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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

Learn about electric current types, Ohm's Law, resistance, drift velocity, conductivity, and more. Explore series and parallel circuits, EMF, resistors, and color codes. Understand internal cell resistance and temperature effects on resistance.

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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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