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C U R R E N T E L E C T R I C I T Y - I 1 . E l e c t r i c C u r r e n t

C U R R E N T E L E C T R I C I T Y - I 1 . E l e c t r i c C u r r e n t 2 . C o n v e n t i o n a l C u r r e n t 3 . D r i ft V e l o c i ty o f e l e c t r o n s a n d c u r r e n t 4 . C u r r e n t D e n s i ty 5 . O h m ’ s L a w

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C U R R E N T E L E C T R I C I T Y - I 1 . E l e c t r i c C u r r e n t

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  1. CURRENTELECTRICITY-I 1.ElectricCurrent 2.ConventionalCurrent 3.DriftVelocityofelectronsandcurrent 4.CurrentDensity 5.Ohm’sLaw 6.Resistance,Resistivity,Conductance&Conductivity 7.Temperaturedependenceofresistance 8.ColourCodesforCarbonResistors 9.SeriesandParallelcombinationofresistors 10.EMFandPotentialDifferenceofacell 11.InternalResistanceofacell 12.SeriesandParallelcombinationofcells

  2. ElectricCurrent: Theelectriccurrentisdefinedasthechargeflowingthroughanysectionoftheconductorinonesecond. I=q/t(iftherateofflowofchargeissteady) I=dq/dt(iftherateofflowofchargevarieswithtime) Differenttypesofcurrent: a)SteadycurrentwhichdoesnotIbc b)&c)Varyingcurrentwhose magnitudevarieswithtimed d)Alternatingcurrentwhose0 anddirectionchangesperiodically a varywithtime t magnitudevariescontinuously

  3. ConventionalCurrent: Conventionalcurrentisthecurrent+- themotionofpositivechargeunderthe+- Conventionalcurrentduetomotionof---+ thatofmotionofelectrons.I+ Driftvelocityisdefinedasthevelocity withwhichthefreeelectronsgetdriftedl effectoftheappliedelectricfield. vd=aτvd=-(eE/m)τI=neAvdI Currentisdirectlyproportional todriftvelocity. vd-driftvelocity,a–acceleration,τ–relaxationtime,E–electricfield, e–electroniccharge,m–massofelectron,n–numberdensityofelectrons, l–lengthoftheconductorandA–Areaofcross-section + + + + - whosedirectionisalongthedirectionof I + - actionofelectricfield. - - electronsisinthedirectionoppositeto + - - + DriftVelocityandCurrent: towardsthepositiveterminalunderthe E A vd- - -

  4. Currentdensity: Currentdensityatapoint,withinaconductor,isthecurrentthroughaunitareaoftheconductor,aroundthatpoint,providedtheareaisperpendiculartothedirectionofflowofcurrentatthatpoint. J=I/A=nevd Invectorform,I=J.A Ohm’sLaw: Theelectriccurrentflowingthroughaconductorisdirectlyproportionaltothepotentialdifferenceacrossthetwoendsoftheconductorwhenphysicalconditionssuchastemperature,mechanicalstrain,etc.remainthesame.I IαVorVαIorV=RI IV 0V

  5. Resistance: Theresistanceofconductoristheoppositionofferedbytheconductortotheflowofelectriccurrentthroughit. R=V/I Resistanceintermsofphysicalfeaturesoftheconductor: m lne2τ specificresistance I=mlResistanceisdirectlyproportionalto Vmlcross-sectionalareaoftheconductor m lResistivitydependsuponnatureof dimensionsoftheconductor. I =neA|vd| whereρ= R=ρA isresistivityor I =neA(e|E| ne2Aτ /m) τ V lengthandinverselyproportionalto = anddependsonnatureofmaterial. ne2Aτ I materialandnotonthegeometrical R= ne2τA

  6. Relationsbetweenvd,ρ,l,E,JandV: ρ=E/J=E/nevd(since,J=I/A=nevd)increases, d increases. (since,E=V/l) decreases. Conductanceandconductivity: Conductanceisthereciprocalofresistance.ItsS.Iunitismho. Conductivityisthereciprocalofresistivity.ItsS.Iunitismho/m. TemperaturedependenceofResistances: m lWhentemperatureincreases,theno.ofcollisions decreases.Therefore,Resistanceincreases. TemperaturecoefficientofResistance:R0–Resistanceat0°C α=orα=t 11 IfR2<R1,thenαis–ve.R2–Resistanceatt2°C Whentemperature vddecreasesandρ Whenlincreases,vd v = E /(neρ) vd = V /(neρl) increasesduetomoreinternalenergyandrelaxationtime R= ne2τA R2–R1 Rt–R0 R–Resistanceatt°C R–Resistanceatt°C R1t2–R2t1 R0t

  7. Colourcodeforcarbonresistors: Thefirsttworingsfromtheendgivethe firsttwosignificantfiguresofBVBGold resistanceinohm.17x100=17±5%Ω Thethirdringindicatesthedecimal multiplier. Thelastringindicatesthetolerancein percentabouttheindicatedvalue.GRBSilver Eg.ABx10C±D%ohm52x106±10%Ω LetterColourNumberColourTolerance BBlack0Gold5% BBrown1Silver10% RRed2Nocolour20% OOrange3 YYellow4 GGreen5 VViolet7GoodWife GGrey8 WWhite9 BVB 52x100=52±20%Ω BBROYofGreatBritainhasVery B Blue 6

  8. AnotherColourcodeforcarbonresistors: i)Thecolourofthebodygivesthefirst significantfigure.RedEndsYellowBodyGoldRing ii)ThecolouroftheendsgivesthesecondBlueDot iii)ThecolourofthedotgivesthedecimalYRBGold multipier. 42x106±5%Ω tolerance. Seriescombinationofresistors: R=R1+R2+R3 R1R2R3Risgreaterthanthegreatestofall. Parallelcombinationofresistors: 123 R2Rissmallerthanthesmallestofall. R3 significantfigure. iv) Thecolourofthering givesthe R1 1/R=1/R+1/R+1/R

  9. Sourcesofemf: Theelectromotiveforceisthemaximumpotentialdifferencebetweenthetwoelectrodesofthecellwhennocurrentisdrawnfromthecell. ComparisonofEMFandP.D: EMFPotentialDifference 1EMFisthemaximumpotentialP.Disthedifferenceofpotentialsdifferencebetweenthetwobetweenanytwopointsinaclosedelectrodesofthecellwhennocircuit. currentisdrawnfromthecell i.e.whenthecircuitisopen. 2ItisindependentoftheItisproportionaltotheresistanceresistanceofthecircuit.betweenthegivenpoints. 3Theterm‘emf’isusedonlyforItismeasuredbetweenanytwothesourceofemf.pointsofthecircuit. 4ItisgreaterthanthepotentialHowever,p.d.isgreaterthanemfdifferencebetweenanytwowhenthecellisbeingcharged.pointsinacircuit.

  10. InternalResistanceofacell: Theoppositionofferedbytheelectrolyteofthecelltotheflowofelectriccurrentthroughitiscalledtheinternalresistanceofthecell. FactorsaffectingInternalResistanceofacell: i)Largertheseparationbetweentheelectrodesofthecell,morethelengthoftheelectrolytethroughwhichcurrenthastoflowandconsequentlyahighervalueofinternalresistance. ii)Greatertheconductivityoftheelectrolyte,lesseristheinternalresistanceofthecell.i.e.internalresistancedependsonthenatureoftheelectrolyte. iii)Theinternalresistanceofacellisinverselyproportionaltothecommonareaoftheelectrodesdippingintheelectrolyte. iv)Theinternalresistanceofacelldependsonthenatureoftheelectrodes. E=V+v =IR+IrEr =I(R+r)v II Thisrelationiscalledcircuitequation. V R I=E/(R+r)

  11. InternalResistanceofacellintermsofE,VandR: E=V+vEr Ir=E-Vv DividingbyIR=V,RIrE–VEV IRVV DeterminationofInternalResistanceofacellbyvoltmetermethod: VV rr II R.B(R)R.B(R) KK EMF(E)ismeasuredPotentialDifference(V)ismeasured =V+Ir I I r=(-1)R = + + Opencircuit(No currentisdrawn) Closedcircuit (Currentisdrawn)

  12. CellsinSeriescombination: Cellsareconnectedinserieswhentheyarejoinedendtoendsothatthesamequantityofelectricitymustflowthrougheachcell. NOTE: sumoftheindividualemfs sameandisidenticalwiththeR currentintheentire arrangement.V 3.Thetotalinternalresistanceofthebatteryisthesumoftheindividualinternalresistances. Totalemfofthebattery=nE(fornno.ofidenticalcells) TotalInternalresistanceofthebattery=nr Totalresistanceofthecircuit=nr+R (i)IfR<<nr,thenI=E/r(ii)Ifnr<<R,thenI=n(E/R) nE nr+Rcomparisontotheexternalresistance,thenthecellsareconnectedinseriestogetmaximumcurrent. E E E r r r 1. Theemfofthebatteryisthe I I 2. Thecurrentineachcellisthe CurrentI= Conclusion:Wheninternalresistanceisnegligiblein

  13. CellsinParallelcombination: Cellsaresaidtobeconnectedinparallelwhentheyarejoinedpositivetopositiveandnegativetonegativesuchthatcurrentisdividedbetweenthecells. NOTE:Er 1.Theemfofthebatteryisthesameasthatofasinglecell. amongthecells. 3.ThereciprocalofthetotalinternalresistanceistheE resistances. Totalemfofthebattery=ER TotalInternalresistanceofthebattery=r/nV Totalresistanceofthecircuit=(r/n)+R (i)IfR<<r/n,thenI=n(E/r)(ii)Ifr/n<<R,thenI=E/R CurrentI=Conclusion:Whenexternalresistanceisnegligiblein connectedinparalleltogetmaximumcurrent. E r 2. Thecurrentintheexternalcircuitisdividedequally r I I sumofthereciprocalsoftheindividualinternal nE nR+r comparisontotheinternalresistance,thenthecellsare

  14. CURRENTELECTRICITY-II 1.Kirchhoff’sLawsofelectricity 2.WheatstoneBridge 3.MetreBridge 4.Potentiometer i)Principle ii)Comparisonofemfofprimarycells

  15. KIRCHHOFF’SLAWS: ILaworCurrentLaworJunctionRule: Thealgebraicsumofelectriccurrentsatajunctioninanyelectricalnetworkisalwayszero. I1I2 I3I1-I2-I3+I4-I5=0 I5 I4 SignConventions: 1.Theincomingcurrentstowardsthejunctionaretakenpositive. 2.Theoutgoingcurrentsawayfromthejunctionaretakennegative. Note:Thechargescannotaccumulateatajunction.Thenumberofchargesthatarriveatajunctioninagiventimemustleaveinthesametimeinaccordancewithconservationofcharges. O

  16. IILaworVoltageLaworLoopRule: Thealgebraicsumofallthepotentialdropsandemf’salonganyclosedpathinanelectricalnetworkisalwayszero. I1E1RI1 R-E1+I1.R1+(I1+I2).R2=0 LoopACDA: I2R3I2-(I1+I2).R2-I2.R3+E2=0 SignConventions: 1.Theemfistakennegativewhenwetraversefrompositivetonegativeterminalofthecellthroughtheelectrolyte. 2.Theemfistakenpositivewhenwetraversefromnegativetopositiveterminalofthecellthroughtheelectrolyte. Thepotentialfallsalongthedirectionofcurrentinacurrentpathanditrisesalongthedirectionoppositetothecurrentpath. 3.Thepotentialfallistakennegative.Note:Thepathcanbetraversed directionoftheloop. LoopABCA: 1 A B I1 2 I2 I1+I2 I1 C D E2 inclockwiseoranticlockwise 4. Thepotentialriseistakenpositive.

  17. B PQ applyingKirchhoff’sJunctionRule.Ig ApplyingKirchhoff’sLoopRulefor:AGC LoopABDA: -I.P-I.G+(I-I).R=0RS I-I1 -(I-I).Q+(I-I+I).S+I.G=0D WhenIg=0,thebridgeissaidtobalanced.IEI Bymanipulatingtheaboveequations,wegetPR Q S WheatstoneBridge: Currentsthrough thearmsareassumed by I1 I1 -Ig I-I1+Ig 1 g 1 I I LoopBCDB: 1 g 1 g g

  18. MetreBridge:R.B(R)X MetreBridgeisbased ontheprincipleofG ABWhenthegalvanometerlcmJ100-lcm currentismadezeroby adjustingthejockeyK bridgewireforthegivenvaluesofknownandunknownresistances, RRAJRAJRl(Since, XRJBXJBX100-llength) Therefore,X=R(100–l)⁄l WheatstoneBridge. positiononthemetre- E Resistanceα

  19. Potentiometer:I+ V V=IR0lcmJ100 A200 300 throughthepotentiometerwire400 ofuniformcrosssectionalarea (A)anduniformcompositionK ofmaterial(ρ),then V=KlorVαl V/lisaconstant. V ofuniformcross-sectionanduniformcompositionisproportionaltoitslengthwhenaconstantcurrent A Principle: E + =Iρl/A theconstant Rh If current flows B Thepotentialdifferenceacrossanylength ofawire 0 l flowsthroughit.

  20. Comparisonofemf’susing I+R.BG obtainedforthecellwhen thepotentiometerwireis0l2J2100 equalandoppositetotheA200l1J1 300 1AJ11 E2=VAJ2=Iρl2/A E1/E2=l1/l2 Note: Thebalancepointwillnotbeobtainedonthepotentiometerwireifthefallofpotentialalongthepotentiometerwireislessthantheemfofthecelltobemeasured. Theworkingofthepotentiometerisbasedonnulldeflectionmethod.Sotheresistanceofthewirebecomesinfinite.Thuspotentiometercanberegardedasanidealvoltmeter. E1 Potentiometer: Thebalancepointis A + E2 E thepotentialatapointon + emfofthecell. E=V Rh B =Iρl/A B 400 K

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