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Chapter 31. Current and Resistance Chapter 31. Current and Resistance Lights, sound systems, microwave ovens, and computers 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 moves through a conductor as what we call a current. Topics: • The Electron Current • Creating a Current • Current and Current Density • Conductivity and Resistivity • Resistance and Ohm’s Law 1 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 2 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What quantity is represented by the symbol J ? Chapter 31. Reading Quizzes A. Resistivity B. Conductivity C. Current density D. Complex impedance E. Johnston’s constant 3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 4 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What quantity is represented by the symbol J ? The electron drift speed in a typical current-carrying wire is A. Resistivity B. Conductivity C. Current density D. Complex impedance E. Johnston’s constant A. B. C. D. E. extremely slow (≈10–4 m/s). moderate (≈ 1 m/s). very fast (≈104 m/s). Could be any of A, B, or C. No numerical values were provided. 6 5 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. All other things being equal, current will be larger in a wire that has a larger value of The electron drift speed in a typical current-carrying wire is A. B. C. D. E. extremely slow (≈10–4 m/s). moderate (≈ 1 m/s). very fast (≈104 m/s). Could be any of A, B, or C. No numerical values were provided. A. B. C. D. E. conductivity. resistivity. the coefficient of current. net charge. potential. 7 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 8 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. All other things being equal, current will be larger in a wire that has a larger value of A. B. C. D. E. The equation I = ∆V/R is called A. Ampère’s law. B.Faraday’s law. C. Ohm’s law. D. Weber’s law. conductivity. resistivity. the coefficient of current. net charge. potential. 10 9 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Electron Current The electron current I is the number of electrons per second that pass through a cross section of a wire. The units of electron current are s-1. The equation I = ∆V/R is called A. Ampère’s law. B. Farady’s law. C. Ohm’s law. D. Weber’s law. N e = i∆ t 11 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 12 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Electric Current The Electron Current i = nAv d Typical Vd is about 10-4 m/s. N e = nV = nA∆x = nAvd ∆t N e = i∆t = nAvd ∆t i = nAv d The drift speed vd is the net speed with which the electrons move, not the speed at which any one electron is bouncing around. 14 13 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Law of Conservation of Current: the electron current is the same at all points in a currentcarrying wire. How long does it take to discharge a capacitor? 0.2 [m] /10-4 [m/s] = 2000 s? The electron current at A is exactly equal to the electron current at B. 15 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 16 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. How long does it take to discharge a capacitor? Establishing the Electric Field in a Wire N e = i∆t = nAv d ∆t ∆t = ∆t = Ne nAv d 1011 = 9 ⋅10 −10 s 8.5 ⋅10 [m ] ⋅ 3.14 ⋅ 4 ⋅10 −6 [m 2 ] ⋅10 − 4 [m / s] 28 −3 18 17 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A Model of Conduction A Model of Conduction ax = v x = vix + a x ∆t = vix + eE ∆t m F eE = m m The energy transfer is the “friction” that raises the temperature of the wire. v x = vix + a x ∆t = vix + eE ∆t m eE vd = v = vix + τ m vd = eE τ m 19 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 20 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Current and Current Density A Model of Conduction eE τ vd = m I ≡( i = nAv d neτAE i= m r dQ , in the direction of E ) dt 1 Ampere = 1 A = 1 coulomb per second = 1 C/s I= The electron current is directly proportional to the electric field strength. Q eN e = = ei ∆t ∆t The direction of the current I in a metal is opposite the direction of motion of the electrons. The current direction in a wire is from the positive terminal of a battery to the negative terminal. 21 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Conservation of Current ∑I in 22 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Current Density in a Wire = ∑ I out I = ei = nevd A J = current density = I = nev d A I = JA 23 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 24 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Conductivity and Resistivity Conductivity and Resistivity J = σE eτE ne 2τ J = nev d = ne ( )= E m m ne 2τ σ = conductivi ty = m 1 m ρ = resistivit y = = 2 σ ne τ 26 25 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Resistance and Ohm’s Law Ohm’s Law The resistance of a long, thin conductor of length L and cross=sectional area A is • Ohm’s law is limited to those materials whose resistance R remains constant—or very nearly so—during use. • The materials to which Ohm’s law applies are called ohmic. The SI unit of resistance is the ohm. 1 ohm = 1 Ω = 1 V/A. The current through a conductor is determined by the potential difference ∆V along its length: • The current through an ohmic material is directly proportional to the potential difference. Doubling the potential difference doubles the current. • Metal and other conductors are ohmic devices. 27 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 28 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 31. Summary Slides 29 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 30 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles General Principles 31 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 32 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles Important Concepts 33 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 34 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts Important Concepts 35 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 36 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications Chapter 31. Questions 37 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. These four wires are made of the same metal. Rank in order, from largest to smallest, the electron currents ia to id. A. B. C. D. E. 38 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. These four wires are made of the same metal. Rank in order, from largest to smallest, the electron currents ia to id. id > ia > ib > ic ib = id > ia = ic ic > ib > ia > id ic > ia = ib > id ib = ic > ia = id A. B. C. D. E. id > ia > ib > ic ib = id > ia = ic ic > ib > ia > id ic > ia = ib > id ib = ic > ia = id 40 39 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Why does the light in a room come on instantly when you flip a switch several meters away? Why does the light in a room come on instantly when you flip a switch several meters 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 from the switch into the wire immediately causes electrons to flow from 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 from switch to the light at the speed of light in an optical fiber. 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 from the switch into the wire immediately causes electrons to flow from 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 from switch to the light at the speed of light in an optical fiber. 41 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 42 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. What are the magnitude and the direction of the current in the fifth wire? What are the magnitude 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 determine 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 determine 43 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 44 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.