Lecture 6 Current and Resistance Ch. 26Loop 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?PowerPoint PresentationWhat is Resistance?Ohm’s LawSlide 11Resistance: What is it? Denote it by RExample Temperature variation of resistivity.Slide 14Resistance at Different TemperaturesPower dissipation resistorsBatteriesWhat is the relationship between Emf, resistance, current, and terminal voltage?Slide 19Combination of resistorsEquivalent ResistanceResistance cubeResistance Cube cont.1Lecture 6 Current and Resistance Ch. 26•Cartoon -Invention of the battery and Voltaic Cell•Warm-up problem•Topics–What is current?–Current density–Conservation of Current–Resistance–Temperature dependence–Ohms Law–Bateries, terminal voltage, imdedance matching–Power dissipation–Combination of resistiors•Demos–Ohms Law demo on overhead projector–T dependence of resistance–Three 100 Watt light bulbs•Puzzles–Resistor network figure out equivalent resistance2Loop of copper wireNothing moving;electrostatic equilibriumNow battery voltage forces charge through the conductor and we have a field in the wire.0=E0≠E3What 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 chargeDensity of electrons1.6 x 10-19 CDivide both sides by t.nqAvtQI =ΔΔ=tnqAv QtAvnq volume volume unit per chargeΔ=ΔΔ×=×=ΔQ4Question 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/cm321922)0815(.106.1104.813cmCampvcmatomsdπ××××=−smdv5105.3−×=The 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/mole5Drift speed of electrons and current densityDirections of current i is defined as the direction of positive charge.(Note positive charge moves in direction of E) electron flow is opposite E.ddnqvJAiJnAqvi===6Currents: Steady motion of charge and conservation of currentCurrent is the same throughout all sections in the diagram below; it is continuous.Current density J does vary.Rule) 2 s(Kirchoff' nd21iii ==7Question: How does the drift speed compare to the instantaneous speed?Instantaneous speed  106 m/s(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.tinsdvvtan11105.3−×≈8Example: 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?sm726194105m10C106.1A10qAvIn×⋅⋅×==−−−For CRTFor CopperTake A The lower the density the higher the speed.26232m10)m10(mm1−−===37313cmelectrons102.1melectrons102.1n ×=×=322cmelectrons105.8n ×=9What is Resistance?The collisions between the electrons and the atoms is the cause of resistance and the cause fo a very slow drift velocity of the electrons. The higher the density, the more collisions you have.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 traveled10Ohm’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 differenceTrue for many materials – not all. Note that Ohms Law 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.Demo: Show Ohm’s LawBest conductorsSilver Copper – oxidizesGold – pretty inertNon-ohmic materialsDiodesSuperconductorsconstant. is E where,LEVVABΔ=−law) s(Ohm' current LEI Δ∝=IVR ==RIVampVoltOhm =11A test of whether or not a material satisfies Ohm’s Lawsatisfied islaw sOhm'constant1Slope ====RRVIIRVHere the slope depends onthe potential difference.Ohm's Law is violated for a pn junction diode.12• 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.mcumALRΩ−−−×≅×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 RNote Conductivity = 1/Resistivity  113Example Temperature variation of resistivity.ρALR =can be positive or negativeConsider two examples of materials at T = 20oC.20 (-m)(C-1)L Area R (20oC)Fe 10 -70.005 6x106 m 1mm2(10-6m2)60,000 Si 640 - 0.075 1 m 1 m2Fe – 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?ρ =ρ201 + α(T − 20)[ ]640 14Condition: RFe = RSi at what temperature?UseρALR =RFe = 10-7 -m [ 1 + .005 (T-20)]26610106mm−×RSi = 640 -m [ 1 + .075 (T-20)]211mmNow, set RFe = RSi and solve for TT – 20 C = – 196 CT = – 176 C or 97 K(pretty low temperature) R =ρ201+α(T −20 C)[ ]LA15Resistance at Different Temperatures T =293K T = 77K (Liquid Nitrogen)Cu .1194  .0152  conductorNb .0235  .0209  impureC .0553 