Solutions to these tests are available online in some places (but not all explanations are good)...

Size: px
Start display at page:

Download "Solutions to these tests are available online in some places (but not all explanations are good)..."

Transcription

1 The Physics GRE

2 Sample test put out by ETS OSU physics website has lots of tips, and 4 additional tests Solutions to these tests are available online in some places (but not all explanations are good)... Study guides and supporting material can be borrowed for use in the PRB...

3 The oscilloscope

4

5 A steady current or a slowly changing potential can be measured by a Voltmeter R V A steady current or a slowly changing current can be measured by an Ammeter R V But the voltage may be oscillating at 10 Khz... that is 10,000 oscillations per second. How should we measure voltages that change quickly?

6 There are two ways of using an oscilloscope The X direction is a uniform rate sweep, so it marks time t Put the voltage V to be measured on the Y terminals Comparing two different voltage sources: Put first voltage on the X terminals Put second voltage on Y terminals

7

8 y max x min y min x max

9 What is the ratio of the frequency of vertical oscillations to the frequency of horizontal oscillations?

10 Example of an analog oscilloscope Lissajous figure, showing a harmonic relationship of 1 horizontal oscillation cycle to 3 vertical oscillation cycles.

11 The Capacitor

12

13 R V I Current flows according to Ohm's law V = IR R Wire has a break, so no current flows V R C There is no conductor between the two plates of a capacitor V So how does any current flow?

14 I The battery pushes electrons out from its negative terminal. In effect this creates a flow of positive charge out of the positive terminal But after a very short time electrons pile up near the end of the wire. They repel each other, pushing back against the pressure from the battery

15 Can we do anything to make the current flow go on longer? Suppose we expand the end of the wire so that it has a large area... Then we can flow out more charge before the 'pushback' stops the current flow

16 Can we do even better? If we could place some positive charges near the negative plate, that would attract the electrons, and reduce the tendency of the electrons to push back... But where would we get such charges from?

17 The capacitor Large area A Store a lot of charge! Small distance d

18 Defining capacitance Q C Q 2Q C 2Q V 2V Voltage is like a 'pressure' More Voltage allows storage of more charge Q / V Units: 1 Coulomb C = Q V Q = CV 1 Farad 1 Volt

19 R C At the start capacitor plates accept charges with no pushback R V So C can be replaced with a wire V I = V R R Q 0 Q 0 V 0 = Q0 C With some charge, the capacitor acts like a 'reverse battery' C R V So C can be replaced with a wire V I = V V 0 R R Q C V V = Q Q C The charge on the capacitor approaches Q = CV R Then there is no net voltage in the circuit, so I =0 V

20 If you quickly vary the voltage, then the capacitor never charges very much There is hardly any 'pushback voltage' R C R V V So in this situation C can be replaced with a wire

21 GR9677

22 V GR9677

23 GR9677

24 GR9677 Q=CV V U C Q=CV Q=CV V C U C U

25 Energy stored in a capacitor Start wth no charge on plates; the energy is zero The battery moves charge from the negative plate to the positive plate Suppose the charges on the plates have reached Q 0 and Q 0 Then the potential difference is Move an additional charge dq 0 V = Q0 C Q 0 Q 0 This needs an energy Thus the total stored energy is de = VdQ 0 = Q0 C dq0 E = Z Q Q 0 =0 Q 0 C dq0 = Q2 2C dq 0 Note that E = Q2 2C = 1 2 CV 2 = 1 2 QV

26 Charging/discharging a capacitor

27 Charging I(t) Q(t) Q(t) R C dq(t) dt = I(t) V The capacitor acts like a 'reverse battery' Solution I(t) V (t) = Q(t) C V V V (t) =I(t)R Q(t) C = I(t)R I(t) =I 0 e I 0 = V R t RC R 1 C dq(t) dt = di(t) dt R V di(t) dt = 1 RC I(t)

28 Discharging I(t) Q(t) Q(t) I(t) V (t) = Q(t) C R C R V (t) =I(t)R Q(t) C 1 C dq(t) dt di(t) dt = I(t)R = di(t) dt R = 1 RC I(t) Solution I(t) =I 0 e t RC I 0 = V 0 R = Q 0 RC Q(T )=Q 0 e t RC

29 GR9277

30 GR9277

31 GR9277

32 GR9277

33 Inductors

34 An inductor is just a coil There is no resistance So if a steady current is passing, there is no effect of the inductor... it is just a piece of ordinary wire with no resistance But if we try to change the current, the inductor does not want to allow that to happen, and it resists the change...

35 When current passes through the coil, there is a magnetic field generated (a) I =0 (b) I > 0 But a magnetic field costs energy, so we cannot immediately go from (a) to (b) What can stop the current from increasing? The coil develops a reverse voltage, which opposes the increase of current...

36 di dt > 0 How much is this reverse voltage? V / di dt V = L di dt Current through an inductor cannot change quickly: the inductor will oppose the change If we make a slow change in the current, the inductor has no effect: it can be ignored

37 39. Which two of the following circuits are highpass filters? (GRO177) (A) I and II (B) I and III (C) I and IV (D) II and III (E) II and IV

38 (GRO177) 39. Which two of the following circuits are highpass filters? (A) I and II (B) I and III (C) I and IV (D) II and III (E) II and IV

39 GR9677

40 High frequency Low frequency GR9677

41 Charging/discharging an inductor

42 Charging V (t) =L di(t) dt R L R V V I(t) I(t) The inductor acts like a 'reverse battery' V V V (t) =I(t)R L di(t) dt = I(t)R Solution I(t) =I 0 (1 e R L t ) di(t) dt = V L R L I(t) I 0 = V R

43 Discharging Current cannot suddenly stop, since the energy in the magnetic field cannot vanish suddenly... So now the inductor has to act like a 'forward battery' V (t) =L( di(t) dt ) R L R L I(t) I(t) V (t) =I(t)R Solution L di(t) dt di(t) = = I(t)R R I(t) I(t) =I 0 e R L t

44 GR In the circuit shown above, the switch S is closed at t = 0. Which of the following best represents the voltage across the inductor, as seen on an oscilloscope? (A) (B) (C) (D) (E)

45 GR In the circuit shown above, the switch S is closed at t = 0. Which of the following best represents the voltage across the inductor, as seen on an oscilloscope? (A) (B) (C) (D) (E)

46 Oscillating currents

47 An oscillating current or voltage source I = I 0 cos(!t) V = V 0 cos(!t) I 0 Average current is zero I 0 Squaring gives positive function, average is 1 2 I2 0 Root mean square current (RMS current) I rms = 1 p 2 I 0

48 Heat dissipated I 2 R = V 2 R = VI No heat dissipated R L C Heat dissipated hi 2 ir = I 2 rmsr

49 40. A series AC circuit with impedance Z consists of resistor R, inductor L, and capacitor C, as shown above. The ideal emf source has a sinusoidal output given by e e max sin wt, and the current is given by I I max sin( wt f). What is the average power dissipated in the circuit? ( I rms is the rootmeansquare current.) (A) I 2 R rms 1 2 rms (B) I R rms (C) I Z rms (D) I R cos f rms (E) I Z 2 cos f

50 40. A series AC circuit with impedance Z consists of resistor R, inductor L, and capacitor C, as shown above. The ideal emf source has a sinusoidal output given by e e max sin wt, and the current is given by I I max sin( wt f). What is the average power dissipated in the circuit? ( I rms is the rootmeansquare current.) (A) I 2 R rms 1 2 rms (B) I R rms (C) I Z rms (D) I R cos f rms (E) I Z 2 cos f

51 RLC circuits

52 (GRO177) 38. An AC circuit consists of the elements shown above, with R = 10,000 ohms, L = 25 millihenries, and C an adjustable capacitance. The AC voltage generator supplies a signal with an amplitude of 40 volts and angular frequency of 1,000 radians per second. For what value of C is the amplitude of the current maximized? (A) 4 nf (B) 40 nf (C) 4 mf (D) 40 mf (E) 400 mf

53 V = L di dt We write I = Re [ I 0 e i! t ] and just write the complex current from now on. I = I 0 e i!t di dt = i!i V =(il!)i Compare to V = IR Reactance il!

54 Q Q I Current I means that I coulombs flow into the plate each second dq dt = I Q = CV C dv dt = I V = V 0 e i!t C(i!V )=I V = I( 1 ic! ) Compare to V = IR Reactance 1 ic!

55 L C il! 1 ic! R V = V 0 e i!t R eff = R 1 ic! il! I = V R eff

56 The current is maximal when the effective resistance is minimal... I = V R eff R eff = R i( R eff 2 = R 2 ( 1 C! L!) 1 C! L!)2 If R, C, L are fixed, and we can only vary!, then R eff is minimal when! = 1 p LC At this frequency we say that the circuit is in RESONANCE

57 GR9277

58 GR9277

59 (GRO177) 38. An AC circuit consists of the elements shown above, with R = 10,000 ohms, L = 25 millihenries, and C an adjustable capacitance. The AC voltage generator supplies a signal with an amplitude of 40 volts and angular frequency of 1,000 radians per second. For what value of C is the amplitude of the current maximized? (A) 4 nf (B) 40 nf (C) 4 mf (D) 40 mf (E) 400 mf

60 (GRO177) 38. An AC circuit consists of the elements shown above, with R = 10,000 ohms, L = 25 millihenries, and C an adjustable capacitance. The AC voltage generator supplies a signal with an amplitude of 40 volts and angular frequency of 1,000 radians per second. For what value of C is the amplitude of the current maximized? (A) 4 nf (B) 40 nf (C) 4 mf (D) 40 mf (E) 400 mf

61 Challenge question

62 GR8677

Alternating Current Circuits

Alternating 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 information

AP Physics C. Electric Circuits III.C

AP 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 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

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

Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies

Ch. 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 information

Learnabout Electronics - AC Theory

Learnabout Electronics - AC Theory Learnabout Electronics - AC Theory Facts & Formulae for AC Theory www.learnabout-electronics.org Contents AC Wave Values... 2 Capacitance... 2 Charge on a Capacitor... 2 Total Capacitance... 2 Inductance...

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

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

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

Chapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively

Chapter 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 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

RLC 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 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 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

Introduction to AC Circuits (Capacitors and Inductors)

Introduction to AC Circuits (Capacitors and Inductors) Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

More 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

A capacitor is a device that stores electric charge (memory devices). A capacitor is a device that stores energy E = Q2 2C = CV 2

A 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 information

EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA

EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA EXPERIMENT 07 TO STUDY DC RC CIRCUIT AND TRANSIENT PHENOMENA DISCUSSION The capacitor is a element which stores electric energy by charging the charge on it. Bear in mind that the charge on a capacitor

More information

Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526)

Assessment 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 information

Assessment Schedule 2016 Physics: Demonstrate understanding electrical systems (91526)

Assessment 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 information

CAPACITORS / ENERGY STORED BY CAPACITORS / CHARGING AND DISCHARGING

CAPACITORS / ENERGY STORED BY CAPACITORS / CHARGING AND DISCHARGING PHYSICS A2 UNIT 4 SECTION 3: CAPACITANCE CAPACITORS / ENERGY STORED BY CAPACITORS / CHARGING AND DISCHARGING # Question CAPACITORS 1 What is current? Current is the rate of flow of charge in a circuit

More information

Alternating Currents. The power is transmitted from a power house on high voltage ac because (a) Electric current travels faster at higher volts (b) It is more economical due to less power wastage (c)

More 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

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

Physics 4 Spring 1989 Lab 5 - AC Circuits

Physics 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 information

1) Opposite charges and like charges. a) attract, repel b) repel, attract c) attract, attract

1) Opposite charges and like charges. a) attract, repel b) repel, attract c) attract, attract ) Opposite charges and like charges. a) attract, repel b) repel, attract c) attract, attract ) The electric field surrounding two equal positive charges separated by a distance of 0 cm is zero ; the electric

More 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

Version 001 CIRCUITS holland (1290) 1

Version 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 information

Impedance. Reactance. Capacitors

Impedance. Reactance. Capacitors Impedance Ohm's law describes the relationship between current and voltage in circuits that are in equilibrium- that is, when the current and voltage are not changing. When we have a situation where the

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 10 6/12/2007 Electricity and Magnetism Induced voltages and induction Self-Inductance RL Circuits Energy in magnetic fields AC circuits and EM waves Resistors, capacitors

More information

A) I B) II C) III D) IV E) V

A) I B) II C) III D) IV E) V 1. A square loop of wire moves with a constant speed v from a field-free region into a region of uniform B field, as shown. Which of the five graphs correctly shows the induced current i in the loop as

More information

SUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r.

SUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r. SUMMARY Phys 53 (University Physics II) Compiled by Prof. Erickson q 1 q Coulomb s Law: F 1 = k e r ˆr where k e = 1 4π =8.9875 10 9 N m /C, and =8.85 10 1 C /(N m )isthepermittivity of free space. Generally,

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

Chapter 30. Inductance. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow

Chapter 30. Inductance. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Chapter 30 Inductance PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Learning Goals for Chapter 30 Looking forward at how a time-varying

More information

Circuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18

Circuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18 Circuit Analysis-II Capacitors in AC Circuits Introduction ü The instantaneous capacitor current is equal to the capacitance times the instantaneous rate of change of the voltage across the capacitor.

More information

5) Ohm s Law gives the relationship between potential difference and current for a.

5) Ohm s Law gives the relationship between potential difference and current for a. ) During any process, the net charge of a closed system. a) increases b) decreases c) stays constant ) In equilibrium, the electric field in a conductor is. a) always changing b) a constant non-zero value

More information

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/ Physics GRE: Electromagnetism G. J. Loges University of Rochester Dept. of Physics & stronomy xkcd.com/567/ c Gregory Loges, 206 Contents Electrostatics 2 Magnetostatics 2 3 Method of Images 3 4 Lorentz

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

Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance

Supplemental 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 information

What happens when things change. Transient current and voltage relationships in a simple resistive circuit.

What happens when things change. Transient current and voltage relationships in a simple resistive circuit. Module 4 AC Theory What happens when things change. What you'll learn in Module 4. 4.1 Resistors in DC Circuits Transient events in DC circuits. The difference between Ideal and Practical circuits Transient

More information

Electromagnetic Induction (Chapters 31-32)

Electromagnetic Induction (Chapters 31-32) Electromagnetic Induction (Chapters 31-3) The laws of emf induction: Faraday s and Lenz s laws Inductance Mutual inductance M Self inductance L. Inductors Magnetic field energy Simple inductive circuits

More 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

ELECTRO MAGNETIC INDUCTION

ELECTRO MAGNETIC INDUCTION ELECTRO MAGNETIC INDUCTION 1) A Circular coil is placed near a current carrying conductor. The induced current is anti clock wise when the coil is, 1. Stationary 2. Moved away from the conductor 3. Moved

More information

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

Mixing Problems. Solution of concentration c 1 grams/liter flows in at a rate of r 1 liters/minute. Figure 1.7.1: A mixing problem.

Mixing Problems. Solution of concentration c 1 grams/liter flows in at a rate of r 1 liters/minute. Figure 1.7.1: A mixing problem. page 57 1.7 Modeling Problems Using First-Order Linear Differential Equations 57 For Problems 33 38, use a differential equation solver to determine the solution to each of the initial-value problems and

More information

2) As two electric charges are moved farther apart, the magnitude of the force between them.

2) As two electric charges are moved farther apart, the magnitude of the force between them. ) Field lines point away from charge and toward charge. a) positive, negative b) negative, positive c) smaller, larger ) As two electric charges are moved farther apart, the magnitude of the force between

More information

Last time. Ampere's Law Faraday s law

Last 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 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

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

Lecture 27: FRI 20 MAR

Lecture 27: FRI 20 MAR Physics 2102 Jonathan Dowling Lecture 27: FRI 20 MAR Ch.30.7 9 Inductors & Inductance Nikolai Tesla Inductors: Solenoids Inductors are with respect to the magnetic field what capacitors are with respect

More information

f = 1 T 6 a.c. (Alternating Current) Circuits Most signals of interest in electronics are periodic : they repeat regularly as a function of time.

f = 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 information

Al-Saudia Virtual Academy Pakistan Online Tuition Online Tutor Pakistan Electricity

Al-Saudia Virtual Academy Pakistan Online Tuition Online Tutor Pakistan Electricity Al-Saudia Virtual Academy Pakistan Online Tuition Online Tutor Pakistan Electricity ELECTRIC NATURE OF MATTER: The electric nature of matter means the ability of a matter to produce charge on it. The addition

More information

Chapter 33. Alternating Current Circuits

Chapter 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 information

Physics 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 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 information

a. Clockwise. b. Counterclockwise. c. Out of the board. d. Into the board. e. There will be no current induced in the wire

a. Clockwise. b. Counterclockwise. c. Out of the board. d. Into the board. e. There will be no current induced in the wire Physics 1B Winter 2012: Final Exam For Practice Version A 1 Closed book. No work needs to be shown for multiple-choice questions. The first 10 questions are the makeup Quiz. The remaining questions are

More information

Direct Current (DC) Circuits

Direct Current (DC) Circuits Direct Current (DC) Circuits NOTE: There are short answer analysis questions in the Participation section the informal lab report. emember to include these answers in your lab notebook as they will be

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

Phys 2025, First Test. September 20, minutes Name:

Phys 2025, First Test. September 20, minutes Name: Phys 05, First Test. September 0, 011 50 minutes Name: Show all work for maximum credit. Each problem is worth 10 points. Work 10 of the 11 problems. k = 9.0 x 10 9 N m / C ε 0 = 8.85 x 10-1 C / N m e

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

AP Physics C. Electricity and Magne4sm Review

AP Physics C. Electricity and Magne4sm Review AP Physics C Electricity and Magne4sm Review Electrosta4cs 30% Chap 22-25 Charge and Coulomb s Law Electric Field and Electric Poten4al (including point charges) Gauss Law Fields and poten4als of other

More information

Yell if you have any questions

Yell 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 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

Note 11: Alternating Current (AC) Circuits

Note 11: Alternating Current (AC) Circuits Note 11: Alternating Current (AC) Circuits V R No phase difference between the voltage difference and the current and max For alternating voltage Vmax sin t, the resistor current is ir sin t. the instantaneous

More information

Coulomb s constant k = 9x10 9 N m 2 /C 2

Coulomb s constant k = 9x10 9 N m 2 /C 2 1 Part 2: Electric Potential 2.1: Potential (Voltage) & Potential Energy q 2 Potential Energy of Point Charges Symbol U mks units [Joules = J] q 1 r Two point charges share an electric potential energy

More information

DOING PHYSICS WITH MATLAB

DOING PHYSICS WITH MATLAB DOING PHYSIS WITH MATAB THE FINITE DIFFERENE METHOD FOR THE NUMERIA ANAYSIS OF IRUITS ONTAINING RESISTORS, APAITORS AND INDUTORS MATAB DOWNOAD DIRETORY N01.m Voltage and current for a resistor, capacitor

More information

Chapter 28. Direct Current Circuits

Chapter 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 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

Capacitance. A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

Capacitance. A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge. Capacitance A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge. a) Parallel-plate capacitor connected to battery. (b) is a circuit

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

18 - ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS ( Answers at the end of all questions ) Page 1

18 - ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS ( Answers at the end of all questions ) Page 1 ( Answers at the end of all questions ) Page ) The self inductance of the motor of an electric fan is 0 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of 8 µ F (

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

Physics Will Farmer. May 5, Physics 1120 Contents 2

Physics Will Farmer. May 5, Physics 1120 Contents 2 Physics 1120 Will Farmer May 5, 2013 Contents Physics 1120 Contents 2 1 Charges 3 1.1 Terms................................................... 3 1.2 Electric Charge..............................................

More information

[1] (b) Fig. 1.1 shows a circuit consisting of a resistor and a capacitor of capacitance 4.5 μf. Fig. 1.1

[1] (b) Fig. 1.1 shows a circuit consisting of a resistor and a capacitor of capacitance 4.5 μf. Fig. 1.1 1 (a) Define capacitance..... [1] (b) Fig. 1.1 shows a circuit consisting of a resistor and a capacitor of capacitance 4.5 μf. S 1 S 2 6.3 V 4.5 μf Fig. 1.1 Switch S 1 is closed and switch S 2 is left

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

Gen. Phys. II Exam 2 - Chs. 21,22,23 - Circuits, Magnetism, EM Induction Mar. 5, 2018

Gen. Phys. II Exam 2 - Chs. 21,22,23 - Circuits, Magnetism, EM Induction Mar. 5, 2018 Gen. Phys. II Exam 2 - Chs. 21,22,23 - Circuits, Magnetism, EM Induction Mar. 5, 2018 Rec. Time Name For full credit, make your work clear. Show formulas used, essential steps, and results with correct

More information

MODULE I. Transient Response:

MODULE I. Transient Response: Transient Response: MODULE I The Transient Response (also known as the Natural Response) is the way the circuit responds to energies stored in storage elements, such as capacitors and inductors. If a capacitor

More information

PHYS 241 EXAM #2 November 9, 2006

PHYS 241 EXAM #2 November 9, 2006 1. ( 5 points) A resistance R and a 3.9 H inductance are in series across a 60 Hz AC voltage. The voltage across the resistor is 23 V and the voltage across the inductor is 35 V. Assume that all voltages

More 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

1 2 U CV. K dq I dt J nqv d J V IR P VI

1 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 information

PHYS 1441 Section 001 Lecture #23 Monday, Dec. 4, 2017

PHYS 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 information

RADIO AMATEUR EXAM GENERAL CLASS

RADIO AMATEUR EXAM GENERAL CLASS RAE-Lessons by 4S7VJ 1 CHAPTER- 2 RADIO AMATEUR EXAM GENERAL CLASS By 4S7VJ 2.1 Sine-wave If a magnet rotates near a coil, an alternating e.m.f. (a.c.) generates in the coil. This e.m.f. gradually increase

More information

Experiment Guide for RC Circuits

Experiment Guide for RC Circuits Guide-P1 Experiment Guide for RC Circuits I. Introduction 1. Capacitors A capacitor is a passive electronic component that stores energy in the form of an electrostatic field. The unit of capacitance is

More information

MAY/JUNE 2006 Question & Model Answer IN BASIC ELECTRICITY 194

MAY/JUNE 2006 Question & Model Answer IN BASIC ELECTRICITY 194 MAY/JUNE 2006 Question & Model Answer IN BASIC ELECTRICITY 194 Question 1 (a) List three sources of heat in soldering (b) state the functions of flux in soldering (c) briefly describe with aid of diagram

More information

Capacitor. Capacitor (Cont d)

Capacitor. Capacitor (Cont d) 1 2 1 Capacitor Capacitor is a passive two-terminal component storing the energy in an electric field charged by the voltage across the dielectric. Fixed Polarized Variable Capacitance is the ratio of

More information

PHYS 2135 Exam II March 20, 2018

PHYS 2135 Exam II March 20, 2018 Exam Total /200 PHYS 2135 Exam II March 20, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each. Choose the best or most nearly correct answer. For questions 6-9, solutions must

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

Lab 10: DC RC circuits

Lab 10: DC RC circuits Name: Lab 10: DC RC circuits Group Members: Date: TA s Name: Objectives: 1. To understand current and voltage characteristics of a DC RC circuit 2. To understand the effect of the RC time constant Apparatus:

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

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

2. The following diagram illustrates that voltage represents what physical dimension?

2. The following diagram illustrates that voltage represents what physical dimension? BioE 1310 - Exam 1 2/20/2018 Answer Sheet - Correct answer is A for all questions 1. A particular voltage divider with 10 V across it consists of two resistors in series. One resistor is 7 KΩ and the other

More information

b) (4) How large is the current through the 2.00 Ω resistor, and in which direction?

b) (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 information

Physics 2B Winter 2012 Final Exam Practice

Physics 2B Winter 2012 Final Exam Practice Physics 2B Winter 2012 Final Exam Practice 1) When the distance between two charges is increased, the force between the charges A) increases directly with the square of the distance. B) increases directly

More information

M. C. Escher: Waterfall. 18/9/2015 [tsl425 1/29]

M. C. Escher: Waterfall. 18/9/2015 [tsl425 1/29] M. C. Escher: Waterfall 18/9/2015 [tsl425 1/29] Direct Current Circuit Consider a wire with resistance R = ρl/a connected to a battery. Resistor rule: In the direction of I across a resistor with resistance

More information

Electrical Engineering Fundamentals for Non-Electrical Engineers

Electrical Engineering Fundamentals for Non-Electrical Engineers Electrical Engineering Fundamentals for Non-Electrical Engineers by Brad Meyer, PE Contents Introduction... 3 Definitions... 3 Power Sources... 4 Series vs. Parallel... 9 Current Behavior at a Node...

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

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

CHEM*3440. Current Convention. Charge. Potential Energy. Chemical Instrumentation. Rudimentary Electronics. Topic 3

CHEM*3440. Current Convention. Charge. Potential Energy. Chemical Instrumentation. Rudimentary Electronics. Topic 3 urrent onvention HEM*3440 hemical nstrumentation Topic 3 udimentary Electronics ONENTON: Electrical current flows from a region of positive potential energy to a region of more negative (or less positive)

More information

REUNotes08-CircuitBasics May 28, 2008

REUNotes08-CircuitBasics May 28, 2008 Chapter One Circuits (... introduction here... ) 1.1 CIRCUIT BASICS Objects may possess a property known as electric charge. By convention, an electron has one negative charge ( 1) and a proton has one

More information

CHAPTER 22 ELECTROMAGNETIC INDUCTION

CHAPTER 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 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

PY3107 Experimental Physics II

PY3107 Experimental Physics II PY3107 Experimental Physics II ock-in Amplifiers MP aughan and F Peters Related Experiments ock-in ab ignal processing and phase sensitive detection using a lock-in amplifier The problem The signal to

More information