the same frequency regardless of the value of R As R decreases, the curve becomes narrower and taller Theoretically, if R = 0 the current would be infinite at resonance Real circuits always have some resistance 33

Driven RLC Circuits Challenge Problem Solutions

Driven 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 information

RLC 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 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 information

Chapter 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 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 information

AC Circuits Homework Set

AC 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 information

I. Impedance of an R-L circuit.

I. Impedance of an R-L circuit. I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC

More information

Sinusoidal Steady-State Analysis

Sinusoidal 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 information

Lecture 24. Impedance of AC Circuits.

Lecture 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 information

Alternating Current Circuits. Home Work Solutions

Alternating 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 information

Chapter 21: RLC Circuits. PHY2054: Chapter 21 1

Chapter 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 information

Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current

Physics 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 information

Electrical Circuit & Network

Electrical 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 information

Learnabout Electronics - AC Theory

Learnabout 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 information

PHYSICS NOTES ALTERNATING CURRENT

PHYSICS 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 information

Yell if you have any questions

Yell 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 information

LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module. What you'll learn in Module 9. Module 9 Introduction

LCR 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 information

20. Alternating Currents

20. 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 information

Sinusoidal Steady-State Analysis

Sinusoidal 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 information

AC Source and RLC Circuits

AC 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 information

Physics-272 Lecture 20. AC Power Resonant Circuits Phasors (2-dim vectors, amplitude and phase)

Physics-272 Lecture 20. AC Power Resonant Circuits Phasors (2-dim vectors, amplitude and phase) Physics-7 ecture 0 A Power esonant ircuits Phasors (-dim vectors, amplitude and phase) What is reactance? You can think of it as a frequency-dependent resistance. 1 ω For high ω, χ ~0 - apacitor looks

More information

Lectures 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 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 information

Lecture 05 Power in AC circuit

Lecture 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 information

Get Discount Coupons for your Coaching institute and FREE Study Material at ELECTROMAGNETIC INDUCTION

Get 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 information

Alternating Current. Chapter 31. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman

Alternating 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 information

EXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection

EXP. 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 information

CIRCUIT ANALYSIS II. (AC Circuits)

CIRCUIT 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, second-order and resonant circuits, damping and

More information

Physics 294H. lectures will be posted frequently, mostly! every day if I can remember to do so

Physics 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 hand-written problem per week) Help-room hours: 12:40-2:40

More information

EE221 - Practice for the Midterm Exam

EE221 - Practice for the Midterm Exam EE1 - Practice for the Midterm Exam 1. Consider this circuit and corresponding plot of the inductor current: Determine the values of L, R 1 and R : L = H, R 1 = Ω and R = Ω. Hint: Use the plot to determine

More information

EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA

EXPERIMENT 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

Electricity & Magnetism Lecture 20

Electricity & 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 information

Exam 3 Solutions. The induced EMF (magnitude) is given by Faraday s Law d dt dt The current is given by

Exam 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

Electrical Engineering Fundamentals for Non-Electrical Engineers

Electrical 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 information

Homwork AC circuits. due Friday Oct 8, 2017

Homwork AC circuits. due Friday Oct 8, 2017 Homwork AC circuits due Friday Oct 8, 2017 Validate your answers (show your work) using a Matlab Live Script and Simulink models. Include these computations and models with your homework. 1 Problem 1 Worksheet

More information

AC Circuits and Electromagnetic Waves

AC Circuits and Electromagnetic Waves AC Circuits and Electromagnetic Waves Physics 102 Lecture 5 7 March 2002 MIDTERM Wednesday, March 13, 7:30-9:00 pm, this room Material: through next week AC circuits Next week: no lecture, no labs, no

More information

1 2 U CV. K dq I dt J nqv d J V IR P VI

1 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 information

PHYS 3900 Homework Set #02

PHYS 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 information

The simplest type of alternating current is one which varies with time simple harmonically. It is represented by

The 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 information

Toolbox: Electrical Systems Dynamics

Toolbox: Electrical Systems Dynamics Toolbox: Electrical Systems Dynamics Dr. John C. Wright MIT - PSFC 05 OCT 2010 Introduction Outline Outline AC and DC power transmission Basic electric circuits Electricity and the grid Image removed due

More information

Chapter 28: Alternating Current

Chapter 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 information

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations Op-Amp Integrator and Op-Amp Differentiator 1 CAPACITANCE AND INDUCTANCE Introduces

More information

Phasors: Impedance and Circuit Anlysis. Phasors

Phasors: 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 information

To investigate further the series LCR circuit, especially around the point of minimum impedance. 1 Electricity & Electronics Constructor EEC470

To investigate further the series LCR circuit, especially around the point of minimum impedance. 1 Electricity & Electronics Constructor EEC470 Series esonance OBJECTIE To investigate further the series LC circuit, especially around the point of minimum impedance. EQUIPMENT EQUIED Qty Apparatus Electricity & Electronics Constructor EEC470 Basic

More information

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1

Chapter 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 information

The Basic Elements and Phasors

The 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 information

INDUCTORS AND AC CIRCUITS

INDUCTORS 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 information

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

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

More information

Electricity and Light Pre Lab Questions

Electricity and Light Pre Lab Questions Electricity and Light Pre Lab Questions The pre lab questions can be answered by reading the theory and procedure for the related lab. You are strongly encouraged to answers these questions on your own.

More information

BASIC NETWORK ANALYSIS

BASIC 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 information

Network Graphs and Tellegen s Theorem

Network 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 information

8.1 Alternating Voltage and Alternating Current ( A. C. )

8.1 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 information

Power Systems - Basic Concepts and Applications - Part I

Power Systems - Basic Concepts and Applications - Part I PDHonline Course E104 (1 PDH) Power ystems Basic Concepts and Applications Part I Instructor: hihmin Hsu PhD PE 01 PDH Online PDH Center 57 Meadow Estates Drive Fairfax A 006658 Phone & Fax: 709880088

More information

Chapter 10: Sinusoidal Steady-State Analysis

Chapter 10: Sinusoidal Steady-State Analysis Chapter 0: Sinusoidal Steady-State Analysis Sinusoidal Sources If a circuit is driven by a sinusoidal source, after 5 tie constants, the circuit reaches a steady-state (reeber the RC lab with t = τ). Consequently,

More information

a + b Time Domain i(τ)dτ.

a + 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 information

FINAL EXAM - Physics Patel SPRING 1998 FORM CODE - A

FINAL EXAM - Physics Patel SPRING 1998 FORM CODE - A FINAL EXAM - Physics 202 - Patel SPRING 1998 FORM CODE - A Be sure to fill in your student number and FORM letter (A, B, C, D, E) on your answer sheet. If you forget to include this information, your Exam

More information

Mixing Problems. Solution of concentration c 1 grams/liter flows in at a rate of r 1 liters/minute. Figure 1.7.1: A mixing problem.

Mixing Problems. Solution of concentration c 1 grams/liter flows in at a rate of r 1 liters/minute. Figure 1.7.1: A mixing problem. page 57 1.7 Modeling Problems Using First-Order Linear Differential Equations 57 For Problems 33 38, use a differential equation solver to determine the solution to each of the initial-value problems and

More information

Three Phase Systems 295

Three Phase Systems 295 Three Phase Systems 95 9. MEASUEMENT OF POE Star-Connected Balanced Load with Neutral Point Power can be measured in this case by connecting a single wattmeter with its current coil in one line and the

More information

Electromagnetic Induction (Chapters 31-32)

Electromagnetic Induction (Chapters 31-32) Electromagnetic Induction (Chapters 31-3) The laws of emf induction: Faraday s and Lenz s laws Inductance Mutual inductance M Self inductance L. Inductors Magnetic field energy Simple inductive circuits

More information

AC Circuits. The Capacitor

AC 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 information

Basics of Network Theory (Part-I)

Basics of Network Theory (Part-I) Basics of Network Theory (PartI). A square waveform as shown in figure is applied across mh ideal inductor. The current through the inductor is a. wave of peak amplitude. V 0 0.5 t (m sec) [Gate 987: Marks]

More information

Notes on Electric Circuits (Dr. Ramakant Srivastava)

Notes 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 information

Wireless charging using a separate third winding for reactive power supply

Wireless charging using a separate third winding for reactive power supply Wireless charging using a separate third winding for reactive power supply Master s thesis in Energy and Environment IAN ŠALKOIĆ Department of Energy and Environment Division of Electric Power Engineering

More information

Unit 21 Capacitance in AC Circuits

Unit 21 Capacitance in AC Circuits Unit 21 Capacitance in AC Circuits Objectives: Explain why current appears to flow through a capacitor in an AC circuit. Discuss capacitive reactance. Discuss the relationship of voltage and current in

More information

HOMEWORK 4: MATH 265: SOLUTIONS. y p = cos(ω 0t) 9 ω 2 0

HOMEWORK 4: MATH 265: SOLUTIONS. y p = cos(ω 0t) 9 ω 2 0 HOMEWORK 4: MATH 265: SOLUTIONS. Find the solution to the initial value problems y + 9y = cos(ωt) with y(0) = 0, y (0) = 0 (account for all ω > 0). Draw a plot of the solution when ω = and when ω = 3.

More information

2B30 Formal Report Simon Hearn Dr Doel

2B30 Formal Report Simon Hearn Dr Doel DEPARTMENT OF PHYSICS & ASTRONOMY SECOND YEAR LAB REPORT DECEMBER 2001 EXPERIMENT E7: STUDY OF AN OSCILLATING SYSTEM DRIVEN INTO RESONANCE PERFORMED BY SIMON HEARN, LAB PARTNER CAROLINE BRIDGES Abstract

More information

EIT Review 1. FE/EIT Review. Circuits. John A. Camara, Electrical Engineering Reference Manual, 6 th edition, Professional Publications, Inc, 2002.

EIT 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 information

Module 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1

Module 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1 Module 4 Single-phase 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 information

In 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 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 information

CHAPTER 2 ELECTRICAL CIRCUITS & FIELDS. In the circuit shown below, the current through the inductor is 2 A (B) (A) (C) (D) 0A

CHAPTER 2 ELECTRICAL CIRCUITS & FIELDS. In the circuit shown below, the current through the inductor is 2 A (B) (A) (C) (D) 0A CHAPTER ELECTRICAL CIRCUITS & FIELDS YEAR 0 ONE MARK MCQ. In the circuit shown below, the current through the inductor is (A) A (B) A + j + j MCQ. (C) A (D) 0A + j The impedance looking into nodes and

More information

CHAPTER FOUR MUTUAL INDUCTANCE

CHAPTER FOUR MUTUAL INDUCTANCE CHAPTER FOUR MUTUAL INDUCTANCE 4.1 Inductance 4.2 Capacitance 4.3 Serial-Parallel Combination 4.4 Mutual Inductance 4.1 Inductance Inductance (L in Henry is the circuit parameter used to describe an inductor.

More information

EE301 Three Phase Power

EE301 Three Phase Power Learning Objectives a. Compute the real, reactive and apparent power in three phase systems b. Calculate currents and voltages in more challenging three phase circuit arrangements c. Apply the principles

More information

Phasor mathematics. Resources and methods for learning about these subjects (list a few here, in preparation for your research):

Phasor 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 information

Exam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses.

Exam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses. Exam 2 Solutions Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1 Part of a long, straight insulated wire carrying current i is bent into a circular

More information

Review of Basic Electrical and Magnetic Circuit Concepts EE

Review of Basic Electrical and Magnetic Circuit Concepts EE Review of Basic Electrical and Magnetic Circuit Concepts EE 442-642 Sinusoidal Linear Circuits: Instantaneous voltage, current and power, rms values Average (real) power, reactive power, apparent power,

More information

Exam 3 Solutions. 1. Which of the following statements is true about the LR circuit shown?

Exam 3 Solutions. 1. Which of the following statements is true about the LR circuit shown? PHY49 Spring 5 Prof. Darin Acosta Prof. Paul Avery April 4, 5 PHY49, Spring 5 Exa Solutions. Which of the following stateents is true about the LR circuit shown? It is (): () Just after the switch is closed

More information

CHAPTER 45 COMPLEX NUMBERS

CHAPTER 45 COMPLEX NUMBERS CHAPTER 45 COMPLEX NUMBERS EXERCISE 87 Page 50. Solve the quadratic equation: x + 5 0 Since x + 5 0 then x 5 x 5 ( )(5) 5 j 5 from which, x ± j5. Solve the quadratic equation: x x + 0 Since x x + 0 then

More information

Lesson 17: Synchronous Machines

Lesson 17: Synchronous Machines Lesson 17: Synchronous Machines ET 332b Ac Motors, Generators and Power Systems Lesson 17_et332b.pptx 1 Learning Objectives After this presentation you will be able to: Explain how synchronous machines

More information

PHY2049 Fall11. Final Exam Solutions (1) 700 N (2) 350 N (3) 810 N (4) 405 N (5) 0 N

PHY2049 Fall11. Final Exam Solutions (1) 700 N (2) 350 N (3) 810 N (4) 405 N (5) 0 N Exam Solutions 1. Three charges form an equilateral triangle of side length d = 2 cm. The top charge is q3 = 3 μc, while the bottom two are q1 = q2 = - 6 μc. What is the magnitude of the net force acting

More information

DEPARTMENT OF NATURAL SCIENCES. PHYS 1112, Exam 3 Section 1 Version 1 December 6, 2004 Total Weight: 100 points

DEPARTMENT OF NATURAL SCIENCES. PHYS 1112, Exam 3 Section 1 Version 1 December 6, 2004 Total Weight: 100 points TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1112, Exam 3 Section 1 Version 1 December 6, 2004 Total Weight: 100 points 1. Check your examination for completeness prior to starting.

More information

Lecture #3. Review: Power

Lecture #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 information

Scanned by CamScanner

Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner t W I w v 6.00-fall 017 Midterm 1 Name Problem 3 (15 pts). F the circuit below, assume that all equivalent parameters are to be found to the left of port

More information

Chapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson

Chapter 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 information

Physics 2B Winter 2012 Final Exam Practice

Physics 2B Winter 2012 Final Exam Practice Physics 2B Winter 2012 Final Exam Practice 1) When the distance between two charges is increased, the force between the charges A) increases directly with the square of the distance. B) increases directly

More information

6.334 Power Electronics Spring 2007

6.334 Power Electronics Spring 2007 MIT OpenCourseWare http://ocw.mit.edu 6.334 Power Electronics Spring 007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Chapter 3 Power Factor and Measures

More information

Complex number review

Complex number review Midterm Review Problems Physics 8B Fall 009 Complex number review AC circuits are usually handled with one of two techniques: phasors and complex numbers. We ll be using the complex number approach, so

More information

Lecture 3: Three-phase power circuits

Lecture 3: Three-phase power circuits 1/24/28 Lecture : Three-phase power circuits 1 nstructor: Dr. Gleb. Tcheslavski Contact: gleb@ee.lamar.edu Office Hours: TBD; Room 2 Class web site: MyLamar ntroduction 2 Almost all electric power generation

More information

EXAM 3: SOLUTIONS. B = B. A 2 = BA 2 cos 0 o = BA 2. =Φ(2) B A 2 = A 1 cos 60 o = A 1 2 =0.5m2

EXAM 3: SOLUTIONS. B = B. A 2 = BA 2 cos 0 o = BA 2. =Φ(2) B A 2 = A 1 cos 60 o = A 1 2 =0.5m2 EXAM : S Q.The normal to a certain m area makes an angle of 6 o with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to

More information

Chapter 15 Power And Harmonics in Nonsinusoidal Systems

Chapter 15 Power And Harmonics in Nonsinusoidal Systems Chapter 15 Power And Harmonics in Nonsinusoidal Systems 15.1. Average power in terms of Fourier series 15.2. RMS value of a waveform 15.3. Power factor THD Distortion and Displacement factors 15.4. Power

More information

Electrochemical methods : Fundamentals and Applications

Electrochemical methods : Fundamentals and Applications Electrochemical methods : Fundamentals and Applications Lecture Note 7 May 19, 2014 Kwang Kim Yonsei University kbkim@yonsei.ac.kr 39 8 7 34 53 Y O N Se I 88.91 16.00 14.01 78.96 126.9 Electrochemical

More information

EECE251. Circuit Analysis I. Set 4: Capacitors, Inductors, and First-Order Linear Circuits

EECE251. Circuit Analysis I. Set 4: Capacitors, Inductors, and First-Order Linear Circuits EECE25 Circuit Analysis I Set 4: Capacitors, Inductors, and First-Order Linear Circuits Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca

More information

ESE319 Introduction to Microelectronics. Output Stages

ESE319 Introduction to Microelectronics. Output Stages Output Stages Power amplifier classification Class A amplifier circuits Class A Power conversion efficiency Class B amplifier circuits Class B Power conversion efficiency Class AB amplifier circuits Class

More information

EDEXCEL NATIONAL CERTIFICATE UNIT 28 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME 3 TUTORIAL 1 - TRIGONOMETRICAL GRAPHS

EDEXCEL NATIONAL CERTIFICATE UNIT 28 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME 3 TUTORIAL 1 - TRIGONOMETRICAL GRAPHS EDEXCEL NATIONAL CERTIFICATE UNIT 28 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME 3 TUTORIAL 1 - TRIGONOMETRICAL GRAPHS CONTENTS 3 Be able to understand how to manipulate trigonometric expressions and apply

More information

Circuits. Fawwaz T. Ulaby, Michel M. Maharbiz, Cynthia M. Furse. Solutions to the Exercises

Circuits. Fawwaz T. Ulaby, Michel M. Maharbiz, Cynthia M. Furse. Solutions to the Exercises Circuits by Fawwaz T. Ulaby, Michel M. Maharbiz, Cynthia M. Furse Solutions to the Exercises Chapter 1: Circuit Terminology Chapter 2: Resisitive Circuits Chapter 3: Analysis Techniques Chapter 4: Operational

More information

Physics 1308 Exam 2 Summer 2015

Physics 1308 Exam 2 Summer 2015 Physics 1308 Exam 2 Summer 2015 E2-01 2. The direction of the magnetic field in a certain region of space is determined by firing a test charge into the region with its velocity in various directions in

More information

ECE145A/218A Course Notes

ECE145A/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 information

Yell if you have any questions

Yell if you have any questions Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 Before Starting All of your grades should now be posted

More information

FE Review 2/2/2011. Electric Charge. Electric Energy ELECTRONICS # 1 FUNDAMENTALS

FE 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 information

Lecture 6: Impedance (frequency dependent. resistance in the s- world), Admittance (frequency. dependent conductance in the s- world), and

Lecture 6: Impedance (frequency dependent. resistance in the s- world), Admittance (frequency. dependent conductance in the s- world), and Lecture 6: Impedance (frequency dependent resistance in the s- world), Admittance (frequency dependent conductance in the s- world), and Consequences Thereof. Professor Ray, what s an impedance? Answers:

More information

Output high order sliding mode control of unity-power-factor in three-phase AC/DC Boost Converter

Output high order sliding mode control of unity-power-factor in three-phase AC/DC Boost Converter Output high order sliding mode control of unity-power-factor in three-phase AC/DC Boost Converter JianXing Liu, Salah Laghrouche, Maxim Wack Laboratoire Systèmes Et Transports (SET) Laboratoire SeT Contents

More information

RC, RL, and LCR Circuits

RC, 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 information

I(t) R L. RL Circuit: Fundamentals. a b. Specifications: E (emf) R (resistance) L (inductance) Switch S: a: current buildup. b: current shutdown

I(t) R L. RL Circuit: Fundamentals. a b. Specifications: E (emf) R (resistance) L (inductance) Switch S: a: current buildup. b: current shutdown RL Circuit: Fundamentals pecifications: E (emf) R (resistance) L (inductance) witch : a: current buildup a b I(t) R L b: current shutdown Time-dependent quantities: I(t): instantaneous current through

More information

Lecture 35: FRI 17 APR Electrical Oscillations, LC Circuits, Alternating Current I

Lecture 35: FRI 17 APR Electrical Oscillations, LC Circuits, Alternating Current I Physics 3 Jonathan Dowling Lecture 35: FRI 7 APR Electrical Oscillations, LC Circuits, Alternating Current I Nikolai Tesla What are we going to learn? A road map Electric charge è Electric force on other

More information