Chapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively


 Owen Henry
 1 years ago
 Views:
Transcription
1 Chapter 3 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively In the LC circuit the charge, current, and potential difference vary sinusoidally (with period T and angular frequency ). The resulting oscillations of the capacitor s electric field and the inductor s magnetic field are said to be electromagnetic oscillations. oscillations the energy stored in the electric field of the capacitor is q UE C L i the energy stored in the magnetic field of the inductor is U B To determine the charge q(t) on the capacitor,put in a voltmeter to measure the potential difference (or voltage) vc that exists across the capacitor C: vc q / C To measure the current, connect a small resistance in series in the circuit and measure the potential difference v across it: v i
2 In an actual LC circuit, the oscillations will not continue indefinitely because there is always some resistance present that will drain energy from the electric and magnetic fields and dissipate it as thermal energy (the circuit may become warmer).
3 The Electrical Mechanical Analogy the analogy between the oscillating LC system and an oscillating block spring system: q corresponds to x, /C correspond to k i corresponds to v, L correspond to m These correspondences suggest that in an LC oscillator, the capacitor is mathematically like the spring in a block spring system and the inductor is like the block. In a block spring system: k block spring system m The correspondences suggest that to find the angular frequency of oscillation for an ideal LC circuit, k Block Spring System LC Oscillator should be replaced by /C and m by L, Element Energy Element Energy L C LC circuit Spring Potential, k x / Block Kinetic, m v / vd x/d t Capacitor Electrical, q / C Inductor Magnetic, L i / i d q/ d t
4 LC Oscillations, Quantitatively The Block Spring Oscillator the total energy of a block spring oscillator: U U b U s m v k x Energy conservation, no friction: du d dv dx 0 m v k x m v k x m d x k x 0 x t X cos t displacement X is the amplitude of the mechanical oscillations, is the angular frequency of the oscillations, and is a phase constant. The LC Oscillator the total energy in an oscillating q LC circuit: U U B U E L i C UB is the energy stored in the magnetic field of the inductor and UE is the energy stored in the electric field of the capacitor. Energy conservation, no resistance: du d di q dq q 0 Li L i C C q t Q cos t charge d q L q 0 LC oscillation C
5 The current of the i t LC oscillator: dq Q sin t I sin t current The angular frequency of the d q I Q LC oscillator: Q cos t L Q cos t Q C cos t L d q q C 0 / LC The phase is determined by the initial conditions. The electrical energy stored in the LC circuit q Q UE cos t C C The magnetic energy stored in the Q UB sin t C UB LC circuit L i L Q sin t Note: U U Q / C E max B max U E U B Q / C constant 3 U E U E max when U B 0 ; U B U B max when U E 0 problem 3
6 Damped Oscillations in an LC Circuit A circuit containing resistance, inductance, and capacitance is called an LC circuit. We shall here discuss only series LC circuits With a resistance present, the total EM energy of the circuit is no longer constant; it decreases with time as energy is transferred to thermal energy in the resistance. Because of this loss of energy, the oscillations of charge, current, and potential difference decrease in amplitude, and the oscillations are damped. du i The rate of energy transferred to thermal energy: d Li q di q dq d q dq L i i L q 0 LC curcuit C d t C C ' / L / L C q Q t / L The electrical energy: U e cos ' t E C C Q t / L U e C Li Q t / L the magnetic energy: U B problem 3 e sin ' t C q Q e t / L cos ' t
7 Alternating Current If the energy is supplied via oscillating emfs and currents, the current is said to be an alternating current, current or ac for short. The nonoscillating current from a battery is said to be a direct current, current or dc. dc These oscillating emfs and currents vary sinusoidally with time, reversing direction (in North America) 0 times per second and thus having frequency f 60 Hz. As the current alternates, so does the magnetic field that surrounds the conductor. This makes possible the use of The advantage of alternating current: Faraday s law of induction. In a generator: ℰ ℰ m sin d t, i I sin d t where d is called the driving angular frequency. frequency the current may not be in phase with the emf. the driving frequency f d d /
8 Forced Oscillations An undamped LC circuits or a damped LC circuits (with small enough ) without any external emf are said to be free oscillations, and the angular frequency / LC is said to be the circuit s natural angular frequency. frequency When the external alternating emf is connected to an LC circuit, the oscillations of charge, potential difference, and current are said to be driven oscillations or forced oscillations., with the driving angular frequency d : Whatever the natural angular frequency of a circuit may be, forced oscillations of charge, current, and potential difference in the circuit always occur at the driving angular frequency d. Three Simple Circuits A esistive Load By the loop rule: ℰ v 0 v ℰ m sin d t v V sin d t V ℰ m i I sin d t 0, v V i sin d t V I resistor v and i are in phase, which means that their corresponding maxima (and minima) occur at the same times.
9 problem 33 A Capacitive Load the potential difference across the capacitor vc V C sin d t qc C v C C V C sin d t d qc d C V C cos d t The current: ic capacitive reactance: X capacitive reactance reactance C d C the SI unit of XC is the ohm, just as for resistance. cos d t sin d t / i C I C sin d t V C IC XC capacitor VC sin d t / XC true for any capacitance in any circuit
10 Problem 34 An Inductive Load the potential difference across the inductance v L V L sin d t L d il d il VL sin d t L VL cos d t The current: i L d i L sin d t d t L d L capacitive reactance: reactance X L d L inductive reactance the SI unit of VL XL is the ohm, just as for XC an for. cos d t sin d t / i L I L sin d t V L I L XL inductor VL sin d t / XL true for any inductance in any circuit
11 Problem 35 Phase and Amplitude elations for Alternating Currents and Voltages Circuit esistance Phase of Phase Constant Amplitude or ecactance the Current or Angle elation Element Symbol esistor In phase with v 0 Capacitor C X C / d C Leads vc by / / V C I C XC Inductor L X L d L Lags v L by / / VL IL XL VI
12 The Series LC Circuit Apply a LC circuit the alternating emf ℰ ℰ m sin d t applied emf i I sin d t The Current Amplitude For the loop rule:ℰ v v C v L ℰ m V V L V C ℰ I I X L I X C where Z X L X C I ℰ X L X C impedance I ℰ Z ℰ [ L / C ] d d I depends on the difference between dl and / dc or, equivalently, the difference between XL and XC. The value of current amplitude
13 The current that we have been describing in this section is the steady state current that occurs after the alternating emf has been applied for some time. When the emf is first applied to a circuit, a brief transient current occurs. Its duration is determined by the time constants LL/ and CC as the inductive and capacitive elements turn on. The Phase Constant V L VC I XL I XC From the plot: tan V I tan X L XC phase constant
14 Three different results for the phase constant XL>XC: The circuit is said to be more inductive than capacitive. XC>XL: The circuit is said to be more capacitive than inductive. XCXL: The circuit is said to be in resonance. purely inductive circuit, where XL is nonzero and XC0, then / (the greatest value of ). In the purely capacitive circuit, where XC is nonzero and XL0, then  / (the least value of ). In the esonance For a given resistance, that amplitude is a maximum when the quantity dl/ dc in the denominator is zero d L d C d L C maximum I the natural angular frequency of the LC circuit is also equal to / L C, the maximum value of I occurs when the driving angular frequency matches the natural angular frequency that is, at resonance. d L C resonance
15 resonance curves peak at their maximum current amplitude I (ℰm/) when d, but the maximum value of I decreases with increasing. The curves also increase in wih (measuring at half the maximum value of I) with increasing. The XL( dl) is small and XC(/ dc) is large. Thus, the circuit is mainly capacitive and the impedance is dominated by the large XC, which keeps For small d, the current low. XC remains dominant but decreases while XL increases. The decrease in XC decreases the impedance, allowing the current I to increase. When the increasing XL and the decreasing XC reach equal values, the current I is As d increases, greatest and the circuit is in resonance, with d. XL becomes more dominant over the decreasing XC. The impedance increases because of XL and the current decreases. As d continue to increase, the increasing In summary: The lowangularfrequency side of a resonance curve is dominated by the capacitor s reactance, the highangular frequency side is dominated by the inductor s reactance, and resonance occurs in the middle. Problem 36
16 Power in AlternatingCurrent Circuits In steadystate operation the average energy stored in the capacitor and inductor together remains constant. The net transfer of energy is thus from the generator to the resistor, where EM energy is dissipated as thermal energy. The instantaneous rate at which energy is dissipated in the resistor P i [ I sin d t ] I sin d t The average rate at which energy is dissipated Pavg T 0 P d t T I T I I rms T 0 sin I d t d t I rms current Pavg I rms average power if we switch to the rms current, we can compute the average rate of energy dissipation for alternatingcurrent circuits just as for directcurrent circuits. V rms V, ℰ rms ℰ rms voltage; rms emf
17 Alternatingcurrent instruments, such as ammeters and voltmeters, are usually calibrated to read Irms, Vrms, and ℰrms. plug an alternatingcurrent voltmeter into a electrical outlet and it reads 0 V, that is an rms voltage. The maximum value of the potential difference at the outlet is 0 V or 70 V. I rms ℰ rms Z ℰ rms X L X C Pavg Pavg ℰ rms I rms cos average power ℰ rms Z I rms ℰ rms I rms cos V ℰm Z I IZ power Z factor The equation is independent of the sign of the phase constant cos cos( ). To maximize the rate at which energy is supplied to a resistive load in an LC circuit, we should keep the power factor cos as close to as possible 0. Problem 37
18 Transformers Energy Transmission equirements an ac circuit with only a resistive load, the power factor cos 0, Pavg ℰ I I V A range of choices of I and of V provided only that the product IV is as required. in the transmission of electrical energy from the generating plant to the consumer, we want the lowest practical current (hence the largest practical voltage) to minimize I losses (often called ohmic losses) in the transmission line. consider a 735 kv line to transmit electrical energy for 000 km. If the current is 500 A and the power factor ~ unity. Thensupply Pavg ℰ I V 500 A 368 MW The resistance of the transmission line is about 0. /km 0 Energy is dissipated due to that resistance at a rate total Pavg I 500 A 0 55 MW ~ 5 % Psupply avg In the other case: I ' I, ℰ ' ℰ / P supply ℰ ' I ' ℰ I avg Pavg I ' 000 A 0 0 MW ~ 65 % Psupply avg the general energy transmission rule:transmit at the highest possible voltage and the lowest possible current.
19 The Ideal Transformer need a device with which we can raise (for transmission) and lower (for use) the ac voltage in a circuit, keeping the product current voltage essentially constant the transformer. The ideal transformer consists of two coils, with different numbers of turns, wound around an iron core. the primary winding, of Np turns, is connected to an AC generator whose emf is The secondary winding, of ℰ ℰ m sin t Ns turns, is connected to load resistance. magnetizing current Imag, lags the primary voltage Vp by 90 (no power is delivered). The sinusoidally changing primary current Imag the primary current, the produces a sinusoidally changing magnetic flux B in the iron core. The core strengthens the flux and to bring it through the secondary winding. Because B varies, it induces an emf ℰturn (d B/) in each turn of the secondary. the emf per turn ℰturn is the same in the primary and the secondary ℰ turn Vp Np Vs Ns V s V p Ns Np transformation of voltage
20 Ns>Np: step up transformer because Vs>Vp ; Ns<Np: step down transformer because Vs<Vp. connect the secondary to the resistive load the generator:, now energy is transferred from An AC Is appears in the secondary circuit, with corresponding energy dissipation rate Is(Vs/) in the resistive load. Is produces its own alternating magnetic flux in the iron core, and this flux induces an opposing emf in the primary windings. 3 Vp of the primary cannot change in response to this opposing emf because it must always be equal to the emf that is provided by the generator. Vp, the generator now produces (in addition to Imag) an AC Ip in the primary circuit; the emf induced by Ip in the primary will exactly cancel the emf induced there by Is. Because the phase constant of Ip is not 90 like that of Imag, this current Ip can transfer energy to the primary. 4 To maintain
21 Assume no energy is lost, conservation of energy requires that I p V p Is Vs I pis Ns Np Ns Vs Np Ns Np Vp Vp eq eq Np Ns Impedance Matching For maximum transfer of energy from an emf device to a load, the impedance of the emf device must equal the impedance of the load. We can match the impedances of the two devices by coupling them through a transformer that has a suitable turns ratio. Solar Activity and PowerGrid Systems problem 38 Selected problems:, 6, 36,50, 58
Electromagnetic Oscillations and Alternating Current. 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3.
Electromagnetic Oscillations and Alternating Current 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3. RLC circuit in AC 1 RL and RC circuits RL RC Charging Discharging I = emf R
More informationRLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is
RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge
More informationAlternating Current Circuits
Alternating Current Circuits AC Circuit An AC circuit consists of a combination of circuit elements and an AC generator or source. The output of an AC generator is sinusoidal and varies with time according
More informationChapter 33. Alternating Current Circuits
Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation  Lower case
More informationChapter 32A AC Circuits. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 32A AC Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should be able to: Describe
More information12 Chapter Driven RLC Circuits
hapter Driven ircuits. A Sources... . A ircuits with a Source and One ircuit Element... 3.. Purely esistive oad... 3.. Purely Inductive oad... 6..3 Purely apacitive oad... 8.3 The Series ircuit...
More informationCh. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies
Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies Induced emf  Faraday s Experiment When a magnet moves toward a loop of wire, the ammeter shows the presence of a current When
More informationPart 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is
1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field
More informationELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT
Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 10 6/12/2007 Electricity and Magnetism Induced voltages and induction SelfInductance RL Circuits Energy in magnetic fields AC circuits and EM waves Resistors, capacitors
More informationAC Circuits Homework Set
Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.
More informationAC Source and RLC Circuits
X X L C = 2π fl = 1/2π fc 2 AC Source and RLC Circuits ( ) 2 Inductive reactance Capacitive reactance Z = R + X X Total impedance L C εmax Imax = Z XL XC tanφ = R Maximum current Phase angle PHY2054: Chapter
More informationDriven RLC Circuits Challenge Problem Solutions
Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs
More informationAlternating Current. Symbol for A.C. source. A.C.
Alternating Current Kirchoff s rules for loops and junctions may be used to analyze complicated circuits such as the one below, powered by an alternating current (A.C.) source. But the analysis can quickly
More informationPhysics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current
Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current People of mediocre ability sometimes achieve outstanding success because they don't know when to quit. Most men succeed because
More informationGeneral Physics (PHY 2140)
General Physics (PHY 40) eminder: Exam this Wednesday 6/3 ecture 04 4 questions. Electricity and Magnetism nduced voltages and induction Selfnductance Circuits Energy in magnetic fields AC circuits and
More informationChapter 21: RLC Circuits. PHY2054: Chapter 21 1
Chapter 21: RC Circuits PHY2054: Chapter 21 1 Voltage and Current in RC Circuits AC emf source: driving frequency f ε = ε sinωt ω = 2π f m If circuit contains only R + emf source, current is simple ε ε
More informationAC Circuits III. Physics 2415 Lecture 24. Michael Fowler, UVa
AC Circuits III Physics 415 Lecture 4 Michael Fowler, UVa Today s Topics LC circuits: analogy with mass on spring LCR circuits: damped oscillations LCR circuits with ac source: driven pendulum, resonance.
More informationElectromagnetic Induction Faraday s Law Lenz s Law SelfInductance RL Circuits Energy in a Magnetic Field Mutual Inductance
Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law SelfInductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic
More informationChapter 31: AC Circuits
hapter 31: A ircuits A urrents and Voltages In this chapter, we discuss the behior of circuits driven by a source of A. Recall that A means, literally, alternating current. An alternating current is a
More informationPhysics 142 AC Circuits Page 1. AC Circuits. I ve had a perfectly lovely evening but this wasn t it. Groucho Marx
Physics 142 A ircuits Page 1 A ircuits I ve had a perfectly lovely evening but this wasn t it. Groucho Marx Alternating current: generators and values It is relatively easy to devise a source (a generator
More informationSolutions to these tests are available online in some places (but not all explanations are good)...
The Physics GRE Sample test put out by ETS https://www.ets.org/s/gre/pdf/practice_book_physics.pdf OSU physics website has lots of tips, and 4 additional tests http://www.physics.ohiostate.edu/undergrad/ugs_gre.php
More informationPhysics for Scientists & Engineers 2
Electromagnetic Oscillations Physics for Scientists & Engineers Spring Semester 005 Lecture 8! We have been working with circuits that have a constant current a current that increases to a constant current
More informationALTERNATING CURRENT
ATENATING UENT Important oints:. The alternating current (A) is generally expressed as ( ) I I sin ω t + φ Where i peak value of alternating current.. emf of an alternating current source is generally
More informationNote 11: Alternating Current (AC) Circuits
Note 11: Alternating Current (AC) Circuits V R No phase difference between the voltage difference and the current and max For alternating voltage Vmax sin t, the resistor current is ir sin t. the instantaneous
More information1 Phasors and Alternating Currents
Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential
More informationEM Oscillations. David J. Starling Penn State Hazleton PHYS 212
I ve got an oscillating fan at my house. The fan goes back and forth. It looks like the fan is saying No. So I like to ask it questions that a fan would say no to. Do you keep my hair in place? Do you
More informationSelfInductance. Φ i. Selfinduction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 111
Lecture  SelfInductance As current i through coil increases, magnetic flux through itself increases. This in turn induces back emf in the coil itself When current i is decreasing, emf is induced again
More informationAlternating Currents. The power is transmitted from a power house on high voltage ac because (a) Electric current travels faster at higher volts (b) It is more economical due to less power wastage (c)
More informationChapter 6. Electromagnetic Oscillations and Alternating Current
hapter 6 Electromagnetic Oscillations an Alternating urrent hapter 6: Electromagnetic Oscillations an Alternating urrent (hapter 31, 3 in textbook) 6.1. Oscillations 6.. The Electrical Mechanical Analogy
More informationPHYSICS NOTES ALTERNATING CURRENT
LESSON 7 ALENAING CUEN Alternating current As we have seen earlier a rotating coil in a magnetic field, induces an alternating emf and hence an alternating current. Since the emf induced in the coil varies
More informationCLUSTER LEVEL WORK SHOP
CLUSTER LEVEL WORK SHOP SUBJECT PHYSICS QUESTION BANK (ALTERNATING CURRENT ) DATE: 0/08/06 What is the phase difference between the voltage across the inductance and capacitor in series AC circuit? Ans.
More informationREACTANCE. By: Enzo Paterno Date: 03/2013
REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE  R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or
More informationThe simplest type of alternating current is one which varies with time simple harmonically. It is represented by
ALTERNATING CURRENTS. Alternating Current and Alternating EMF An alternating current is one whose magnitude changes continuously with time between zero and a maximum value and whose direction reverses
More informationELECTROMAGNETIC 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 informationInductance, RL and RLC Circuits
Inductance, RL and RLC Circuits Inductance Temporarily storage of energy by the magnetic field When the switch is closed, the current does not immediately reach its maximum value. Faraday s law of electromagnetic
More informationELECTROMAGNETIC INDUCTION AND FARADAY S LAW
ELECTROMAGNETIC INDUCTION AND FARADAY S LAW Magnetic Flux The emf is actually induced by a change in the quantity called the magnetic flux rather than simply py by a change in the magnetic field Magnetic
More informationGet Discount Coupons for your Coaching institute and FREE Study Material at ELECTROMAGNETIC INDUCTION
ELECTROMAGNETIC INDUCTION 1. Magnetic Flux 2. Faraday s Experiments 3. Faraday s Laws of Electromagnetic Induction 4. Lenz s Law and Law of Conservation of Energy 5. Expression for Induced emf based on
More informationCircuit AnalysisII. Circuit AnalysisII Lecture # 5 Monday 23 rd April, 18
Circuit AnalysisII Capacitors in AC Circuits Introduction ü The instantaneous capacitor current is equal to the capacitance times the instantaneous rate of change of the voltage across the capacitor.
More information1 2 U CV. K dq I dt J nqv d J V IR P VI
o 5 o T C T F 3 9 T K T o C 73.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC L pv nrt 3 Ktr nrt 3 CV R ideal monatomic gas 5 CV R ideal diatomic gas w/o vibration V W pdv V U Q W W Q e Q Q e Carnot
More informationChapter 32. Inductance
Chapter 32 Inductance Joseph Henry 1797 1878 American physicist First director of the Smithsonian Improved design of electromagnet Constructed one of the first motors Discovered selfinductance Unit of
More informationHandout 10: Inductance. SelfInductance and inductors
1 Handout 10: Inductance SelfInductance and inductors In Fig. 1, electric current is present in an isolate circuit, setting up magnetic field that causes a magnetic flux through the circuit itself. This
More informationPHYS 1441 Section 001 Lecture #23 Monday, Dec. 4, 2017
PHYS 1441 Section 1 Lecture #3 Monday, Dec. 4, 17 Chapter 3: Inductance Mutual and Self Inductance Energy Stored in Magnetic Field Alternating Current and AC Circuits AC Circuit W/ LRC Chapter 31: Maxwell
More informationCHAPTER 22 ELECTROMAGNETIC INDUCTION
CHAPTER 22 ELECTROMAGNETIC INDUCTION PROBLEMS 47. REASONING AND Using Equation 22.7, we find emf 2 M I or M ( emf 2 ) t ( 0.2 V) ( 0.4 s) t I (.6 A) ( 3.4 A) 9.3 0 3 H 49. SSM REASONING AND From the results
More informationALTERNATING CURRENT. with X C = 0.34 A. SET UP: The specified value is the rootmeansquare current; I. EXECUTE: (a) V = (0.34 A) = 0.12 A.
ATENATING UENT 3 3 IDENTIFY: i Icosωt and I I/ SET UP: The specified value is the rootmeansquare current; I 34 A EXEUTE: (a) I 34 A (b) I I (34 A) 48 A (c) Since the current is positive half of the time
More informationSelfinductance A timevarying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying current.
Inductance Selfinductance A timevarying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying current. Basis of the electrical circuit element called an
More informationLecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1
Physics 1 ecture 1 esonance and power in A circuits Physics 1 ecture 1, Slide 1 I max X X = w I max X w e max I max X X = 1/w I max I max I max X e max = I max Z I max I max (X X ) f X X Physics 1 ecture
More informationInduction_P1. 1. [1 mark]
Induction_P1 1. [1 mark] Two identical circular coils are placed one below the other so that their planes are both horizontal. The top coil is connected to a cell and a switch. The switch is closed and
More informationLecture 39. PHYC 161 Fall 2016
Lecture 39 PHYC 161 Fall 016 Announcements DO THE ONLINE COURSE EVALUATIONS  response so far is < 8 % Magnetic field energy A resistor is a device in which energy is irrecoverably dissipated. By contrast,
More informationECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance
ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations OpAmp Integrator and OpAmp Differentiator 1 CAPACITANCE AND INDUCTANCE Introduces
More informationChapter 30 Self Inductance, Inductors & DC Circuits Revisited
Chapter 30 Self Inductance, Inductors & DC Circuits Revisited SelfInductance and Inductors Self inductance determines the magnetic flux in a circuit due to the circuit s own current. B = LI Every circuit
More informationPhysics 1502: Lecture 25 Today s Agenda
Physics 1502: Lecture 25 Today s Agenda Announcements: Midterm 2: NOT Nov. 6 Following week Homework 07: due Friday net week AC current esonances Electromagnetic Waves Mawell s Equations  evised Energy
More informationChapter 32. Inductance
Chapter 32 Inductance Inductance Selfinductance A timevarying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying current. Basis of the electrical circuit
More informationTRANSFORMERS B O O K P G
TRANSFORMERS B O O K P G. 4 4 4449 REVIEW The RMS equivalent current is defined as the dc that will provide the same power in the resistor as the ac does on average P average = I 2 RMS R = 1 2 I 0 2 R=
More informationActive Figure 32.3 (SLIDESHOW MODE ONLY)
RL Circuit, Analysis An RL circuit contains an inductor and a resistor When the switch is closed (at time t = 0), the current begins to increase At the same time, a back emf is induced in the inductor
More informationELEC ELE TRO TR MAGNETIC INDUCTION
ELECTRO MAGNETIC INDUCTION Faraday Henry 17911867 1797 1878 Laws: Faraday s Laws : 1) When ever there is a change in magnetic flux linked with a coil, a current is generated in the coil. The current
More informationBook Page cgrahamphysics.com Transformers
Book Page 444449 Transformers Review The RMS equivalent current is defined as the dc that will provide the same power in the resistor as the ac does on average P average = I 2 RMS R = 1 2 I 0 2 R= V RMS
More informationYell if you have any questions
Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored
More informationPhysics272 Lecture 20. AC Power Resonant Circuits Phasors (2dim vectors, amplitude and phase)
Physics7 ecture 0 A Power esonant ircuits Phasors (dim vectors, amplitude and phase) What is reactance? You can think of it as a frequencydependent resistance. 1 ω For high ω, χ ~0  apacitor looks
More informationPH 2222C Fall Electromagnetic Oscillations and Alternating Current. Lectures 1819
H  Fall 0 Electroagnetic Oscillations and Alternating urrent ectures 89 hapter 3 (Halliday/esnick/Walker, Fundaentals of hysics 8 th edition) hapter 3 Electroagnetic Oscillations and Alternating urrent
More informationInductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits
Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Selfinductance A timevarying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying
More informationImpedance/Reactance Problems
Impedance/Reactance Problems. Consider the circuit below. An AC sinusoidal voltage of amplitude V and frequency ω is applied to the three capacitors, each of the same capacitance C. What is the total reactance
More informationLearning Material Ver 1.2
RLC Resonance Trainer Learning Material Ver.2 Designed & Manufactured by: 4A, Electronic Complex, Pardesipura, Indore 452 00 India, Tel.: 97342500, Telefax: 9734202959, Toll free: 800035050, Email:
More informationExam 2 Solutions. PHY2054 Spring Prof. Paul Avery Prof. Pradeep Kumar Mar. 18, 2014
Exam 2 Solutions Prof. Paul Avery Prof. Pradeep Kumar Mar. 18, 2014 1. A series circuit consists of an open switch, a 6.0 Ω resistor, an uncharged 4.0 µf capacitor and a battery with emf 15.0 V and internal
More informationPhysics 102 Spring 2007: Final Exam MultipleChoice Questions
Last Name: First Name: Physics 102 Spring 2007: Final Exam MultipleChoice Questions 1. The circuit on the left in the figure below contains a battery of potential V and a variable resistor R V. The circuit
More informationElectromagnetic Induction (Chapters 3132)
Electromagnetic Induction (Chapters 313) 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 informationHandout 11: AC circuit. AC generator
Handout : AC circuit AC generator Figure compares the voltage across the directcurrent (DC) generator and that across the alternatingcurrent (AC) generator For DC generator, the voltage is constant For
More information20. Alternating Currents
University of hode sland DigitalCommons@U PHY 204: Elementary Physics Physics Course Materials 2015 20. lternating Currents Gerhard Müller University of hode sland, gmuller@uri.edu Creative Commons License
More informationRLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:
RLC Series Circuit In this exercise you will investigate the effects of changing inductance, capacitance, resistance, and frequency on an RLC series AC circuit. We can define effective resistances for
More informationPHYSICS. Chapter 30 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 30 Lecture RANDALL D. KNIGHT Chapter 30 Electromagnetic Induction IN THIS CHAPTER, you will learn what electromagnetic induction is
More informationAssessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526)
NCEA evel 3 Physics (91526) 2016 page 1 of 5 Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526) Evidence Statement NØ N1 N 2 A 3 A 4 M 5 M 6 E 7 E 8 0 1A 2A 3A 4A or
More informationExam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field
Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,
More informationPhysics 4 Spring 1989 Lab 5  AC Circuits
Physics 4 Spring 1989 Lab 5  AC Circuits Theory Consider the series inductorresistorcapacitor circuit shown in figure 1. When an alternating voltage is applied to this circuit, the current and voltage
More informationElectrical Engineering Fundamentals for NonElectrical Engineers
Electrical Engineering Fundamentals for NonElectrical Engineers by Brad Meyer, PE Contents Introduction... 3 Definitions... 3 Power Sources... 4 Series vs. Parallel... 9 Current Behavior at a Node...
More informationAlternating Current. Chapter 31. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman
Chapter 31 Alternating Current PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 8_8_2008 Topics for Chapter 31
More informationChapter 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 selfinductance. An inductor is formed by taken
More informationPhysics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33
Session 33 Physics 115 General Physics II AC: RL vs RC circuits Phase relationships RLC circuits R. J. Wilkes Email: phy115a@u.washington.edu Home page: http://courses.washington.edu/phy115a/ 6/2/14 1
More informationAlternating Current Circuits. Home Work Solutions
Chapter 21 Alternating Current Circuits. Home Work s 21.1 Problem 21.11 What is the time constant of the circuit in Figure (21.19). 10 Ω 10 Ω 5.0 Ω 2.0µF 2.0µF 2.0µF 3.0µF Figure 21.19: Given: The circuit
More informationOscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1
Oscillations and Electromagnetic Waves March 30, 2014 Chapter 31 1 Three Polarizers! Consider the case of unpolarized light with intensity I 0 incident on three polarizers! The first polarizer has a polarizing
More informationRLC Circuits. 1 Introduction. 1.1 Undriven Systems. 1.2 Driven Systems
RLC Circuits Equipment: Capstone, 850 interface, RLC circuit board, 4 leads (91 cm), 3 voltage sensors, Fluke mulitmeter, and BNC connector on one end and banana plugs on the other Reading: Review AC circuits
More information1) Opposite charges and like charges. a) attract, repel b) repel, attract c) attract, attract
) Opposite charges and like charges. a) attract, repel b) repel, attract c) attract, attract ) The electric field surrounding two equal positive charges separated by a distance of 0 cm is zero ; the electric
More informationPESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru 100 Department of Electronics & Communication Engineering
QUESTION PAPER INTERNAL ASSESSMENT TEST 2 Date : /10/2016 Marks: 0 Subject & Code: BASIC ELECTRICAL ENGINEERING 15ELE15 Sec : F,G,H,I,J,K Name of faculty : Dhanashree Bhate, Hema B, Prashanth V Time :
More informationMAY/JUNE 2006 Question & Model Answer IN BASIC ELECTRICITY 194
MAY/JUNE 2006 Question & Model Answer IN BASIC ELECTRICITY 194 Question 1 (a) List three sources of heat in soldering (b) state the functions of flux in soldering (c) briefly describe with aid of diagram
More information8.1 Alternating Voltage and Alternating Current ( A. C. )
8  ALTENATING UENT Page 8. Alternating Voltage and Alternating urrent ( A.. ) The following figure shows N turns of a coil of conducting wire PQS rotating with a uniform angular speed ω with respect to
More informationAC vs. DC Circuits. Constant voltage circuits. The voltage from an outlet is alternating voltage
Circuits AC vs. DC Circuits Constant voltage circuits Typically referred to as direct current or DC Computers, logic circuits, and battery operated devices are examples of DC circuits The voltage from
More informationIntroduction to AC Circuits (Capacitors and Inductors)
Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/
More informationName:... Section:... Physics 208 Quiz 8. April 11, 2008; due April 18, 2008
Name:... Section:... Problem 1 (6 Points) Physics 8 Quiz 8 April 11, 8; due April 18, 8 Consider the AC circuit consisting of an AC voltage in series with a coil of selfinductance,, and a capacitor of
More informationREVIEW EXERCISES. 2. What is the resulting action if switch (S) is opened after the capacitor (C) is fully charged? Se figure 4.27.
REVIEW EXERCISES Circle the letter of the correct answer to each question. 1. What is the current and voltage relationship immediately after the switch is closed in the circuit in figure 427, which shows
More informationCourse Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits
ourse Updates http://www.phys.hawaii.edu/~varner/phys272spr10/physics272.html eminders: 1) Assignment #10 due Today 2) Quiz # 5 Friday (hap 29, 30) 3) Start A ircuits Alternating urrents (hap 31) In this
More informationConventional PaperI2011 PARTA
Conventional PaperI0 PARTA.a Give five properties of static magnetic field intensity. What are the different methods by which it can be calculated? Write a Maxwell s equation relating this in integral
More informationPHYS 241 EXAM #2 November 9, 2006
1. ( 5 points) A resistance R and a 3.9 H inductance are in series across a 60 Hz AC voltage. The voltage across the resistor is 23 V and the voltage across the inductor is 35 V. Assume that all voltages
More informationExam 3 Solutions. The induced EMF (magnitude) is given by Faraday s Law d dt dt The current is given by
PHY049 Spring 008 Prof. Darin Acosta Prof. Selman Hershfield April 9, 008. A metal rod is forced to move with constant velocity of 60 cm/s [or 90 cm/s] along two parallel metal rails, which are connected
More informationElectrical Circuit & Network
Electrical Circuit & Network January 1 2017 Website: www.electricaledu.com Electrical Engg.(MCQ) Question and Answer for the students of SSC(JE), PSC(JE), BSNL(JE), WBSEDCL, WBSETCL, WBPDCL, CPWD and State
More informationPhysics 240 Fall 2005: Exam #3 Solutions. Please print your name: Please list your discussion section number: Please list your discussion instructor:
Physics 4 Fall 5: Exam #3 Solutions Please print your name: Please list your discussion section number: Please list your discussion instructor: Form #1 Instructions 1. Fill in your name above. This will
More informationEXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA
EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA DISCUSSION The capacitor is a element which stores electric energy by charging the charge on it. Bear in mind that the charge on a capacitor
More informationChapter 30. Inductance
Chapter 30 Inductance Self Inductance When a time dependent current passes through a coil, a changing magnetic flux is produced inside the coil and this in turn induces an emf in that same coil. This induced
More informationElectromagnetic Field Theory Chapter 9: Timevarying EM Fields
Electromagnetic Field Theory Chapter 9: Timevarying EM Fields Faraday s law of induction We have learned that a constant current induces magnetic field and a constant charge (or a voltage) makes an electric
More informationPhysics 240 Fall 2005: Exam #3. Please print your name: Please list your discussion section number: Please list your discussion instructor:
Physics 240 Fall 2005: Exam #3 Please print your name: Please list your discussion section number: Please list your discussion instructor: Form #1 Instructions 1. Fill in your name above 2. This will be
More informationI. Impedance of an RL circuit.
I. Impedance of an RL circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the RL circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC
More informationELECTRO MAGNETIC INDUCTION
ELECTRO MAGNETIC INDUCTION 1) A Circular coil is placed near a current carrying conductor. The induced current is anti clock wise when the coil is, 1. Stationary 2. Moved away from the conductor 3. Moved
More information