[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
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