Continuing our discussion on Capacitors
|
|
- Dulcie Irma Carr
- 5 years ago
- Views:
Transcription
1 Continuing our discussion on Capacitors
2 Cylindrical Capacitors (I) Two concentric conducting cylinders of length L and radii R and R. We determine the electric field between the cylinders using Gauss s Law: we imagine a cylinder in between the other two. The enclosed charge is Q, and the field is radial: E(πrL)=Q/ε 0 R < R << L r E = V C = πlε = V Q V 0 V Q r rˆ where V is the magnitude of = R R πlε 0 = ln( R R ) r r E dr = R R Q Q dr = ln( R πlε r πlε 0 the potential difference...a 0 R ) positive quantity
3 Cylindrical Capacitors (II) If (R R )<< L, then the cylindrical capacitor acts much like a parallel plate capacitor. We revisit our integral for the potential difference. narrow, so we approximate the integral by taking dr V C = V V This has the form of and plate area = R R πrlε 0 R R A = r r E dr = R R πrl (the area of Q Q R dr πlε r πlε 0 The interval from R 0 the curved surface of a cylinder). ( R R ) is very / the capacitance of a parallel plate capacitor with spacing d = R R R R R and r to R R. R
4 Spherical Capacitors Two concentric conducting spheres of radii R and R. (hard to build ) R < R We know already the field between the two spheres: it is radial with magnitude E=kQ/r. R Q Q R V C = = V Q V = V k = R R R R r r E dr = = 4πε 0 ( R R ) R R R R Q k dr r R R = kq R R
5 A parallel plate capcitor has an area of A = cm = X0-4 m and a plate separation of d = mm = X0-3 m. Find its capacitance. What is the capacitance if the plate separation is increased to 3mm?
6 Quiz: Case Case Q Q d -Q d -Q The capacitance of the conductors.
7 Quiz: 50 V V Case A Case B The capacitance of the conductors.
8 Quiz: If the area of the plates of a parallel-plate capacitor is doubled, the capacitance is a. not changed b. doubled c. halved d. quadrupled e. quartered
9 Energy Stored in a Capacitor If plates of a charged capacitor are connected together by a conductor, charge will transfer from one plate to the other until the two are uncharged. The energy stored in a capacitor may be considered as being stored in the electric field created between plates as the capacitor is charged The electric field is proportional to the charge E=Q/ε o A for two plates
10 Energy Stored in a Capacitor (I) uncharged capacitor Ll du = Vdq= q C dq Move charge from one plate to the other This action required work --- how much? U = Q q C dq = Q C 0 This result applies to any capacitor, regardless of its geometry. As the stored energy increases as C and the potential difference V increases. = QV = CV
11 Energy Stored in a Capacitor (II) We can also store (or extract) energy by moving the capacitor plates. r E d,v,c Q Q r E Q Q d,v,c The work done is E ( d d). The potential increases from V to V = d d V. The capacitance decreases from C to C = d d C.
12 Energy Stored in the Electric Field Let s express the energy stored in a parallel plate capacitor in terms of its internal electric field: U = CV Then the energy per unit volume is u = e ε 0 A d = ε 0E ( Ed ) = ε E ( Ad ) We call this the energy density of the electric field 0 { volume inside of capacitor This expression is in fact valid for any electric field.
13 Combinations of Capacitors Individual capacitors can be connected into combinations. We can calculate the equivalent capacitance of these combinations. parallel connection: the capacitors have the same potential difference placed across them series connection: the capacitors have the same charge stored in them
14 Important: Not every connection is series or parallel!!! Although this would not usually occur in a circuit constructed by a professional, it can happen in nature, or in amateur (!) circuits, that some capacitances are neither in series nor in parallel. Each pair is a series combination, and the two pairs are in parallel to each other. Now, none of the capacitors are in series or in parallel with any other.
15 Parallel Capacitor Combinations The total charge stored is Q=Q Q The potential difference is V=V a V b Thus, the equivalent capacitance is C = Q V = Q Q V = Q V Q V = C C
16 Series Capacitor Combinations The total charge stored is Q=C V =C V The potential difference is V=V V Thus, the equivalent capacitance is C = Q V = Q V V = Q Q Q = C C C C C = C C
17 The equivalent capacitance for series and parallel arrangements may be determined by considering the following relationships For capacitors arranged in Series: Thus, the equivalent capacitance is C = Q V = Q V V = Q Q Q = C C C C C = C C For capacitors arranged in Parallel: Thus, the equivalent capacitance is C = Q V = Q Q V = Q V Q V = C C So a practical problem
18 Find the equivalent capacitance between a and b for the combination of capacitors shown below
19 Find the equivalent capacitance between a and b for the combination of capacitors shown below C C C 3 The equivalent capacitance of this combination is C C C 3
20 What is the equivalent capacitance?
21 Now let s discuss capacitors with dielectrics. A dielectric is a nonconducting material such as rubber glass wax What happens to a capacitor when a dielectric is inserted between the conducting surfaces? Let s consider a parallel plate capacitor.
22 When a dielectric is inserted between the plates of a charged capacitor The charge on the plates remains unchanged But the potential difference as recorded by an electrostatic voltmeter is reduced from V O to V = V O κ
23 This means that the capacitance increases by a factor, к So when a dielectric material is inserted between the plates of a capacitor, the capacitance increases. If the dielectric completely fills the space between the plates, the capacitance increases by a dimensionless factor, к, called the dielectric constant.
24 Dielectrics part Consider this problem: A metal slab is inserted into the capacitor. The charges in the plates induce an equal charge density on the surfaces of the slab, so that E=0 inside the slab. This action reduces the potential difference between the two plates, and so increases the capacitance. The conducting slab is completely polarized. The electric field inside the slab is completely zero.
25 Dielectrics part If we stick in an insulator, there will be a partial polarization at the surface, and a partial reduction of the electric field. Since the charges in the plates are free to move, we call that the free charge density, σ f. The charges in the insulator are bound to atoms (not free to move), and so we call that the bound charge density, σ b. The full electric field is E 0 = σ f ε 0. The reduced field in the insulator is E = σ f σ b ε 0
26 Dielectrics part 3 An insulator placed in a capacitor in this way affects the Field. Some materials have a larger effect on the Field than others. The ratio of the full Field to the reduced Field is the dielectric constant of the material. κ = E 0 E = σ f σ f σ b We also sometimes speak of the permittivity of the material. ε = κε 0
27 Dielectrics in Capacitors If the dielectric completely fills the volume of the capacitor, then the potential (field) is reduced by the factor k and thus the capacitance will be increased by k. for a C C = κ = κc parallel plate capacitor this ε o 0 A d may be written as
28 Practical reasons for using dielectrics We saw that we could use a conductor in between the plates to increase the capacitance, but there is always the chance of the inserted conductor touching the plates! Dielectrics don t have that problem. It is easier to maintain a precise separation of the two plates if there is a material in between the two plates to hold them in place. So, even just inserting a weak dielectric (κ ~ ) has a practical function. The dielectric breakdown field of air is only 3x0 6 V/m. Much higher fields can be maintained in a capacitor if a dielectric is used in the gap instead of air.
29 Table of Dielectrics
30 What if the dielectric doesn t fill the gap? = For the basic parallel plate capacitor with an air gap, C = ε 0 A d ( ( ) 0. m ) = 8.85 pf/m =. pf m If we fill the gap with a dielectric of κ =, C = κε 0 A d = 44. pf The partly filled gap is just two capacitors in series! We add them in the usual way. C = ε 0 A d 4 ( ) κε 0 A ( 3d 4) A = ε 0 d 4 3 κ = 35.4 pf
31 Energy Stored in a Capacitor with a Dielectric The increase in capacitance means an increase in energy stored, for a given potential. U = CV Then the energy per unit volume is u = e ε 0 A d = ε 0E ( Ed ) = ε E ( Ad ) 0 { volume inside of capacitor
32 However, with a and dielectric inserted the capacitance is C = κc and so the potential energy becomes u e 0 U = CV U = κc0v the energy per unit volume becomes = κε 0 E given by
33 The energy of a capacitor is raised when a diaelectric is inserted. This means that Work is done on the dielectric which draws it into the capacitor. This then implies that a force must act on the dielectric which draws it into the capacitor. This force originates from the nonuniform nature of the electric field of the capacitor near its edges
34 The nonuniform electric field near the edges of a parallel plate capacitor causes a dielectric to be pulled into the capacitor
35 To Your Groups
36 STOP
Chapter 25. Capacitance
Chapter 25 Capacitance 1 1. Capacitors A capacitor is a twoterminal device that stores electric energy. 2 2. Capacitance The figure shows the basic elements of any capacitor two isolated conductors of
More informationClass 5 : Conductors and Capacitors
Class 5 : Conductors and Capacitors What is a conductor? Field and potential around conductors Defining and evaluating capacitance Potential energy of a capacitor Recap Gauss s Law E. d A = Q enc and ε
More informationDefinition of Capacitance
Definition of Capacitance The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the potential difference between the conductors Q C = ΔV The SI
More informationCapacitors (Chapter 26)
Capacitance, C Simple capacitive circuits Parallel circuits Series circuits Combinations Electric energy Dielectrics Capacitors (Chapter 26) Capacitors What are they? A capacitor is an electric device
More information(21/703) At what distance from a point charge of 8µC would the potential equal 3.6X10 4 V?
(/73) At what distance from a point charge of 8µC would the potential equal 3.6X 4 V? (6/73) A positron has the same charge as a proton but the same mass as an electron. Suppose a positron moves 5. cm
More informationChapter 26. Capacitance and Dielectrics
Chapter 26 Capacitance and Dielectrics Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters in power supplies energy-storing
More informationCapacitance. Chapter 21 Chapter 25. K = C / C o V = V o / K. 1 / Ceq = 1 / C / C 2. Ceq = C 1 + C 2
= Chapter 21 Chapter 25 Capacitance K = C / C o V = V o / K 1 / Ceq = 1 / C 1 + 1 / C 2 Ceq = C 1 + C 2 Copyright 25-2 Capacitance 25.01 Sketch a schematic diagram of a circuit with a parallel-plate capacitor,
More informationChapter 24 Capacitance and Dielectrics
Chapter 24 Capacitance and Dielectrics Lecture by Dr. Hebin Li Goals for Chapter 24 To understand capacitors and calculate capacitance To analyze networks of capacitors To calculate the energy stored in
More informationReading: Electrostatics 3. Key concepts: Capacitance, energy storage, dielectrics, energy in the E-field.
Reading: Electrostatics 3. Key concepts: Capacitance, energy storage, dielectrics, energy in the E-field. 1.! Questions about charging and discharging capacitors. When an uncharged capacitor is connected
More informationChapter 18. Circuit Elements, Independent Voltage Sources, and Capacitors
Chapter 18 Circuit Elements, Independent Voltage Sources, and Capacitors Ideal Wire _ + Ideal Battery Ideal Resistor Ideal Capacitor Series Parallel An ideal battery provides a constant potential difference
More informationCan current flow in electric shock?
Can current flow in electric shock? Yes. Transient current can flow in insulating medium in the form of time varying displacement current. This was an important discovery made by Maxwell who could predict
More informationPhysics 202, Exam 1 Review
Physics 202, Exam 1 Review Logistics Topics: Electrostatics + Capacitors (Chapters 21-24) Point charges: electric force, field, potential energy, and potential Distributions: electric field, electric potential.
More informationChapter 24. Capacitance and Dielectrics Lecture 1. Dr. Armen Kocharian
Chapter 24 Capacitance and Dielectrics Lecture 1 Dr. Armen Kocharian Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters
More informationPhysics 202, Exam 1 Review
Physics 202, Exam 1 Review Logistics Topics: Electrostatics (Chapters 21-24.6) Point charges: electric force, field, potential energy, and potential Distributions: electric field, electric potential. Interaction
More informationChapter 24: Capacitance and Dielectrics
Chapter 24: Capacitance and Dielectrics When you compress/stretch a spring, we are storing potential energy This is the mechanical method to store energy It is also possible to store electric energy as
More informationFriday July 11. Reminder Put Microphone On
Friday July 11 8:30 AM 9:0 AM Catch up Lecture 3 Slide 5 Electron projected in electric field problem Chapter 23 Problem 29 Cylindrical shell problem surrounding wire Show Faraday Ice Pail no chrage inside
More informationCapacitors And Dielectrics
1 In this small e-book we ll learn about capacitors and dielectrics in short and then we ll have some questions discussed along with their solutions. I ll also give you a practices test series which you
More informationCapacitor: any two conductors, one with charge +Q, other with charge -Q Potential DIFFERENCE between conductors = V
Physics 2102 Gabriela González Capacitor: any two conductors, one with charge +Q, other with charge -Q Potential DIFFERENCE between conductors = V Units of capacitance: Farad (F) = Coulomb/Volt -Q +Q Uses:
More informationChapter 24: Capacitance and Dielectrics
Chapter 24: Capacitance and Dielectrics When you compress/stretch a spring, we are storing potential energy This is the mechanical method to store energy It is also possible to store electric energy as
More informationUniversity Physics (PHY 2326)
Chapter 23 University Physics (PHY 2326) Lecture 5 Electrostatics Electrical energy potential difference and electric potential potential energy of charged conductors Capacitance and capacitors 3/26/2015
More informationChapter 24 Capacitance and Dielectrics
Chapter 24 Capacitance and Dielectrics 1 Capacitors and Capacitance A capacitor is a device that stores electric potential energy and electric charge. The simplest construction of a capacitor is two parallel
More informationElectric Potential. Capacitors (Chapters 28, 29)
Electric Potential. Capacitors (Chapters 28, 29) Electric potential energy, U Electric potential energy in a constant field Conservation of energy Electric potential, V Relation to the electric field strength
More informationChapter 24 Capacitance, Dielectrics, Electric Energy Storage
Chapter 24 Capacitance, Dielectrics, Electric Energy Storage Units of Chapter 24 Capacitors (1, 2, & 3) Determination of Capacitance (4 & 5) Capacitors in Series and Parallel (6 & 7) Electric Energy Storage
More informationParallel Plate Capacitor, cont. Parallel Plate Capacitor, final. Capacitance Isolated Sphere. Capacitance Parallel Plates, cont.
Chapter 6 Capacitance and Dielectrics Capacitors! Capacitors are devices that store electric charge! Examples of where capacitors are used include:! radio receivers (tune frequency)! filters in power supplies!
More informationCapacitance and capacitors. Dr. Loai Afana
apacitance and capacitors apacitors apacitors are devices that store energy in an electric field. apacitors are used in many every-day applications Heart defibrillators amera flash units apacitors are
More informationDepartment of Physics. PHYS MAJOR 2 EXAM Test Code: 015. Monday 1 st May 2006 Exam Duration: 2hrs (from 6:30pm to 8:30pm)
Department of Physics PHYS1005 MJOR EXM Test Code: 015 Monday 1 st May 006 Exam Duration: hrs (from 6:30pm to 8:30pm) Name: Student Number: Section Number: Version 15 Page 1 1. Each of the four capacitors
More informationW05D1 Conductors and Insulators Capacitance & Capacitors Energy Stored in Capacitors
W05D1 Conductors and Insulators Capacitance & Capacitors Energy Stored in Capacitors W05D1 Reading Assignment Course Notes: Sections 3.3, 4.5, 5.1-5.4 1 Outline Conductors and Insulators Conductors as
More informationCapacitance and Dielectrics
Chapter 24 Capacitance and Dielectrics PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 24 To understand capacitors
More informationChapter 26. Capacitance and Dielectrics
Chapter 26 Capacitance and Dielectrics Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters in power supplies to eliminate
More informationwhich checks. capacitance is determined entirely by the dimensions of the cylinders.
4.3. IDENTIFY and SET UP: It is a parallel-plate air capacitor, so we can apply the equations of Section 4.. EXEUTE: (a) (b) = ε 0 A d (c) V ab so Q V = so 0 ab V ab 6 Q 0. 48 0 = = = 604 V. 45 0 F 3 d
More informationCapacitance, 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 informationElectric Field of a uniformly Charged Thin Spherical Shell
Electric Field of a uniformly Charged Thin Spherical Shell The calculation of the field outside the shell is identical to that of a point charge. The electric field inside the shell is zero. What are the
More informationPhysics 212. Lecture 7. Conductors and Capacitance. Physics 212 Lecture 7, Slide 1
Physics 212 Lecture 7 Conductors and Capacitance Physics 212 Lecture 7, Slide 1 Conductors The Main Points Charges free to move E = 0 in a conductor Surface = Equipotential In fact, the entire conductor
More informationLook over. examples 1, 2, 3, 5, 6. Look over. Chapter 25 section 1-8. Chapter 19 section 5 Example 10, 11
PHYS Look over hapter 5 section -8 examples,, 3, 5, 6 PHYS Look over hapter 7 section 7-9 Examples 8, hapter 9 section 5 Example 0, Things to Know ) How to find the charge on a apacitor. ) How to find
More informationChapter 24: Capacitance and Dielectrics
hapter 4: apacitance and Dielectrics apacitor: two conductors (separated by an insulator) usually oppositely charged a + b - ab proportional to charge = / ab (defines capacitance) units: F = / pc4: The
More informationAP Physics C. Electric Potential and Capacitance. Free Response Problems
AP Physics C Electric Potential and Capacitance Free Response Problems 1. Two stationary point charges + are located on the y-axis at a distance L from the origin, as shown above. A third charge +q is
More informationChapter 24 Capacitance and Dielectrics
Chapter 24 Capacitance and Dielectrics 1 Capacitors and Capacitance A capacitor is a device that stores electric potential energy and electric charge. The simplest construction of a capacitor is two parallel
More informationCAPACITANCE: CHAPTER 24. ELECTROSTATIC ENERGY and CAPACITANCE. Capacitance and capacitors Storage of electrical energy. + Example: A charged spherical
CAPACITANCE: CHAPTER 24 ELECTROSTATIC ENERGY an CAPACITANCE Capacitance an capacitors Storage of electrical energy Energy ensity of an electric fiel Combinations of capacitors In parallel In series Dielectrics
More informationRoll Number SET NO. 42/1
Roll Number SET NO. 4/1 INDIAN SCHOOL MUSCAT FIRST TERM EXAMINATION PHYSICS CLASS: XII Sub. Code: 04 Time Allotted: Hrs 0.04.018 Max. Marks: 70 General Instructions: 1. All questions are compulsory. There
More informationChapter 26. Capacitance and Dielectrics
Chapter 26 Capacitance and Dielectrics Capacitors Capacitors are devices that store electric charge Examples of where capacitors are used include: radio receivers filters in power supplies to eliminate
More informationPhysics (
Exercises Question 2: Two charges 5 0 8 C and 3 0 8 C are located 6 cm apart At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero
More informationPhysics Electricity & Op-cs Lecture 8 Chapter 24 sec Fall 2017 Semester Professor
Physics 24100 Electricity & Op-cs Lecture 8 Chapter 24 sec. 1-2 Fall 2017 Semester Professor Kol@ck How Much Energy? V 1 V 2 Consider two conductors with electric potentials V 1 and V 2 We can always pick
More information(3.5.1) V E x, E, (3.5.2)
Lecture 3.5 Capacitors Today we shall continue our discussion of electrostatics and, in particular, the concept of electrostatic potential energy and electric potential. The main example which we have
More informationC = V Q. To find the capacitance of two conductors:
Capacitance Capacitance is a measure of the ability of two conductors to store charge when a given potential difference is established between them. Two conductors, on one of which is charge +Q and on
More informationCapacitance and Dielectrics
Capacitance and Dielectrics 1 Definition of Capacitance A capacitor consists of two conductors separated by an insulator. The capacitance of a given capacitor depends on its geometry and on the material
More informationPhysics 2102 Gabriela González
Physics 2102 Gabriela González Any two charged conductors form a capacitor. Capacitance : C= Q/V Simple Capacitors: Parallel plates: C = ε 0 A/d Spherical : C = ε 0 4πab/(b-a) Cylindrical: C = ε 0 2πL/ln(b/a)
More informationChapter 16. Electric Energy and Capacitance
Chapter 16 Electric Energy and Capacitance Electric Potential Energy The electrostatic force is a conservative force It is possible to define an electrical potential energy function with this force Work
More informationChapter 24: Capacitance and dielectrics
Chapter 24: Capacitance and dielectrics Capacitor: a device store electric energy How to define capacitance In parallel and/or in series Electric energy stored in a capacitor Dielectric materials Capacitor:
More informationChapter 26. Capacitance and Dielectrics
Chapter 26 Capacitance and Dielectrics Circuits and Circuit Elements Electric circuits are the basis for the vast majority of the devices used in society. Circuit elements can be connected with wires to
More informationAP Physics C Electricity & Magnetism Mid Term Review
AP Physics C Electricity & Magnetism Mid Term Review 1984 37. When lighted, a 100-watt light bulb operating on a 110-volt household circuit has a resistance closest to (A) 10-2 Ω (B) 10-1 Ω (C) 1 Ω (D)
More informationCapacitors II. Physics 2415 Lecture 9. Michael Fowler, UVa
Capacitors II Physics 2415 Lecture 9 Michael Fowler, UVa Today s Topics First, some review then Storing energy in a capacitor How energy is stored in the electric field Dielectrics: why they strengthen
More informationLecture 20. March 22/24 th, Capacitance (Part I) Chapter , Pages
Lecture 0 March /4 th, 005 Capacitance (Part I) Reading: Boylestad s Circuit Analysis, 3 rd Canadian Edition Chapter 10.1-6, Pages 8-94 Assignment: Assignment #10 Due: March 31 st, 005 Preamble: Capacitance
More informationExam 1 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1
Exam 1 Solutions Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1 A rod of charge per unit length λ is surrounded by a conducting, concentric cylinder
More informationPHYSICS - CLUTCH CH 24: CAPACITORS & DIELECTRICS.
!! www.clutchprep.com CONCEPT: CAPACITORS AND CAPACITANCE A CAPACITOR is formed by two surfaces of equal/opposite charge brought close together - Separation of charge potential energy stored Connecting
More informationshown in Fig. 4, is initially uncharged. How much energy is stored in the two capacitors after the switch S is closed for long time?
Chapter 25 Term 083 Q13. Each of the two 25-µF capacitors, as shown in Fig. 3, is initially uncharged. How many Coulombs of charge pass through ammeter A after the switch S is closed for long time? A)
More informationChapter 24: Capacitance and Dielectrics. Capacitor: two conductors (separated by an insulator) usually oppositely charged. (defines capacitance)
hapter 4: apacitance and Dielectrics apacitor: two conductors (separated by an insulator) usually oppositely charged a b - ab proportional to charge / ab (defines capacitance) units: F / pc4: The parallel
More information5: Capacitors July 8, 2008
5: Capacitors July 8, 2008 5.1 Definition A capacitor is a structure which has a certain capacity to hold an electric charge. It is essentially the simplest possible battery. The typical example of a capacitor,
More information= (series) Capacitors in series. C eq. Hence. Capacitors in parallel. Since C 1 C 2 V 1 -Q +Q -Q. Vab V 2. C 1 and C 2 are in series
Capacitors in series V ab V + V Q( + C Vab + Q C C C Hence C C eq eq + C C C (series) ) V ab +Q -Q +Q -Q C and C are in series C V V C +Q -Q C eq C eq is the single capacitance equivalent to C and C in
More informationGeneral Physics - E&M (PHY 1308) - Lecture Notes. General Physics - E&M (PHY 1308) Lecture Notes
General Physics - E&M (PHY 1308) Lecture Notes Lecture 009: Using Capacitors SteveSekula, 15 February 2011 (created 14 February 2011) Discuss the energy stored in a capacitor Discuss how to use capacitors
More informationElectric Potential Energy Conservative Force
Electric Potential Energy Conservative Force Conservative force or field is a force field in which the total mechanical energy of an isolated system is conserved. Examples, Gravitation, Electrostatic,
More informationF 13. The two forces are shown if Q 2 and Q 3 are connected, their charges are equal. F 12 = F 13 only choice A is possible. Ans: Q2.
Q1. Three fixed point charges are arranged as shown in Figure 1, where initially Q 1 = 10 µc, Q = 15 µc, and Q 3 = 5 µc. If charges Q and Q 3 are connected by a very thin conducting wire and then disconnected,
More informationAgenda for Today. Elements of Physics II. Capacitors Parallel-plate. Charging of capacitors
Capacitors Parallel-plate Physics 132: Lecture e 7 Elements of Physics II Charging of capacitors Agenda for Today Combinations of capacitors Energy stored in a capacitor Dielectrics in capacitors Physics
More informationA) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 2, 3, 1, 4 D) 2, 4, 1, 3 E) 3, 2, 4, 1. Page 2
1. Two parallel-plate capacitors with different plate separation but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is NOT the same for
More informationCapacitance. 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 informationiclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed?
1 iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed? q A: C->2 C0 B: C-> C0 C: C-> C0/2 D: C->- C0 E: C->-2 C0 2 iclicker A metal ball of
More informationAgenda for Today. Elements of Physics II. Capacitors Parallel-plate. Charging of capacitors
Capacitors Parallel-plate Physics 132: Lecture e 7 Elements of Physics II Charging of capacitors Agenda for Today Combinations of capacitors Energy stored in a capacitor Dielectrics in capacitors Physics
More informationPhysics (
Question 2.12: A charge of 8 mc is located at the origin. Calculate the work done in taking a small charge of 2 10 9 C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).
More informationSolution to Quiz 2. April 18, 2010
Solution to Quiz April 8, 00 Four capacitors are connected as shown below What is the equivalent capacitance of the combination between points a and b? a µf b 50 µf c 0 µf d 5 µf e 34 µf Answer: b (A lazy
More informationSharpen thinking about connections among electric field, electric potential difference, potential energy
PHYS 2015 -- Week 6 Sharpen thinking about connections among electric field, electric potential difference, potential energy Apply the ideas to capacitance and the parallel plate capacitor For exclusive
More informationReview. Spring Semester /21/14. Physics for Scientists & Engineers 2 1
Review Spring Semester 2014 Physics for Scientists & Engineers 2 1 Notes! Homework set 13 extended to Tuesday, 4/22! Remember to fill out SIRS form: https://sirsonline.msu.edu Physics for Scientists &
More informationCapacitance & Capacitors, Energy Stored in Capacitors Challenge Problems
Problem 1: Capacitance & Capacitors, Energy Stored in Capacitors Challenge Problems A parallel-plate capacitor is charged to a potential V 0, charge Q 0 and then disconnected from the battery. The separation
More informationExam 2 Practice Problems Part 1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Exam 2 Practice Problems Part 1 Problem 1 Electric Field and Charge Distributions from Electric Potential An electric potential V ( z ) is described
More information13 - ELECTROSTATICS Page 1 ( Answers at the end of all questions )
3 - ELECTROSTATICS Page ) Two point charges 8 and - are located at x = 0 and x = L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is
More informationChapter 25. Capacitance
Chapter 25 Capacitance 25.2: Capacitance: 25.2: Capacitance: When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: q+ and q-. However, we refer to the charge of a
More informationToday in Physics 122: capacitors
Today in Physics 122: capacitors Parallelplate and cylindrical capacitors: calculation of capacitance as a review in the calculation of field and potential Dielectrics in capacitors Capacitors, dielectrics
More informationClass 6 : Insulating Materials
Class 6 : Insulating Materials What is an insulator? Electric dipoles Polarization of an insulator, and how it modifies electric field Electric displacement Boundary conditions for E Recap (1) Maxwell
More informationChapter 19 Electric Potential and Electric Field
Chapter 19 Electric Potential and Electric Field The electrostatic force is a conservative force. Therefore, it is possible to define an electrical potential energy function with this force. Work done
More informationEnergy stored in a capacitor W = \ q V. i q1. Energy density in electric field i. Equivalent capacitance of capacitors in series
The Language of Physics Cwcihor Two conductors of any size or shape carrying equal and opposite charges are called a capacitor. The charge on the capacitor is directly proportional to the potential difference
More informationThis work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.
University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 07. Capacitors I Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License
More informationPhysics 169. Luis anchordoqui. Kitt Peak National Observatory. Thursday, February 22, 18
Physics 169 Kitt Peak National Observatory Luis anchordoqui 1 4.1 Capacitors A capacitor is a system of two conductors that carries equal and opposite charges A capacitor stores charge and energy in the
More informationLecture 7. Capacitors and Electric Field Energy. Last lecture review: Electrostatic potential
Lecture 7. Capacitors and Electric Field Energy Last lecture review: Electrostatic potential V r = U r q Q Iclicker question The figure shows cross sections through two equipotential surfaces. In both
More informationHIGH VOLTAGE TECHNIQUES Basic Electrode Systems (3)
HIGH VOLTAGE TECHNIQES Basic Electrode Systems (3) Assistant Professor Suna BOLAT KRÖGER Eastern Mediterranean niversity Department of Electric & Electronic Engineering 1 Basic electrode systems Different
More informationCapacitance and Dielectrics. Chapter 26 HW: P: 10,18,21,29,33,48, 51,53,54,68
Capacitance and Dielectrics Chapter 26 HW: P: 10,18,21,29,33,48, 51,53,54,68 Capacitors Capacitors are devices that store electric charge and energy Examples of where capacitors are used include: radio
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 7 Electrostatics and electrodynamics Capacitance and capacitors capacitors with dielectrics Electric current current and drift speed resistance and Ohm s law http://www.physics.wayne.edu/~apetrov/phy2140/
More informationPhysics 142 Electrostatics 3 Page 1. Electrostatics 3. Get your facts first; then you can distort them as you please. Mark Twain
Physics 142 Electrostatics 3 Page 1 Electrostatics 3 Get your facts first; then you can distort them as you please. Mark Twain The E-field has energy stored in it that can be useful Like other forms of
More informationPH 222-2A Spring 2015
PH -A Spring 15 Capacitance Lecture 7 Chapter 5 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 5 Capacitance In this chapter we will cover the following topics: -Capacitance
More informationPotentials and Fields
Potentials and Fields Review: Definition of Potential Potential is defined as potential energy per unit charge. Since change in potential energy is work done, this means V E x dx and E x dv dx etc. The
More informationConsider a point P on the line joining the two charges, as shown in the given figure.
Question 2.1: Two charges 5 10 8 C and 3 10 8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
More informationPhysics 240 Fall 2003: Exam #1. Please print your name: Please list your discussion section number: Please list your discussion instructor:
Physics 4 Fall 3: Exam #1 Please print your name: Please list your discussion section number: Please list your discussion instructor: Form #1 Instructions 1. Fill in your name above. This will be a 1.5
More informationClass 6. Capacitance and Capacitors. Physics 106. Winter Press CTRL-L to view as a slide show. Class 6. Physics 106.
and in and Energy Winter 2018 Press CTRL-L to view as a slide show. From last time: The field lines are related to the field as follows: What is the electric potential? How are the electric field and the
More informationChapter 17. Potential and Capacitance
Chapter 17 Potential and Capacitance Potential Voltage (potential) is the analogue of water pressure while current is the analogue of flow of water in say gal/min or Kg/s Think of a potential as the words
More informationHollow Conductors. A point charge +Q is placed at the center of the conductors. The induced charges are: 1. Q(I1) = Q(I2) = -Q; Q(O1) = Q(O2)= +Q
O2 I2 O1 I1 Hollow Conductors A point charge +Q is placed at the center of the conductors. The induced charges are: 1. Q(I1) = Q(I2) = -Q; Q(O1) = Q(O2)= +Q 2. Q(I1) = Q(I2) = +Q; Q(O1) = Q(O2)= -Q 3.
More informationGeneral Physics II. Conducting concentric spheres Two concentric spheres of radii R and r. The potential difference between the spheres is
apacitors and Dielectrics The ideas of energy storage in E-fields can be carried a step further by understanding the concept of "apacitance" onsider a sphere with a total charge, Q, and a radius, R From
More informationFREE Download Study Package from website: &
EXERISE- * MARK IS MORE THAN ONE ORRET QUESTIONS. SETION A : DEFINITION OF APAIT ITANE A. A. When 0µ charge is given to an isolated conductor of capacitance 5µF. Find out following (i) Potential of the
More informationLESSON 2 PHYSICS NOTES
LESSON 2 ELECTROSTATIC POTENTIAL AND CAPACITANCE SECTION I ELECTROSTATIC POTENTIAL ELECTRIC FIELD IS CONSERVATIVE In an electric field work done by the electric field in moving a unit positive charge from
More informationChapter 10. Electrostatics
Chapter 10 Electrostatics 3 4 AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A solid conducting sphere
More information1. zero. Where an electric field line crosses an equipotential surface, the angle between the field line and the equipotential is
Week 5 Where an electric field line crosses an equipotential surface, the angle between the field line and the equipotential is 1. zero 2. between zero and 90 3. 90 4. not enough information given to
More informationEnergy Stored in Capacitors
Energy Stored in Capacitors U = 1 2 qv q = CV U = 1 2 CV 2 q 2 or U = 1 2 C 37 Energy Density in Capacitors (1) We define the, u, as the electric potential energy per unit volume Taking the ideal case
More informationPhys102 Second Major-181 Zero Version Coordinator: Kunwar, S Monday, November 19, 2018 Page: 1
Coordinator: Kunwar, S Monday, November 19, 2018 Page: 1 Q1. A neutral metal ball is suspended by a vertical string. When a positively charged insulating rod is placed near the ball (without touching),
More informationPhysics Jonathan Dowling. Final Exam Review
Physics 2102 Jonathan Dowling Physics 2102 Final Exam Review A few concepts: electric force, field and potential Electric force: What is the force on a charge produced by other charges? What is the force
More information