Physics 9 Friday, April 18, 2014
|
|
- Felicia Tate
- 5 years ago
- Views:
Transcription
1 Physics 9 Friday, April 18, 2014 Turn in HW12. I ll put HW13 online tomorrow. For Monday: read all of Ch33 (optics) For Wednesday: skim Ch34 (wave optics) I ll hand out your take-home practice final exam (due just before Reading Days start, 10% of grade) by Wednesday. If you want to learn more about diodes, LEDs, and p-n junctions, here are two YouTube videos that are ( extremely ) informative, but maybe a little slow: Today: mainly high-pass & low-pass filters. Also, we can try analyzing a multi-battery circuit together for practice.
2
3 Quick demos/hand-arounds: Three-way stairway light switch. Household light switch with bulb & battery. Take apart Wednesday s transformer.
4 What are the two solutions to the equation z = 0
5 What are the two solutions to the equation z = 0 Define i = 1. Then solution to above equation is z = ±i. Complex numbers: z = x + iy, where x, y R. real part of z: Re(z) = x. imaginary part of z: Im(z) = y. (Note: it s y, not iy.) addition: (a + ib) + (c + id) = (a + c) + i(b + d) multiplication: (a + ib) (c + id) = (ac bd) + i(bc + ad) division: a + ib c + id = (a + ib)(c id) (c + id)(c id) = (ac + bd) + i(bc ad) c 2 + d 2
6 Represent complex numbers as vectors on complex plane. Then adding (4 + 2i) + ( 1 + 3i) = (3 + 5i) is just like adding vectors. (4, 2) + ( 1, 3) = (3, 5)
7 Sometimes a vector in a plane is most conveniently represented (x,y). Sometimes it s more convenient to use length and angle: x = R cos θ y = R sin θ R = x 2 + y 2 tan θ = y/x Sometimes a complex number is most conveniently written R cos θ + ir sin θ instead of x + iy.
8
9 That shocking t-shirt depends on DeMoivre s Theorem: e iθ = cos θ + i sin θ If you take that equation as true, and plug in θ = π, then e iπ = cos π + i sin π = ( 1) + i(0) = 1 To prove this, use taylor series: e θ = 1 + θ + θ2 2 + θ3 6 + θ θ θ θ e iθ = 1 + (iθ) + (iθ)2 2 + (iθ)3 6 then using i 2 = 1, i 4 = 1, etc., you get + (iθ) (iθ) (iθ) (iθ) e iθ = 1 + iθ θ2 2 iθ3 6 + θ i θ5 120 θ6 720 i θ
10 e iθ = 1 + iθ θ2 2 iθ3 6 + θ i θ5 120 θ6 720 i θ Meanwhile, we can expand cos θ and sin θ: cos θ = 1 θ2 2 + θ4 24 θ sin θ = θ θ3 6 + θ5 120 θ So then cos θ + i sin θ has the same talyor series as e iθ. e iθ = cos θ + i sin θ That means I can write a complex number as x + iy = R cos θ + i sin θ = Re iθ where R = x 2 + y 2 and tan θ = x/y.
11 How does this relate to AC circuits? Textbook is drawing oscillating quantities as little arrows that turn ccw at frequency f = ω/(2π). At time t, the vertical position of the tip of each arrow represents voltage V (t), current I(t), etc. In this example (inductor), V (t) and I(t) are 90 out of phase. Notice that if you took the I(t) arrow and multiplied it by i = 1, it would line up with the V (t) arrow if you interpret the arrows as lying in the complex plane. The part we are graphing at each instant to get V (t) or I(t) is the vertical (imaginary) component of the arrow.
12 The part we are graphing at each instant to get V (t) or I(t) is the vertical (imaginary) component of the arrow. The current phasor arrow in the graph is the complex number I(t) = I max e iωt = I max (cos(ωt) + i sin(ωt)) whose vertical (imaginary) component is I(t) = Im(I(t)) = I max sin(ωt) (The imaginary part of a complex number is a real number!)
13 The part we are graphing at each instant to get V (t) or I(t) is the vertical (imaginary) component of the arrow. The voltage phasor arrow in the graph is the complex number V(t) = V max e iωt+π/2 = iv max e iωt = V max ( sin(ωt) + i cos(ωt)) whose vertical (imaginary) component is V (t) = Im(V(t)) = V max cos(ωt) We got the 90 phase shift between V and I just by multiplying by i = 1. Using complex numbers, V(t) is proportional to I(t), even if there is a phase shift between them.
14 For a resistor, V = IR. There is no phase shift between voltage and current. The complex phasor arrows are: V(t) = V max e iωt I(t) = (V max /R)e iωt The vertical components (the actual voltage and current) are: V (t) = Im(V(t)) = V max sin(ωt) I(t) = Im(I(t)) = (V max /R) sin(ωt)
15 For a capacitor, Q = CV, which means I = C dv. The phase of dt the current is 90 ahead of the phase of the voltage. The complex voltage phasor arrow is: V(t) = V max e iωt Taking the derivative to get the current gives: I(t) = C dv(t) = C iω V max e iωt dt So I(t) and V(t) are proportional, in spite of the phase shift: I(t) = (iωc) V(t)
16 For an inductor, V = L di. The phase of the current is 90 dt behind the phase of the voltage. The complex current phasor arrow is: I(t) = I max e iωt Taking the derivative to get the voltage gives: V(t) = L di(t) = L iω I max e iωt dt So I(t) and V(t) are proportional, in spite of the phase shift: V(t) = (iωl) I(t)
17 The derivative of e iωt is simple: just multiply by iω. The derivative is proportional to the original. de iωt dt But with sines and cosines: d sin(ωt) dt = iωe iωt = ω cos(ωt) d cos(ωt) = ω sin(ωt) dt That s a pain, because derivative is not proportional to original. So we pretend that voltage and current are complex, writing: V(t) = Ve iωt I(t) = Ie iωt This lets us write V = IZ where Z is called the impedance. This lets us treat resistors, capacitors, and inductors in a unified way.
18 We pretend that voltage and current are complex, writing: V(t) = Ve iωt I(t) = Ie iωt To get instantaneous V (t) or I(t), take the vertical (imaginary) part of the complex phasor: V (t) = Im(V(t)) I(t) = Im(I(t)) Usually, you care more about the amplitude. To get the amplitude, just take the magnitude of the complex phasor: V max = V(t) I max = I(t) We ll see how this works in a minute. It s easier than you think. (Most people use the real (horizontal) component to get the instantaneous V (t) or I(t), but I m using the vertical (imaginary) component for consistency with the book s phasor diagrams. Also, engineers use j = 1, because they use lowercase i for current.)
19 Generalized Ohm s law: V = IZ For a resistor, Z = R. V(t) = I(t) R = Z R = R For an inductor, Z = iωl (where i = 1 ) V(t) = L di(t) dt = (iωl) I(t) = Z L = iωl For a capacitor, Z = 1 (iωc) = i/(ωc). I(t) = C dv(t) dt = (iωc) V(t) = Z C = 1/(iωC) Z = R + ix. Real part of impedance is called resistance. Imaginary part is called reactance: X L = ωl. X C = 1/(ωC). Whew! That was the hard part. Now the fun part.
20 Let s take AC signal source E(t) as our input signal, and V cb (t) (across R 2 ) as our output signal. How does the output amplitude compare with the input amplitude? What happens to V out when R 2 R 1? algebra = V out V in = V cb(t) E(t) = R 2 R 1 + R 2
21 Now replace one resistor with a capactor. Just by replacing resistance with impedance we can analyze the circuit in exactly the same way as the previous one. Which impedance is smaller at high frequency? What happens to the amplitude of V out (V across the capacitor) as the frequency changes?
22 Now swap resistor and capactor. Which impedance is smaller at high frequency? What happens to the amplitude of V out (voltage across the resistor) as the frequency changes?
23
24 The graphs show V out V in vs. frequency for low-pass filter (left) and high-pass filter (right).
25 ( ) The graphs show log Vout 10 V in vs. log 10 (frequency) for low-pass filter (left) and high-pass filter (right).
26
27
28
29 Quick way to get total current drawn from the batteries. R 1 + (R 5 (R 2 + (R 3 R 4 )))) = 160 Ω I batt = 3 V 160 Ω
30 Predict the relative brightness for the three bulbs (assuming the bulbs are identical). (A) A < B < C (B) A < B = C (C) A = B = C (D) A > B = C (E) A > B > C
31 You just predicted A > B = C when all 3 bulbs are present. Now predict what will happen to the brightness of bulbs A and B if bulb C is unscrewed. (A) A and B will both become brighter. (B) A and B will both become dimmer. (C) A will become brighter, and B will become dimmer. (D) A will become dimmer, and B will become brighter. (E) The brightness of A and B will not change.
32 If you were to build this circuit, when would bulb A be brighter? (A) A is brighter when the switch is open (B) A is brighter when the switch is closed (C) A is the same brightness in both cases
33 How does the resistance of bulb B compare with the resistance of a closed switch? (A circuit diagram usually shows a switch in its open position, as this one does.) (A) a closed switch has much smaller resistance than bulb B (B) a closed switch has much larger resistance than bulb B (C) the resistance of a closed switch is similar to the resistance of bulb B
34 By the way, what is the resistance of an open switch? (Is it very easy or is it very difficult for current to flow through an open switch?) (A) an open switch has a very small resistance, effectively zero (B) an open switch has a very large resistance, effectively infinite
35 Physics 9 Friday, April 18, 2014 Turn in HW12. I ll put HW13 online tomorrow. For Monday: read all of Ch33 (optics) For Wednesday: skim Ch34 (wave optics) I ll hand out your take-home practice final exam (due just before Reading Days start, 10% of grade) by Wednesday. If you want to learn more about diodes, LEDs, and p-n junctions, here are two YouTube videos that are ( extremely ) informative, but maybe a little slow: If you found today s discussion of filters interesting and mostly understandable (and you get an A or A+ in Phys 009), then you re qualified to take my electronics course (Phys 364), which is entirely lab-based (like a studio). Tu/Th 2 5pm. Filters, amplifiers, transistors, Arduinos, etc.
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 informationAnnouncements: Today: more AC circuits
Announcements: Today: more AC circuits I 0 I rms Current through a light bulb I 0 I rms I t = I 0 cos ωt I 0 Current through a LED I t = I 0 cos ωt Θ(cos ωt ) Theta function (is zero for a negative argument)
More informationSupplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance
Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance Complex numbers Complex numbers are expressions of the form z = a + ib, where both a and b are real numbers, and i
More informationPhysics 9 Monday, April 7, 2014
Physics 9 Monday, April 7, 2014 Handing out HW11 today, due Friday. Finishes induced emf; starts circuits. For today: concepts half of Ch31 (electric circuits); read equations half for Wednesday. Annotated
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 informationComplex number review
Midterm Review Problems Physics 8B Fall 009 Complex number review AC circuits are usually handled with one of two techniques: phasors and complex numbers. We ll be using the complex number approach, so
More informationI. Impedance of an R-L circuit.
I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC
More informationLecture 24. Impedance of AC Circuits.
Lecture 4. Impedance of AC Circuits. Don t forget to complete course evaluations: https://sakai.rutgers.edu/portal/site/sirs Post-test. You are required to attend one of the lectures on Thursday, Dec.
More informationLaboratory I: Impedance
Physics 331, Fall 2008 Lab I - Handout 1 Laboratory I: Impedance Reading: Simpson Chapter 1 (if necessary) & Chapter 2 (particularly 2.9-2.13) 1 Introduction In this first lab we review the properties
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 informationSinusoids and Phasors
CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying
More informationCircuit 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 informationz = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1)
11 Complex numbers Read: Boas Ch. Represent an arb. complex number z C in one of two ways: z = x + iy ; x, y R rectangular or Cartesian form z = re iθ ; r, θ R polar form. (1) Here i is 1, engineers call
More informationSCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self-paced Course
SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING Self-paced Course MODULE 26 APPLICATIONS TO ELECTRICAL CIRCUITS Module Topics 1. Complex numbers and alternating currents 2. Complex impedance 3.
More informationPHYS 3900 Homework Set #02
PHYS 3900 Homework Set #02 Part = HWP 2.0, 2.02, 2.03. Due: Mon. Jan. 22, 208, 4:00pm Part 2 = HWP 2.04, 2.05, 2.06. Due: Fri. Jan. 26, 208, 4:00pm All textbook problems assigned, unless otherwise stated,
More informationL L, R, C. Kirchhoff s rules applied to AC circuits. C Examples: Resonant circuits: series and parallel LRC. Filters: narrowband,
Today in Physics 1: A circuits Solving circuit problems one frequency at a time. omplex impedance of,,. Kirchhoff s rules applied to A circuits. it V in Examples: esonant circuits: i series and parallel.
More informationChapter 10: Sinusoids and Phasors
Chapter 10: Sinusoids and Phasors 1. Motivation 2. Sinusoid Features 3. Phasors 4. Phasor Relationships for Circuit Elements 5. Impedance and Admittance 6. Kirchhoff s Laws in the Frequency Domain 7. Impedance
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 informationExperiment 3: Resonance in LRC Circuits Driven by Alternating Current
Experiment 3: Resonance in LRC Circuits Driven by Alternating Current Introduction In last week s laboratory you examined the LRC circuit when constant voltage was applied to it. During this laboratory
More informationPhysics 294H. lectures will be posted frequently, mostly! every day if I can remember to do so
Physics 294H l Professor: Joey Huston l email:huston@msu.edu l office: BPS3230 l Homework will be with Mastering Physics (and an average of 1 hand-written problem per week) Help-room hours: 12:40-2:40
More informationElectronics. Basics & Applications. group talk Daniel Biesinger
Electronics Basics & Applications group talk 23.7.2010 by Daniel Biesinger 1 2 Contents Contents Basics Simple applications Equivalent circuit Impedance & Reactance More advanced applications - RC circuits
More informationHarman Outline 1A CENG 5131
Harman Outline 1A CENG 5131 Numbers Real and Imaginary PDF In Chapter 2, concentrate on 2.2 (MATLAB Numbers), 2.3 (Complex Numbers). A. On R, the distance of any real number from the origin is the magnitude,
More informationElectricity & Magnetism Lecture 20
Electricity & Magnetism Lecture 20 Today s Concept: AC Circuits Maximum currents & voltages Phasors: A Simple Tool Electricity & Magne?sm Lecture 20, Slide 1 Other videos: Prof. W. Lewin, MIT Open Courseware
More informationMathematical Review for AC Circuits: Complex Number
Mathematical Review for AC Circuits: Complex Number 1 Notation When a number x is real, we write x R. When a number z is complex, we write z C. Complex conjugate of z is written as z here. Some books use
More informationWave Phenomena Physics 15c
Wave Phenomena Physics 15c Lecture Harmonic Oscillators (H&L Sections 1.4 1.6, Chapter 3) Administravia! Problem Set #1! Due on Thursday next week! Lab schedule has been set! See Course Web " Laboratory
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 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 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 informationEE100Su08 Lecture #11 (July 21 st 2008)
EE100Su08 Lecture #11 (July 21 st 2008) Bureaucratic Stuff Lecture videos should be up by tonight HW #2: Pick up from office hours today, will leave them in lab. REGRADE DEADLINE: Monday, July 28 th 2008,
More informationWave Phenomena Physics 15c
Wave Phenomena Physics 15c Lecture Harmonic Oscillators (H&L Sections 1.4 1.6, Chapter 3) Administravia! Problem Set #1! Due on Thursday next week! Lab schedule has been set! See Course Web " Laboratory
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques
More informationLectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011
Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits Nov. 7 & 9, 2011 Material from Textbook by Alexander & Sadiku and Electrical Engineering: Principles & Applications,
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 20 121101 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Chapters 1-3 Circuit Analysis Techniques Chapter 10 Diodes Ideal Model
More informationElectric Circuit Theory
Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1
More informationEE 40: Introduction to Microelectronic Circuits Spring 2008: Midterm 2
EE 4: Introduction to Microelectronic Circuits Spring 8: Midterm Venkat Anantharam 3/9/8 Total Time Allotted : min Total Points:. This is a closed book exam. However, you are allowed to bring two pages
More informationPhysics 2020 Lab 5 Intro to Circuits
Physics 2020 Lab 5 Intro to Circuits Name Section Tues Wed Thu 8am 10am 12pm 2pm 4pm Introduction In this lab, we will be using The Circuit Construction Kit (CCK). CCK is a computer simulation that allows
More informationPhasors: Impedance and Circuit Anlysis. Phasors
Phasors: Impedance and Circuit Anlysis Lecture 6, 0/07/05 OUTLINE Phasor ReCap Capacitor/Inductor Example Arithmetic with Complex Numbers Complex Impedance Circuit Analysis with Complex Impedance Phasor
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 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. 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 informationPhysics 405/505 Digital Electronics Techniques. University of Arizona Spring 2006 Prof. Erich W. Varnes
Physics 405/505 Digital Electronics Techniques University of Arizona Spring 2006 Prof. Erich W. Varnes Administrative Matters Contacting me I will hold office hours on Tuesday from 1-3 pm Room 420K in
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis
More informationf = 1 T 6 a.c. (Alternating Current) Circuits Most signals of interest in electronics are periodic : they repeat regularly as a function of time.
Analogue Electronics (Aero).66 66 Analogue Electronics (Aero) 6.66 6 a.c. (Alternating Current) Circuits Most signals of interest in electronics are periodic : they repeat regularly as a function of time.
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 informationCircuits Advanced Topics by Dr. Colton (Fall 2016)
ircuits Advanced Topics by Dr. olton (Fall 06). Time dependence of general and L problems General and L problems can always be cast into first order ODEs. You can solve these via the particular solution
More informationSinusoidal Steady-State Analysis
Sinusoidal Steady-State Analysis Almost all electrical systems, whether signal or power, operate with alternating currents and voltages. We have seen that when any circuit is disturbed (switched on or
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 informationPhysics 102 Spring 2007: Final Exam Multiple-Choice Questions
Last Name: First Name: Physics 102 Spring 2007: Final Exam Multiple-Choice 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 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 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 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 informationAssessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526)
NCEA Level 3 Physics (91526) 2015 page 1 of 6 Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526) Evidence Q Evidence Achievement Achievement with Merit Achievement
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 informationPower lines. Why do birds sitting on a high-voltage power line survive?
Power lines At large distances, the resistance of power lines becomes significant. To transmit maximum power, is it better to transmit high V, low I or high I, low V? (a) high V, low I (b) low V, high
More informationConsider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current.
AC power Consider a simple RC circuit We might like to know how much power is being supplied by the source We probably need to find the current R 10! R 10! is VS Vmcosωt Vm 10 V f 60 Hz V m 10 V C 150
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 informationVibrations and Waves Physics Year 1. Handout 1: Course Details
Vibrations and Waves Jan-Feb 2011 Handout 1: Course Details Office Hours Vibrations and Waves Physics Year 1 Handout 1: Course Details Dr Carl Paterson (Blackett 621, carl.paterson@imperial.ac.uk Office
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 informationA capacitor is a device that stores electric charge (memory devices). A capacitor is a device that stores energy E = Q2 2C = CV 2
Capacitance: Lecture 2: Resistors and Capacitors Capacitance (C) is defined as the ratio of charge (Q) to voltage (V) on an object: C = Q/V = Coulombs/Volt = Farad Capacitance of an object depends on geometry
More informationProf. Anyes Taffard. Physics 120/220. Voltage Divider Capacitor RC circuits
Prof. Anyes Taffard Physics 120/220 Voltage Divider Capacitor RC circuits Voltage Divider The figure is called a voltage divider. It s one of the most useful and important circuit elements we will encounter.
More informationPhysics 115. AC circuits Reactances Phase relationships Evaluation. General Physics II. Session 35. R. J. Wilkes
Session 35 Physics 115 General Physics II AC circuits Reactances Phase relationships Evaluation R. J. Wilkes Email: phy115a@u.washington.edu 06/05/14 1 Lecture Schedule Today 2 Announcements Please pick
More informationClicker Session Currents, DC Circuits
Clicker Session Currents, DC Circuits Wires A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? 1) it decreases
More informationPhysics 9 Wednesday, November 28, 2018
Physics 9 Wednesday, November 28, 2018 HW10 due Friday. For today, you read Mazur ch31 (electric circuits) The main goals for the electricity segment (the last segment of the course) are for you to feel
More informationWith this expanded version of what we mean by a solution to an equation we can solve equations that previously had no solution.
M 74 An introduction to Complex Numbers. 1 Solving equations Throughout the calculus sequence we have limited our discussion to real valued solutions to equations. We know the equation x 1 = 0 has distinct
More informationECE 201 Fall 2009 Final Exam
ECE 01 Fall 009 Final Exam December 16, 009 Division 0101: Tan (11:30am) Division 001: Clark (7:30 am) Division 0301: Elliott (1:30 pm) Instructions 1. DO NOT START UNTIL TOLD TO DO SO.. Write your Name,
More informationBasic Electronics. Introductory Lecture Course for. Technology and Instrumentation in Particle Physics Chicago, Illinois June 9-14, 2011
Basic Electronics Introductory Lecture Course for Technology and Instrumentation in Particle Physics 2011 Chicago, Illinois June 9-14, 2011 Presented By Gary Drake Argonne National Laboratory Session 2
More informationParallel Resistors (32.6)
Parallel Resistors (32.6) Resistors connected at both ends are called parallel resistors The important thing to note is that: the two left ends of the resistors are at the same potential. Also, the two
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 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 information1 (2n)! (-1)n (θ) 2n
Complex Numbers and Algebra The real numbers are complete for the operations addition, subtraction, multiplication, and division, or more suggestively, for the operations of addition and multiplication
More informationChapter 9 Objectives
Chapter 9 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 9 Objectives Understand the concept of a phasor; Be able to transform a circuit with a sinusoidal source into the frequency domain using phasor
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 informationParallel Resistors (32.6)
Parallel Resistors (32.6) Resistors connected at both ends are called parallel resistors Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1 Parallel Resistors (32.6)
More informationPHYS 1444 Section 003 Lecture #12
PHYS 1444 Section 003 Lecture #12 Monday, Oct. 10, 2005 EMF and Terminal Voltage Resisters in series and parallel Kirchhoff s Rules EMFs in series and parallel RC Circuits Today s homework is homework
More informationExperiment 4. RC Circuits. Observe and qualitatively describe the charging and discharging (decay) of the voltage on a capacitor.
Experiment 4 RC Circuits 4.1 Objectives Observe and qualitatively describe the charging and discharging (decay) of the voltage on a capacitor. Graphically determine the time constant τ for the decay. 4.2
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 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 informationSinusoidal Steady-State Analysis
Sinusoidal Steady-State Analysis Mauro Forti October 27, 2018 Constitutive Relations in the Frequency Domain Consider a network with independent voltage and current sources at the same angular frequency
More informationMasteringPhysics: Assignment Print View. Problem 30.50
Page 1 of 15 Assignment Display Mode: View Printable Answers phy260s08 homework 13 Due at 11:00pm on Wednesday, May 14, 2008 View Grading Details Problem 3050 Description: A 15-cm-long nichrome wire is
More information09/29/2009 Reading: Hambley Chapter 5 and Appendix A
EE40 Lec 10 Complex Numbers and Phasors Prof. Nathan Cheung 09/29/2009 Reading: Hambley Chapter 5 and Appendix A Slide 1 OUTLINE Phasors as notation for Sinusoids Arithmetic with Complex Numbers Complex
More informationSchedule. 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 informationLCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module. What you'll learn in Module 9. Module 9 Introduction
Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing
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 informationEE40 Lecture 11 Josh Hug 7/19/2010
EE40 Lecture Josh 7/9/200 Logistical Things Lab 4 tomorrow Lab 5 (active filter lab) on Wednesday Prototype for future lab for EE40 Prelab is very short, sorry. Please give us our feedback Google docs
More informationb) (4) How large is the current through the 2.00 Ω resistor, and in which direction?
General Physics II Exam 2 - Chs. 19 21 - Circuits, Magnetism, EM Induction - Sep. 29, 2016 Name Rec. Instr. Rec. Time For full credit, make your work clear. Show formulas used, essential steps, and results
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 informationP441 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 informationName: Lab: M8 M2 W8 Th8 Th11 Th2 F8. cos( θ) = cos(θ) sin( θ) = sin(θ) sin(θ) = cos. θ (radians) θ (degrees) cos θ sin θ π/6 30
Name: Lab: M8 M2 W8 Th8 Th11 Th2 F8 Trigonometric Identities cos(θ) = cos(θ) sin(θ) = sin(θ) sin(θ) = cos Cosines and Sines of common angles Euler s Formula θ (radians) θ (degrees) cos θ sin θ 0 0 1 0
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 informationLecture 05 Power in AC circuit
CA2627 Building Science Lecture 05 Power in AC circuit Instructor: Jiayu Chen Ph.D. Announcement 1. Makeup Midterm 2. Midterm grade Grade 25 20 15 10 5 0 10 15 20 25 30 35 40 Grade Jiayu Chen, Ph.D. 2
More informationCircuit 3. Name Student ID
Name Student ID last first Score II. [10 pts total] The following questions are based on your experience in the lab. The questions are not related to each other. Please assume that all batteries are ideal
More information2.1 The electric field outside a charged sphere is the same as for a point source, E(r) =
Chapter Exercises. The electric field outside a charged sphere is the same as for a point source, E(r) Q 4πɛ 0 r, where Q is the charge on the inner surface of radius a. The potential drop is the integral
More informationDesign Engineering MEng EXAMINATIONS 2016
IMPERIAL COLLEGE LONDON Design Engineering MEng EXAMINATIONS 2016 For Internal Students of the Imperial College of Science, Technology and Medicine This paper is also taken for the relevant examination
More informationChapter 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 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 informationProf. Anyes Taffard. Physics 120/220. Foundations Circuit elements Resistors: series & parallel Ohm s law Kirchhoff s laws Complex numbers
Prof. Anyes Taffard Physics 120/220 Foundations Circuit elements Resistors: series & parallel Ohm s law Kirchhoff s laws Complex numbers Foundations Units: ü Q: charge [Coulomb] ü V: voltage = potential
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 informationProf. Shayla Sawyer CP08 solution
What does the time constant represent in an exponential function? How do you define a sinusoid? What is impedance? How is a capacitor affected by an input signal that changes over time? How is an inductor
More informationMATH 135: COMPLEX NUMBERS
MATH 135: COMPLEX NUMBERS (WINTER, 010) The complex numbers C are important in just about every branch of mathematics. These notes 1 present some basic facts about them. 1. The Complex Plane A complex
More informationCapacitance. A different kind of capacitor: Work must be done to charge a capacitor. Capacitors in circuits. Capacitor connected to a battery
Capacitance The ratio C = Q/V is a conductor s self capacitance Units of capacitance: Coulomb/Volt = Farad A capacitor is made of two conductors with equal but opposite charge Capacitance depends on shape
More information