PES 1120 Spring 2014, Spendier Lecture 36/Page 1
|
|
- Mitchell Conley
- 6 years ago
- Views:
Transcription
1 PES 0 Spring 04, Spenier ecture 36/Page Toay: chapter 3 - R circuits: Dampe Oscillation - Driven series R circuit - HW 9 ue Wenesay - FQs Wenesay ast time you stuie the circuit (no resistance) The total energy of the system is conserve an oscillates between magentic an electric potential energy. We notice that this circuit is analogous to a spring-mass system (simple harmonic oscillator) without friction. However, we know that typically there is resistance in the circuit (wires, resistors, internal resistance). So, what o you think happens if we put a resistor in series with the capacitor an inuctor? Remember that with the resistor, the total energy will ecrease ue to the power issipate in the resistor. R circuit: Dampe Oscillation A circuit containing resistance, inuctance, an capacitance is calle an R circuit. Figure shows a series R circuit. As the charge containe in the circuit oscillates back an forth through the resistance, electromagnetic energy is issipate as thermal energy, amping (ecreasing the amplitue of) the oscillations. the capacitor is initially charge to Q 0. After the switch is close current will begin to flow. However, unlike the circuit energy will be issipate through the resistor. The rate at which energy is issipate is U t i( t) R where the negative sign on the right-han sie implies that the total energy q( t) i( t) U U E U B
2 PES 0 Spring 04, Spenier ecture 36/Page is ecreasing. After substituting for the left-han sie of the above equation, we obtain the following ifferential equation: q( t) q i( t) i i( t) R t t q use i( t) t q( t) i ( ) ( ) ( ) i t i t i t R t q( t) q q t t q t R q t R 0 q( t) 0 i not show these steps This expression shoul remin you of the equation for ampe simple harmonic oscillations. The general solution is: initial conition: q(t=0) = Q 0 t R q( t) Q0e cos t 4 R R ' ( angular frequency) ( amping factor) 4 - The amping effect is ue to the presence of resistance R. - The amping factor γ etermines the rate at which the response is ampe. - If R=0, the circuit is sai to be lossless an the oscillatory response will continue. How o these oscillations look like?
3 PES 0 Spring 04, Spenier ecture 36/Page 3 a) Unerampe circuit (small resistance R) With a relatively small resistor, 4 R then there are oscillations whose amplitue ecreases exponentially in time. The ampe oscillation exhibite by the unerampe response is known as ringing. It stems from the ability of the an to transfer energy back an forth between them. b) ritically ampe circuit (larger resistance R) 4 R then the system no longer oscillates, but instea amps own as quickly as is possible. ' R 0 4 All the other properties (i(t), E(t), B(t), U E (t), U B (t)) will also ecay in amplitue over time until all electromagnetic energy has been lost to heat. A an D Until now, we have ealt with circuits where the source of EMF (e.g., the battery) has a constant value. This is known as a irect current (D) source. For many reasons however, much of the worl s power is not elivere as a uniirectional EMF. For commercial an resiential electricity, A current is use. The main reason for this is the with a changing current, Faraay's aw of inuction can be use to inuce EMFs/currents in other circuits. This is the main iea behin transformers, which we will iscuss next lecture.
4 PES 0 Spring 04, Spenier ecture 36/Page 4 We just saw that for an R circuit, energy is taken away from the circuit as heat in the resistor. Therefore the oscillating current ies away over time. Not very useful for commercial electricity. - So how can we stop this ecay over time? We coul put energy at the same rate as it is being lost! Alternating EMF So, now we want to examine how the circuit elements we have behave when they are riven with an alternating current (A) source. An A source supplies an EMF which follows a cosine epenency: ( t) sin( t)... imum emf amplitue... riving angular frequency After an initial transient time, an A current will flow in the circuit as a response to the riving voltage source. The current, written as i( t) I sin( t ) will oscillate with the same frequency as the voltage source an may be out of phase with the emf. Driven series R circuit We are now reay to apply the alternating emf ( t) sin( t) to the full R circuit. Because R,, an are in series, the same current i( t) I sin( t ) is riven in all three of them. We wish to fin the current amplitue I an the phase constant.
5 PES 0 Spring 04, Spenier ecture 36/Page 5 Applying Kirchhoff s loop rule, we obtain i q( t) ( t) VR ( t) V ( t) V ( t) ( t) i( t) R 0 t which leas to the following ifferential equation: i q( t) i( t) R sin( t) t Assuming that the capacitor is initially uncharge so that i(t)=+q/t is proportional to the increase of charge in the capacitor, the above equation can be rewritten as ( ) R sin( t) q q q t t t One possible solution to this equation is q( t) Q cos( t ) where the imum charge amplitue is Q R /( ). The corresponing current is q i( t) Q0 sin t t with an imum current amplitue I Q0 R /( ) an phase
6 PES 0 Spring 04, Spenier ecture 36/Page 6 tan R (Note book uses a ifferent way of eriving these results) We can see that the quantities X an X must have the same units as resistance. They are calle "inuctive reactance (X )" an the "capacitive reactance (X )". Resonance in an R circuit I Q 0 R /( ) gives the current amplitue I in an R circuit as a function of the riving angular frequency ω of the external alternating emf.for a given resistance R, that amplitue is a imum when the quantity 0 that is when: ( X X ) Because the natural angular frequency ω of the circuit is also equal to /, the imum value of I occurs when the riving angular frequency matches the natural angular frequency that is, at resonance. Thus, in an R circuit, resonance an imum current amplitue I occur when (resonance)
7 PES 0 Spring 04, Spenier ecture 36/Page 7 Usefulness of Reactances X an X Notice that the reactances are epenent on the angular frequency, (the resistance is not). As ω 0 (D), there is no inuctive effect X goes to zero an current is passe through the inuctor, while no current is passe through the capacitor X iverges. As ω gets large, X goes to zero an current is passe through the capacitor, while no current is passe through the inuctor X gets large because of the quickly changing current. We can use these properties to create frequency filters. - Inuctors are use as low-pass filters. - apacitors are use as high-pass filters. - In combination, you can create a cross-over circuit. The inuctor an capacitor fee low frequencies mainly fee low frequencies mainly to the woofer an high frequencies mainly to the tweeter.
Chapter 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 informationChapter 31: RLC Circuits. PHY2049: Chapter 31 1
Chapter 31: RLC Circuits PHY049: Chapter 31 1 LC Oscillations Conservation of energy Topics Dampe oscillations in RLC circuits Energy loss AC current RMS quantities Force oscillations Resistance, reactance,
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 informationPhysics 4B. Chapter 31: Questions: 2, 8, 12 Exercises & Problems: 2, 23, 24, 32, 41, 44, 48, 60, 72, 83. n n f
Physics 4B Solutions to hapter 1 HW hapter 1: Questions:, 8, 1 Exercises & Probles:,, 4,, 41, 44, 48, 60, 7, 8 Question 1- (a) less; (b) greater Question 1-8 (a) 1 an 4; (b) an Question 1-1 (a) lea; (b)
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 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 informationChapter 3. Modeling with First-Order Differential Equations
Chapter 3 Moeling with First-Orer Differential Equations i GROWTH AND DECAY: The initial-value problem x = kx, x(t 0 ) = x 0, (1) where k is a constant of proportionality, serves as a moel for iverse phenomena
More informationHomework 7 Due 18 November at 6:00 pm
Homework 7 Due 18 November at 6:00 pm 1. Maxwell s Equations Quasi-statics o a An air core, N turn, cylinrical solenoi of length an raius a, carries a current I Io cos t. a. Using Ampere s Law, etermine
More informationCapacitance: The ability to store separated charge C=Q/V. Capacitors! Capacitor. Capacitance Practice SPH4UW 24/08/2010 Q = CV
SPH4UW Capacitors! Capacitance: The ability to store separate charge C=Q/V Charge Q on plates V = V V B = E 0 Charge 2Q on plates V = V V B =2E 0 E=E 0 B E=2E 0 B Physics 102: Lecture 4, Slie 1 Potential
More informationInductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits
Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the timevarying
More informationPhysics 11b Lecture #15
Physics 11b ecture #15 and ircuits A ircuits S&J hapter 3 & 33 Administravia Midterm # is Thursday If you can t take midterm, you MUST let us (me, arol and Shaun) know in writing before Wednesday noon
More informationInductance, RL Circuits, LC Circuits, RLC Circuits
Inductance, R Circuits, C Circuits, RC Circuits Inductance What happens when we close the switch? The current flows What does the current look like as a function of time? Does it look like this? I t Inductance
More informationC R. Consider from point of view of energy! Consider the RC and LC series circuits shown:
ircuits onsider the R and series circuits shown: ++++ ---- R ++++ ---- Suppose that the circuits are formed at t with the capacitor charged to value. There is a qualitative difference in the time development
More informationInductance. Slide 2 / 26. Slide 1 / 26. Slide 4 / 26. Slide 3 / 26. Slide 6 / 26. Slide 5 / 26. Mutual Inductance. Mutual Inductance.
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 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 informationHandout 10: Inductance. Self-Inductance and inductors
1 Handout 10: Inductance Self-Inductance 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 informationsinb2ωtg to write this as
Chapter 31 13. (a) The charge (as a function of tie) is given by q= Qsinωt, where Q is the axiu charge on the capacitor an ω is the angular frequency of oscillation. A sine function was chosen so that
More informationc h L 75 10
hapter 31 1. (a) All the energy in the circuit resies in the capacitor when it has its axiu charge. The current is then zero. f Q is the axiu charge on the capacitor, then the total energy is c c h h U
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 informationUNIT V: OSCILLATIONS
UNIT V: OSCILLATIONS Introuction: Motion of boies can be broaly classifie into three categories: [] Translational motion [] Rotational motion [3] Vibrational / Oscillatory motion Translational motion:
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 informationElectromagnetic 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 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 informationPhysics 2112 Unit 19
Physics 11 Unit 19 Today s oncepts: A) L circuits and Oscillation Frequency B) Energy ) RL circuits and Damping Electricity & Magnetism Lecture 19, Slide 1 Your omments differential equations killing me.
More informationPhysics 212. Lecture 11. RC Circuits. Change in schedule Exam 2 will be on Thursday, July 12 from 8 9:30 AM. Physics 212 Lecture 11, Slide 1
Physics 212 Lecture 11 ircuits hange in schedule Exam 2 will be on Thursday, July 12 from 8 9:30 AM. Physics 212 Lecture 11, Slide 1 ircuit harging apacitor uncharged, switch is moved to position a Kirchoff
More information1. A1, B3 2. A1, B2 3. A3, B2 4. A2, B2 5. A3, B3 6. A1, B1 7. A2, B1 8. A2, B3 9. A3, B1
peden (jp5559) Time onstants peden (0100) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Test is Thursday!
More informationPhysics 4 Spring 1989 Lab 5 - AC Circuits
Physics 4 Spring 1989 Lab 5 - AC Circuits Theory Consider the series inductor-resistor-capacitor circuit shown in figure 1. When an alternating voltage is applied to this circuit, the current and voltage
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 informationPES 1120 Spring 2014, Spendier Lecture 35/Page 1
PES 0 Spring 04, Spendier Lecture 35/Page Today: chapter 3 - LC circuits We have explored the basic physics of electric and magnetic fields and how energy can be stored in capacitors and inductors. We
More informationDirect-Current Circuits. Physics 231 Lecture 6-1
Direct-Current Circuits Physics 231 Lecture 6-1 esistors in Series and Parallel As with capacitors, resistors are often in series and parallel configurations in circuits Series Parallel The question then
More informationSlide 1 / 26. Inductance 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 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 informationDesigning Information Devices and Systems II Spring 2019 A. Sahai, J. Roychowdhury, K. Pister Midterm 1: Practice
EES 16B Designing Information Devices an Systems II Spring 019 A. Sahai, J. Roychowhury, K. Pister Miterm 1: Practice 1. Speaker System Your job is to construct a speaker system that operates in the range
More informationLecture 6: Control of Three-Phase Inverters
Yoash Levron The Anrew an Erna Viterbi Faculty of Electrical Engineering, Technion Israel Institute of Technology, Haifa 323, Israel yoashl@ee.technion.ac.il Juri Belikov Department of Computer Systems,
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 informationConservation laws a simple application to the telegraph equation
J Comput Electron 2008 7: 47 51 DOI 10.1007/s10825-008-0250-2 Conservation laws a simple application to the telegraph equation Uwe Norbrock Reinhol Kienzler Publishe online: 1 May 2008 Springer Scienceusiness
More information2.4 Harmonic Oscillator Models
2.4 Harmonic Oscillator Models In this section we give three important examples from physics of harmonic oscillator models. Such models are ubiquitous in physics, but are also used in chemistry, biology,
More informationCourse Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits
ourse Updates http://www.phys.hawaii.edu/~varner/phys272-spr10/physics272.html eminders: 1) Assignment #10 due Today 2) Quiz # 5 Friday (hap 29, 30) 3) Start A ircuits Alternating urrents (hap 31) In this
More 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 informationAs light level increases, resistance decreases. As temperature increases, resistance decreases. Voltage across capacitor increases with time LDR
LDR As light level increases, resistance decreases thermistor As temperature increases, resistance decreases capacitor Voltage across capacitor increases with time Potential divider basics: R 1 1. Both
More informationPhysics 115C Homework 4
Physics 115C Homework 4 Problem 1 a In the Heisenberg picture, the ynamical equation is the Heisenberg equation of motion: for any operator Q H, we have Q H = 1 t i [Q H,H]+ Q H t where the partial erivative
More informationChapter 31: RLC Circuits. PHY2049: Chapter 31 1
hapter 31: RL ircuits PHY049: hapter 31 1 L Oscillations onservation of energy Topics Damped oscillations in RL circuits Energy loss A current RMS quantities Forced oscillations Resistance, reactance,
More informationMATH 56A: STOCHASTIC PROCESSES CHAPTER 3
MATH 56A: STOCHASTIC PROCESSES CHAPTER 3 Plan for rest of semester (1) st week (8/31, 9/6, 9/7) Chap 0: Diff eq s an linear recursion (2) n week (9/11...) Chap 1: Finite Markov chains (3) r week (9/18...)
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 information2.4 Models of Oscillation
2.4 Models of Oscillation In this section we give three examples of oscillating physical systems that can be modeled by the harmonic oscillator equation. Such models are ubiquitous in physics, but are
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 informationModule 25: Outline Resonance & Resonance Driven & LRC Circuits Circuits 2
Module 25: Driven RLC Circuits 1 Module 25: Outline Resonance & Driven LRC Circuits 2 Driven Oscillations: Resonance 3 Mass on a Spring: Simple Harmonic Motion A Second Look 4 Mass on a Spring (1) (2)
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 informationChapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively
Chapter 3 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively In the LC circuit the charge, current, and potential difference vary sinusoidally (with period T and angular
More 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 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 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 informationFinal Exam Physics 7b Section 2 Fall 2004 R Packard. Section Number:
Final Exam Physics 7b Section 2 Fall 2004 R Packard Name: SID: Section Number: The relative weight of each problem is stated next to the problem. Work the easier ones first. Define physical quantities
More informationChapter 28. Direct Current Circuits
Chapter 28 Direct Current Circuits Circuit Analysis Simple electric circuits may contain batteries, resistors, and capacitors in various combinations. For some circuits, analysis may consist of combining
More informationPHYS 272 (Spring 2018): Introductory Physics: Fields Problem-solving sessions
Figure 1: Problem 1 Figure 2: Problem 2 PHYS 272 (Spring 2018): Introductory Physics: Fields Problem-solving sessions (1). A thin rod of length l carries a total charge Q distributed uniformly along its
More informationSelf-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1
Lecture - Self-Inductance 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 informationPhysics 102: Lecture 7 RC Circuits
Physics 102: Lecture 7 C Circuits Physics 102: Lecture 7, Slide 1 C Circuits Circuits that have both resistors and capacitors: K Na Cl C ε K ε Na ε Cl S With resistance in the circuits, capacitors do not
More informationChapter 21. Ac Circuits
Chapter 21 Ac Circuits AC current Transformer Transforms AC voltage UP or DOWN Historical basis for AC Grid your use George Westinghouse (AC) vs Edison (DC) Losses due to resistance in wire and eddy currents
More informationVersion 001 CIRCUITS holland (1290) 1
Version CIRCUITS holland (9) This print-out should have questions Multiple-choice questions may continue on the next column or page find all choices before answering AP M 99 MC points The power dissipated
More informationElectricity & Optics
Physics 241 Electricity & Optics Lecture 12 Chapter 25 sec. 6, 26 sec. 1 Fall 217 Semester Professor Koltick Circuits With Capacitors C Q = C V V = Q C + V R C, Q Kirchhoff s Loop Rule: V I R V = V I R
More informationPhysics 115. General Physics II. Session 24 Circuits Series and parallel R Meters Kirchoff s Rules
Physics 115 General Physics II Session 24 Circuits Series and parallel R Meters Kirchoff s Rules R. J. Wilkes Email: phy115a@u.washington.edu Home page: http://courses.washington.edu/phy115a/ 5/15/14 Phys
More informationDirect Current Circuits. February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1
Direct Current Circuits February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1 Kirchhoff s Junction Rule! The sum of the currents entering a junction must equal the sum of the currents leaving
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 information6.003 Homework #7 Solutions
6.003 Homework #7 Solutions Problems. Secon-orer systems The impulse response of a secon-orer CT system has the form h(t) = e σt cos(ω t + φ)u(t) where the parameters σ, ω, an φ are relate to the parameters
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 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 informationChapter 30 Inductance and Electromagnetic Oscillations
Chapter 30 Inductance and Electromagnetic Oscillations Units of Chapter 30 30.1 Mutual Inductance: 1 30.2 Self-Inductance: 2, 3, & 4 30.3 Energy Stored in a Magnetic Field: 5, 6, & 7 30.4 LR Circuit: 8,
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 informationMath 342 Partial Differential Equations «Viktor Grigoryan
Math 342 Partial Differential Equations «Viktor Grigoryan 6 Wave equation: solution In this lecture we will solve the wave equation on the entire real line x R. This correspons to a string of infinite
More informationu t v t v t c a u t b a v t u t v t b a
Nonlinear Dynamical Systems In orer to iscuss nonlinear ynamical systems, we must first consier linear ynamical systems. Linear ynamical systems are just systems of linear equations like we have been stuying
More informationPhysics 2212 GJ Quiz #4 Solutions Fall 2015
Physics 2212 GJ Quiz #4 Solutions Fall 215 I. (17 points) The magnetic fiel at point P ue to a current through the wire is 5. µt into the page. The curve portion of the wire is a semicircle of raius 2.
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 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 informationDynamics of the synchronous machine
ELEC0047 - Power system ynamics, control an stability Dynamics of the synchronous machine Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct These slies follow those presente in course
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 self-inductance Unit of
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 informationPhysics-272 Lecture 20. AC Power Resonant Circuits Phasors (2-dim vectors, amplitude and phase)
Physics-7 ecture 0 A Power esonant ircuits Phasors (-dim vectors, amplitude and phase) What is reactance? You can think of it as a frequency-dependent resistance. 1 ω For high ω, χ ~0 - apacitor looks
More informationThe derivative of a function f(x) is another function, defined in terms of a limiting expression: f(x + δx) f(x)
Y. D. Chong (2016) MH2801: Complex Methos for the Sciences 1. Derivatives The erivative of a function f(x) is another function, efine in terms of a limiting expression: f (x) f (x) lim x δx 0 f(x + δx)
More informationInductive & Capacitive Circuits. Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur
Inductive & Capacitive Circuits Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur LR Circuit LR Circuit (Charging) Let us consider a circuit having an inductance
More informationSelf-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current.
Inductance Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current. Basis of the electrical circuit element called an
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 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 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 informationElectrical Circuits Lab Series RC Circuit Phasor Diagram
Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is
More informationUNIT 4:Capacitors and Dielectric
UNIT 4:apacitors an Dielectric SF7 4. apacitor A capacitor is a evice that is capable of storing electric charges or electric potential energy. It is consist of two conucting plates separate by a small
More information= e = e 3 = = 4.98%
PHYS 212 Exam 2 - Practice Test - Solutions 1E In order to use the equation for discharging, we should consider the amount of charge remaining after three time constants, which would have to be q(t)/q0.
More informationLecture 12 Chapter 28 RC Circuits Course website:
Lecture 12 Chapter 28 RC Circuits Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 28: Section 28.9 RC circuits Steady current Time-varying
More informationYour Comments. THIS IS SOOOO HARD. I get the concept and mathematical expression. But I do not get links among everything.
Your omments THIS IS SOOOO HAD. I get the concept and mathematical expression. But I do not get links among everything. ery confusing prelecture especially what happens when switches are closed/opened
More informationElectricity and Magnetism DC Circuits Resistance-Capacitance Circuits
Electricity and Magnetism DC Circuits Resistance-Capacitance Circuits Lana Sheridan De Anza College Feb 12, 2018 Last time using Kirchhoff s laws Overview two Kirchhoff trick problems resistance-capacitance
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2003 Experiment 17: RLC Circuit (modified 4/15/2003) OBJECTIVES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8. Spring 3 Experiment 7: R Circuit (modified 4/5/3) OBJECTIVES. To observe electrical oscillations, measure their frequencies, and verify energy
More informationApplications of Second-Order Differential Equations
Applications of Second-Order Differential Equations ymy/013 Building Intuition Even though there are an infinite number of differential equations, they all share common characteristics that allow intuition
More informationModule 24: Outline. Expt. 8: Part 2:Undriven RLC Circuits
Module 24: Undriven RLC Circuits 1 Module 24: Outline Undriven RLC Circuits Expt. 8: Part 2:Undriven RLC Circuits 2 Circuits that Oscillate (LRC) 3 Mass on a Spring: Simple Harmonic Motion (Demonstration)
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 self-inductance,, and a capacitor of
More informationGoal of this chapter is to learn what is Capacitance, its role in electronic circuit, and the role of dielectrics.
PHYS 220, Engineering Physics, Chapter 24 Capacitance an Dielectrics Instructor: TeYu Chien Department of Physics an stronomy University of Wyoming Goal of this chapter is to learn what is Capacitance,
More informationLast time. Ampere's Law Faraday s law
Last time Ampere's Law Faraday s law 1 Faraday s Law of Induction (More Quantitative) The magnitude of the induced EMF in conducting loop is equal to the rate at which the magnetic flux through the surface
More informationIMPORTANT Read these directions carefully:
Physics 208: Electricity and Magnetism Common Exam 2, October 17 th 2016 Print your name neatly: First name: Last name: Sign your name: Please fill in your Student ID number (UIN): _ - - Your classroom
More information9. M = 2 π R µ 0 n. 3. M = π R 2 µ 0 n N correct. 5. M = π R 2 µ 0 n. 8. M = π r 2 µ 0 n N
This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 00 0.0 points A coil has an inductance of 4.5 mh, and the current
More informationAP Physics C. Electric Circuits III.C
AP Physics C Electric Circuits III.C III.C.1 Current, Resistance and Power The direction of conventional current Suppose the cross-sectional area of the conductor changes. If a conductor has no current,
More informationLast lecture. Today s menu. Capacitive sensing elements. Capacitive sensing elements (cont d...) Examples. General principle
Last lecture esistive sensing elements: Displacement sensors (potentiometers). Temperature sensors. Strain gauges. Deflection briges. Toay s menu Capacitive sensing elements. Inuctive sensing elements.
More informationIntegration Review. May 11, 2013
Integration Review May 11, 2013 Goals: Review the funamental theorem of calculus. Review u-substitution. Review integration by parts. Do lots of integration eamples. 1 Funamental Theorem of Calculus In
More information