Lecture 15. LC Circuit. LC Oscillation - Qualitative. LC Oscillator

Size: px
Start display at page:

Download "Lecture 15. LC Circuit. LC Oscillation - Qualitative. LC Oscillator"

Transcription

1 Lecture 5 Phys. 07: Waves and Light Physics Department Yarmouk University 63 Irbid Jordan &KDSWHUElectromagnetic Oscillations and Alternating urrent L ircuit In this chapter you will see how the electric charge varies with time in a circuit made up of an inductor L, and a capacitor. From another point of view, we shall discuss how energy shuttles back and forth between the magnetic field of the inductor and the electric field of the capacitor. Dr. Nidal Ershaidat L Fig. Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 L Oscillation - Qualitative The energy stored in the capacitor is called the electric energy because it is associated with the energy stored between the capacitor plates as electric field. Which is eual to: The energy stored in the inductors is call the magnetic energy because it is associated with the energy stored in the inductor as magnetic field Which is eual to: U B Li U E Fig. -a Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 3 L Oscillator onsider the L circuit. According to Kirchhoff s second law: the (algebraic) sum of potential differences euals zero, i.e. V L V 0 + di L + 0 di V L L d di d I d d L L Thus we get a homogeneous linear nd order DE: &+ & ω 0 where ω L V Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 4

2 L Oscillator We know that the solution is of the form: Q cos ( ωt which is similar to x x cos( ωt The current in this circuit is given by: ( ωt I sin( ω i Q ωsin t ( ω which is similar to v v0 sin t 0 5 Electric and Magnetic Energy Oscillations Q U E cos ( ω t U B L i Lω Q sin ω t + φ ω Lω L U Q sin ω t + φ B Q U U E + U B Animation of L ircuit ( ω x x cos t 0 6 Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 L Oscillation - Energy The inductor and capacitor transfer energy from one to the other as shown below: Fig. 3 Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture The Electrical Mechanical Analogy L Oscillation - Energy The Energy in Two Oscillating Systems ompared Block Spring System Element Spring Block dx v Energy K x m v L Oscillator Element apacitor Inductor Energy L i d i Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 8

3 Lecture 6 Phys. 07: Waves and Light Physics Department Yarmouk University 63 Irbid Jordan 3UREOHPVRQElectromagnetic Oscillations and Alternating urrent Problem 33-5 The freuency of oscillation of a certain L circuit is 00 khz. At time t 0, plate A of the capacitor has maximum positive charge. At what times t > 0 will (a) plate A again have maximum positive charge, (b) the other plate of the capacitor have maximum positive charge, and (c) the inductor have maximum magnetic field? 0 Dr. Nidal Ershaidat L Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 Problem Solution a) harge on the capacitor () t Q cos( ωt at t 0 Q Q Q cos φ φ 0 Q cosω t b) Q at t T / f / µ s at t T /. 5 µ s c) The Magnetic field is maximum when the current is maximum and that occurs at t T/4 when 0, at t.5 µs not that: i I sin ω t i I at t T / 4 Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 Problem 33-3 In the circuit shown in Fig the switch is kept in position a for a long time. It is then thrown to position b. (a) alculate the freuency of the resulting oscillating current. (b) What is the amplitude of the current oscillations? Solution a) f π L f 75 Hz π b) I Q ω π f Q Q V 6.µ F 34.0V 0. 8µ I π A Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 3

4 Problem 33-7 The energy in an oscillating L circuit containing a.5 H inductor is 5.70 µj. The maximum charge on the capacitor is 75.0 µ. Find (a) the mass: The mass m corresponds to the inductance, i.e. m.5 kg. b) the spring constant: The spring constant k corresponds to the reciprocal of the capacitance. Since the total energy is given by U Q /, where Q is the maximum charge on the capacitor and is the capacitance then: Q F k 37 N m U J.69 0 Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 3 Problem 33-7 c) the maximum displacement, The maximum displacement x m corresponds to the maximum charge, thus x m m 75.0 µm and (d) the maximum speed for a mechanical system with the same period. The maximum speed v m corresponds to the maximum current. The maximum current is: I Q ω Q L Thus v m/s A (.5 H )(.69 0 F ) Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 4 Problem 33-7 In an oscillating L circuit, L 5.0 mh and 7.80 mf. At time t 0 the current is 9.0 ma, the charge on the capacitor is 3.80 m, and the capacitor is charging. (a) What is the total energy in the circuit? The total energy U is the sum of the energies in the inductor and capacitor. If is the charge on the capacitor, is the capacitance, i is the current, and L is the inductance, then: i L U U E + U B + ( ) ( 9. 0 A) ( H ) F.98 0 J.98 µ J Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 5 Problem 33-7 (b) What is the maximum charge on the capacitor? Solve U Q / for the maximum charge Q: Q U ( F )(.98 0 J ) (c) What is the maximum current? U ( F ) I. 6 ma L H (d) If the charge on the capacitor is given by Q cos(ωt, what is the phase angle φ? If 0 is the charge on the capacitor at time t 0, then : 0 Q cos φ µ φ cos cos ± 49.6 Q 5.56µ Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 6 4

5 Problem 33-7 (e) Suppose the data are the same, except that the capacitor is discharging at t 0. What then is φ? Now you want the derivative to be negative and sinφ to be positive. Take φ For φ +46.9, the charge on the capacitor is decreasing; for φ , it is increasing. To check this, calculate the derivative of with respect to time, evaluated for t 0. You should get - ω Q sinφ. You want this to be positive. Since sin(+46.9 ) is positive and sin(-46.9 ) is negative, the correct value for increasing charge is φ Next Lecture hapter 5 Electromagnetic Waves Dr. N. Ershaidat Phys. 07 hapter 4: Electromagnetic Oscillations and Alternating urrent Lecture 5 (QGRI/HFWXUH 5

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1

Chapter 31: RLC Circuits. PHY2049: Chapter 31 1 hapter 31: RL ircuits PHY049: hapter 31 1 L Oscillations onservation of energy Topics Damped oscillations in RL circuits Energy loss A current RMS quantities Forced oscillations Resistance, reactance,

More information

C R. Consider from point of view of energy! Consider the RC and LC series circuits shown:

C 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 information

PES 1120 Spring 2014, Spendier Lecture 35/Page 1

PES 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 information

Physics 212. Lecture 8. Today's Concept: Capacitors. Capacitors in a circuits, Dielectrics, Energy in capacitors. Physics 212 Lecture 8, Slide 1

Physics 212. Lecture 8. Today's Concept: Capacitors. Capacitors in a circuits, Dielectrics, Energy in capacitors. Physics 212 Lecture 8, Slide 1 Physics 212 Lecture 8 Today's oncept: apacitors apacitors in a circuits, Dielectrics, Energy in capacitors Physics 212 Lecture 8, Slide 1 Simple apacitor ircuit Q +Q -Q Q= Q Battery has moved charge Q

More information

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

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

More information

INDUCTANCE Self Inductance

INDUCTANCE Self Inductance NDUTANE 3. Self nductance onsider the circuit shown in the Figure. When the switch is closed the current, and so the magnetic field, through the circuit increases from zero to a specific value. The increasing

More information

Inductance, RL and RLC Circuits

Inductance, 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 information

Physics 11b Lecture #15

Physics 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 information

12 Chapter Driven RLC Circuits

12 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 information

Chapter 3: Capacitors, Inductors, and Complex Impedance

Chapter 3: Capacitors, Inductors, and Complex Impedance hapter 3: apacitors, Inductors, and omplex Impedance In this chapter we introduce the concept of complex resistance, or impedance, by studying two reactive circuit elements, the capacitor and the inductor.

More information

Alternating Current Circuits. Home Work Solutions

Alternating Current Circuits. Home Work Solutions Chapter 21 Alternating Current Circuits. Home Work s 21.1 Problem 21.11 What is the time constant of the circuit in Figure (21.19). 10 Ω 10 Ω 5.0 Ω 2.0µF 2.0µF 2.0µF 3.0µF Figure 21.19: Given: The circuit

More information

Physics 2112 Unit 19

Physics 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 information

Inductance, RL Circuits, LC Circuits, RLC Circuits

Inductance, 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 information

Physics for Scientists & Engineers 2

Physics 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 information

Inductance. Slide 2 / 26. Slide 1 / 26. Slide 4 / 26. Slide 3 / 26. Slide 6 / 26. Slide 5 / 26. Mutual Inductance. Mutual Inductance.

Inductance. 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 information

MASSACHUSETTS 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 8.02 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 information

Handout 10: Inductance. Self-Inductance and inductors

Handout 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 information

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

ELECTROMAGNETIC 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 information

Lecture 39. PHYC 161 Fall 2016

Lecture 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 information

AC Circuits Homework Set

AC Circuits Homework Set Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.

More information

Inductance, Inductors, RL Circuits & RC Circuits, LC, and RLC Circuits

Inductance, 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 information

ALTERNATING CURRENT

ALTERNATING 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 information

Review: Inductance. Oscillating Currents. Oscillations (cont d) LC Circuit Oscillations

Review: Inductance. Oscillating Currents. Oscillations (cont d) LC Circuit Oscillations Oscillating urrents h.30: Induced E Fields: Faraday s aw h.30: ircuits h.3: Oscillations and A ircuits eview: Inductance If the current through a coil of wire changes, there is an induced ef proportional

More information

mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel

mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel esson 6 Solution of urrent in Parallel and Seriesparallel ircuits n the last lesson, the following points were described:. How to compute the total impedance/admittance in series/parallel circuits?. How

More information

EM Oscillations. David J. Starling Penn State Hazleton PHYS 212

EM 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 information

Example 1 Physical Sizes of Capacitors

Example 1 Physical Sizes of Capacitors apacitance (R. Bolton - 0) apacitance Physics, 7th Edition, utnell & Johnson hapter 9.5, 0. Pages 586-59, 68-630 (R. Bolton - 0) apacitance Example Physical Sizes of apacitors The value of capacitance

More information

Chapter 29. Electric Potential: Charged Conductor

Chapter 29. Electric Potential: Charged Conductor hapter 29 Electric Potential: harged onductor 1 Electric Potential: harged onductor onsider two points (A and B) on the surface of the charged conductor E is always perpendicular to the displacement ds

More information

ALTERNATING CURRENT. with X C = 0.34 A. SET UP: The specified value is the root-mean-square current; I. EXECUTE: (a) V = (0.34 A) = 0.12 A.

ALTERNATING CURRENT. with X C = 0.34 A. SET UP: The specified value is the root-mean-square 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 root-mean-square 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 information

Schedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review.

Schedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review. Schedule Date Day lass No. 0 Nov Mon 0 Exam Review Nov Tue Title hapters HW Due date Nov Wed Boolean Algebra 3. 3.3 ab Due date AB 7 Exam EXAM 3 Nov Thu 4 Nov Fri Recitation 5 Nov Sat 6 Nov Sun 7 Nov Mon

More information

9. 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

9. 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 information

Course Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits

Course 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 information

Chapter 31: AC Circuits

Chapter 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 information

Electricity and Magnetism. Capacitance

Electricity and Magnetism. Capacitance Electricity and Magnetism apacitance Sources of Electric Potential A potential difference can be created by moving charge from one conductor to another. The potential difference on a capacitor can produce

More information

---------------------------------------------------------------------------------------------------------- PHYS 2326 University Physics II Class number ---------------------------------------------------------------------------------------------------------------------

More information

Chapter 6 Objectives

Chapter 6 Objectives hapter 6 Engr8 ircuit Analysis Dr urtis Nelson hapter 6 Objectives Understand relationships between voltage, current, power, and energy in inductors and capacitors; Know that current must be continuous

More information

BME/ISE 3511 Bioelectronics - Test Five Review Notes Fall 2015

BME/ISE 3511 Bioelectronics - Test Five Review Notes Fall 2015 BME/ISE 35 Bioelectronics - Test Five Review Notes Fall 205 Test Five Topics: RMS Resistive Power oss (I 2 R) A Reactance, Impedance, Power Factor R ircuit Analysis alculate Series R Impedance alculate

More information

Physics 142 AC Circuits Page 1. AC Circuits. I ve had a perfectly lovely evening but this wasn t it. Groucho Marx

Physics 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 information

19. LC and RLC Oscillators

19. LC and RLC Oscillators University of Rhode Island Digitaloons@URI PHY 204: Eleentary Physics II Physics ourse Materials 2015 19. L and RL Oscillators Gerhard Müller University of Rhode Island, guller@uri.edu reative oons License

More information

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

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase circuits ersion EE T, Kharagpur esson 6 Solution of urrent in Parallel and Seriesparallel ircuits ersion EE T, Kharagpur n the last lesson, the following points were described:. How

More information

Chapter 30 Inductance and Electromagnetic Oscillations

Chapter 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 information

Chapter 32. Inductance

Chapter 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 information

Lecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1

Lecture 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 information

On my honor, I have neither given nor received unauthorized aid on this examination.

On my honor, I have neither given nor received unauthorized aid on this examination. Instructor: Profs. Andrew Rinzler, Paul Avery, Selman Hershfield PHYSICS DEPARTMENT PHY 049 Exam 3 April 7, 00 Name (print, last first): Signature: On my honor, I have neither given nor received unauthorized

More information

Self-inductance A time-varying current in a circuit produces an induced emf opposing the emf that initially set up the time-varying current.

Self-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 information

Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current

Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current People of mediocre ability sometimes achieve outstanding success because they don't know when to quit. Most men succeed because

More information

First Order RC and RL Transient Circuits

First Order RC and RL Transient Circuits First Order R and RL Transient ircuits Objectives To introduce the transients phenomena. To analyze step and natural responses of first order R circuits. To analyze step and natural responses of first

More information

RC Circuits. Equipment: Capstone with 850 interface, RLC circuit board, 2 voltage sensors (no alligator clips), 3 leads V C = 1

RC Circuits. Equipment: Capstone with 850 interface, RLC circuit board, 2 voltage sensors (no alligator clips), 3 leads V C = 1 R ircuits Equipment: apstone with 850 interface, RL circuit board, 2 voltage sensors (no alligator clips), 3 leads 1 Introduction The 3 basic linear circuits elements are the resistor, the capacitor, and

More information

Look over. examples 1, 2, 3, 5, 6. Look over. Chapter 25 section 1-8. Chapter 19 section 5 Example 10, 11

Look over. examples 1, 2, 3, 5, 6. Look over. Chapter 25 section 1-8. Chapter 19 section 5 Example 10, 11 PHYS Look over hapter 5 section -8 examples,, 3, 5, 6 PHYS Look over hapter 7 section 7-9 Examples 8, hapter 9 section 5 Example 0, Things to Know ) How to find the charge on a apacitor. ) How to find

More information

P441 Analytical Mechanics - I. RLC Circuits. c Alex R. Dzierba. In this note we discuss electrical oscillating circuits: undamped, damped and driven.

P441 Analytical Mechanics - I. RLC Circuits. c Alex R. Dzierba. In this note we discuss electrical oscillating circuits: undamped, damped and driven. Lecture 10 Monday - September 19, 005 Written or last updated: September 19, 005 P441 Analytical Mechanics - I RLC Circuits c Alex R. Dzierba Introduction In this note we discuss electrical oscillating

More information

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

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

More information

PHYS General Physics for Engineering II FIRST MIDTERM

PHYS General Physics for Engineering II FIRST MIDTERM Çankaya University Department of Mathematics and Computer Sciences 2010-2011 Spring Semester PHYS 112 - General Physics for Engineering II FIRST MIDTERM 1) Two fixed particles of charges q 1 = 1.0µC and

More information

Physics 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. 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 information

Oscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1

Oscillations 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 information

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. 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 information

Capacitance. PHY2049: Chapter 25 1

Capacitance. PHY2049: Chapter 25 1 apacitance PHY049: hapter 5 1 oulomb s law Electric fields Equilibrium Gauss law What You Know: Electric Fields Electric fields for several charge configurations Point Dipole (along axes) Line Plane (nonconducting)

More information

Physics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33

Physics 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 information

Module 24: Outline. Expt. 8: Part 2:Undriven RLC Circuits

Module 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 information

Active Figure 32.3 (SLIDESHOW MODE ONLY)

Active 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 information

Chapter 28: Alternating Current

Chapter 28: Alternating Current hapter 8: Alternating urrent Phasors and Alternating urrents Alternating current (A current) urrent which varies sinusoidally in tie is called alternating current (A) as opposed to direct current (D).

More information

Your Comments. THIS IS SOOOO HARD. I get the concept and mathematical expression. But I do not get links among everything.

Your 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 information

Maxwell s Equations & Electromagnetic Waves. The Equations So Far...

Maxwell s Equations & Electromagnetic Waves. The Equations So Far... Maxwell s Equations & Electromagnetic Waves Maxwell s equations contain the wave equation Velocity of electromagnetic waves c = 2.99792458 x 1 8 m/s Relationship between E and B in an EM wave Energy in

More information

Induction_P1. 1. [1 mark]

Induction_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 information

AC Circuits III. Physics 2415 Lecture 24. Michael Fowler, UVa

AC 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 information

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic

More information

Driven RLC Circuits Challenge Problem Solutions

Driven RLC Circuits Challenge Problem Solutions Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs

More information

Inductors. Hydraulic analogy Duality with capacitor Charging and discharging. Lecture 12: Inductors

Inductors. Hydraulic analogy Duality with capacitor Charging and discharging. Lecture 12: Inductors Lecture 12: nductors nductors Hydraulic analogy Duality with capacitor Charging and discharging Robert R. McLeod, University of Colorado http://hilaroad.com/camp/projects/magnet.html 99 Lecture 12: nductors

More information

Self-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1

Self-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 information

not to scale Show that the potential difference between the plates increases to about 80 V. Calculate the energy that is now stored by the capacitor.

not to scale Show that the potential difference between the plates increases to about 80 V. Calculate the energy that is now stored by the capacitor. Q1.The figure below shows a capacitor of capacitance 370 pf. It consists of two parallel metal plates of area 250 cm 2. A sheet of polythene that has a relative permittivity 2.3 completely fills the gap

More information

Name:... Section:... Physics 208 Quiz 8. April 11, 2008; due April 18, 2008

Name:... 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 information

1 Phasors and Alternating Currents

1 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 information

Lecture 4: R-L-C Circuits and Resonant Circuits

Lecture 4: R-L-C Circuits and Resonant Circuits Lecture 4: R-L-C Circuits and Resonant Circuits RLC series circuit: What's V R? Simplest way to solve for V is to use voltage divider equation in complex notation: V X L X C V R = in R R + X C + X L L

More information

Chapter 32. Inductance

Chapter 32. Inductance Chapter 32 Inductance 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

More information

Louisiana State University Physics 2102, Exam 3 April 2nd, 2009.

Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),

More information

DC and AC Impedance of Reactive Elements

DC and AC Impedance of Reactive Elements 3/6/20 D and A Impedance of Reactive Elements /6 D and A Impedance of Reactive Elements Now, recall from EES 2 the complex impedances of our basic circuit elements: ZR = R Z = jω ZL = jωl For a D signal

More information

PROBLEMS TO BE SOLVED IN CLASSROOM

PROBLEMS TO BE SOLVED IN CLASSROOM PROLEMS TO E SOLVED IN LSSROOM Unit 0. Prerrequisites 0.1. Obtain a unit vector perpendicular to vectors 2i + 3j 6k and i + j k 0.2 a) Find the integral of vector v = 2xyi + 3j 2z k along the straight

More information

Oscillations. Tacoma Narrow Bridge: Example of Torsional Oscillation

Oscillations. Tacoma Narrow Bridge: Example of Torsional Oscillation Oscillations Mechanical Mass-spring system nd order differential eq. Energy tossing between mass (kinetic energy) and spring (potential energy) Effect of friction, critical damping (shock absorber) Simple

More information

NAME: PHYSICS 6B SPRING 2011 FINAL EXAM ( VERSION A )

NAME: PHYSICS 6B SPRING 2011 FINAL EXAM ( VERSION A ) NAME: PHYSCS 6B SPRNG 2011 FNAL EXAM ( VERSON A ) Choose the best answer for each of the following multiple-choice questions. There is only one answer for each. Questions 1-2 are based on the following

More information

RLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:

RLC 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 information

Circuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18

Circuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18 Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)

More information

2.4 Models of Oscillation

2.4 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 information

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

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

More information

AN019. A Better Approach of Dealing with Ripple Noise of LDO. Introduction. The influence of inductor effect over LDO

AN019. A Better Approach of Dealing with Ripple Noise of LDO. Introduction. The influence of inductor effect over LDO Better pproach of Dealing with ipple Noise of Introduction It has been a trend that cellular phones, audio systems, cordless phones and portable appliances have a requirement for low noise power supplies.

More information

Slide 1 / 26. Inductance by Bryan Pflueger

Slide 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 information

Handout 11: AC circuit. AC generator

Handout 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 information

Solutions to PHY2049 Exam 2 (Nov. 3, 2017)

Solutions to PHY2049 Exam 2 (Nov. 3, 2017) Solutions to PHY2049 Exam 2 (Nov. 3, 207) Problem : In figure a, both batteries have emf E =.2 V and the external resistance R is a variable resistor. Figure b gives the electric potentials V between the

More information

TEST 2 3 FIG. 1. a) Find expression for a capacitance of the device in terms of the area A and d, k 1 and k 2 and k 3.

TEST 2 3 FIG. 1. a) Find expression for a capacitance of the device in terms of the area A and d, k 1 and k 2 and k 3. TEST Giving or receiving aid in any examination is cause for dismissal from the university. Perform the necessary calculation in the spaces provided. If additional space is required, use the backs of the

More information

Chapter 21: RLC Circuits. PHY2054: Chapter 21 1

Chapter 21: RLC Circuits. PHY2054: Chapter 21 1 Chapter 21: RC Circuits PHY2054: Chapter 21 1 Voltage and Current in RC Circuits AC emf source: driving frequency f ε = ε sinωt ω = 2π f m If circuit contains only R + emf source, current is simple ε ε

More information

Physics 2112 Unit 20. Outline: Driven AC Circuits Phase of V and I Conceputally Mathematically With phasors

Physics 2112 Unit 20. Outline: Driven AC Circuits Phase of V and I Conceputally Mathematically With phasors Physics 2112 Unit 20 Outline: Driven A ircuits Phase of V and I onceputally Mathematically With phasors Electricity & Magnetism ecture 20, Slide 1 Your omments it just got real this stuff is confusing

More information

ET4119 Electronic Power Conversion 2011/2012 Solutions 27 January 2012

ET4119 Electronic Power Conversion 2011/2012 Solutions 27 January 2012 ET4119 Electronic Power Conversion 2011/2012 Solutions 27 January 2012 1. In the single-phase rectifier shown below in Fig 1a., s = 1mH and I d = 10A. The input voltage v s has the pulse waveform shown

More information

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

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

More information

EE 205 Dr. A. Zidouri. Electric Circuits II. Frequency Selective Circuits (Filters) Low Pass Filter. Lecture #36

EE 205 Dr. A. Zidouri. Electric Circuits II. Frequency Selective Circuits (Filters) Low Pass Filter. Lecture #36 EE 05 Dr. A. Zidouri Electric ircuits II Frequency Selective ircuits (Filters) ow Pass Filter ecture #36 - - EE 05 Dr. A. Zidouri The material to be covered in this lecture is as follows: o Introduction

More information

INTC 1307 Instrumentation Test Equipment Teaching Unit 6 AC Bridges

INTC 1307 Instrumentation Test Equipment Teaching Unit 6 AC Bridges IHLAN OLLEGE chool of Engineering & Technology ev. 0 W. lonecker ev. (8/6/0) J. Bradbury INT 307 Instrumentation Test Equipment Teaching Unit 6 A Bridges Unit 6: A Bridges OBJETIVE:. To explain the operation

More information

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance

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

More information

Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is

Part 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 information

FINAL EXAM - Physics Patel SPRING 1998 FORM CODE - A

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

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 140) Lecture 6 lectrodynamics Direct current circuits parallel and series connections Kirchhoff s rules circuits Hours of operation: Monday and Tuesday Wednesday and Thursday Friday,

More information

APPLICATIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS

APPLICATIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS APPLICATIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration

More information

Chapter 2: Capacitor And Dielectrics

Chapter 2: Capacitor And Dielectrics hapter 2: apacitor And Dielectrics In this chapter, we are going to discuss the different ways that a capacitor could be arranged in a circuit and how its capacitance could be increased. Overview apacitor

More information

2.4 Harmonic Oscillator Models

2.4 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 information

ε induced Review: Self-inductance 20.7 RL Circuits Review: Self-inductance B induced Announcements

ε induced Review: Self-inductance 20.7 RL Circuits Review: Self-inductance B induced Announcements Announcements WebAssign HW Set 7 due this Friday Problems cover material from Chapters 20 and 21 We re skipping Sections 21.1-21.7 (alternating current circuits) Review: Self-inductance induced ε induced

More information