# Chapter 31. Current and Resistance. What quantity is represented by the symbol J?

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1 Chapter 31. Current and Resistance Lights, sound systes, icrowave ovens, and coputers are all connected by wires to a battery or an electrical outlet. How and why does electric current flow through a wire? Chapter Goal: To learn how and why charge oves through a conductor as what we call a current. Chapter 31. Current and Resistance Topics: The Electron Current Creating a Current Current and Current Density Conductivity and Resistivity Resistance and Oh s Law 1 2 What quantity is represented by the sybol J? Chapter 31. Reading Quizzes A. Resistivity B. Conductivity C. Current density D. Coplex ipedance E. Johnston s constant 3 4

2 What quantity is represented by the sybol J? The electron drift speed in a typical current-carrying wire is A. Resistivity B. Conductivity C. Current density D. Coplex ipedance E. Johnston s constant A. extreely slow ( 10 4 /s). B. oderate ( 1 /s). C. very fast ( 10 4 /s). D. Could be any of A, B, or C. E. No nuerical values were provided. 5 6 The electron drift speed in a typical current-carrying wire is A. extreely slow ( 10 4 /s). B. oderate ( 1 /s). C. very fast ( 10 4 /s). D. Could be any of A, B, or C. E. No nuerical values were provided. All other things being equal, current will be larger in a wire that has a larger value of A. conductivity. B. resistivity. C. the coefficient of current. D. net charge. E. potential. 7 8

3 All other things being equal, current will be larger in a wire that has a larger value of A. conductivity. B. resistivity. C. the coefficient of current. D. net charge. E. potential. The equation I V/R is called A. Apère s law. B.Faraday s law. C. Oh s law. D. Weber s law The Electron Current The equation I V/R is called A. Apère s law. B. Farady s law. C. Oh s law. D. Weber s law. The electron current I is the nuber of electrons per second that pass through a cross section of a wire. The units of electron current are s -1. N e i t 11 12

4 The Electric Current The Electron Current i nav d N N e e nv na x nav t i t nav t d d i nav d Typical V d is about 10-4 /s. The drift speed v d is the net speed with which the electrons ove, not the speed at which any one electron is bouncing around The Law of Conservation of Current: the electron current is the sae at all points in a currentcarrying wire. How long does it take to discharge a capacitor? 0.2 [] /10-4 [/s] 2000 s? The electron current at A is exactly equal to the electron current at B

5 How long does it take to discharge a capacitor? Establishing the Electric Field in a Wire N e i t nav d t N e t nav d t s [ ] [ ] 10 [ / s] A Model of Conduction A Model of Conduction F a x v x v ix + a t v x t ix + The energy transfer is the friction that raises the teperature of the wire. 19 v v x v ix + a t v x v v d ix + ix τ + t v d τ 20

6 v d A Model of Conduction τ i nav d Current and Current Density dq r I (, in the direction of E) dt 1 Apere 1 A 1 coulob per second 1 C/s i neτae The electron current is directly proportional to the electric field strength. 21 Q en I e ei t t The direction of the current I in a etal is opposite the direction of otion of the electrons. The current direction in a wire is fro the positive terinal of a battery to the negative terinal. 22 Conservation of Current I I in out The Current Density in a Wire I ei nev d A I J current density A I JA nev d 23 24

7 Conductivity and Resistivity Conductivity and Resistivity J σe J nev d 2 e τ E ne τ ne ( ) E 2 τ ne σ conductivi ty 1 ρ resistivit y 2 σ ne τ Resistance and Oh s Law Oh s Law The resistance of a long, thin conductor of length L and crosssectional area A is The SI unit of resistance is the oh. 1 oh 1 Ω 1 V/A. The current through a conductor is deterined by the potential difference V along its length: Oh s law is liited to those aterials whose resistance R reains constant or very nearly so during use. The aterials to which Oh s law applies are called ohic. The current through an ohic aterial is directly proportional to the potential difference. Doubling the potential difference doubles the current. Metal and other conductors are ohic devices

8 Chapter 31. Suary Slides General Principles General Principles 31 32

9 General Principles Iportant Concepts Iportant Concepts Iportant Concepts 35 36

10 Applications Chapter 31. Questions These four wires are ade of the sae etal. Rank in order, fro largest to sallest, the electron currents i a to i d. These four wires are ade of the sae etal. Rank in order, fro largest to sallest, the electron currents i a to i d. A. i d > i a > i b > i c B. i b i d > i a i c C. i c > i b > i a > i d D. i c > i a i b > i d E. i b i c > i a i d A. i d > i a > i b > i c B. i b i d > i a i c C. i c > i b > i a > i d D. i c > i a i b > i d E. i b i c > i a i d 39 40

11 Why does the light in a roo coe on instantly when you flip a switch several eters away? A. Electrons travel at the speed of light through the wire. B. Because the wire between the switch and the bulb is already full of electrons, a flow of electrons fro the switch into the wire iediately causes electrons to flow fro the other end of the wire into the lightbulb. C. The switch sends a radio signal which is received by a receiver in the light which tells it to turn on. D. Optical fibers connect the switch with the light, so the signal travels fro switch to the light at the speed of light in an optical fiber. Why does the light in a roo coe on instantly when you flip a switch several eters away? A. Electrons travel at the speed of light through the wire. B. Because the wire between the switch and the bulb is already full of electrons, a flow of electrons fro the switch into the wire iediately causes electrons to flow fro the other end of the wire into the lightbulb. C. The switch sends a radio signal which is received by a receiver in the light which tells it to turn on. D. Optical fibers connect the switch with the light, so the signal travels fro switch to the light at the speed of light in an optical fiber What are the agnitude and the direction of the current in the fifth wire? What are the agnitude and the direction of the current in the fifth wire? A. 15 A into the junction B. 15 A out of the junction C. 1 A into the junction D. 1 A out of the junction E. Not enough data to deterine A. 15 A into the junction B. 15 A out of the junction C. 1 A into the junction D. 1 A out of the junction E. Not enough data to deterine 43 44

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