Physics 2102 Lecture 13: WED 11 FEBPowerPoint PresentationSlide 3Slide 4Dielectric ConstantSlide 6ExampleExampleSummaryWhat are we going to learn? A road mapSlide 11Slide 12Slide 13Resistivity and TemperaturePower in electrical circuitsPhysics 2102 Physics 2102 Lecture 13: WED 11 FEBLecture 13: WED 11 FEBCapacitors III / Current & Capacitors III / Current & ResistanceResistancePhysics 2102Jonathan DowlingCh25.6–7QuickTime™ and a decompressorare needed to see this picture.Ch26.1–3QuickTime™ and a decompressorare needed to see this picture.Georg Simon Ohm (1789-1854)We Are Borg.Resistance Is Futile!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 electrostatic force on the central particle due to the other particles?F≠E! Units!F≠E!Most common mistake to Compute Magnitude and Direction of Electric Field instead of Electric Force at Central Point. FThis problem from our slides first week of class.xq3x–LF13F32Charges Alone Could Cancel to Left and To Right. Must discuss Big & Small Charge versus Small and Big Distance: Q vs. 1/r2Common mistake: To putq3 at –L to Left “By Symmetry” This would only make sense if q3 and q2 were held and q1 was free. But we are told q1 and q2 are fixed and q3 is free to move. So no symmetry! Common mistake: Wrong x.This is Sample Problem from Book We worked on Board € r F 31=r 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 capacitor plates is filled by a dielectric, the capacitance INCREASES by a factor •This is a useful, working definition for dielectric constant.•Typical values of are 10–200+Q–QDIELECTRICC = A/dC = A/dThe and the constant o are both called dielectric constants. The has no units (dimensionless).The and the constant o are both called dielectric constants. The has no units (dimensionless).Atomic ViewEmolEcapMolecules set up counter E field Emol that somewhat cancels out capacitor field Ecap. This avoids sparking (dielectric breakdown) by keeping field inside dielectric small. Hence the bigger the dielectric constant the more charge you can store on the capacitor.Example Example •Capacitor has charge Q, voltage V•Battery remains connected while dielectric 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 = C (increases)•Qnew = (C)V = Q (increases).•Since Vnew = V, Enew = V/d=E (same)dielectric slabEnergy stored? u=0E2/2 => u=0E2/2 = E2/2SummarySummary• Any two charged conductors form a capacitor.• Capacitance : C= Q/V• Simple Capacitors:Parallel plates: C = 0 A/dSpherical : C = 4 0 ab/(b-a)Cylindrical: C = 2 0 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=0E2/2• Capacitor with a dielectric: capacitance increases C’=kCWhat are we going to What are we going to learn?learn?A road mapA road map•Electric charge Electric force on other electric charges Electric field, and electric potential•Moving electric charges : current •Electronic circuit components: batteries, resistors, capacitors•Electric currents Magnetic field Magnetic force on moving charges•Time-varying magnetic field Electric Field•More circuit components: inductors. •Electromagnetic waves light waves•Geometrical Optics (light rays). •Physical optics (light waves)The resistance is related to the potential we need to apply to a device to drive a given current through it. The larger the resistance, the larger the potential we need to drive the same current. ) (abbr. OhmAmpereVolt [R] :Units Ω≡=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 move erratically, colliding with the nuclei all the time: this is what we call “resistance”.Resistance is NOT Resistance is NOT Futile!Futile!€ i ≡dqdt =Cs ⎡ ⎣ ⎢ ⎤ ⎦ ⎥≡ Ampere[ ]= A[ ]€ i ≡dqdt =Cs ⎡ ⎣ ⎢ ⎤ ⎦ ⎥≡ Ampere[ ]= A[ ]Jr :VectorEr as direction Same∫⋅= AdJirr that suchEiJdAIf surface is perpendicular to a constant electric field, 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==dvenJrr=Current density and Current density and drift speeddrift 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 different things go on.Metal“field lines”resistivity:JEJErrρρ == vectors,as or, Resistivity is associatedwith a material, resistancewith respect to a deviceconstructed with the material.ρσ1 :tyConductivi =Example:ALV+-AiJLVE == ,LARAiLV==ρALR ρ=Makes sense!For a given material: resistance LessThickerresistance MoreLonger →→Resistivity and Resistivity and resistanceresistance( resistance: R=V/I )€ ρ ≡ Ωm[ ]= Ohm⋅meter[ ]€ ρ ≡ Ωm[ ]= Ohm⋅meter[ ]Resistivity and Resistivity and TemperatureTemperature• At what temperature would the
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