Chapter 27 Lecture - Faculty/Staff Websites & Bios

PHYSICSFOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH4/EChapter 27 LectureRANDALL D. KNIGHT

Chapter 27 Current and ResistanceIN THIS CHAPTER, you will learn how and whycharge moves through a wire as a current. 2017 Pearson Education, Inc.Slide 27-2

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Chapter 27 Content, Examples, andQuickCheck Questions 2017 Pearson Education, Inc.Slide 27-8

Electric Current How does a capacitor get discharged? Figure (a) shows a charged capacitor in equilibrium. Figure (b) shows a wire discharging the capacitor. As the capacitor is discharging, there is a current in thewire. 2017 Pearson Education, Inc.Slide 27-9

Electric Current When a current is flowing, the conductors are not inelectrostatic equilibrium. Though you cannot see current directly, there arecertain indicators that current is present in a wire. 2017 Pearson Education, Inc.Slide 27-10

Charge Carriers The outer electrons ofmetal atoms are onlyweakly bound to thenuclei. In a metal, the outerelectrons becomedetached from theirparent nuclei to form afluid-like sea of electronsthat can move through thesolid. Electrons are the chargecarriers in metals. 2017 Pearson Education, Inc.Slide 27-11

The Electron Current We define theelectron current ieto be the number ofelectrons persecond that passthrough a crosssection of theconductor. The number Ne ofelectrons that passthrough the crosssection during thetime interval Δt is 2017 Pearson Education, Inc.Slide 27-12

The Electron Current If the number density ofconduction electrons isne, then the totalnumber of electrons inthe shaded cylinder isNe neV neAΔx neAvdΔt So the electron currentis 2017 Pearson Education, Inc.Slide 27-13

The Electron Density In most metals,each atomcontributes onevalence electron tothe sea ofelectrons. Thus the numberof conductionelectrons ne is thesame as thenumber of atomsper cubic meter. 2017 Pearson Education, Inc.Slide 27-14

Example 27.1 The Size of the Electron Current 2017 Pearson Education, Inc.Slide 27-15

Discharging a Capacitor How long should ittake to discharge thiscapacitor? A typical drift speedof electron currentthrough a wire isvd 10–4 m/s. At this rate, it wouldtake an electronabout 2000 s (overhalf an hour) to travel20 cm. But real capacitors discharge almost instantaneously! What’s wrong with our calculation? 2017 Pearson Education, Inc.Slide 27-16

Discharging a Capacitor The wire is already fullof electrons! We don’t have to waitfor electrons to moveall the way through thewire from one plate toanother. We just need toslightly rearrange thecharges on the platesand in the wire. 2017 Pearson Education, Inc.Slide 27-17

Creating a Current A book on a tablewill slow down andstop unless youcontinue pushing. Analogously, thesea of electronswill slow down andstop unless youcontinue pushingwith an electricfield. 2017 Pearson Education, Inc.Slide 27-18

Establishing the Electric Field in a Wire The figure showstwo metal wiresattached to theplates of acharged capacitor. This is anelectrostaticsituation. What will happen ifwe connect thebottom ends of thewires together? 2017 Pearson Education, Inc.Slide 27-19

Establishing the Electric Field in a Wire Within a very briefinterval of time( 10–9 s) ofconnecting thewires, the sea ofelectrons shiftsslightly. The surface chargeis rearranged into anonuniformdistribution, asshown in the figure. 2017 Pearson Education, Inc.Slide 27-20

Establishing the Electric Field in a Wire The nonuniform distribution of surface charges along awire creates a net electric field inside the wire thatpoints from the more positive end toward the morenegative end of the wire. This is the internal electric field that pushes the electroncurrent through the wire. 2017 Pearson Education, Inc.Slide 27-21

A Model of Conduction Within a conductorin electrostaticequilibrium, there isno electric field. In this case, anelectron bouncesback and forthbetween collisions,but its averagevelocity is zero. 2017 Pearson Education, Inc.Slide 27-22

A Model of Conduction In the presence of anelectric field, theelectric force causeselectrons to movealong parabolictrajectories betweencollisions. Because of thecurvature of thetrajectories, there is aslow net motion in the“downhill” direction. 2017 Pearson Education, Inc.Slide 27-23

A Model of Conduction The graphshows thespeed of anelectron duringmultiplecollisions. The averagedrift speed is 2017 Pearson Education, Inc.Slide 27-24

Electron CurrentElectronCurrent Theelectric fieldstrength E in a wire of crosssection A causes an electron current: The electron density ne and the mean time betweencollisions τ are properties of the metal. The electron current is directly proportional to theelectric field strength. 2017 Pearson Education, Inc.Slide 27-25

Example 27.3 Collisions in a Copper Wire 2017 Pearson Education, Inc.Slide 27-26

Example 27.3 Collisions in a Copper Wire 2017 Pearson Education, Inc.Slide 27-27

Current If CurrentQ is the total amount of charge that has movedpast a point in a wire, we define the current I inthe wire to be the rate of charge flow:current is the rate at which charge flows The SI unit for current is the coulomb per second,which is called the ampere. 1 ampere 1 A 1 C/s The conventional current I and the electron currentie are related by 2017 Pearson Education, Inc.Slide 27-28

Current Note that the direction of the current I in a metal isopposite to the direction of the electron current ie. 2017 Pearson Education, Inc.Slide 27-29

The Current Density in a WireTheCurrentDensityinwirea Wire ThecurrentdensityJ in ais the current persquare meter of cross section: The current density has units of A/m2. 2017 Pearson Education, Inc.Slide 27-30

Example 27.4 Finding the Electron Drift Speed 2017 Pearson Education, Inc.Slide 27-31

Conservation of Current The figure shows twolightbulbs in the wireconnecting two chargedcapacitor plates. As the capacitordischarges, the currentthrough both bulbs isexactly the same! The rate of electronsleaving a lightbulb (orany other device) isexactly the same as therate of electronsentering the lightbulb. 2017 Pearson Education, Inc.Slide 27-32

Charge Conservation and Current Due to conservation of charge, the current must be thesame at all points in a current-carrying wire. 2017 Pearson Education, Inc.Slide 27-33

Kirchhoff’s Junction Law For a junction, the law ofconservation of currentrequires thatwhere the Σ symbolmeans summation. This basicconservationstatement is calledKirchhoff’s junctionlaw. 2017 Pearson Education, Inc.Slide 27-34

Conductivity and Resistivity The conductivity of a material is Conductivity, like density, characterizes a materialas a whole. The current density J is related to the electric fieldE by The resistivity tells us how reluctantly the electronsmove in response to an electric field: 2017 Pearson Education, Inc.Slide 27-35

Conductivity and ResistivityThis woman is measuring her percentage body fat bygripping a device that sends a small electric currentthrough her body. Because muscle and fat have differentresistivities, the amount of current allows the fat-to-muscleratio to be determined. 2017 Pearson Education, Inc.Slide 27-36

Conductivity and Resistivity 2017 Pearson Education, Inc.Slide 27-37

Example 27.5 The Electric Field in a Wire 2017 Pearson Education, Inc.Slide 27-38

Superconductivity In 1911, the Dutchphysicist KamerlinghOnnes discovered thatcertain materialssuddenly anddramatically lose allresistance to currentwhen cooled below acertain temperature. This complete loss ofresistance at lowtemperatures is calledsuperconductivity. 2017 Pearson Education, Inc.Superconductors have unusualmagnetic properties. Here asmall permanent magnetlevitates above a disk of the hightemperature superconductorYBa2Cu3O7 that has been cooledto liquid-nitrogen temperature.Slide 27-39

Resistance and Ohm’s Law The figure shows a sectionof a conductor in which anelectric field E is creatingcurrent I by pushing thecharge carriers. The field strength is The current density isJ I/A E/ρ So the current is relatedto ΔV by 2017 Pearson Education, Inc.Slide 27-40

Resistance and Ohm’s Law The current through a conductor is proportional tothe potential difference between its ends. We define the resistance R of a long, thin conductorof length L and cross-sectional area A to be The SI unit of resistance is the ohm. 1 ohm 1 Ω 1 V/A The current through a conductor is determined bythe potential difference ΔV along its length: 2017 Pearson Education, Inc.Slide 27-41

Batteries and Current A battery is a source ofpotential difference ΔVbat. The battery creates apotential differencebetween the ends of thewire. The potential differencein the wire creates anelectric field in the wire. The electric field pushesa current I through thewire. The current in the wire isI ΔVwire/R 2017 Pearson Education, Inc.Slide 27-42

Ohm’s Law Ohm’s law is limited tothose materials whoseresistance R remainsconstant—or verynearly so—during use. The materials to which Ohm’s law applies are called ohmic. The current through an ohmic material is directly proportionalto the potential difference; doubling the potential differencedoubles the current. Metal and other conductors are ohmic devices. 2017 Pearson Education, Inc.Slide 27-43

Nonohmic Materials Some materials and devices are nonohmic,meaning that the current through the device is notdirectly proportional to the potential difference. Diodes, batteries, and capacitors are all nonohmicdevices. 2017 Pearson Education, Inc.Slide 27-44

Battery-Wire-Resistor-Wire Circuit The figure shows aresistor connected toa battery with currentcarrying wires. Current must beconserved; hence thecurrent I through theresistor is the same asthe current in eachwire. The next two slidesshow how the electricpotential variesthrough the circuit. 2017 Pearson Education, Inc.Slide 27-45

Battery-Wire-Resistor-Wire Circuit 2017 Pearson Education, Inc.Slide 27-46

Battery-Wire-Resistor-Wire Circuit 2017 Pearson Education, Inc.Slide 27-47

Example 27.7 A Battery and a Resistor 2017 Pearson Education, Inc.Slide 27-48

Chapter 27 Summary Slides 2017 Pearson Education, Inc.Slide 27-49

General Principles 2017 Pearson Education, Inc.Slide 27-50

General Principles 2017 Pearson Education, Inc.Slide 27-51

General Principles 2017 Pearson Education, Inc.Slide 27-52

Important Concepts 2017 Pearson Education, Inc.Slide 27-53

Important Concepts 2017 Pearson Education, Inc.Slide 27-54

Important Concepts 2017 Pearson Education, Inc.Slide 27-55

Applications 2017 Pearson Education, Inc.Slide 27-56

The electric field strength . Electron Current . E. in a wire of cross-section . A. causes an electron current: The electron density . n. e. and the mean time between collisions τ are properties of the metal. The electron current is directly proportional to the electric field strength. Electron Current