INTRODUCTION SELF INDUCTANCE. Introduction. Self inductance. Mutual inductance. Transformer. RLC circuits. AC circuits


 Fay Perry
 1 years ago
 Views:
Transcription
1 Chapter 13 INDUCTANCE Introduction Self inductance Mutual inductance Transformer RLC circuits AC circuits Magnetic energy Summary INTRODUCTION Faraday s important contribution was his discovery that achangingmagneticflux induces an emf in a circuit. Hisrelationisgivenas: = Φ where the electromotive force is given by: I = ( E + v B) l and the magnetic flux Φ is given by: Φ = B S The negative sign in Faraday s law is a statement of Lenz s Law. Faraday s Law encompasses two phenomena, the induced electric fieldinafixed circuit due toachangingmagneticflux, and motional emf due to motion of the circuit in a magnetic field. Einstein s Theory of Relativity shows that these two phenomena are manifestations of the same physics that result from changing frames of reference. It was shown that independent of whether the circuit moves or not, Faraday s law is equivalent to the statement that: I E l = B S This relation is derived easily from Faraday s Law for the special case of a fixed circuit since then only B is time dependent. Faraday s Law provides a direct linkage of electric and magnetic fields that occurs for dynamical situations, that is changing magnetic fields. It leads to the Figure 1 Self inductance in a circuit. The light bulbs serve as voltmeters. When the current is switched on the light across the inductance is bright because of the large emf across this coil while the coil across the resistor is low because the current is low. In the steady case only the bulb across the resistor is bright because of the voltage drop. When the circuit is broken the energy stored in the self inductance is dissipated in the bulb across the inductance. fact that the circulation of the electric field can be nonzero for changing magnetic flux in a closed circuit. Faraday s law underlies much of the technology that is used in modern life. This chapter probes technical aspects of induction. SELF INDUCTANCE According to Faraday s Law, a changing magnetic flux in a circuit induces an emf that resists such a change. Consider an isolated circuit. If the current in this circuit changes then the magnetic field produced by the current in this circuit will induce an emf in the same circuit. This is called the back emf because it opposes the change in the magnetic flux enclosed by the circuit, that is, the circuit exhibits inertia. This is called self inductance and is illustrated by the demonstration where turning off the magnet current causes a current to flow in the light bulb in the circuit shown in figure 1. Consider that this circuit is designated by the letter Then the flux in circuit due to the current in the same circuit will be written as Φ. Using Faraday s law we have: = Φ This can be written as: = Φ = where the self inductance is defined as: 97
2 Figure 2 Self inductance of a solenoid. Figure 3 Mutual inductance. MUTUAL INDUCTANCE Φ Note the negative sign in the equation for emf which results from Faraday s law. Example: Self inductance of a solenoid. Consider that the solenoid has turns, length radius, and carries a current as shown in figure 2. Ampère s Law can be used to show that the magnetic field in a solenoid is axial with a magnitude: = 0 The flux linkage Φ, taking into account that the field is uniform across the solenoid, and that it is linked times since the coil has turns. Φ = B S = 2 2 = 0 2 Thus the self inductance is given as: = Φ 2 = 0 2 The self inductance is just a simple geometric number for any coil. NB, Many books use =turns per unit length in his formula, whereas these notes use =thetotal number of turns; be careful not to get confused. The SI unit of inductance is the Henry after the US scientist. The SI unit of magnetic flux Φ is the weber. Thus, since = Φ = = The Henry is a large unit. For example, for the above case let =10 3, =002, =01 and 0 =410 7, then =16. For this coil, if =10 3 per second, then the induced back emf will be 16 volts. Mutual inductance is the induced emf in one circuit due to a changing field produced by a second circuit. Faraday s Law can be written as: = Φ = Φ = where the mutual inductance is defined as: Φ Calculation of the mutual inductance for any pair of circuits can be a complicated integral. One uses the Biot Savart law to compute the B field at circuit due to circuit B = 0 4 I dl cr 2 Knowing the magnetic field, then one can compute the flux linkage in circuit due to the field produced by circuit. Φ = B S Φ = I 0 dl cr S 4 2 Thus the mutual inductance is given by Φ = I 0 4 dl cr S 2 This complicated double integral can be simplified mathematically using Stokes Theorem, to give that: = I I 0 l l 4 This nontrivial step gives that the double integral is a symmetric geometric factor. This relation is called Neumann s Formula. 98
3 = Φ = 0 2 You can easily compute the mutual inductance due to the magnetic flux due to in and you will obtain the same mutual inductance relation. Typical values might be = =10 3 =01 =001 then one obtains =40. Figure 4 Concentric solenoids The above proof can be repeated for the emf in due to a changing current in circuit. Thatis; = Φ = Φ = leading to mutual inductance = I I 0 l l = = 4 That is; the mutual inductance is symmetrical whether one is considering the flux in due to or vice versa. Thus we can write for the two coils that: = = where the mutual inductance is a geometrical factor expressing the degree of coupling of the magnetic flux between two separate circuits. Note the negative sign remaining from Faraday s and Lenz s laws. Mutual inductance between two concentric solenoids In general the computation of mutual inductance is non trivial. However, one can easily calculate the mutual inductance between concentric solenoids. Consider the system shown in figure 4 where the radii of the coils are such that. The magnetic field in due to circuit is = 0 The field from only extends over an area 2. Thus the flux linkage in circuit due to the magnetic flux from is: Φ = 2 = 0 2 Thus the mutual inductance is: TRANSFORMER The transformer is a nice example of use of inductance. Consider two tightlycoupled circuits such as two concentric solenoids with an alternating emf applied to the primary coil and a resistor dissipating energy connected to the secondary coil. Consider that all of the magnetic flux Φ goes through both coils. Then the flux linkage for the primary circuit is Φ = Φ while the flux linkage for the secondary is Φ = Φ If the magnetic flux is time dependent then we have Φ = Similarly for the secondary Φ = Eliminating Φ gives = That is the voltage ratio equals the turns ratio. The perfect transformer does not dissipate energy in the transformer, thus we must have power conserved, that is: = Thus: = The non perfect transformer can be solved using Kirchhoff s loop rule that the sum of emfs around the primary circuit equals zero: =0 where we have to include the induced emf due to self inductance as well as the mutual inductance term. For the secondary the voltage across the resistor = Then Kirchhoff s loop rule gives: 99
4 =0 Multiply the first equation by and the second equation by andthentakethedifference of these equations gives ( )=( 2 ) Obviously the closest coupling of magnetic flux occurs for self inductance where a coil is coupled perfectly to the magnetic flux it generates. Thus we must have that: Figure 5 The transformer. Figure 6 RLC circuit. Thus : RLC CIRCUITS 2 For perfect coupling of magnetic flux between the coupled circuits, then: 2 = In the case of perfect coupling then the righthand side of the previous equation relating the emfs is zero, therefore: It is useful to consider the response of simple circuits involving resistance, capacitance, and inductance. The response of general LRC circuits to AC input signals is important because of many applications to technology. However, the discussion of such response requires a detailed discussion of both the amplitude and phase of the output relative to the input waveforms. The following is a brief summary of some concepts of AC circuits. Consider the series combination of, and shown in figure 6. Assume that initially the capacitor is charged with charge 0 when the switch is closed at atime =0. Using Kirchhoff s loop rule, and knowing that voltage across the capacitor = then: = For perfect coupling this equation gives the same equationsasgivenabove; = = = Note that the transformer only works for oscillating currents and emf s, otherwise =0However, the ratio of voltages is independent of frequency in this elementary theory. For perfect coupling and a resistive load, then the primary and secondary waveforms are in phase and the solution is simple. The ability of the transformer to easily and efficiently transform voltages for AC power is the reason that AC is used for power distribution. = From charge conservation, Kirchhoff s node rule, we have: + =0 Using these two equations gives a second order differential equation =0 100
5 Figure 7 Damped RLC circuit response compared with undampedsolutionwhenr=0. Since = this also can be written as: =0 If you have studied second order homogeneous differential equations you will know that the solution for 1 light damping, that is, 2 4 is: 2 Figure 8 When the motion is overdamped 2 leading to an exponetial decay. When 1 = 2 4 the 2 system is critically damped leading to the most rapid damping. Critical damping is used for meter systems to ensure that the needle reaches the correct value in the shortest time. where: () = 0 2 [ sin + cos ] 2 = The time dependence is that of a damped harmonic oscillation with angular frequency and damping time constant = 2 as shown in figure 7. Note that for =0there is no damping and one has a constant harmonic oscillation with angular frequency = 1 For the damped case the frequency is slightly reduced. On the other hand, when the relation 2 for 2 is negative leading to an imaginary value for producing a nonoscillatory overdamped motion that decays exponentially as shown in figure 8. If one applies an sinusoidal voltage from a power supply then one will have the phenomena of resonance when the applied frequency approaches the resonant frequency of the circuit as will be dicussed next lecture. Tesla Coil The Tesla coil provides a nice example of RLC circuits coupled to transformers. The first transformer raises the Hz primary voltage to 15,60Hz.The small spark gap breaks down at 15 kv stimulating the Figure 9 The Tesla coil. 101
6 Figure 11 The series resonant circuit and the corresponding phasor diagram. Capacitor C Since = and from charge conservation Figure 10 Phase relations between current (solid line) and voltage (shaded) for a resistor, capacitor, and inductor. The phasor diagram is shown on the right. LC circuit to oscillate at about 500 khz. The rate of change of current in the primary of the second transformer is 10,000 times what it would be at 60 Hz. The turns ratio for the second coil then produces 300 kv across the final spark gap. AC CIRCUITS This discussion leads naturally to the topic of AC circuits which is of considerable technical importance. This relates to the response of R,L,C circuits to an applied sinusoidal voltage. This topic is not included in this course and the examinations because of the mathematical complexity. However, for your education it is useful to recognize the basic elements of AC circuits. Consider an applied voltage that is a cosine function of time = 0 cos It is useful to define an impedance by Resistor Ohm slawgivesthat = = = 0 cos Thus the current and voltage are in phase as shown in figure 10a and the impedance is = = = = 0 sin = 0 cos( + 2 ) Thus as shown in figure 10b for a capacitor the current leads the voltage by 90 and the impedance is = 1 and 90 out of phase. This is obvious in that you can only change the voltage across a capacitor by having current flow into the capacitor to change the stored charge. Inductor L Since by Kirchhoff s rules for circuit figure 10c, =0 Thus 0 cos = By integration this gives 0 sin = This can be rewritten as = 0 cos( 2 ) Thus for an inductor the the current lags the voltage by 90 and the impedance is = and 90 out of phase. This is obvious in the the back emf opposes change of the field, that is the current when a voltage is applied. 102
7 Thus using Kirchhoff s rules for the RLC circuit in figure 11 it can be seen that the magnitude of the effective impedance can be calculate using Pythagorus Theorem to have a magnitude given by " = 2 + µ 1 # and the voltage leads the current by a phase angle µ 1 =tan 1 Figure 12 Build up of magnetic energy as the current increases in a RL circuit connected to a battery after the switch is closed at t=0. This series is an example of the fact that any combination of passive impedances can be represented as a net load having a resultant complex impedance such that V = I where has an inphase resistive component = cos and a reactive, or out of phase, component Figure 13 LC circuit. = sin It is interesting that the resistive load dissipates power where = = where the factor of 12 comes from the fact that the average of (cos ) 2 over one complete cycle is 12. However a reactive load does not dissipate power since the voltage and current are out of phase then the product of gives a (cos sin ) term which averages to zero over one complete cycle of oscillation. Because of the mathematical complexity of this topic this discussion will not be pursued further. It is suggested that you skim over chapter 31 of Giancoli to get an broader impression of this topic. MAGNETIC ENERGY Energy stored in Inductor Since forces occur between magnetic circuits, energy must be stored in the magnetic field. Consider the system shown in figure 12. Using Kirchhoff s loop rule we have: 0 = + Consider that in a time dt, a charge = flows. The work done by the battery is given by 0 This equals: 0 = 2 + This is equivalent to the statement that the energy provided by the battery equals the energy dissipated in the resistor plus the energy stored in the self inductance. Thus we have that the energy stored in the inductance is: = Integrating the energy from =0to the final value gives the magnetic energy stored in the self inductance as: = 0 = Consider a simple LC circuit, shown in figure 13, with oscillating current and charge. The total energy is distributed between the capacitor and the inductor as: = + = Note that the energy oscillates between the capacitor, when Q is maximum and =0 to the inductor when =0and I is a maximum. This is analogous to 103
8 Ampère s law gives the magnetic field inside the toroid is () = 0 2 Integrating over the rectangular cross section inside the toroid windings, gives the magnetic flux inside the windings to be Φ = () = 0 2 Figure14 Nturntoriodwithinnerradius, outer radius, andthickness. harmonic oscillations of a pendulum where the energy oscillates between kinetic energy and potential energy. The inertia in the inductance is analogous to moment of inertia in the kinetic energy term for angular motion of the pendulum. The energy stored in the capacitor is analogous to the gravitational potential energy stored at the extreme positions of the pendulum oscillation. Energy Density in a Magnetic Field It is more useful to express the stored magnetic energy density in terms of the magnetic field B just as the electric energy density was expressed in terms of the electric field E Inthecaseoftheelectricfield, the stored electric energy for a capacitor, of = was used to show that the electric energy can be expressed as the integral of the electric energy density in vacuum = Thus the total stored energy in the electric field in vacuum 1 = where the integral is taken over all space For the magnetic fielditwillbeshownlaterthat the magnetic energy = can be expressed in terms of the magnetic energy density in vacuum = Thus the total stored energy in the magnetic field in vacuum is 1 2 = 2 0 The equivalence of this expression and = can be illustrated by considering the toriod shown in figure 14. Φ = 0 2 ln( ) Thus the flux linkage for the N turns wrapped around the toroid is Φ = Φ = ln( ) This gives that the self inductance = Φ = ln( ) Therefore the stored magnetic energy = = 0 4 ()2 ln( ) Consider the integral of = Knowing that () = 0 2 and that the volume element of a ring inside the torus is d =2 gives = 1 µ That is = 0 4 ()2 = = 0 4 ()2 ln( ) which is the same relation obtained using = That is, the two expressions for magnetic energy give the same answer for this case. In fact it can be proven, using vector differential calculus, that this is always true. As a result, the most general expression for the total electromagnetic energy can be written in terms of the electric and magnetic fields as given by the integral over all space of the energy density = =( ) 2 0 ( ) 2 0 This is especially useful for discussions of electromagnetic waves. 104
9 SUMMARY The concepts of self inductance and mutual inductance and some applications have been discussed. It was shown that the induced emf in an isolated circuit can be written as: = where the self inductance L is defined as: Φ Similarly, the coupling between two circuits is given by = where the mutual inductance is defined as: Φ Elements of the response of circuits with L, R, and C were discussed as well as applications to the transformer and the induction coil. It was shown that the energy stored in an inductor is given by = Thus the total energy stored in a circuit having both inductors and capacitors is: = + = It is especially useful to express the total energy stored in an electromagnetic field in terms the energy density of the E and B fields. = ( ) This form will be used in discussing electromagnetic radiation. Reading assignment: Giancoli, Chapter 30 plus skim through Chapter
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 informationEðlisfræði 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 informationCircuits 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 informationHomework #11 20311721 Physics 2 for Students of Mechanical Engineering
Homework #11 20311721 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 informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More information1) 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 informationCoupled 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 informationFall 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 informationLast 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 informationNZQA 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 informationAlternating Current RL Circuits
Alternating Current RL Circuits Objectives. To understand the voltage/current phase behavior of RL circuits under applied alternating current voltages, and. To understand the current amplitude behavior
More informationElectromagnetic 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 informationExperiment A5. Hysteresis in Magnetic Materials
HYSTERESIS IN MAGNETIC MATERIALS A5 1 Experiment A5. Hysteresis in Magnetic Materials Objectives This experiment illustrates energy losses in a transformer by using hysteresis curves. The difference betwen
More information1. 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 informationSolution 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 informationEdmund 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 informationChapter 30 Inductance
Chapter 30 Inductance  Mutual Inductance  SelfInductance and Inductors  MagneticField Energy  The R Circuit  The C Circuit  The RC Series Circuit . Mutual Inductance  A changing current in
More informationInduced 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 informationPhysics 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 informationChapter 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 informationBASIC ELECTRONICS AC CIRCUIT ANALYSIS. December 2011
AM 5202 BASIC ELECTRONICS AC CIRCUIT ANALYSIS December 2011 DISTRIBUTION RESTRICTION: Approved for Pubic Release. Distribution is unlimited. DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM FORT
More informationEDEXCEL 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 informationDiodes have an arrow showing the direction of the flow.
The Big Idea Modern circuitry depends on much more than just resistors and capacitors. The circuits in your computer, cell phone, Ipod depend on circuit elements called diodes, inductors, transistors,
More informationMagnetic Field of a Circular Coil Lab 12
HB 112607 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 information45. The peak value of an alternating current in a 1500W 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 5W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,
More informationDirection 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 informationProf. 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 informationInductance and Magnetic Energy
Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance... 113 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops... 115 11. SelfInductance... 115 Example 11. SelfInductance
More informationCourse 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 informationScott Hughes 7 April 2005. Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005. Lecture 15: Mutual and Self Inductance.
Scott Hughes 7 April 2005 151 Using induction Massachusetts nstitute of Technology Department of Physics 8022 Spring 2005 Lecture 15: Mutual and Self nductance nduction is a fantastic way to create EMF;
More informationPhysics 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 informationW03 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 informationCHAPTER 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 informationLab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response
Capacitor and Inductor Transient Response Capacitor Theory Like resistors, capacitors are also basic circuit elements. Capacitors come in a seemingly endless variety of shapes and sizes, and they can all
More informationAn Introduction to the Mofied Nodal Analysis
An Introduction to the Mofied Nodal Analysis Michael Hanke May 30, 2006 1 Introduction Gilbert Strang provides an introduction to the analysis of electrical circuits in his book Introduction to Applied
More informationEE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits
EE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits 1. Introduction and Goal: Exploring transient behavior due to inductors and capacitors in DC circuits; gaining experience with lab instruments.
More informationDirect versus Alternating Current Things We Can Measure
Phil Sherrod W4PHS Direct versus Alternating Current Things We Can Measure Direct Current (DC) Alternating Current (AC) Voltage Voltage (peak, RMS) Current Current (peak, effective) Power True power, Apparent
More informationChapter 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 informationLesson 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 informationPractice Problems  Chapter 33 Alternating Current Circuits
Multiple Choice Practice Problems  Chapter 33 Alternating Current Circuits 4. A highvoltage powerline operates at 500 000 Vrms and carries an rms current of 500 A. If the resistance of the cable is
More informationAlternatingCurrent Circuits
hapter 1 Alternatingurrent ircuits 1.1 A Sources... 11. Simple A circuits... 13 1..1 Purely esistive load... 13 1.. Purely Inductive oad... 15 1..3 Purely apacitive oad... 17 1.3 The Series ircuit...
More information2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?
Extra Questions  2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux
More information12. Transformers, Impedance Matching and Maximum Power Transfer
1 1. Transformers, Impedance Matching and Maximum Power Transfer Introduction The transformer is a device that takes AC at one voltage and transforms it into another voltage either higher or lower than
More informationReading assignment: All students should read the Appendix about using oscilloscopes.
10. A ircuits* Objective: To learn how to analyze current and voltage relationships in alternating current (a.c.) circuits. You will use the method of phasors, or the vector addition of rotating vectors
More information1. E&M induction requires change, of the intensity of a magnetic field or of motion in a magnetic field.
Chapter 25 EXERCISE key 1. E&M induction requires change, of the intensity of a magnetic field or of motion in a magnetic field. 2. Magnetic induction will not occur in nylon, since it has no magnetic
More informationCURRENT ELECTRICITY INTRODUCTION TO RESISTANCE, CAPACITANCE AND INDUCTANCE
CURRENT ELECTRICITY INTRODUCTION TO RESI STANCE, CAPACITANCE AND INDUCTANCE P R E A M B L E This problem is adapted from an online knowledge enhancement module for a PGCE programme. It is used to cover
More informationExtra Questions  1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A
Extra Questions  1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated
More informationLet 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 informationAlternating 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 informationCHAPTER  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 PHYSICSII (w.e.f 201314) Chapter ONE: WAVES CHAPTER  1 1.1 INTRODUCTION 1.2 Transverse and longitudinal waves 1.3 Displacement
More informationChapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits. Copyright 2009 Pearson Education, Inc.
Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits 301 Mutual Inductance Mutual inductance: a changing current in one coil will induce a current in a second coil: Coil 1 produces a flux
More informationApplication Note. So You Need to Measure Some Inductors?
So You Need to Measure Some nductors? Take a look at the 1910 nductance Analyzer. Although specifically designed for production testing of inductors and coils, in addition to measuring inductance (L),
More information* Biot Savart s Law Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No.
* Biot Savart s Law Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B PPT No. 17 Biot Savart s Law A straight infinitely long wire is carrying
More informationInductors & 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 informationElectromagnetism Laws and Equations
Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E and Dfields............................................. Electrostatic Force............................................2
More informationName Date Day/Time of Lab Partner(s) Lab TA
Name Date Day/Time of Lab Partner(s) Lab TA Objectives LAB 7: AC CIRCUITS To understand the behavior of resistors, capacitors, and inductors in AC Circuits To understand the physical basis of frequencydependent
More informationBharathwaj Muthuswamy EE100 Active Filters
Bharathwaj Muthuswamy EE100 mbharat@cory.eecs.berkeley.edu 1. Introduction Active Filters In this chapter, we will deal with active filter circuits. Why even bother with active filters? Answer: Audio.
More informationElectroMagnetic Induction. AP Physics B
ElectroMagnetic Induction AP Physics B What is E/M Induction? Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current. Michael Faraday
More informationModule P5.4 AC circuits and electrical oscillations
F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P5.4 Opening items. Module introduction.2 Fast track questions.3 Ready to study? 2 AC circuits 2. Describing alternating currents
More informationA 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 informationPHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA
PHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationAC Generators. Basic Generator
AC Generators Basic Generator A basic generator consists of a magnetic field, an armature, slip rings, brushes and a resistive load. The magnetic field is usually an electromagnet. An armature is any number
More informationLecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)
Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1 Roadmap: How Does This Work? 2 Processor Board 3 More Detailed Roadmap
More informationCritical thinfilm processes such as deposition and etching take place in a vacuum
WHITEPAPER INTRODUCING POWER SUPPLIES AND PLASMA Critical thinfilm processes such as deposition and etching take place in a vacuum SYSTEMS chamber in the presence of a plasma. A plasma is an electrically
More information12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its selfinductance?
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 selfinductance? From Equation 325, L = E=(dI =dt) = 40 V=(100 A/s) = 0.4 H. 15. A cardboard
More informationPhasors. Phasors. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department. ^ V cos (wt + θ) ^ V sin (wt + θ)
V cos (wt θ) V sin (wt θ) by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Vector
More informationSeries & Parallel Impedance Parameters and Equivalent Circuits
Chroma ystems olutions, Inc. eries & arallel Impedance arameters and Equivalent Circuits Keywords: Impedance, capacitance, resistance Title: roduct Family: eries & arallel Impedance arameters and Equivalent
More informationChapter 14 Magnets and
Chapter 14 Magnets and Electromagnetism How do magnets work? What is the Earth s magnetic field? Is the magnetic force similar to the electrostatic force? Magnets and the Magnetic Force! We are generally
More informationMarch 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 informationAP R Physics C Electricity and Magnetism Syllabus
AP R Physics C Electricity and Magnetism Syllabus 1 Prerequisites and Purposes of AP R C E & M AP R Physics C Electricity and Magnetism is the second course in a twocourse sequence. It is offered in the
More informationInductance. Motors. Generators
Inductance Motors Generators Selfinductance Selfinductance 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 informationPhysics 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 informationExperiment #11: LRC Circuit (Power Amplifier, Voltage Sensor)
Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage
More informationFirst Year (Electrical & Electronics Engineering)
Z PRACTICAL WORK BOOK For The Course EE113 Basic Electrical Engineering For First Year (Electrical & Electronics Engineering) Name of Student: Class: Batch : Discipline: Class Roll No.: Examination Seat
More informationApril 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 informationStudent 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 informationInductors in AC Circuits
Inductors in AC Circuits Name Section Resistors, inductors, and capacitors all have the effect of modifying the size of the current in an AC circuit and the time at which the current reaches its maximum
More informationVectors and Phasors. A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles. Owen Bishop
Vectors and phasors Vectors and Phasors A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles Owen Bishop Copyrught 2007, Owen Bishop 1 page 1 Electronics Circuits
More informationThree phase circuits
Three phase circuits THREE PHASE CIRCUITS THREEPHASE ADVANTAGES 1. The horsepower rating of threephase motors and the kva rating of threephase transformers are 150% greater than singlephase motors
More information13 ELECTRIC MOTORS. 13.1 Basic Relations
13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical actuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This
More information1. The diagram below represents magnetic lines of force within a region of space.
1. The diagram below represents magnetic lines of force within a region of space. 4. In which diagram below is the magnetic flux density at point P greatest? (1) (3) (2) (4) The magnetic field is strongest
More informationChapter 25 Alternating Currents
Physics Including Human Applications 554 Chapter 25 Alternating Currents GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each
More information5. Measurement of a magnetic field
H 5. Measurement of a magnetic field 5.1 Introduction Magnetic fields play an important role in physics and engineering. In this experiment, three different methods are examined for the measurement of
More informationEE301 Lesson 14 Reading: 10.110.4, 10.1110.12, 11.111.4 and 11.1111.13
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 informationDOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4
DOEHDBK1011/392 JUNE 1992 DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4 U.S. Department of Energy Washington, D.C. 20585 FSC6910 Distribution Statement A. Approved for public release;
More informationVOLTAGE REGULATOR AND PARALLEL OPERATION
VOLTAGE REGULATOR AND PARALLEL OPERATION Generator sets are operated in parallel to improve fuel economy and reliability of the power supply. Economy is improved with multiple paralleled generators by
More informationAP 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" = R # C. Create your sketch so that Q(t=τ) is sketched above the delineated tic mark. Your sketch. 1" e " t & (t) = Q max
Physics 241 Lab: Circuits DC Source http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html Name: Section 1: 1.1. Today you will investigate two similar circuits. The first circuit is
More information9.1 Variable currents 1: Discharging a capacitor
Scott Hughes 8 March 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005 Lecture 9: Variable currents; Thévenin equivalence 9.1 Variable currents 1: Discharging a capacitor
More informationRLC Circuits. OBJECTIVES To observe free and driven oscillations of an RLC circuit.
ircuits It doesn t matter how beautiful your theory is, it doesn t matter how smart you are. If it doesn t agree with experiment, it s wrong. ichard Feynman (19181988) OBJETIVES To observe free and driven
More informationExperiment V: The AC Circuit, Impedance, and Applications to High and Low Pass Filters
Experiment : The AC Circuit, Impedance, and Applications to High and Low Pass Filters I. eferences Halliday, esnick and Krane, Physics, ol. 2, 4th Ed., Chapters 33 Purcell, Electricity and Magnetism, Chapter
More informationCHAPTER 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 informationChapter 35 Alternating Current Circuits
hapter 35 Alternating urrent ircuits acircuits Phasor Diagrams Resistors, apacitors and nductors in acircuits R acircuits acircuit power. Resonance Transformers ac ircuits Alternating currents and
More informationTransformer circuit calculations
Transformer circuit calculations 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 informationPS6.2 Explain the factors that determine potential and kinetic energy and the transformation of one to the other.
PS6.1 Explain how the law of conservation of energy applies to the transformation of various forms of energy (including mechanical energy, electrical energy, chemical energy, light energy, sound energy,
More informationMAGNETISM 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 informationDEGREE: 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 informationCandidate 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 informationThe Time Constant of an RC Circuit
The Time Constant of an RC Circuit 1 Objectives 1. To determine the time constant of an RC Circuit, and 2. To determine the capacitance of an unknown capacitor. 2 Introduction What the heck is a capacitor?
More informationImpedance Matching and Matching Networks. Valentin Todorow, December, 2009
Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing  Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines
More information