PHY2054: Chapter 171Current and ResistancePHY2054: Chapter 172What You Will Learn in This ChapterÎNature of electric currentÎDrift speed and currentÎCurrent and voltage measurementsÎConductivity and resistivityÎOhm’s lawÎTemperature variations of resistanceÎSuperconductorsÎPower in electric circuitsÎElectrical activity in the heartPHY2054: Chapter 173CurrentÎThe electric current is defined as (a) Amount of charge per time (b) Amount of charge per volume (c) Amount of charge per area (d) Amount of charge (e) None of theseqItΔ=ΔPHY2054: Chapter 174EMFÎEMF 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 – chargePHY2054: Chapter 175Common dry cell batteryPHY2054: Chapter 176Electric 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:+-V+-orqItΔ=ΔPHY2054: Chapter 177Direction of the currentÎIn conductors, electrons are free and carry the chargeÎBut direction of current is defined as flowing from the positive to the negative terminal+++---PHY2054: Chapter 178Example 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−==××PHY2054: Chapter 179Current 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 move with average drift speed vd, Δx = vdΔtÎThus, current can be written in terms of basic quantities()eQnAxqΔ= Δ()edQnAvtqΔ= ΔedQinqAvtΔ==Δ-----IPHY2054: Chapter 1710Example of Drift SpeedÎ10A flowing through a copper wire of diameter 2mm Density of Cu = 8.92 g/cm3= 8920 kg/m3 1 free electron per Cu atom Atomic mass ACu= 63.5ÎFind drift speed vdusing e is charge Find A: Still need ne= density of electrons = number density of Cu atomsedineAv=()223 623.14 10 3.14 10 mArπ−−==× =×191.6 10e−=×28 3Cu323Cu892018.4610 /m63.5 10 /6.02 10enmρ−=×= =×××PHY2054: Chapter 1711Example of Drift Speed (cont.)ÎSolve for electron drift speed vdÎThus vdis 0.24 mm/sec: ~1 hour to move 1 mÎCalculate thermal speed vrmsÎThis is ~ 5 × 108times larger than drift speed!()()()428 19 6102.4 10 m/s8.46 10 1.6 10 3.14 10deivneA−−−== =××× ×235rms3133 1.38 10 3001.17 10 m/s9.11 10BekTvm−−×× ×== =××231rms22eBmv k T=T ≅ 300KPHY2054: Chapter 1712Electrons in the WireÎ If the electrons move so slowly through the wire, why does the light go on right away when we flip a switch?1. Household wires have almost no resistance2. The electric field inside the wire travels much faster3. Light switches do not involve currents4. None of the aboveThink of what happens when you turn on a hose full of water. Water atend of hose comes out immediately because of push by pressure wave.PHY2054: Chapter 1713Electrons in the Wire, Part 2 Î Okay, so the electric field in a wire travels quickly. But, didn’t we just learn that E = 0 inside a conductor?1. True, it can’t be the electric field after all!!2. The electric field travels along the outside of the conductor3. E = 0 inside the conductor applies only to static charges4. None of the abovePHY2054: Chapter 1714Resistance and Ohm’s LawÎOhm’s law is an empirical observation: for most materials the current is proportional to the applied voltageÎWe write the constant of proportionality as R and call it the “resistance”, measured in ohms (Ω)ÎExample, 120 V applied to a material gives I = 15 A. R = 120/15 = 8ΩÎMost materials are “ohmic”, i.e. obey Ohm’s law over a very wide range of applied voltages Common “nonohmic” materials are semiconductors such as silicon & germanium for which current rises exponentially with
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