[1]

Instructions:4 All questions are compulsory. There are 27 questions in all 4 This question paper has four sections : Section A, Section B, Section C, and Section D. 4 Section A contains five questions of one mark each, Section B contains seven questions of two marks each,

Section C contains twelve questions of three marks each, Section D contains three questions of five marks each. 4 There is no overall choice. However, an internal choice has been provided in two questions of one marks, two

questions of two marks, four questions of three marks and three questions of five marks weightage. You have to attempt only one of the choices in such questions.

Section – A

1. DefineoneTeslausingtheexpressionforthemagneticforceactingonaparticleofcharge‘q’ movingwithvelocity v inamagneticfield

B . [1]OR

Twodipoles,madefromcharges± ±q and Q respectively,haveequaldipolemoments.Givethe(i)ratiobetweenthe‘separations’ofthesetwopairsofcharges,(ii)anglebetweenthedipoleaxisofthesetwodipoles.

2. Professor C.V. Raman surprised his students by suspending freely a tiny light ball in atransparentvacuumchamberbyshiningalaserbeamonit.WhichpropertyofEMwaveswasheexhibiting?Giveonemoreexampleofthisproperty? [1]

3. Whyisitfoundexperimentallydifficulttodetectneutrinosinnuclearb-decay? [1]4. Themagneticfluxthreadingacoilchangesfrom12×10–3Wbto6×10–3Wbin0.01s.Calculate

theinducedemf. [1]OR

ThegivengraphshowsvariationofchargeqversuspotentialdifferenceVfortwocapacitorsC1 andC2.BoththecapacitorshavesameplateseparationbutplateareaofC2isgreaterthanthatofC1.Whichline(AorB)correspondstoC1andWhy?

A

B

V

q

5. Thegraphshowninthefigurerepresentsaplotofcurrentversusvoltageforagivensemiconductor.Identifytheregion,ifany,overwhichthesemiconductorhasanegativeresistance. [1]

B

AC

Voltage(v)

Current(mA)

(2018-19)Date : ___________Duration : 3 Hrs. Max. Marks : 70

ClassXIIPhysics

Sample Paper

[2]

Section – B

6. Fivecharges,qeachareplacedatthecornersofaregularpentagonofside'a'andcentreO. (i) WhatwillbetheelectricfieldatOifthechargefromoneofthecorners(sayA)isremoved? (ii) WhatwillbetheelectricfieldatOifthechargeqatAisreplacedby-q? [2]

OR Twochargesqand–3qareplacedonx-axisseparatedbydistanced.Whereathirdcharge2q

shouldbeplacedsuchthatitwillnotexperienceanyforce?7. Writetwopropertiesofequipotentialsurfaces.Depictequipotentialsurfacesduetoanisolated

pointcharge. [2]8. Writetwopropertieseachofamaterialsuitableformaking(i)apermanentmagnet,and(ii)an

electromagnet. [2]OR

(i) Statetheconditionunderwhichalargemagnificationcanbeachievedinanastronomicaltelescope.

(ii) Give two reasons to explain why a reflecting telescope is preferred over a refractingtelescope.

9. (i) Whatistheimportanceofaradialmagneticfieldandhowisitproduced? (ii) Whyisitthatwhileusingamovingcoilgalvanometerasavoltmeterahighresistancein

seriesisrequiredwhereasinanammeterashuntisused? [2]10. (i) StateBiot-Savart’slawinvectorformexpressingthemagneticfieldduetoanelementdl

���

carryingcurrentIatadistance r fromtheelement. (ii) Writetheexpressionforthemagnitudeofthemagneticfieldatthecentreofacircular

loopofradiusrcarryingasteadycurrentI.Drawthefieldlinesduetothecurrentloop. [2]

11. Howiselectromagneticwaveproduced?DrawasketchofaplaneEMwavepropagatingalongX-axisdepictingthedirectionsoftheoscillatingelectricandmagneticfield. [2]

12. Defineionizationenergy.Howwouldtheionizationenergychangewhenelectroninhydrogenatom is replacedbyaparticle ofmass200 times thatof the electronbuthaving the samecharge? [2]

Section – C

13. Define the term ‘amplitudemodulation’.Explainany two factorswhich justify theneed formodulatingalowfrequencybasebandsignal. [3]

OR Inthefirstexcitedstateofhydrogenatom,itsradiusisfoundtobe21.2×10–11m.Calculate

itsBohrradiusinthegroundstate.Alsocalculatethetotalenergyoftheatominthesecondexcitedstate.

14. Givereasonsforthefollowing: (i) TheZenerdiodeisfabricatedbyheavilydopingboththepandnsidesofthejunction. (ii) Aphotodiode,whenusedasadetectorofopticalsignalsisoperatedunderreversebias. (iii) ThebandgapofthesemiconductorusedforfabricationofvisibleLED’smustatleastbe

1.8eV. [3]15. (i) Statethelawofradioactivedecay.WritetheSIunitof‘activity’. (ii) Thereare4 2 106× radioactivenucleiinagivenradioactivesample.Ifthehalflifeofthe

sampleis20s,howmanynucleiwilldecayin10s? [3]16. (i) Drawthegraphshowingthevariationofde-Brogliewavelengthlofaparticleofchargeq

andmassmwiththeunderrootofacceleratingpotential. (ii) Anelectronandprotonhavethesamede-Brogliewavelengths.Explain,whichofthetwo

hasmorekineticenergy. [3]

[3]

(i) UnploarisedlightofintensityI0passesthroughtwopolaroidsP1andP2suchthatpass-axisofP2makesanangleqwiththepass-axisofP1.PlotagraphshowingthevariationofintensityoflighttransmittedthroughP2astheangleqvariesfromzeroto180°.

(ii) AthirdpolaroidP3isplacedbetweenP1andP2withpassaxisofP3makinganangleb withthatofP1.IfI1,I2andI3representtheintensitiesoflighttransmittedbyP1,P2andP3 determinethevaluesofangleaandbforwhichI1 = I2 = I3.

17. (a) StateHuygen’sprinciple.Usingthisprincipledrawadiagramtoshowhowaplanewavefrontincidentattheinterfaceofthetwomediagetsrefractedwhenitpropagatesfromararertoadensermedium.HenceverifySnell’slawofrefraction. [3]

(b) Whenmonochromaticlighttravelsfromararertoadensermedium,explainthefollowinggivingreasons:

(i) Isthefrequencyofreflectedandrefractedlightsameasthefrequencyofincidentlight?

(ii) Doesthedecreaseinspeedimplyareductionintheenergycarriedbylightwave?18. Drawaschematicraydiagramofreflectingtelescopeshowinghowrayscomingformadistant

object are received at the eye-piece. Write its two important advantages over a refractingtelescope. [3]

OR (i) Drawaraydiagramdepictingtheformationoftheimagebyanastronomicaltelescopein

normaladjustment. (ii) Youaregiventhefollowingthreelenses.Whichtwolenseswillyouuseasaneyepieceand

asanobjectivetoconstructanastronomicaltelescope?Givereason.

Lenses Power (D) Aperture (cm)L1 3 8L2 6 1L3 10 1

19. WriteMaxwell’sgeneralizationofAmpere’sCircuitalLaw.Showthatintheprocessofcharging

acapacitor,thecurrentproducedwithintheplatesofthecapacitoris iddt

=∈0Φε .

WhereΦeistheelectricfluxproducedduringchargingofthecapacitorplates. [3]20. A source of ac voltageV =V0 sinwt is connected across a pure inductor of inductance L.

Derivetheexpressionsfortheinstantaneouscurrentinthecircuit.Showthataveragepowerdissipatedinthecircuitiszero. [3]

OR (i) Inthefollowing‘diagram‘S’isasemiconductor.Wouldyouincreaseordecreasethevalue

ofRtokeepthereadingoftheammeterAconstantwhenSisheated?Givereasonforyouranswer.

A

V S

R

– +

(ii) Draw the circuit diagram of a photodiode and explain its working. Draw its I/Vcharacteristics.

21. Define mutual inductance between a pair of coils. Derive an expression for the mutualinductanceoftwolongcoaxialsolenoidsofsamelengthwoundoneovertheother. [3]

22. (i) Obtainanexpressionforcyclotronfrequency. (ii) Adeuteronandaprotonareacceleratedbythecyclotron.Canbothbeacceleratedwith

thesameoscillatorfrequency?Givereasontojustifyyouranswer. [3]

OR

[4]

along its length.Thenullpoints forthetwoprimarycellsofemfe1ande2connected inthemannershownareobtainedatadistanceof120cmand300cmfromtheendA.Find(i)e1/e2 (ii)positionofnullpointforthecelle1.

Howisthesensitivityofapotentiometerincreased? [3]

BA120cm

310cm

e2e1

e1 e2

24. (i) Derivetheexpressionforelectricfieldatapointontheequatoriallineofanelectricdipole. (ii) Depict theorientationof thedipole in (i) stable, (ii)unstableequilibrium inauniform

electricfield. [3]

Section – D25. (i) AnelectricdipoleofmomentPisplacedinuniformelectricfield

E. Writetheexpressionforthetorque τ experiencedbythedipole.Identifytwopairsofperpendicularvectorsintheexpression.Showdiagrammaticallytheorientationofthedipoleinthefieldforwhichthetorqueis(i)themaximum,(ii)halfofthemaximumvalue,(ii)Zero.

(ii) Twopointcharges4mCand+1mCareseparatedbydistanceof2minair.Findthepointonthelinejoiningchargesatwhichthenetelectricfieldonthesystemiszero? [5]

OR (i) Obtainanexpressionforintensityofelectricfieldinendonposition,i.e.,axialpositionof

anelectricdipole. (ii) Drawtheequipotentialsurfacesduetoanelectricdipole.Locate thepointswherethe

potentialduetothedipoleiszero.26. (i) Iff=+0.5m,whatisthepowerofthelens? [5] (ii) Theradiiofcurvatureofthefacesofadoubleconvexlensare10cmand15cm.Itsfocal

lengthis12cmwhatistherefractingindexofglass? (iii) Aconvexlenshas20cmfocallengthinair.Whatisitsfocallengthinwater? (Refractiveindexair-water=1.33,refractiveindexforair-glass=1.5)

OR (i) Provethatforaconcavemirror,theradiusofcurvatureistwicethefocallengthforsmall

apertureascomparedtoitsradiusofcurvature. (ii) Withthehelpofasuitablediagram,derivethemirrorformulaforaconcavemirror.27. (i) Differentiatebetweenthreesegmentsofatransistoronthebasisoftheirsizeandlevelof

doping. [5] (ii) Howisatransistorbiasedtobeinactivestate? (iii) Withthehelpofnecessarycircuitdiagram,describebrieflyhown-p-ntransistorinCE

configurationamplifiesasmallsinusoidalinputvoltage.Writetheexpressionfortheaccurrentgain.

OR Drawthecircuitdiagramofann-p-ntransistorwithemitter-basejunctionforwardbiasedand

collectorbasejunctionreversebiased.Describebrieflyhowthemotionofchargecarriersinthetransistorconstitutestheemittercurrent(IE),thebasecurrent(IB)andthecollectorcurrent(IC).HencededucetherelationIE = IB + IC.

vvvvv

23. In thefigure a longuniformpotentiometerwireAB ishaving a constant potential gradient

[5]

1. Tesla is when a charge of 1C,moving with velocity 1m/s, perpendicular in the region ofmagneticfield,experiencesaforceof1N. [1]

F q q B= ×( )

B F

qv=

1Tesla=1Na–1m–1

=1W/m2

OR Asp = qa,wehave

aa

qQ'

= [½]

and q=0. [½]2. The properties of electromagnetic waves are similar to other waves as it exerts radiation

pressure.Atinyballcanbesuspendedfreelyinatransparentvacuumchamberbyshiningalaserbeamonitaselectromagneticwaveexertsradiationpressure.Also,accordingtohim,thetailsofthecometsareduetoradiationpressure.

3. Neutrinosareneutral(chargeless)(almost)masslessparticlesthathardlyinteractwithmatter. Alternatively.Theneutrinoscanpernetratelargequantityofmatterwithoutanyinteraction.

4. εφ φ

=−

=× − ×

=− −

i f

tV12 10 6 10

0 010 6

3 3

.. [½]

OR ForC1 LineB Sinceslope(q/V)oflineBislesserthanthatofLineA5. TheresistanceofamaterialcanbefoundoutbytheslopeofthecurveVasI,PartBCofthe

curveshowsthenegativeresistanceaswiththeincreaseincurrent,voltagedecreases.6. Aq

BqEq

DqCq

or

a

(i) 1

4 02πεqr

[1]

(ii) 14

2

02πεqr

along OA� ���

(2018-19)Date : ___________Duration : 3 Hrs. Max. Marks : 70

ClassXIIPhysics

Hints/Solutions to Sample Paper

[6]

fieldwillbe

E q

r=

14 0

2πε which is along OA.

� ���

(ii) Ifachargeqisreplacedbycharge–qatpointA,theregeneratesanetelectricfieldatpointOasaresultof-2qcharge,so

Oq q

q

q q

q qd d

q q

O

–2q

AtPon2q,forceduetoqistotheleftandthatdueto–3qistotheright.d

x

qP

2q –3q

\

24

64

2

02

2

02

qx

qd xπε πε

=+( )

\ (d+x)2=3x2

\ 2x2–2dx–d2=0

\ x d d= ±

232

Asthenegativechargewillbeinbetweenqand-3q,henceitisunacceptable.

x d d d= + = +( )2

32 2

1 3 totheleftofq.

7. Characteristicsofequalpotentialsurfaces: (i) Thesearealwaysperpendiculartofieldlines. (ii) Noworkisdoneinmovingthetestchargefromonepointofequipotentialsurfacetothe

other. O—N reducing the distance of source charge, the electric field becomes strong and

equipotential surface comes closer. For an isolated point charge, the equipotentialsurfacesareshownbelow.

8. (i) Twopropertiesformakingpermanentmagnet (ii) Twopropertiesformakinganelectromagnet. (i) Formainpermanentmagnet: (a) Highretentively (b) Lowcoercivity (c) Lowpermeability

Detailed answer : (i) IfachargeqisrevolvedfrompointA,anegativechargeisdevelopedatAwhereelectric

[7]

OR

(i) mffe

= 0

Byincreasingf0ordecreasingfe (ii) (a) Nochromaticaberration (b) Nosphericalaberration (c) Mechanicaladvantage-lowweight,easiertosupport. (d) Mirrorsareeasytoprepare. (e) Moreeconomical9. (i) Importanceandproductionofradialmagneticfield:Inaradialmagneticfield,magnetic

torqueremainsmaximumeverywhere. Itisproducedduetocylindricalpolepiecesandsoftironcore. (ii) Voltmeter : Ahighresistanceinseriesisrequiredwhenmovingcoilgalvanometerisused

asvoltmeter tomakesure thata lowcurrentshould travel throughvoltmeterwithoutchangingthepotentialdifferencethanneedstobemeasured.

Ammeter : Ashuntisusedwhenamovingcoilgalvanometerisusedasammeterastomakesure about not such change in total resistance of the circuit with actual current value offollowingcurrent.

10. (i) AccordingtoBiot-Savart'slaw,themagneticfieldduetoacurrentelementdl���carrying

currentIatapointPwithpositionvector r isgivenby

dB I dl r

r

� ��� �=

×

µπ0

34

P

I

ar

(ii) BIr

=µ0

2 Fieldlines:

11. Electromagneticwavesareproducedduetooscillating/acceleratingchargedparticles.

12. Theminimumenergy,requiredtofreetheelectronfromthegroundstateofthehydrogenatom,isknowaslionizationenergy.

(ii) Formakingelectromagnet: (a) Highpermeability (b) Lowretentively (c) Lowcoactivity

[8]

LonizationEnergyisgivenbyE mchi e E m0

4

02 2 08

= ∝ε

. .,

Since, ionizationenergy isdirectlyproportional tomass. IonizationEnergywillbecome200times.

13. (i) It istheprocessofsuperpositionof information/messagesignaloveracarrierwaveinsuch away that the amplitude of carrierwave is varied according to the informationsignal/messagesignal.

Directtransmission,ofthelowfrequencybasebandinfomationsignal,isnotpossibleduetothefollowingreasons:

Size of Antenna :fortransmittingasignal,minimumheightofantennashouldbel4

,

with the help ofmodulationwavelength of signal decreases, hence height of antennabecomesmanageable.

(ii) Effective power radiated by an antenna :Effectivepowerradiatedbyanatennavariesinverselyasl2,henceeffectivepowerradiatedintothespace,bytheatenna,increases.

(iii) Toavoidmixingupofsignalsformdifferenttransmitters.OR

r0=21.2×10–11m

Firstexcitedstatemeans,n=2 r1=r0n

2

or r rn0

12=

r m0

1121 2 104

=× −.

=5.3×10–11m

E

n= −

13 62.

E = −

13 622

.

=–3.4eV14. (i) Aheavydopingmakesthedepletionregionverythin.Thismakestheelectricfieldofthe

junctionveryhigh,even forasmall reversebiasvoltage.This in turnhelps theZenerdiodetoactasavoltageregulator'.

(ii) Whenoperatedunderreversebias,thephotodiodecandetectthechangesincurrentwiththechangesinlightintensitymoreeasilyasfractionalchangeinchargecarriersislargeinreversebias.

(iii) Thephotonenergy,ofvisiblelightphotonsvariesfromabout1.8eVto3eV.HenceforvisibleLED's,thesemiconductormusthaveabandgapof1.8eV.

15. (i) Statement :Rateofdecayofagivenradioactivesampleisdirectlyproportionaltothetotalnumberofundecayednucleipresentinthesample.

Alternatively : − ∝

dNdt

N

Unit→becquerel(Bq)

(ii) NN

n

0

12

=

n t

T= = =

1 2

1020

12/

⇒ N = × ×

4 2 10 1

26

1 2/

=4×106nuclei

[9]

V

lK.E.

λ =

hmeV2

(ii) Foranelectronandproton qp=qe

mp>me

Sincewavelength, λ =hmqV2

, andbothparticleshave samede-Brogliewavelength,l

andKineticenergyisgivenbyqV

\ hmK E

hm K Ep p2 2. . . .

=

⇒ me(K.E.)e=mp(K.E.)p \ mp>me

\ K.E.ofelectronwillbemore.OR

(i) Therequiredgraphwouldhavetheformasshownbelow:

(i)

p

I

Op2

UsingI2 = I1cos2q

(ii) I1=LighttransmittedbyP1

I3=LighttramittedbyP3 = I1cos2b

I2=LighttransmittedbyP2

= I3cos2(q – b)

\ I2 = I3

I1cos2bcos2(q – b)=I1cos

2b q = b Also,I1 = I2 I1 = I1cos

2q or cos2q=1 \ q=0°orp Thereforeb=0°orp17. (a) Huygens Principle (i) Eachpointofthewavefrontisasourceofasecondarydisturbanceandsecondarywavelets

emanatingfromthesepointsspreadoutinalldirectionswiththespeedofthewave. (ii) Thenewpositionofthewavefrontatalatertimecanbefoundusingtheproductvtwhere

visthespeedandtisthetime. (iii) Energypropagatesinthedirectionperpendiculartothewavefront.

16. (i) Wavelengthofaparticleisgivenby

[10]

REFRACTION OF PLANE WAVES USING HUYGENS PRINCIPLE Refractionofaplanewave:–Letv1andv2bethespeedoflightinmedium1andmedium2.

SupposeaplanewavefrontABisincidentonPP'atananglei.

LettbethetimetakenbythewavefronttotraveldistanceBCinmedium1.Thus,BC=v1t. InthesametimethewavefronttravelsdistanceAEinmedium2.Thus,AE=v2tandCEwould

representtherefractedwavefront.

In,;sin i BCAC

v tAC

= = 1 In,DAEC sinr AEAC

v tAC

= = 2

whereiandraretheanglesofincidenceofrefraction.

\ sinsin

ir

vv

= 1

2

...(i)

Now, n cv

n cv1

12

2= =and

\ nn

vv

2

1

1

2= orn21=

vv

1

2 ...(ii)

From(i)and(ii), sinsin

ir

n= 21

ThisistheSnell'slawofrefraction. (b) (i) Frequencyisthepropertyofsource.Hence,frequencydoesnotchangewhenlightis

reflectedorrefracted (ii) No,decreaseinspeeddoesnotimplyreductioninenergycarriedbylightwave.Thisis

becausethefrequencydoesnotchangeandaccordingtotheformulaE=hn,energywillbeindependentofspeed.

[11]

18. Objectivemirror

Eyepiece

SecondaryMirror

2

Advantages : (i) Largegatheringpower (ii) Largemagnifyingpower (iii) Nochromaticaberration (iv) Sphericalaberrationisalsoremoved (v) Easymechanicalsupport (vi) Largeresolvingpower(anytwo) [½+½]

OR (i) Raydiagramofastronomicaltelescope

Objective Eyepices

EB′

A′

Oaba

fe

fo

[Note;Deduct½markifthe‘arrowsarenotmarked] (ii) ObjectiveLens:LensL1 [½] EyepieceLens:LensL3 [½] Reason: Theobjectiveshouldhavelargeapertureandlargefocallengthwhiletheeyepieceshould

havesmallapertureandsmallfocallength. [½]19. Ampere’scircuitallawisgivenbyas

φ µ� ���B dl ic. − 0

Butforacircuitcontainingcapacitor,duringitscharging/dischargingthecurrentwithintheplatesofthecapacitorvaries,(producingdisplacementcurrentii) [1]

Maxwell,isgivenas� ����B dl i ic d. = +∫ µ µ0 0 [1]

During theprocessofchargingofcapacitor,electricflux (f)betweentheplatesofcapacitorchangeswithtime,whichproducesthecurrentwithintheplatesofcapacitor.

Thiscurrent,beingproportionalto ddtf , wehave i d

dtd = εφ

0 [1]20. Derivationofinstantaneouscurrent [2] Derivationofaveragepowerdissipated [1] Given:V=V0sinwt

V L di

dt=

⇒ di VLdt= L

V=V0sinwt

\ dtVL

tdt= 0 sinω

[12]

Integratine, IVL

t= − 0

ωωcos

\ IVL

t= − 0

ωωcos

IVL00=

ω Averagepower,

P V dtiV

? = ∫00

=−∫

VL

t tdtT

02

0ωω ωsin cos

=−∫

VL

t dtT

02

022

ωωsin( )

=0OR

(i) Rwouldbeincreased. ResistanceofS(asemiconductor)decreasesonheating (ii) Photodiodediagram

p-side n-side

PL+–

mA

mv>E1

Whenthephotodiodeisilluminatedwithlight(photons)(withenergy)(hv)greaterthantheenergygap(Eg)ofthesemiconductor),thenelectron-holepairsaregeneratedduetotheabsorptionofphotons.Duetojunctionfield,electronsandholesareseparatedbeforetheyrecombine.Electronsarecollectedonn-sideandholesarecollectedonp-sidegivingrisetoanemf.

Whenanexternalloadconnected,currentflows. V-lCharacteristicsofthediode:

L1L2L3L4

L1>L2>L3>L4

mA

L

I

V

mA

21. (i) Mutualinductance,isnumericallyequaltotheinducedemfinthesecondarycoilwhenthecurrentintheprimarycoilchangesbyunity.

Alternatively, Mutual inductance in numerically equal to the magnetic flux linked with one coil/

secondarycoilwhenunitcurrentflowsthroughtheothercoil/primarycoil.

[13]

LetacurrentI2flowinthesecondarycoil

\ BN il2

0 2 2=µ

Fluxlinkedwiththeprimarycoil

=µ0 2 1 1 2N N A i

l=M12i2

Hence,MN N Al12

0 2 1 2=µ

=m0n2n1A1l

Here, nNlnNl1

12

2=

;

22. (i) Derivationoftheexpressionforcyclotronfrequency (ii) Reasonjustificationforthecorrectanswer

(i) mvr

qvB2=

r mv

qB=

Frequencyofrevolution v( ) = 1Time Period

T r

vmv

vBq= =2 2π π

=2πmBq

\ f qBm

=2π

(ii) No Themass of the twoparticles, ie., deuteronandproton, is different.Since (cyclotron)

frequency depends inversely on the mass, they cannot be accelerated by the sameoscillatorfrequency.

Detailed answer: Acyclotronworksonlywhenthefrequencyoftherevolutionofparticleisequaltothefrequency

ofoscillation.

\ Massofprotonanddeuteronaredifferent m mmd p=( ) ∝2 1 and v [½]

\ Frequencyofrevolutionofprotonanddeuteronisdifferent,sotheycantbeacceleratedwithsameoscillatorfrequency. [½]

[14]

23. (i) Letkbethepotentialgradientinvolt/cm Thene1 + e2=300kande1 – e2=120k \ e1=210kande2=90k

Hence, εε1

2

73

=

(ii) ase1=210k \ Balancinglengthforcelle1is

l

k11 210= =ε

cm

Thesensitivityofapotentiometerwirecanbeincreasedbydecreasingpotentialgradienteitherthroughincreasinglengthofthepotentiometerwire.

24. Derivationofexpressionofelectricfieldonequatoriallineofelectricdipole Depictionoforientationforstableandunstableequilibriuminelectricfield

q PO′ OE–qr

EatP

E+q

P

q–q

(i) Letthepoint'P'beatbeatadistance'r'fromthemidpointofthedipole.

E qr a

q+ =+( )4 0

2 2πε

E qr a

q− =−

+( )4 02 2πε

Bothareequalandtheirdirectionsareasshowninthefigurehencenetelectricfield � �E E E pq q= − +( )

+ − cos θ [½]

= −

+( )2

4 02 2 3 2qa

r ap

πε/

[½]

(ii) Stableequilibriumq=0° [½]

E

+q-q p

Unstableequilibriumq=180° [½]

P–q+q

E

25. (i) LetadipoleABissituatedintheuniformelectricfield

E.

[15]

E→

F

F –qA

2l

B+q

q

Thetorqueondipoleis,

τ = ×p E p, where isdipolemoment.

Twopairsofperpendicularvectorsare

τ τ and and and p E intheexpression.

Thetorqueisthemaximum,whenq=90°whichisshowninfollowingdiagram:

P

–q

90°

+q E→

Themaximumvalueoftorque=pE

Thehalfofmaximumvalue = pE2

So,wehavepEsinq =pE2

or sin θ θ= = °12

30or

Thearrangementisasgivenbeloworshownasbelow:

E→

–q

2l+q

30°

Forzerovalueoftorque,sinq=0orq=0°,whichisshownasbelow:

E→

+q–q

2

(ii) TwopointchargesqA=4mCandqB+1mCarelocated2mapartinairasshownPisthemid-pointoflineAB.

A B

2-x2m

P

+1mC4mC

x

Distancebetweenthetwocharge,AB=2m \ PA=xm,PB=2–xm NetelectricfieldatpointP=E Electricfieldatpointpcausedby+4mCcharge,

[16]

E

PAN C1

6

02

4 104

=×

( )

−

πε/ along I'A

MagnitudeofelectricfieldatpointPcausedby+1mCcharge,

E

PBN C2

6

02

1 10

4=

+ ×

( )

−

πε/ along PB

Now,4 104

1 104 2

6

02

6

02

×=

+ ×

−( )

− −

πε πεx x or, (2–x)24=(x)21 16–16x+3x2=0

gives x x= =43

4, , possiblepointonthelinewillbe

x =

43

OR (i) ReferSMbook,Part-I (ii) ReferSMbook,Part-I26. f=0.5m

P

fD= = = +

1 10 5

2.

(ii) R1=+10cm,R2=–15cm f=+12cm

1 1 1 1

1 2fn

R Ra g= −( ) −

112

1 110

115

= −( ) −−

a gn

112

1 16

= −( ) ×a gn

ang =1.5

(iii) fa=+20cm,anw=1.33,ang=1.5 fw=?

1 1 1 1

1 2fn

R Raa g= −( ) −

1 1 1

20 0 51

101 2R R− =

×=

. Whenlensplacedinafter

1 1 1 1

1 2fnn R Rw

a g

a w= −

−

1 1 51 33

1 110fw

= −

×

..

fw =

×10 1 330 17

..

fw = +78 2. cm

[17]

(i) ReferSMbook,Part-II (ii) ReferSMbook,Part-II

27. (i) Emitter : Itisofmoderatesizeandheavilydoped

Base :Itisverythinandlightlydoped. Collector : Itismoderatelydopedandlargerinsize. (ii) ReferSMbook,Part-II (iii) ReferSMbook,Part-II

OR

(ii) ReferSMbook,Part-II (ii) Thecircuitdiagramofatransistor,workingasanamplifier, initsCEmode, isshown

here.

– + – +

VCDVFE

IE IC

OutputSignal

InputSignal

If a small sinusoidal voltage is superimposed on the dc base by connecting the source ofthis signal in serieswithVBB supply.Then thebase currentwillhave sinusoidal variationssuperposedonthevaluesIB.Asaconsequence,thecollectorcurrentalsowillhavesinusoidalvariationsuperimposedonthevalueofICproducinginturncorrespondingchangeintheoutputvoltageV0. [1½]

vvvvv

OR