Chapter 30 Inductance

Size: px
Start display at page:

Download "Chapter 30 Inductance"

Transcription

1 Chapter 30 Inductance - Mutual Inductance - Self-Inductance and Inductors - Magnetic-Field Energy - The R- Circuit - The -C Circuit - The -R-C Series Circuit

2 . Mutual Inductance - A changing current in coil causes B and a changing magnetic flux through coil that induces emf in coil. ε N dφ B Magnetic flux through coil : N B M Φ i Mutual inductance of two coils: M ε dφ B N M M M N Φ i B M is a constant that depends on geometry of the coils M.

3 - If a magnetic material is present, M will depend on magnetic properties. If relative permeability (K m ) is not constant (M not proportional to B) Φ B not proportional to i (exception). ε ε M M Mutual inductance: emf opposes the flux change M N Φ i B NΦ i B - Only a time-varying current induces an emf. Units of inductance: Henry Weber/A V s/a J/A Ex. 30.

4 . Self Inductance and Inductors - When a current is present in a circuit, it sets up B that causes a magnetic flux that changes when the current changes emf is induced. enz s law: a self-induced emf opposes the change in current that caused it Induced emf makes fficult variations in current. NΦ i B Self-inductance dφ N B ε Self-induced emf

5 Inductors as Circuit Elements Inductors oppose variations in the current through a circuit. -In DC-circuit, helps to maintain a steady current (despite fluctuations in applied emf). In AC circuit, helps to suppress fast variations in current. - Reminder of Kirchhoff s loop rule: the sum of potential fferences around any closed loop is zero because E produced by charges stributed around circuit is conservative E c. -The magnetically induced electric field within the coils of an inductor is nonconservative (E n ). - If R 0 in inductor s coils very small E required to move charge through coils total E through coils E c + E n 0. Since E c 0 E c -E n accumulation of charge on inductor s terminals and surfaces of its conductors to produce that field. E n dl

6 - E n 0 only within the inductor. b a b a E E n c dl dl E c E + n 0 (at each point within the inductor s coil) - Self-induced emf opposes changes in current. Potential fference between terminals of an inductor: Vab Va Vb V ab is associated with conservative, electrostatic forces, despite the fact that E associated with the magnetic induction is non-conservative Kirchhoff s loop rule can be used. - If magnetic flux is concentrated in region with a magnetic material µ 0 in eqs. must be replaced by µ K m µ 0.

7

8 3. Magnetic-Field Energy - Establishing a current in an inductor requires an input of energy. An inductor carrying a current has energy stored in it. Energy Stored in an Inductor Rate of transfer of energy into : P Vabi i Energy supplied to inductor during : du P i Total energy U supplied while the current increases from zero to I: U I i 0 I Energy stored in an inductor - Energy flows into an ideal (R 0) inductor when current in inductor increases. The energy is not ssipated, but stored in and released when current decreases.

9 Magnetic Energy Density r A N π µ 0 0 ) ( r I N A r U V U u π µ π 0 I r A N I U π µ -The energy in an inductor is stored in the magnetic field within the coil, just as the energy of a capacitor is stored in the electric field between its plates. Ex: toroidal solenoid (B confined to a finite region of space within its core). V (πr) A Energy per unit volume: u U/V magnetic energy density

10 µ µ 0 B u B u ( ) 0 µ π B r I N r NI B π µ 0 Magnetic energy density in vacuum Magnetic energy density in a material

11 4. The R- Circuit - An inductor in a circuit makes it fficult for rapid changes in current to occur due to induced emf. Current-Growth in an R- Circuit At t 0 Switch closed. v ab I R v bc ε i R 0 ε ir ε R i

12 initial final ε 0 ε R I ( t 0 i 0 V ab 0) ε I R ( t f / 0) i ε R ( ) R i ' i' ( ε ) R t 0 0 i ln ( ε R) ε R R ' R Current in R- circuit: t ε i e R ( R ) t

13 ε e ( R )t t 0 i 0, / ε / t i ε/r, / 0 Time constant for an R- circuit: τ R At t τ, the current has risen to (-/e) (63 % ) of its final value. Power supplied by the source: ε i i R Power ssipated by R + i Power stored in inductor

14 Current-Decay in an R- Circuit i I 0 e ( R )t t 0 I 0 Τ /R for current to decrease to /e (37 % of I 0 ). Total energy in circuit: 0 i R + i No energy supplied by a source (no battery present)

15 5. The -C Circuit - In -C circuit, the charge on the capacitor and current through inductor vary sinusoidally with time. Energy is transferred between magnetic energy in inductor (U B ) and electric energy in capacitor (U E ). As in simple harmonic motion, total energy remains constant.

16 -C Circuit t 0 C charged Q C V m C scharges through inductor. Because of induced emf in, the current does not change instantaneously. I starts at 0 until it reaches I m. During C scharge, the potential in C induced emf in. When potential in C 0 induced emf 0 maximum I m. During the scharge of C, the growing current in leads to magnetic field energy stored in C (in its electric field) becomes stored in (in magnetic field). After C fully scharged, some i persists (cannot change instantaneously), C charges with contrary polarity to initial state. As current decreases B decreases induced emf in same rection as current that slows decrease in current. At some point, B 0, i 0 and C fully charged with V m (-Q on left plate, contrary to initial state). If no energy loses, the charges in C oscillate back and forth infinitely electrical oscillation. Energy is transferred from capacitor E to inductor B.

17 Electrical Oscillations in an -C Circuit Shown is + i dq/ (rate of change of q in left plate). If C scharges dq/<0 counter clockwise i is negative. Kirchhoff s loop rule: d q x + q C 0 Acos( ω t + ϕ) -C circuit q C Analogy to eq. for harmonic oscillator: 0 d x k + x m 0 q Q cos t ( ω +ϕ) dq i ω Qsin( ωt + ϕ) ω C Angular frequency of oscillation ω π f If at t 0 Q max in C, i 0 φ 0 If at t 0, q0 φ ±π/ rad

18 Energy in an -C Circuit Analogy with harmonic oscillator (mass attached to spring): E total 0.5 k A KE + U elas 0.5 m v x k x (A oscillation amplitude) v x ± k m A x Mechanical oscillations - For -C Circuit: Q C i + q C Total energy initially stored in C energy stored in + energy stored in C (at given t). i ± C Q q Electrical oscillations

19

20 6. The -R-C Series Circuit Because of R, the electromagnetic energy of system is ssipated and converted to other forms of energy (e.g. internal energy of circuit materials). [Analogous to friction in mechanical system]. - Energy loses in R i R U B in when C completely scharged < U E Q /C - Small R circuit still oscillates but with damped harmonic motion circuit underdamped. - arge R no oscillations (e out) critically damped. - Very large R circuit overdamped C charge approaches 0 slowly.

21 Analyzing an -R-C Circuit ir q C 0 (i dq/) d q R dq + + q C 0 For R < 4/C: (underdamped) q Ae ( R / ) t cos C R 4 t + ϕ A, φ are constants ω ' C R 4 underdamped -R-C series circuit

22 Inductors in series: eq + Inductors in parallel: / eq / + /

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one

More information

April 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii.

April 1. Physics 272. Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html. Prof. Philip von Doetinchem philipvd@hawaii. Physics 272 April 1 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 164 Summary Gauss's

More information

Chapter 30 Inductance

Chapter 30 Inductance Chapter 30 Inductance In this chapter we investigate the properties of an inductor in a circuit. There are two kinds of inductance mutual inductance and self-inductance. An inductor is formed by taken

More information

Inductance and Magnetic Energy

Inductance and Magnetic Energy Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance... 11-3 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops... 11-5 11. Self-Inductance... 11-5 Example 11. Self-Inductance

More information

Eðlisfræði 2, vor 2007

Eðlisfræði 2, vor 2007 [ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has

More information

Induced voltages and Inductance Faraday s Law

Induced voltages and Inductance Faraday s Law Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic

More information

Inductance. Motors. Generators

Inductance. Motors. Generators Inductance Motors Generators Self-inductance Self-inductance occurs when the changing flux through a circuit arises from the circuit itself. As the current increases, the magnetic flux through a loop due

More information

Last time : energy storage elements capacitor.

Last time : energy storage elements capacitor. Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because

More information

Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering

Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering 2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An externally produced magnetic field of

More information

Solution Derivations for Capa #11

Solution Derivations for Capa #11 Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the

More information

Lecture 22. Inductance. Magnetic Field Energy. Outline:

Lecture 22. Inductance. Magnetic Field Energy. Outline: Lecture 22. Inductance. Magnetic Field Energy. Outline: Self-induction and self-inductance. Inductance of a solenoid. The energy of a magnetic field. Alternative definition of inductance. Mutual Inductance.

More information

Fall 12 PHY 122 Homework Solutions #10

Fall 12 PHY 122 Homework Solutions #10 Fall 12 PHY 122 Homework Solutions #10 HW10: Ch.30 Q5, 8, 15,17, 19 P 1, 3, 9, 18, 34, 36, 42, 51, 66 Chapter 30 Question 5 If you are given a fixed length of wire, how would you shape it to obtain the

More information

CHAPTER 30: Inductance, Electromagnetic Oscillations, and AC Circuits

CHAPTER 30: Inductance, Electromagnetic Oscillations, and AC Circuits HAPTE 3: Inductance, Electromagnetic Oscillations, and A ircuits esponses to Questions. (a) For the maximum value of the mutual inductance, place the coils close together, face to face, on the same axis.

More information

Objectives. Capacitors 262 CHAPTER 5 ENERGY

Objectives. Capacitors 262 CHAPTER 5 ENERGY Objectives Describe a capacitor. Explain how a capacitor stores energy. Define capacitance. Calculate the electrical energy stored in a capacitor. Describe an inductor. Explain how an inductor stores energy.

More information

RUPHYS ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman

RUPHYS ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman Signed in as Jolie Cizewski, Instructor Help Sign Out RUPHYS2272014 ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman Course Home Assignments Roster

More information

March 20. Physics 272. Spring 2014 Prof. Philip von Doetinchem

March 20. Physics 272. Spring 2014  Prof. Philip von Doetinchem Physics 272 March 20 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 129 Summary No magnetic

More information

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H). INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes

More information

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13 CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how

More information

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49 Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large

More information

Physics 2102 Lecture 19. Physics 2102

Physics 2102 Lecture 19. Physics 2102 Physics 2102 Jonathan Dowling Physics 2102 Lecture 19 Ch 30: Inductors and RL Circuits Nikolai Tesla What are we going to learn? A road map Electric charge Electric force on other electric charges Electric

More information

Your Comments. This was a very confusing prelecture. Do you think you could go over thoroughly how the LC circuits work qualitatively?

Your Comments. This was a very confusing prelecture. Do you think you could go over thoroughly how the LC circuits work qualitatively? Your omments I am not feeling great about this mierm...some of this stuff is really confusing still and I don't know if I can shove everything into my brain in time, especially after spring break. an you

More information

EEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate

EEE1001/PHY1002. Magnetic Circuits. The circuit is of length l=2πr. B andφ circulate 1 Magnetic Circuits Just as we view electric circuits as related to the flow of charge, we can also view magnetic flux flowing around a magnetic circuit. The sum of fluxes entering a point must sum to

More information

Module 22: Inductance and Magnetic Field Energy

Module 22: Inductance and Magnetic Field Energy Module 22: Inductance and Magnetic Field Energy 1 Module 22: Outline Self Inductance Energy in Inductors Circuits with Inductors: RL Circuit 2 Faraday s Law of Induction dφ = B dt Changing magnetic flux

More information

Course Syllabus: AP Physics C Electricity and Magnetism

Course Syllabus: AP Physics C Electricity and Magnetism Course Syllabus: AP Physics C Electricity and Magnetism Course Description: AP Physics C is offered as a second year physics course to students who are planning to major in the physical sciences or in

More information

Direction of Induced Current

Direction of Induced Current Direction of Induced Current Bar magnet moves through coil Current induced in coil A S N v Reverse pole Induced current changes sign B N S v v Coil moves past fixed bar magnet Current induced in coil as

More information

Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )

Outline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... ) Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor Non-Ideal Inductor Dr. P.J. Randewijk

More information

W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören

W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018 - Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and

More information

A Capacitor Paradox. Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (July 10, 2002; updated June 16, 2013)

A Capacitor Paradox. Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (July 10, 2002; updated June 16, 2013) Problem A Capacitor Paradox Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 085 (July 0, 00; updated June 6, 03) Two capacitors of equal capacitance C are connected in parallel

More information

DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING

DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING SESSION WEEK COURSE: Physics II DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING DESCRIPTION GROUPS (mark ) Indicate YES/NO If the session needs 2

More information

Inductors & Inductance. Electronic Components

Inductors & Inductance. Electronic Components Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered

More information

PHY2049 Exam #2 Solutions Fall 2012

PHY2049 Exam #2 Solutions Fall 2012 PHY2049 Exam #2 Solutions Fall 2012 1. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial segments. The circuits

More information

1. Title Electrical fundamentals II (Mechanics Repair and Maintenance)

1. Title Electrical fundamentals II (Mechanics Repair and Maintenance) 1. Title Electrical fundamentals II (Mechanics Repair and Maintenance) 2. Code EMAMBG429A 3. Range The knowledge is needed for a wide range of aircraft repair and maintenance works,e.g. applicable to aircrafts,

More information

Magnetic Circuits. Outline. Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples

Magnetic Circuits. Outline. Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples Magnetic Circuits Outline Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples 1 Electric Fields Magnetic Fields S ɛ o E da = ρdv B V = Q enclosed S da =0 GAUSS GAUSS

More information

ES250: Electrical Science. HW7: Energy Storage Elements

ES250: Electrical Science. HW7: Energy Storage Elements ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;

More information

Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits. Copyright 2009 Pearson Education, Inc.

Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits. Copyright 2009 Pearson Education, Inc. Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits 30-1 Mutual Inductance Mutual inductance: a changing current in one coil will induce a current in a second coil: Coil 1 produces a flux

More information

Physics 6C, Summer 2006 Homework 2 Solutions

Physics 6C, Summer 2006 Homework 2 Solutions Physics 6C, Summer 006 Homework Solutions All problems are from the nd edition of Walker. Numerical values are different for each student. Chapter 3 Problems. Figure 3-30 below shows a circuit containing

More information

Chapter 27 Electromagnetic Induction

Chapter 27 Electromagnetic Induction For us, who took in Faraday s ideas so to speak with our mother s milk, it is hard to appreciate their greatness and audacity. Albert Einstein 27.1 ntroduction Since a current in a wire produces a magnetic

More information

Time dependent circuits - The RC circuit

Time dependent circuits - The RC circuit Time dependent circuits - The circuit Example 1 Charging a Capacitor- Up until now we have assumed that the emfs and resistances are constant in time, so that all potentials, currents and powers are constant

More information

Chapter 11. Inductors ISU EE. C.Y. Lee

Chapter 11. Inductors ISU EE. C.Y. Lee Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive

More information

Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration

More information

PHY114 S11 Term Exam 3

PHY114 S11 Term Exam 3 PHY4 S Term Exam S. G. Rajeev Mar 2 20 2:0 pm to :45 pm PLEASE write your workshop number and your workshop leader s name at the top of your book, so that you can collect your graded exams at the workshop.

More information

ELECTRICAL ENGINEERING Vol. I - Direct Current and Alternating Current Systems - N. Rajkumar DIRECT CURRENT AND ALTERNATING CURRENT SYSTEMS

ELECTRICAL ENGINEERING Vol. I - Direct Current and Alternating Current Systems - N. Rajkumar DIRECT CURRENT AND ALTERNATING CURRENT SYSTEMS DIRECT CURRENT AND ALTERNATING CURRENT SYSTEMS N. Rajkumar, Research Fellow, Energy Systems Group, City University Northampton Square, London EC1V 0HB, UK Keywords: Electrical energy, direct current, alternating

More information

Capacitors and Inductors

Capacitors and Inductors P517/617 ec2, P1 Capacitors and Inductors 1) Capacitance: Capacitance (C) is defined as the ratio of charge (Q) to voltage () on an object. Define capacitance by: C = Q/ = Coulombs/olt = Farad. Capacitance

More information

EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors

EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors Chapter 19 DC Electrical Circuits Topics in Chapter 19 EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors

More information

Inductors. AC Theory. Module 3

Inductors. AC Theory. Module 3 Module 3 AC Theory What you ll learn in Module 3. Section 3.1 Electromagnetic Induction. Magnetic Fields around Conductors. The Solenoid. Section 3.2 Inductance & Back e.m.f. The Unit of Inductance. Factors

More information

NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians

NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers

More information

12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its self-inductance?

12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its self-inductance? 12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its self-inductance? From Equation 32-5, L = -E=(dI =dt) = 40 V=(100 A/s) = 0.4 H. 15. A cardboard

More information

Physics 9 Fall 2009 Homework 8 - Solutions

Physics 9 Fall 2009 Homework 8 - Solutions 1. Chapter 34 - Exercise 9. Physics 9 Fall 2009 Homework 8 - s The current in the solenoid in the figure is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop?

More information

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao. D.C Machines

Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao. D.C Machines D.C Machines 1 Introduction The steam age signalled the beginning of an industrial revolution. The advantages of machines and gadgets in helping mass production and in improving the services spurred the

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2014

Candidate Number. General Certificate of Education Advanced Level Examination June 2014 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday

More information

Physics 1653 Exam 3 - Review Questions

Physics 1653 Exam 3 - Review Questions Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

More information

Magnetic Field of a Circular Coil Lab 12

Magnetic Field of a Circular Coil Lab 12 HB 11-26-07 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment- coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,

More information

Electromagnetic Induction

Electromagnetic Induction Electromagnetic Induction Lecture 29: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Mutual Inductance In the last lecture, we enunciated the Faraday s law according to

More information

Charge and Discharge of a Capacitor

Charge and Discharge of a Capacitor Charge and Discharge of a Capacitor INTRODUCTION Capacitors 1 are devices that can store electric charge and energy. Capacitors have several uses, such as filters in DC power supplies and as energy storage

More information

Experiment #9: RC and LR Circuits Time Constants

Experiment #9: RC and LR Circuits Time Constants Experiment #9: RC and LR Circuits Time Constants Purpose: To study the charging and discharging of capacitors in RC circuits and the growth and decay of current in LR circuits. Part 1 Charging RC Circuits

More information

AP Physics C: Electricity and Magnetism: Syllabus 3

AP Physics C: Electricity and Magnetism: Syllabus 3 AP Physics C: Electricity and Magnetism: Syllabus 3 Scoring Components SC1 SC2 SC3 SC SC5 SC6 SC7 The course provides and provides instruction in electrostatics. The course provides and provides instruction

More information

CHAPTER - 1. Chapter ONE: WAVES CHAPTER - 2. Chapter TWO: RAY OPTICS AND OPTICAL INSTRUMENTS. CHAPTER - 3 Chapter THREE: WAVE OPTICS PERIODS PERIODS

CHAPTER - 1. Chapter ONE: WAVES CHAPTER - 2. Chapter TWO: RAY OPTICS AND OPTICAL INSTRUMENTS. CHAPTER - 3 Chapter THREE: WAVE OPTICS PERIODS PERIODS BOARD OF INTERMEDIATE EDUCATION, A.P., HYDERABAD REVISION OF SYLLABUS Subject PHYSICS-II (w.e.f 2013-14) Chapter ONE: WAVES CHAPTER - 1 1.1 INTRODUCTION 1.2 Transverse and longitudinal waves 1.3 Displacement

More information

RUPHYS2272015 ( RUPHY227F2015 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman

RUPHYS2272015 ( RUPHY227F2015 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman Signed in as Jolie Cizewski, Instructor Help Sign Out RUPHYS2272015 ( RUPHY227F2015 ) My Courses Course Settings University Physics with Modern Physics, 14e Young/Freedman Course Home Assignments Roster

More information

A Resonant Circuit. I. Equipment

A Resonant Circuit. I. Equipment Physics 14 ab Manual A Resonant Circuit Page 1 A Resonant Circuit I. Equipment Oscilloscope Capacitor substitution box Resistor substitution box Inductor Signal generator Wires and alligator clips II.

More information

45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across?

45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across? PHYS Practice Problems hapters 8- hapter 8. 45. The peak value of an alternating current in a 5-W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,

More information

Faraday s Law of Induction

Faraday s Law of Induction Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction...10-10.1.1 Magnetic Flux...10-3 10.1. Lenz s Law...10-5 10. Motional EMF...10-7 10.3 Induced Electric Field...10-10 10.4 Generators...10-1

More information

Physics 9 Fall 2009 Homework 6 - Solutions

Physics 9 Fall 2009 Homework 6 - Solutions . Chapter 32 - Exercise 8. Physics 9 Fall 29 Homework 6 - s How much power is dissipated by each resistor in the figure? First, let s figure out the current in the circuit. Since the two resistors are

More information

Chapter 35 Alternating Current Circuits

Chapter 35 Alternating Current Circuits hapter 35 Alternating urrent ircuits ac-ircuits Phasor Diagrams Resistors, apacitors and nductors in ac-ircuits R ac-ircuits ac-ircuit power. Resonance Transformers ac ircuits Alternating currents and

More information

) 0.7 =1.58 10 2 N m.

) 0.7 =1.58 10 2 N m. Exam 2 Solutions Prof. Paul Avery Prof. Andrey Korytov Oct. 29, 2014 1. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides, each with length L = 15 cm as

More information

Generate Electricity While Cycling

Generate Electricity While Cycling International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869, Volume-1, Issue-7, September 2013 Generate Electricity While Cycling Shubhankar Paul Abstract This paper will propose

More information

Coupled Inductors. Introducing Coupled Inductors

Coupled Inductors. Introducing Coupled Inductors Coupled Inductors From power distribution across large distances to radio transmissions, coupled inductors are used extensively in electrical applications. Their properties allow for increasing or decreasing

More information

Chapter 7 Direct-Current Circuits

Chapter 7 Direct-Current Circuits Chapter 7 Direct-Current Circuits 7. Introduction...7-7. Electromotive Force...7-3 7.3 Resistors in Series and in Parallel...7-5 7.4 Kirchhoff s Circuit Rules...7-7 7.5 Voltage-Current Measurements...7-9

More information

Problem Solving 8: RC and LR Circuits

Problem Solving 8: RC and LR Circuits MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Problem Solving 8: RC and LR Circuits Section Table and Group (e.g. L04 3C ) Names Hand in one copy per group at the end of the Friday Problem

More information

Let s examine the response of the circuit shown on Figure 1. The form of the source voltage Vs is shown on Figure 2. R. Figure 1.

Let s examine the response of the circuit shown on Figure 1. The form of the source voltage Vs is shown on Figure 2. R. Figure 1. Examples of Transient and RL Circuits. The Series RLC Circuit Impulse response of Circuit. Let s examine the response of the circuit shown on Figure 1. The form of the source voltage Vs is shown on Figure.

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3 - MAGNETISM and INDUCTION

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3. OUTCOME 3 - MAGNETISM and INDUCTION EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 3 - MAGNETISM and INDUCTION 3 Understand the principles and properties of magnetism Magnetic field:

More information

Capacitors in Circuits

Capacitors in Circuits apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively

More information

Introduction to Complex Numbers in Physics/Engineering

Introduction to Complex Numbers in Physics/Engineering Introduction to Complex Numbers in Physics/Engineering ference: Mary L. Boas, Mathematical Methods in the Physical Sciences Chapter 2 & 14 George Arfken, Mathematical Methods for Physicists Chapter 6 The

More information

RLC Resonant Circuits

RLC Resonant Circuits C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document

More information

Electrical Machines II. Week 1: Construction and theory of operation of single phase transformer

Electrical Machines II. Week 1: Construction and theory of operation of single phase transformer Electrical Machines II Week 1: Construction and theory of operation of single phase transformer Transformers Overview A transformer changes ac electric power at one frequency and voltage level to ac electric

More information

Student Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics

Student Name Instructor Name. High School or Vocational Center Grade. COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Student Name Instructor Name High School or Vocational Center Grade COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Electronics Please check below each skill the student has mastered as described,

More information

Aircraft Electrical System

Aircraft Electrical System Chapter 9 Aircraft Electrical System Introduction The satisfactory performance of any modern aircraft depends to a very great degree on the continuing reliability of electrical systems and subsystems.

More information

A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle

A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle Page 1 of 15 Abstract: The wireless power transfer link between two coils is determined by the properties of the

More information

Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010. Dr.Prapun Suksompong 1 June 16, 2010

Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010. Dr.Prapun Suksompong 1 June 16, 2010 Sirindhorn International Institute of Technology Thammasat University School of Information, Computer and Communication Technology Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010 Dr.Prapun

More information

Chapter 12 Driven RLC Circuits

Chapter 12 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 information

EE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits

EE 221 Circuits II. Chapter 13 Magnetically Coupled Circuits EE Circuits II Chapter 3 Magnetically Coupled Circuits Magnetically Coupled Circuits 3. What is a transformer? 3. Mutual Inductance 3.3 Energy in a Coupled Circuit 3.4 inear Transformers 3.5 Ideal Transformers

More information

Power Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore.

Power Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore. Power Electronics Prof. K. Gopakumar Centre for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture - 1 Electric Drive Today, we will start with the topic on industrial drive

More information

RC Circuits. 1 Introduction. 2 Capacitors

RC Circuits. 1 Introduction. 2 Capacitors 1 RC Circuits Equipment DataStudio with 750 interface, RLC circuit board, 2 voltage sensors (no alligator clips), 2x35 in. leads, 12 in. lead Reading Review operation of DataStudio oscilloscope. Review

More information

Lecture 10. Resistor Circuits, Batteries and EMF

Lecture 10. Resistor Circuits, Batteries and EMF Lecture 10. Resistor Circuits, Batteries and EMF Outline: Connection of Resistors: In Parallel and In Series. Batteries. Non-ideal batteries: internal resistance. Potential distribution around a complete

More information

104 Practice Exam 2-3/21/02

104 Practice Exam 2-3/21/02 104 Practice Exam 2-3/21/02 1. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero

More information

DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4

DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4 DOE-HDBK-1011/3-92 JUNE 1992 DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4 U.S. Department of Energy Washington, D.C. 20585 FSC-6910 Distribution Statement A. Approved for public release;

More information

Circuits. PHY2049: Chapter 27 1

Circuits. PHY2049: Chapter 27 1 Circuits PHY2049: Chapter 27 1 What You Already Know Nature of current Current density Drift speed and current Ohm s law Conductivity and resistivity Calculating resistance from resistivity Power in electric

More information

Chapter 7. DC Circuits

Chapter 7. DC Circuits Chapter 7 DC Circuits 7.1 Introduction... 7-3 Example 7.1.1: Junctions, branches and loops... 7-4 7.2 Electromotive Force... 7-5 7.3 Electrical Energy and Power... 7-9 7.4 Resistors in Series and in Parallel...

More information

2 A bank account for electricity II: flows and taxes

2 A bank account for electricity II: flows and taxes PHYS 189 Lecture problems outline Feb 3, 2014 Resistors and Circuits Having introduced capacitors, we now expand our focus to another very important component of a circuit resistors. This entails more

More information

Alternating Current Circuits and Electromagnetic Waves

Alternating Current Circuits and Electromagnetic Waves Arecibo, a large radio telescope in Puerto Rico, gathers electromagnetic radiation in the form of radio waves. These long wavelengths pass through obscuring dust clouds, allowing astronomers to create

More information

Lesson 3 DIRECT AND ALTERNATING CURRENTS. Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks.

Lesson 3 DIRECT AND ALTERNATING CURRENTS. Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks. Lesson 3 DIRECT AND ALTERNATING CURRENTS Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks. Objectives. When you have completed this lesson, you should be able

More information

CHAPTER 28 ELECTRIC CIRCUITS

CHAPTER 28 ELECTRIC CIRCUITS CHAPTER 8 ELECTRIC CIRCUITS 1. Sketch a circuit diagram for a circuit that includes a resistor R 1 connected to the positive terminal of a battery, a pair of parallel resistors R and R connected to the

More information

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

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

1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole.

1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole. Exam Name 1) Magnetic field lines come out of the south pole of a magnet and enter at the north pole. 2) Which of the following statements is correct? A) Earth's north pole is magnetic north. B) The north

More information

Physics 2220 Module 09 Homework

Physics 2220 Module 09 Homework Physics 2220 Module 09 Homework 01. A potential difference of 0.050 V is developed across the 10-cm-long wire of the figure as it moves though a magnetic field perpendicular to the page. What are the strength

More information

1. 1. Right Hand Rule Practice. Using the the right hand rule, find find the the direction of of the the missing information in in the the diagram.

1. 1. Right Hand Rule Practice. Using the the right hand rule, find find the the direction of of the the missing information in in the the diagram. 1. 1. Right Hand Rule Practice Using the the right hand rule, find find the the direction of of the the missing information in in the the diagram. (A) (A) up up (C) (C) left left (B) (B) down (D) (D) right

More information

MAGNETISM MAGNETISM. Principles of Imaging Science II (120)

MAGNETISM MAGNETISM. Principles of Imaging Science II (120) Principles of Imaging Science II (120) Magnetism & Electromagnetism MAGNETISM Magnetism is a property in nature that is present when charged particles are in motion. Any charged particle in motion creates

More information

Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

More information

MEASURING INSTRUMENTS. By: Nafees Ahmed, Asstt, Prof, EE Deptt, DIT, Dehradun

MEASURING INSTRUMENTS. By: Nafees Ahmed, Asstt, Prof, EE Deptt, DIT, Dehradun MEASURING INSTRUMENTS By: Nafees Ahmed, Asstt, Prof, EE Deptt, DIT, Dehradun MEASURING INSTRUMENTS The device used for comparing the unknown quantity with the unit of measurement or standard quantity is

More information