PHY2049: Chapter 261Current and ResistancePHY2049: Chapter 262What You Will Learn in This ChapterÎNature of electric currentÎDrift speed, current and current densityÎCurrent and voltage measurementsÎConductivity and resistivityÎOhm’s lawÎTemperature variations of resistanceÎSuperconductorsÎPower in electric circuitsÎElectrical activity in the heartPHY2049: Chapter 263The electric current is defined asÎAmount of charge per timeÎAmount of charge per areaÎAmount of charge per volumeÎAmount of chargePHY2049: Chapter 264EMFÎEMF device performs work on charge carriers Converts energy to electrical energy Moves carriers from low potential to high potential Maintains potential difference across terminalsÎVarious types of EMF devices Battery Electrolytic reaction Generator Magnetic field Fuel cell Oxidation of fuel Solar cell Electromagnetic energy Thermopile Nuclear decayÎExample: battery Two electrodes (different metals) Immersed in electrolyte (dilute acid) One electrode develops + charge, the other – chargePHY2049: Chapter 265Common dry cell batteryPHY2049: Chapter 266Electric CurrentÎConnecting the terminals of a battery across device leads to an electric circuit Charge begins to flow: electric current Units: 1 Coulomb/s = 1 Ampere (A)ÎSymbol:tqIΔΔ=+-V+-orPHY2049: Chapter 267Direction of the currentÎIn conductors, electrons are free and carry the charge But direction of current is defined as flowing from the positive to the negative terminal So current points in opposite direction from electron movementIn the wire, electrons movevery slowly (0.05 mm/s).~ 1 meter per 5 hours!!+++--------IPHY2049: Chapter 268Example of Electron FlowÎConsider a current of 1A. Find the number of electrons flowing past a point per secondÎSo, in one second, number of electrons passing a point is1 A 1 coulomb / secqtΔ=⇒Δ18191 coulomb6.2 10 electrons1.6 10eN−==××PHY2049: Chapter 269Current and Electron Drift SpeedÎConsider a material where current (electrons) is flowing Let ne= # free charge carriers / m3 Let q = charge per charge carrier Let A = cross sectional area of materialÎTotal charge ΔQ in volume element moving past a pointÎIf charges moving with drift speed vd, then Δx = vdΔtÎThus, current can be written in terms of basic quantities()eQnAxqΔ= Δ()edQnAvtqΔ= ΔedQinqAvtΔ==Δ-----xΔAusing VAxΔ=ΔPHY2049: Chapter 2610Example of Drift SpeedÎ10A flowing through a copper wire of diameter 2mm Density of Cu = 8.92 g/cm3 1 free electron per Cu atom Atomic mass ACu= 63.5ÎFind drift speed vdusing e is electron charge Find A: Still need ne= density of electrons (#/m3)edineAv=()223 623.14 10 3.14 10 mArπ−−==× =×191.6 10e−=×328 3Cu323Cu8.92 101 8.5 10 / m63.5 10 /6.02 10enmρ−×=×= =×××PHY2049: Chapter 2611Example of Drift Speed (cont.)ÎSolve for electron drift speed vdÎThus vdis 0.24 mm/sec: ~1 hour to move 1 mÎBut electrons actually move ~ 106m/s in material! This is ~ 4 × 109times larger than drift speed()( )( )428 19 6102.4 10 m/s8.5 10 1.6 10 3.14 10deivneA−−−== =××× ×PHY2049: Chapter 2612Electrons in the WireÎIf the electrons move so slowly through the wire, why does the light go on right away when we flip a switch? Household wires have almost no resistance The electric field inside the wire travels much faster Light switches do not involve currents None of the aboveLike a hose full of water whenyou turn on the faucetPHY2049: Chapter 2613Electrons in the Wire, Part 2 ÎOkay, so the electric field in a wire travels quickly. But, didn’t we just learn that E = 0 inside a conductor? True, it can’t be the electric field after all!! The electric field travels along the outside of the conductor E = 0 inside the conductor applies only to static charges None of the aboveEMF source constantly replenishes E fieldPHY2049: Chapter 2614Current DensityUniform currentSurface of area A(normal to current)2"current density" (A/m )IJJA≡=PHY2049: Chapter 2615Current Density ExampleÎPrevious example: I = 10 A flowing in 2mm diameter wire()223 623.14 10 3.14 10 mArπ−−==× =×726103.2 10 A/m3.14 10IJA−== ××PHY2049: Chapter 2616Current Density (More General)SId=⋅∫JAJSVariable J,curved surfaceDifference between I and J:• I depends on overall geometry• J(x) is a “local” quantity definedat any point in spacePHY2049: Chapter 2617Why Use Current Density?ÎI depends on material properties + shape, size of surfaceÎJ depends only on properties at a point in space J(x) depends on material properties and E field at point x Useful when shape is complex or applied field is non-uniformÎConsider equation for current and drift velocityÎGet current density J = i / AÎvdhas magnitude/direction at any point in space ⇒ vectorÎThis is “atomic-level” definition of
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