Physics 2102Physics 2102Lecture 13: WED 11 FEBLecture 13: WED 11 FEBCapacitors III / Current & ResistanceCapacitors III / Current & ResistancePhysics 2102Jonathan DowlingCh25.6–7Ch26.1–3Georg Simon Ohm (1789-1854)We Are Borg.Resistance IsFutile!Exam 01:Sec. 2 (Dowling) Average: 67/100A: 90–100 B: 80–89 C: 60–79 D: 50–59Graders:Q1/P1: Dowling (NICH 453, MWF 10:30AM-11:30AM)Q2/P2: Schafer (NICH 222B, MW 1:30-2:30 PMQ3/P3: Buth (NICH 222A, MF 2:30-3:30 PM )Q4/P4: Lee (NICH 451, WF 2:30-3:30 PMSolutions:http://www.phys.lsu.edu/classes/spring2009/phys2102/Go over the solutions NOW.Material will reappear on FINAL!(ii) (4 pts) What is the direction of the net electrostaticforce on the central particle due to the other particles?F≠E! Units!F≠E!Most common mistaketo Compute Magnitudeand Direction ofElectric Field insteadof Electric Force atCentral Point.FThis problem from our slides first week of class.xq3x–LF13F32Charges Alone Could Cancel toLeft and To Right. Mustdiscuss Big & Small Chargeversus Small and Big Distance:Q vs. 1/r2Common mistake: To putq3 at –L to Left “By Symmetry” Thiswould only make sense if q3 and q2were held and q1 was free. But weare told q1 and q2 are fixed and q3 isfree to move. So no symmetry!Common mistake: Wrong x.This is Sample Problem from Book We worked on Board ! ! F 31=! F 32 " k q3q1r312=k q3q2r3124kQ2x2=kQ2x # L( )2 " 4x2=1x # L( )24 x # L( )2= x2 " ± 2 x # L( )= x+2 x # L( )= x or # 2 x # L( )= xx = 2L or x = 2L / 3Not to right.Dielectric ConstantDielectric Constant• If the space between capacitorplates is filled by a dielectric,the capacitance INCREASES bya factor κ• This is a useful, workingdefinition for dielectric constant.• Typical values of κ are 10–200+Q–QDIELECTRICC = κε0 A/dThe κ and the constantε=κεo are both calleddielectric constants. The κhas no units (dimensionless).Atomic ViewEmolEcapMolecules set upcounter E field Emolthat somewhat cancelsout capacitor field Ecap.This avoids sparking(dielectric breakdown)by keeping field insidedielectric small.Hence the bigger thedielectric constant themore charge you canstore on the capacitor.ExampleExample• Capacitor has charge Q, voltage V• Battery remains connected whiledielectric slab is inserted.• Do the following increase,decrease or stay the same:– Potential difference?– Capacitance?– Charge?– Electric field?dielectric slabExampleExample• Initial values:capacitance = C; charge = Q;potential difference = V;electric field = E;• Battery remains connected•V is FIXED; Vnew = V (same)•Cnew = κC (increases)•Qnew = (κC)V = κQ (increases).• Since Vnew = V, Enew = V/d=E (same)dielectric slabEnergy stored? u=ε0E2/2 => u=κε0E2/2 = εE2/2SummarySummary• Any two charged conductors form a capacitor.• Capacitance : C= Q/V• Simple Capacitors:Parallel plates: C = ε0 A/dSpherical : C = 4π ε0 ab/(b-a)Cylindrical: C = 2π ε0 L/ln(b/a)• Capacitors in series: same charge, not necessarily equal potential;equivalent capacitance 1/Ceq=1/C1+1/C2+…• Capacitors in parallel: same potential; not necessarily same charge;equivalent capacitance Ceq=C1+C2+…• Energy in a capacitor: U=Q2/2C=CV2/2; energy density u=ε0E2/2• Capacitor with a dielectric: capacitance increases C’=kCWhat are we going to learn?What are we going to learn?A road mapA road map• Electric chargeè Electric force on other electric chargesè Electric field, and electric potential• Moving electric charges : current• Electronic circuit components: batteries, resistors,capacitors• Electric currents è Magnetic fieldè Magnetic force on moving charges• Time-varying magnetic field è Electric Field• More circuit components: inductors.• Electromagnetic waves è light waves• Geometrical Optics (light rays).• Physical optics (light waves)The resistance is related to the potential we need to apply to a deviceto drive a given current through it. The larger the resistance, the largerthe potential we need to drive the same current.) (abbr. OhmAmpereVolt [R] :Units !"=Georg Simon Ohm (1789-1854)"a professor who preaches such heresies is unworthy to teach science.” Prussian minister of education 1830iVR !iRVRVi == and : thereforeandOhm’s lawsDevices specifically designed to have a constant value of R are calledresistors, and symbolized byElectrons are not “completely free to move” in a conductor. They moveerratically, colliding with the nuclei all the time: this is what we call“resistance”.Resistance is NOT Futile!Resistance is NOT Futile!! i "dqdt =Cs# $ % & ' ( " Ampere[ ]= A[ ]J! :VectorE! as direction Same!"= AdJi!! that suchEiJdAIf surface is perpendicular to a constant electricfield, then i=JA, or J=i/ADrift speed: vd :Velocity at which electrons move in order to establish a current.EiLACharge q in the length L of conductor:eLAnq )(=n =density of electrons, e =electric chargedvLt =ddveAnvLeLAntqi ===enJeAnivd==dvenJ!!=Current density and drift speedCurrent density and drift speedThe current is the flux of the current density!2mAmpere][ =JUnits:These two devices could have the same resistanceR, when measured on the outgoing metal leads.However, it is obvious that inside of them differentthings go on.Metal“field lines”resistivity:JEJE!!!!== vectors,as or, Resistivity is associatedwith a material, resistancewith respect to a deviceconstructed with the material.!"1 :tyConductivi =Example:ALV+-AiJLVE == ,LARAiLV==!ALR!=Makes sense!For a given material: resistance LessThickerresistance MoreLonger !!Resistivity Resistivity and resistanceand resistance( resistance: R=V/I )! "# $m[ ]= Ohm % meter[ ]Resistivity Resistivity and Temperatureand Temperature• At what temperature would the resistance ofa copper conductor be double its resistance at20.0°C?• Does this same "doubling temperature" holdfor all copper conductors, regardless of shapeor size?Resistivity depends ontemperature: ρ = ρ0(1+α (T-T0) )baPower in electrical circuitsPower in electrical circuitsA battery “pumps” charges through theresistor (or any device), by producing apotential difference V between points aand b. How much work does the batterydo to move a small amount of charge dqfrom b to a?dW!= –dU!= -dq•V!=!(dq/dt)•dt•V= iV•dtThe battery “power” is the work it does per unit time: P!=!dW/dt!=!iVP=iV is true for the battery pumping charges through any device. If thedevice follows Ohm’s law (i.e., it is a
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