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UVA PHYS 632 - Lecture 6 Current and Resistance Chp. 27

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Lecture 6 Current and Resistance Chp. 27Loop of copper wireWhat is Current?Question What causes charges to move in the wire?Drift speed of electrons and current densityCurrents: Steady motion of charge and conservation of currentQuestion: How does the drift speed compare to the instantaneous speed?What is Resistance?Ohm’s LawPowerPoint PresentationResistance: What is it? Denote it by RExample Temperature variation of resistivity.Slide 13Power dissipation resistorsBatteriesWhat is the relationship between Emf, resistance, current, and terminal voltage?Slide 17Slide 18Combination of resistorsEquivalence of two versions of Ohm’s LawWarm-up Set 6What is the electric field in a sphere of uniform distribution of positive charge. (nucleus of protons)Slide 23Find the capacitance of a ordinary piece of coaxial cable (TV cable)Capacitance of two concentric spherical shellsModel of coaxial cable for calculation of capacitanceLecture 6 Current and Resistance Chp. 27•Cartoon -Invention of the battery and Voltaic Cell•Opening Demo - Lemon Battery•Warm-up problem•Physlet •Topics•Demos–Lemon Battery estimate internal resistance–Ohms Law demo on overhead projector–T dependence of resistance–Three 100 Watt light bulbs•Puzzles–Resistor network figure out equivalent resistanceLoop of copper wireNothing moving;electrostatic equilibriumNow battery forces charge through the conductor. We have a field in the wire.0=E0≠EWhat is Current?It is the amount of positive charge that moves past a certain point per unit time. + + + + + ++ +ILAmpondCoulombtQI ==ΔΔ=secCopper wire with voltage across itALtv Δ=ΔDrift velocity of chargeQ = charge per unit volume x volumenq x AvtQ = nqAv tDensity of electrons1.6 x 10-19 CDivide both sides by t.nqAvtQI =ΔΔ=Question What causes charges to move in the wire?How many charges are available to move?Example What is the drift velocity for 1 Amp of current flowing through a 14 gauge copper wire of radius 0.815 mm?Drift velocity€ vd=InqAΜ=oNn ρ= 8.4x1022 atoms/cm3€ vd=18.4 ×1022• 1.6 ×10−19• π(.0815)2€ vd= 3.5 ×10−5msThe higher the density the smaller the drift velocityI = 1 Ampq = 1.6x10-19 CA = (.0815 cm)2 = 8.9 grams/cm 3No = 6x1023 atoms/moleM = 63.5 grams/moleDrift speed of electrons and current densityDirections of current i is defined as the direction of positive charge.ddnqvJAiJnAqvi===(Note positive charge moves in direction of E) electron flow is opposite E.Currents: Steady motion of charge and conservation of currenti = i1 + i2(Kirchoff’s 2nd rule)Current is the same throughout all sections in the diagram below; it is continuous.Current density J does vary.Question: How does the drift speed compare to the instantaneous speed?Instantaneous speed  106 m/svd  3.5x10-11 • vinstant (This tiny ratio is why Ohm’s Law works so well for metals.)At this drift speed 3.5x10-5 m/s, it would take an electron 8 hours to go 1 meter. Question: So why does the light come on immediately when you turn on the light switch?It’s like when the hose is full of water and you turn the faucet on, it immediately comes out the ends. The charge in the wire is like the water. A wave of electric field travels very rapidly down the wire, causing the free charges to begin drifting.Example: Recall typical TV tube, CRT, or PC monitor. The electron beam has a speed 5x107 m/s. If the current is I = 100 microamps, what is n?smCAqAvIn7619410510106.110ו•×==−−−Take A = 1mm2 = (10-3)2 = 10-6 m2n = 8.5x1022 e/cm3n = 1.2x1013 e/m3 = 1.2x107 e/cm3 For CRTFor CopperThe lower the density the higher the speed.What is Resistance?The collisions between the electrons and the atoms is the cause of resistance and a very slow drift velocity of the electrons. The higher density, the more collisions.The dashed lines represent the straight line tracks of electrons in between collisions•Electric field is off.•Electric field is on. When the field is on, the electron traveled drifted further to BI.e-field offfield onextra distance electron traveledOhm’s LawWant to emphasize here that as long as we have current (charge moving) due to an applied potential, the electric field is no longer zero inside the conductor.I• •A BLPotential differenceVB - VA = E LConstant EI = current  E L (Ohm’s Law)True for many materials – not all. Note that this is an experimental observation and is not a true law.Constant of proportionality between V and I is known as the resistance. The SI unit for resistance is called the ohm.V = RI R = V/I Ohm = volt/ampDemo: Show Ohm’s LawBest conductorsSilver – w/ sulpherCopper – oxidizesGold – pretty inertNon-ohmic materialsDiodesSuperconductorsA test of whether or not a material satisfies Ohm’s LawV = IRI = V/RSlope = 1/R = constantOhm’s Law is satisfied.Here the slope depends on the potential difference. Ohm’s Law is violated.• Depends on shape, material, temperature.• Most metals: R increases with increasing T• Semi-conductors: R decreases with increasing TDefine a new constant which characterizes materials.ResistivityLAR=ρALρALR =Demo: Show temperature dependence of resistanceFor materials  = 10-8 to 1015 ohms-metersExample: What is the resistance of a 14 gauge Cu wire? Find the resistance per unit length.mcu mALRΩ−−−×≅×Ω×==3238108)10815(.14.3107.1ρBuild circuits with copper wire. We can neglect the resistance of the wire. For short wires 1-2 m, this is a good approximation.Resistance: What is it? Denote it by RExample Temperature variation of resistivity. = 20 [ 1 +  (T-20) ]ρALR =can be positive or negativeConsider two examples of materials at T = 20oC.(-m)(k-1)L Area R (20oC)Fe 10-7.005 6x106 m 1mm2(10-6m2) 60,000 Si 640 -.075 1 m 1 m2640 Fe – conductor - a long 6x106 m wire.Si – insulator - a cube of Si 1 m on each sideQuestion: You might ask is there a temperature where a conductor and insulator are one and the same?Condition: RFe = RSi at what temperature?UseρALR == 20 [ 1 +  (T-20) ] ALRFe = 10-7 -m [ 1 + .005 (T-20)]26610106mm−×RSi = 640 -m [ 1 + .075 (T-20)]211mmSet RFe = RSi and solve for TT – 20 = -196C (pretty low temperature)T = -176CResistance at different TemperaturesCu .1194  .0152  conductorNb .0235  .0209  impureC .0553  .069  semiconductorT = 300 K = 77 KPower


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