# Energy / Dielectrics in Capacitors

Save this PDF as:

Size: px
Start display at page:

Download "Energy / Dielectrics in Capacitors"

## Transcription

1 Energy / Dielectrics in apacitors Polar dielectrics, like Water. In an Electric field Phys Lecture G. Rybka Q/ Q Q/ U Useful stuff Q Q

2 We ended last time looking at this clicker Q 0 3 Q 3 Q 3 Which of the following is NOT necessarily true: A) 0 B) total > ) 3 D) Q Q 3 E) + 3 is in parallel with battery (same ) total is in parallel with 3 ;; total + 3 Q: When might this be true? Q and Q 3 same since capacitors in series in parallel with combination of and 3 ;; same Δ

3 Reminder: Energy of a apacitor We obtain the energy stored in a charged capacitor by alculating the work provided (usually by a battery) to charge a capacitor to +/- Q: Incremental work dw needed to add dq to capacitor at voltage : - + Q/ q dw dq( ) dq The total work W to charge to Q is then given by: W Q qdq 0 Q We will use U as in Potential Energy Three equivalent forms: W U Q Q

4 licker Two identical parallel plate capacitors are connected to a battery. is then disconnected from the battery and the separation between the plates of both capacitors is doubled. d d d d What is the relation between U, the energy stored in, and U, the energy stored in? (a) U < U (b) U U (c) U > U After The charge on has not changed. The voltage on has not changed. U ½ Q /;; smaller;; U up U ½ ;; smaller;; U down Or, think that the work done to separate the plates with fixed charge in meant takes more Energy And, Energy in decreased. harge must leave in order to reduce the electric field so that the potential difference remains the same.

5 Questions Suppose the capacitor shown here is charged to Q and then the battery disconnected. d A Now suppose I pull the plates further apart so that the final separation is d. How do the quantities Q, U,, E, change? Q: U: : E: : remains the same.. no way for charge to leave. increases.. add energy to system by separating decreases.. Separation d increases;; A/d remains the same.. depends only on charge density increases.. equal to E x d, and d increases How much do these quantities change answers: d U d d U d d d

6 Dielectrics Empirical observation: Yes, it s an insulator Inserting a non-conducting material between the plates of a capacitor changes the ALUE of the capacitance. Definition: The dielectric constant of a material is the ratio of the capacitance when filled with the dielectric to that without it. i.e. 0 is always > (e.g., glass 5.6;; water 78)

7 Dielectric onstants Of arious Materials

8 Dielectrics By adding a dielectric you are just making a new capacitor with larger capacitance (factor of ) 0 Q Q A good thing because It is hard to make big capacitors with just air gaps Permits more energy to be stored than otherwise

9 What is going on? Parallel Plate Example harge a parallel plate capacitor filled with vacuum (air) to potential difference 0. Q 0 0 is deposited on each plate. E 0 σ/ε 0 Insert material with dielectric constant. harge Q remains constant Induced dipoles in material align Bulk middle is neutral Effective opposite E field added to original field gives SMALLER net E between plates: E E 0 / E d à smaller for same Q. Q/ à 0

10 What about GAUSS' LAW? How can field decrease if charge remains the same?? Answer: the dielectric becomes polarized in the presence of the field due to Q. E E 0» The molecules partially align with the field.» The field inside the dielectric (from the dipoles) opposes the original field and is responsible for the reduction in the effective field Rewrite Gauss' Law in presence of a dielectric:! E! ds q 0 ε0 ε 0 E ds q This form of Gauss' Law can be used in vacuum or dielectric alike where q represents the "free" charge.!!

11 licker Two parallel plate capacitors are identical except has half of the space between the plates filled with a material of dielectric constant. Both capacitors have charge Q ompare E, the electric field in the air of, and E, the electric field in the air of +Q E? -Q +Q E? -Q (a) E < E (b) E E (c) E > E The key here is to realize that the electric field in the air in must be equal to the electric field in the dielectric in!! The top plane is a conductor à equipotential surface. The bottom plane is a conductor à equipotential surface. is proportional to E d For this to happen, the charge density on each plane must be nonuniform to create equal electric fields!! Since >, for the same charge, <. onsequently, E < E.

12 heckpoint 8 Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After has been charged and disconnected, it is filled with a dielectric. The dielectric increases ;; > Q remains the same Q/ so decreases Alternately, recall E reduced à E E 0 /

13 heckpoint 0 Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After has been charged and disconnected, it is filled with a dielectric. A) B) ) Just learned > for same Q, so Recall Also, since Q unchanged, larger implies lower U

14 heckpoint The two capacitors are now connected to each other by wires as shown. How will the charge redistribute itself, if at all? A. The charges will flow so that the charge on will become equal to the charge on. B. The charges will flow so that the energy stored in will become equal to the energy stored in. The charges will flow so that the potential difference across will become the same as the potential difference across. D. No charges will flow. The charge on the capacitors will remain what it was before they were connected. must be the same! Q: U: Q Q Q Q U U U U

15 licker and Typical alculation x 0 0 x 0 /4 An air- gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. What is Q f, the final charge on the capacitor? First a licker: What changes when the dielectric added? A) Only B) only Q ) only D) and Q E) and Q Adding dielectric changes the physical capacitor does not change and changes changes Q changes

16 x 0 0 alculation Now, Strategic Analysis: alculate new capacitance Apply definition of capacitance to determine Q onsider to be two capacitances, and, in parallel x 0 /4 An air- gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. What is Q f, the final charge on the capacitor? Parallel plate capacitor: ε 0 A/d A 3 / 4 A 0 d d 0 3 / 4 (ε 0 A 0 /d 0 ) 3 / 4 0

17 alculation x 0 0 An air- gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. 3 / 4 0 What is Q f, the final charge on the capacitor? Parallel plate capacitor filled with dielectric: ε 0 A/d A / 4 A 0 d d 0 ¼(ε 0 A 0 /d 0 ) / 4 0

18 alculation x 0 0 An air- gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. What is Q f, the final charge on the capacitor? 3 / 4 0 / 4 0 parallel combination of and : + 0 ( 3 / 4 + / 4 )

19 alculation x 0 0 An air- gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. 3 / 4 0 What is Q f, the final charge on the capacitor? / 4 0 What is Q? 0 ( 3 / 4 + / 4 ) Q Q f Q

20 Reminder: Where is the Energy Stored? Answer: in the Electric field itself onsider energy stored by a constant field in a parallel plate capacitor: U Q The Electric field is given by: E Q ( Aε / d ) The energy density u in the field is given by: σ Q Þ ε 0 ε 0 A U E ε0ad u U volume U Ad 0 ε0e Units: 3 J m

21 licker b a onsider two cylindrical capacitors, each of length L. has inner radius a and outer radius b. has inner radius a and outer radius b. If both capacitors are given the same amount of charge, what is the relation between U, the energy stored in, and U, the energy stored in? b a (a) U < U (b) U U (c) U > U U U Q Q U U ln ln ( b / a) ( b / a) Q πε0l b ln a

22 Energy expressions in apacitors (various forms) From: Q/ Q Q/

### Capacitance and Dielectrics. Physics 231 Lecture 4-1

apacitance and Dielectrics Physics 3 Lecture 4- apacitors Device for storing electrical energy which can then be released in a controlled manner onsists of two conductors, carrying charges of q and q,

More information

### Capacitance. IV. Capacitance. 1a. Leyden Jar. Battery of Leyden Jars. A. The Electric Condenser. B. Dielectrics. C. Energy in Electric Field

IV. apacitance apacitance A. The Electric ondenser B. Dielectrics Revised: Feb5. Energy in Electric Field Sections.7-9 and 3.8 in book A. The Electric ondenser 3. History of the apacitor 4 ) History of

More information

### Fall 12 PHY 122 Homework Solutions #4

Fall 12 PHY 122 Homework Solutions #4 Chapter 23 Problem 45 Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10-30 C.m at a point 4.1 x 10-9 m away if this point is (a)

More information

### Chapter 26. Capacitance and Dielectrics

Chapter 26 Capacitance and Dielectrics Capacitors Capacitors are devices that store electric charge Examples where capacitors are used: radio receivers filters in power supplies energy-storing devices

More information

### February 6. Physics 272. Spring 2014 Prof. Philip von Doetinchem

Physics 272 February 6 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 216 Summary Charges

More information

### physics 111N electric potential and capacitance

physics 111N electric potential and capacitance electric potential energy consider a uniform electric field (e.g. from parallel plates) note the analogy to gravitational force near the surface of the Earth

More information

### Capacitors. February 5, 2014 Physics for Scientists & Engineers 2, Chapter 24 1

Capacitors February 5, 2014 Physics for Scientists & Engineers 2, Chapter 24 1 Review! The electric potential energy stored in a capacitor is given by! The field energy density stored in a parallel plate

More information

### Coefficient of Potential and Capacitance

Coefficient of Potential and Capacitance Lecture 12: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We know that inside a conductor there is no electric field and that

More information

### Electric Fields in Dielectrics

Electric Fields in Dielectrics Any kind of matter is full of positive and negative electric charges. In a dielectric, these charges cannot move separately from each other through any macroscopic distance,

More information

### Electricity & Optics

Physics 24100 Electricity & Optics Lecture 9 Chapter 24 sec. 3-5 Fall 2012 Semester Matthew Jones Thursday s Clicker Question To double the capacitance of a parallel plate capacitor, you should: (a) Double

More information

### Capacitance, Resistance, DC Circuits

This test covers capacitance, electrical current, resistance, emf, electrical power, Ohm s Law, Kirchhoff s Rules, and RC Circuits, with some problems requiring a knowledge of basic calculus. Part I. Multiple

More information

### Problem Solving 4: Capacitance, Stored Energy, Capacitors in Parallel and Series, Dielectrics

Problem Solving 4: Capacitance, Stored Energy, Capacitors in Parallel and Series, Dielectrics Section Table Names Hand in one copy per group at the end of the Friday Problem Solving Session. OBJECTIVES

More information

### Chapter 25: Capacitance

Chapter 25: Capacitance Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone. Albert Einstein 25.1 Introduction Whenever

More information

### Lesson 6 Capacitors and Capacitance Lawrence B. Rees 2007. You may make a single copy of this document for personal use without written permission.

Lesson 6 apacitors and apacitance Lawrence B. Rees 7. You may make a single copy of this document for personal use without written permission. 6. Introduction In 745 Pieter van Musschenbroek, while trying

More information

### Chapter 7: Polarization

Chapter 7: Polarization Joaquín Bernal Méndez Group 4 1 Index Introduction Polarization Vector The Electric Displacement Vector Constitutive Laws: Linear Dielectrics Energy in Dielectric Systems Forces

More information

### Exam 1 Solutions. PHY2054 Fall 2014. Prof. Paul Avery Prof. Andrey Korytov Sep. 26, 2014

Exam 1 Solutions Prof. Paul Avery Prof. Andrey Korytov Sep. 26, 2014 1. Charges are arranged on an equilateral triangle of side 5 cm as shown in the diagram. Given that q 1 = 5 µc and q 2 = q 3 = 2 µc

More information

### Chapter 4. Electrostatic Fields in Matter

Chapter 4. Electrostatic Fields in Matter 4.1. Polarization A neutral atom, placed in an external electric field, will experience no net force. However, even though the atom as a whole is neutral, the

More information

### 2 A Dielectric Sphere in a Uniform Electric Field

Dielectric Problems and Electric Susceptability Lecture 10 1 A Dielectric Filled Parallel Plate Capacitor Suppose an infinite, parallel plate capacitor with a dielectric of dielectric constant ǫ is inserted

More information

### 1 of 7 3/23/2010 2:45 PM

1 of 7 3/23/2010 2:45 PM Chapter 30 Homework Due: 8:00am on Tuesday, March 23, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]

More information

### Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b to 2Q, while keeping the conductors in the same positions.

More information

### CHAPTER 26 ELECTROSTATIC ENERGY AND CAPACITORS

CHAPTER 6 ELECTROSTATIC ENERGY AND CAPACITORS. Three point charges, each of +q, are moved from infinity to the vertices of an equilateral triangle of side l. How much work is required? The sentence preceding

More information

### Chapter 17: Electric Potential

hapter 17: Electric Potential Electric Potential Energy Electric Potential How are the E-field and Electric Potential related? Motion of Point harges in an E-field apacitors Dielectrics 1 Electric Potential

More information

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 802 Spring 2013 Conflict Exam Two Solutions Problem 1 (25 points): answers without work shown will not be given any credit A uniformly charged

More information

### Physics 1653 Exam 3 - Review Questions

Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

More information

Last Name: First Name: Physics 102 Spring 2006: Exam #2 Multiple-Choice Questions 1. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged

More information

### RC Cola. I was really confused about the calculus that lead to the current equation. Could you derive this in class? - We ll do that today

ola was really confused about the calculus that lead to the current euation. ould you derive this in class? - We ll do that today Phys 122 Lecture 15 G. ybka Business Exam Thursday! (no circuits on this

More information

### HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 22.P.053 The figure below shows a portion of an infinitely

More information

### PHYS-2020: General Physics II Course Lecture Notes Section II

PHYS-2020: General Physics II Course Lecture Notes Section II Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and

More information

### ( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011

Phy 49 Fall 11 Solutions 1. Three charges form an equilateral triangle of side length d = 1 cm. The top charge is q = - 4 μc, while the bottom two are q1 = q = +1 μc. What is the magnitude of the net force

More information

### 14 Capacitors in Series & Parallel

hapter 4 apacitors in Series & Parallel 4 apacitors in Series & Parallel The method of ever-simpler circuits that we used for circuits with more than one resistor can also be used for circuits having more

More information

### RC Circuits. Honors Physics Note 002 c Alex R. Dzierba Honors Physics P222 - Spring, 2004

R ircuits Honors Physics Note 2 c Alex R. Dziera Honors Physics P222 - Spring, 24 Introduction This note concerns the ehavior of circuits that include cominations of resistors, capacitors and possily a

More information

### LAB ELEC3.COMP From Physics with Computers, Vernier Software and Technology, 2003

APAITORS LAB ELE3.OMP From Physics with omputers, Vernier Software and Technology, 2003 INTRODUTION The charge q on a capacitor s plate is proportional to the potential difference V across the capacitor.

More information

### Exam 2 Practice Problems Part 1 Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Exam Practice Problems Part 1 Solutions Problem 1 Electric Field and Charge Distributions from Electric Potential An electric potential V ( z

More information

### Chapter 18 Electric Forces and Electric Fields. Key Concepts:

Chapter 18 Lectures Monday, January 25, 2010 7:33 AM Chapter 18 Electric Forces and Electric Fields Key Concepts: electric charge principle of conservation of charge charge polarization, both permanent

More information

### Pre-Lab 7 Assignment: Capacitors and RC Circuits

Name: Lab Partners: Date: Pre-Lab 7 Assignment: Capacitors and RC Circuits (Due at the beginning of lab) Directions: Read over the Lab Handout and then answer the following questions about the procedures.

More information

### Electrical Energy, Potential and Capacitance. AP Physics B

Electrical Energy, Potential and Capacitance AP Physics B Electric Fields and WORK In order to bring two like charges near each other work must be done. In order to separate two opposite charges, work

More information

### AP2 Electrostatics. Three point charges are located at the corners of a right triangle as shown, where q 1. are each 1 cm from q 3.

Three point charges are located at the corners of a right triangle as shown, where q 1 = q 2 = 3 µc and q 3 = -4 µc. If q 1 and q 2 are each 1 cm from q 3, what is the magnitude of the net force on q 3?

More information

### Experiment: RC Circuits

Phy23: General Physics III Lab page 1 of 5 OBJETIVES Experiment: ircuits Measure the potential across a capacitor as a function of time as it discharges and as it charges. Measure the experimental time

More information

### EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13

CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how

More information

### Electric Field Mapping Lab 3. Precautions

HB 09-25-07 Electric Field Mapping Lab 3 1 Electric Field Mapping Lab 3 Equipment mapping board, U-probe, resistive boards, templates, dc voltmeter (431B), 4 long leads, 16 V dc for wall strip Reading

More information

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the voltage at a point in space is zero, then the electric field must be A) zero. B) positive.

More information

### Multiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields

Multiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields 63 When a positive charge q is placed in the field created by two other charges Q 1 and Q 2, each a distance r away from q, the

More information

### Electrostatics Problems

Name AP Physics B Electrostatics Problems Date Mrs. Kelly 1. How many excess electrons are contained in a charge of 30 C? 2. Calculate and compare the gravitational and electrostatic force between an electron

More information

### Capacitors in Circuits

apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively

More information

### Capacitors and Resistors: Capacitor Time Constants

Not the Flux Kind A capacitor is comprised of a pair of conductors surrounding some non-conducting region (either empty space or a dielectric). The point of these things is to store energy in the electric

More information

### Course Syllabus: AP Physics C Electricity and Magnetism

Course Syllabus: AP Physics C Electricity and Magnetism Course Description: AP Physics C is offered as a second year physics course to students who are planning to major in the physical sciences or in

More information

### Electric Forces and Fields. Charge Coulomb's Law Electric Fields Conductors & Insulators Parallel plates Dipoles

Electric Forces and Fields Charge Coulomb's Law Electric Fields Conductors & Insulators Parallel plates Dipoles 1 Friction causes these effects Pollen sticks to bees Dust sticks to TV Static cling of clothes

More information

### Problem 4.48 Solution:

Problem 4.48 With reference to Fig. 4-19, find E 1 if E 2 = ˆx3 ŷ2+ẑ2 (V/m), ε 1 = 2ε 0, ε 2 = 18ε 0, and the boundary has a surface charge density ρ s = 3.54 10 11 (C/m 2 ). What angle does E 2 make with

More information

### Capacitors. We charge a capacitor by connecting the two plates to a potential difference, such as a battery:

RC Circuits PHYS 1112L Capacitors A capacitor is an electrical component that stores charge. The simplest capacitor is just two charged metal plates separated by a non-conducting material: In the diagram

More information

### Lecture 14 Capacitance and Conductance

Lecture 14 Capacitance and Conductance ections: 6.3, 6.4, 6.5 Homework: ee homework file Definition of Capacitance capacitance is a measure of the ability of the physical structure to accumulate electrical

More information

### Experiment 2: Faraday Ice Pail

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2009 OBJECTIVES Experiment 2: Faraday Ice Pail 1. To explore the charging of objects by friction and by contact. 2. To explore the

More information

### Physics 2220 Module 09 Homework

Physics 2220 Module 09 Homework 01. A potential difference of 0.050 V is developed across the 10-cm-long wire of the figure as it moves though a magnetic field perpendicular to the page. What are the strength

More information

### Lab 4 - Capacitors & RC Circuits

Lab 4 Capacitors & RC Circuits L41 Name Date Partners Lab 4 Capacitors & RC Circuits OBJECTIVES To define capacitance and to learn to measure it with a digital multimeter. To explore how the capacitance

More information

### Electromagnetic Induction

Electromagnetic Induction Lecture 29: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Mutual Inductance In the last lecture, we enunciated the Faraday s law according to

More information

### Experiment 9 ~ RC Circuits

Experiment 9 ~ RC Circuits Objective: This experiment will introduce you to the properties of circuits that contain both resistors AND capacitors. Equipment: 18 volt power supply, two capacitors (8 µf

More information

### Chapter 18. Electric Forces and Electric Fields

My lecture slides may be found on my website at http://www.physics.ohio-state.edu/~humanic/ ------------------------------------------------------------------- Chapter 18 Electric Forces and Electric Fields

More information

### Capacitance. Apparatus: RC (Resistor-Capacitor) circuit box, voltmeter, power supply, cables

apacitance Objective: To observe the behavior of a capacitor charging and discharging through a resistor; to determine the effective capacitance when capacitors are connected in series or parallel. Apparatus:

More information

### Exam 1 Practice Problems Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8 Spring 13 Exam 1 Practice Problems Solutions Part I: Short Questions and Concept Questions Problem 1: Spark Plug Pictured at right is a typical

More information

### How to transform, with a capacitor, thermal energy into usable work.

How to transform, with a capacitor, thermal energy into usable work. E. N. Miranda 1 CONICET CCT Mendoza 55 Mendoza, Argentina and Facultad de Ingeniería Universidad de Mendoza 55 Mendoza, Argentina Abstract:

More information

### " - angle between l and a R

Magnetostatic Fields According to Coulomb s law, any distribution of stationary charge produces a static electric field (electrostatic field). The analogous equation to Coulomb s law for electric fields

More information

### Measurement of Capacities, Charging and Discharging of Capacitors

95 arl von Ossietzky niversity Oldenburg Faculty V - Institute of Physics Module Introductory laboratory course physics Part I Measurement of apacities, harging and Discharging of apacitors Keywords: apacitor,

More information

### PH 212 07-31-2015 Physics 212 Exam-3 Solution NAME: Write down your name also on the back of the package of sheets you turn in.

PH 1 7-31-15 Physics 1 Exam-3 Solution NAME: Write down your name also on the back of the package of sheets you turn in. SIGNATURE and ID: Return this hard copy exam together with your other answer sheets.

More information

### Answer, Key Homework 11 David McIntyre 1 1 A

nswer, Key Homework 11 avid Mcntyre 1 This print-out should have 36 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

More information

### A wave lab inside a coaxial cable

INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)76273-X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera

More information

### Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).

INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes

More information

### Recitation 6 Chapter 21

Recitation 6 hapter 21 Problem 35. Determine the current in each branch of the circuit shown in Figure P21.35. 3. Ω 5. Ω 1. Ω 8. Ω 1. Ω ɛ 2 4 12 Let be the current on the left branch (going down), be the

More information

### AP Physics C: Electricity and Magnetism: Syllabus 2

AP Physics C: Electricity and Magnetism: Syllabus 2 Scoring Components SC1 SC2 SC SC SC5 SC6 SC7 The course provides and provides instruction in electrostatics. The course provides and provides instruction

More information

### Ch. 20 Electric Circuits

Ch. 0 Electric Circuits 0. Electromotive Force Every electronic device depends on circuits. Electrical energy is transferred from a power source, such as a battery, to a device, say a light bulb. Conducting

More information

### ELECTRICITYt. Electromagnetism

ELECTRICITYt Electromagnetism Subject area : Physics Topic focus : magnetic properties, magnetic field, the Earth s magnetic field, magnetic field of an electric wire. Learning Aims : Polarity of bar magnets

More information

### Slide 1 / 26. Inductance. 2011 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

### Force on Moving Charges in a Magnetic Field

[ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

More information

### Problem 1 (25 points)

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2012 Exam Three Solutions Problem 1 (25 points) Question 1 (5 points) Consider two circular rings of radius R, each perpendicular

More information

### Exercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F

Exercises on Voltage, Capacitance and Circuits Exercise 1.1 Instead of buying a capacitor, you decide to make one. Your capacitor consists of two circular metal plates, each with a radius of 5 cm. The

More information

### Physics 9 Summer 2010 Midterm Solutions

Physics 9 Summer 010 Midterm s For the midterm, you may use one sheet of notes with whatever you want to put on it, front and back Please sit every other seat, and please don t cheat! If something isn

More information

### Capacitors and a Galvanometer

Capacitors and a Galvanometer Object To investigate, understand and verify how capacitances are added together both in series and parallel and to consider the leakage of a capacitor. Also to employ a galvanometer

More information

### Vessel holding water. Charged capacitor. Questions. Question 1

ELEN236 Capacitors This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

More information

### Your Comments. This was a very confusing prelecture. Do you think you could go over thoroughly how the LC circuits work qualitatively?

Your omments I am not feeling great about this mierm...some of this stuff is really confusing still and I don't know if I can shove everything into my brain in time, especially after spring break. an you

More information

### Electric Forces & Fields, Gauss s Law, Potential

This test covers Coulomb s Law, electric fields, Gauss s Law, electric potential energy, and electric potential, with some problems requiring a knowledge of basic calculus. Part I. Multiple Choice +q +2q

More information

### Profs. A. Petkova, A. Rinzler, S. Hershfield. Exam 2 Solution

PHY2049 Fall 2009 Profs. A. Petkova, A. Rinzler, S. Hershfield Exam 2 Solution 1. Three capacitor networks labeled A, B & C are shown in the figure with the individual capacitor values labeled (all units

More information

### Chapter 22: Electric Flux and Gauss s Law

22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we

More information

### Capacitors. Goal: To study the behavior of capacitors in different types of circuits.

Capacitors Goal: To study the behavior of capacitors in different types of circuits. Lab Preparation A capacitor stores electric charge. A simple configuration for a capacitor is two parallel metal plates.

More information

### ELECTRICAL CHARACTERISTICS OF TRANSMISSION LINES

Page 1 of 6 ELECTRICAL CHARACTERISTICS OF TRANSMISSION LINES Transmission lines are generally characterized by the following properties: balance-to-ground characteristic impedance attenuation per unit

More information

### v 2 = v a(x x 0 ) and v = 0 a = v2 0 2d = K md F net = qe = ma E = ma e = K ed = V/m dq = λ ds de r = de cosθ = 1 λ ds = r dθ E r =

Physics 11 Honors Final Exam Spring 003 Name: Section: Closed book exam. Only one 8.5 11 formula sheet (front and back side) can be used. Calculators are allowed. Use the scantron forms (pencil only!)

More information

### Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

More information

### The current that flows is determined by the potential difference across the conductor and the resistance of the conductor (Ohm s law): V = IR P = VI

PHYS1000 DC electric circuits 1 Electric circuits Electric current Charge can move freely in a conductor if an electric field is present; the moving charge is an electric current (SI unit is the ampere

More information

### Components in Series, Parallel, and Combination

Components in Series, Parallel, and Combination Kirchoff s Laws VOLTAGE LAW: A series circuit of voltages across the various components must add up to be equal to the voltage applied to the circuit. CURRENT

More information

### HW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 24.P.021 (a) Find the energy stored in a 20.00 nf capacitor

More information

### Last time : energy storage elements capacitor.

Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because

More information

### Gravitational Fields: Review

Electric Fields Review of gravitational fields Electric field vector Electric fields for various charge configurations Field strengths for point charges and uniform fields Work done by fields & change

More information

### 104 Practice Exam 2-3/21/02

104 Practice Exam 2-3/21/02 1. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero

More information

### Physics 2212 GH Quiz #4 Solutions Spring 2015

Physics 1 GH Quiz #4 Solutions Spring 15 Fundamental Charge e = 1.6 1 19 C Mass of an Electron m e = 9.19 1 31 kg Coulomb constant K = 8.988 1 9 N m /C Vacuum Permittivity ϵ = 8.854 1 1 C /N m Earth s

More information

### Lab 5 RC Circuits. What You Need To Know: Physics 226 Lab

Lab 5 R ircuits What You Need To Know: The Physics In the previous two labs you ve dealt strictly with resistors. In today s lab you ll be using a new circuit element called a capacitor. A capacitor consists

More information

### Magnetic Dipoles. Magnetic Field of Current Loop. B r. PHY2061 Enriched Physics 2 Lecture Notes

Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to

More information

### 45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across?

PHYS Practice Problems hapters 8- hapter 8. 45. The peak value of an alternating current in a 5-W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,

More information

### CAPACITIVE REACTANCE. We have already discussed the operation of a capacitor in a DC circuit, however let's just go over the main principles again.

Reading 13 Ron Bertrand VK2DQ http://www.radioelectronicschool.com CAPACITOR IN A DC CIRCUIT CAPACITIVE REACTANCE We have already discussed the operation of a capacitor in a DC circuit, however let's just

More information

### The oil condition sensor increases the function range of the thermal oil level sensor. The oil condition sensor measures the following variables:

WDS Wiring Diagram System meeknet.co.uk/e64 Page 1 of 6 Oil condition sensor Oil condition sensor The oil condition sensor increases the function range of the thermal oil level sensor. The oil condition

More information

### Chapter 11- Electricity

Chapter 11- Electricity Course Content Definition of Electricity Circuit Diagrams Series and Parallel Circuits Calculating total resistances Measurement of Electricity Ammeters and Voltmeters Ohm s Law

More information

### 1. Purpose Experimental verification of an exponential dependency between two physical quantities. Perform numerical evaluations.

Experimental Science P9: Capacitor charge and discharge 1. Purpose Experimental verification of an exponential dependency between two physical quantities. Perform numerical evaluations. 2. Introduction

More information

### CHAPTER 19: DC Circuits. Answers to Questions

HAPT 9: D ircuits Answers to Questions. The birds are safe because they are not grounded. Both of their legs are essentially at the same voltage (the only difference being due to the small resistance of

More information

### Chapter 3. Gauss s Law

3 3 3-0 Chapter 3 Gauss s Law 3.1 Electric Flux... 3-2 3.2 Gauss s Law (see also Gauss s Law Simulation in Section 3.10)... 3-4 Example 3.1: Infinitely Long Rod of Uniform Charge Density... 3-9 Example

More information