()-12th phy(2009)

15
Series S S O RoliN o . | ( 1 4. 5wr xF {s rF{-W{ 10.15 q ' i Code No . 6ts i. Candidates must write t h e Codeon t h e title page o f t h e answer-book' q-fr$T?fi o'ts 61 5d{-gk-6T b ge-W q{ sfiI{q ft{qii t 6,r ffiqiifi, wEw ffi | TqTA I Tfi-q,{ qT fufl{uT Tqi6 rf ds 6F{ tqq xw-qd sl q.et 3*t 5512 Maximum Marhs : 70 eTfEndq eiq : 70 L _r r^ri", . A \ l rtuL orlr\ t\. (;nt please checkthat this question paper contains 15 printed pages' code number given on th e right hand side of th e question paper should' be written on th e title page of th e answer-book by th e candidate' PleasecheckthatthisquestionpapercontainsS0questions' please write down th e serial Number of th e qudstion before attempting it . o 15 minutes time ha s been allotted to read this question paper' Th e question paper will be distributed at 10.15a.m. From 10.15 a.m' t o 10'30 a'm'' t he ,trra*t t will read th e question paper only an d will no t write an y answer on th e answer script during this period' 1 5 ? ffi*g+5-w.F*it Fqqf fr 6,'t d fs $T swT-sr d m .q{q t r o a a a O ifi'r siR {6 fit t q6a, T{{ 4l q-.di t ftq 15 fr={e fl qqq Rqr r*-qT qrt'qT I 10.15 qi t 10.30 q} gq 3i-qfq + d{q i e-fl-sfRqT q{ 4li Eil{ rfr ffii I PHYSICS (Theory) dFrd,funlq tffiol Timeallowed: 3 hours fr?ttftaw4:3qr) 5512 P.T. O .

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SeriesSSO

Roli No.

| ( 1 4 .

5wr xF

{s rF{-W{

10.15q'i

Code No.

6ts i.

Candidatesmust wr i te the Code on

the t i t le page of the answer-book '

q-fr$T?fio'ts615d{-gk-6Tb ge-W

q{ sfiI{q ft{qii t

6,r ffiqiifi, wEw ffi |

TqTA I Tfi-q,{ qT fufl{uTTqi6 rf

ds 6F{ tqq xw-qd sl q.et 3*t

5512

Maximum Marhs : 70

eTfEndqeiq : 70

L_rr^ri",. A\lrtuL or l r \ t\. (;nt

please check that this question paper contains 15 printed pages'

code number given on the right hand side of the question paper should'be

written on the title page of the answer-bookby the candidate'

P leasechecktha t th isquest ionpapercon ta insS0quest ions '

please write down the serial Number of the qudstion before

attempting it.

o 15 minutes time has been allotted to read this question paper' The question

paper will be distributed at 10.15 a.m. From 10.15 a.m' to 10'30 a'm'' the

,trra*t t will read the question paper only and will not write any answer on

the answer script during this period'

15?

ffi*g+5-w.F*it

Fqqf fr 6,'t d fs $T swT-srd m .q{qt r

o

a

a

a

O

ifi'r siR fdq{T {6 fit tq6a, T{{

4l q-.dit ftq 15 fr={efl qqq Rqr

r*-qTqrt'qTI 10.15qi t 10.30q}

gq 3i-qfq+ d{q i e-fl-sfRqTq{ 4li Eil{ rfr ffii I

PHYSICS(Theory)

dFrd,funlqtffiol

Timeallowed:3 hours

f r?t t f taw4:3qr)

5512P.T .O.

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General Instruetions :

O All questions are eompulsory.

(ii) There a.reB0 questions_in totar. euestions r to g carry one markeach,questionsg to 18 ca*y t*i *iiir"r"ri:oriir',ins tg to 2zcdrry three marks each and, questions2g to bd ,";;; fi.ae markseach.

(iiil There is no ouerall choice.Howeuer, an internal choice has beenprouided i_none questionof tyo *orrrr, one question of three marksand ail three questions of fiue morki each-.you haue to attemptonly one of the choicesin'such questions(iu)

(u)

Use of calculators is not permitted,.

You may use the foilowing uaruesof physicar constantswhereuernecessary:

c=3*108ms- l

h = 6.626x 10-u Js

e = 1-602x 10-1sC

Vo=4n x 10-7TmA-r

4neo

=9x109Nm2<:a

Mass of electronDu = 9.1 x 10-31kg

Mass of neutron h' i I.678 x 10-27kg

Boltzmann'sconstantk _ 1.8g1x 10_28JK_1

Avogadro'snumber NA = 6.022x 1023/ mol-l

Radius of earth = 6400 kmFpTa fdir r

(i) v'fi qw qM d I(iil .tsvfl{-q-r

tgu s0tw d r y.r-+r0scrd6 r*r q6 eiq w i, swg d rs f y-&. ys+dr eiqw d, vra 19 + zz t sdq-wi dTqef+ qr idEryw28 t Sot

ydayw fTaai6 +r d I(iiil wq-w t sw qr dd fu"1 ,A d I detTfr,d r# ard qn wr l, d?4;r*i fl-A (m ry-+d efr qfq ffi qrfl dfi'y7n t eildtw aqa ,En Bqr'Tqrd / @ vr# + s'qdiE+4nEq, t c'frf,-qo xra aTqrard r

--.4-.

t

2

.\

55t2

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it't *e3tiei * slqhT41Wfu rd'd t

t:) qai enapq7d eyq ffifsn tifua ffi + qt'ii w wql'Trmr vfrArl,= 'e

c=3x108- r -1

h = 6.626x 10*34Js

e = 1.602x 10-1eC

Vo=4n x 10-7TmA-1

1=9x1o9N^2c-2

4neo

{A-{iq 41 {i-dfr me = 9'1 x 10-31kg

{ciq 41 €6fd ffi., i 1.675 x 10-27kg

Aa{$qH trlais k = 1'381 x 1o-23J K-l

qT-cM 41 €cqT NA = 6'022 x 1023/ mol-1

ytql ql F-q - 64oo km

1. whar is rhc rorl' done rn mving a test charge q through a distance of

I rr -r-f tc e+ntorlat nris of an electric dipole ?

ffi AgdE€-d* qq{fr 3iqTt ruRrT fs€i' q-<rqTrrqThTq 4J 1 cm (fr ffi A

;Tq fr f+.-d4rq.rdf+qTqrdTe ?-Y" ^

2. How would the angular separation of interference fringes in Young's

double slit experiment change when the distance between the slits and

screenis doubled? asf Ym"

.i'T+ RFfr nqiTq fflR* f,r{rqt + etq 4i $ d gJqTeG q"{qfro"rurffi

t +Mq yq.n={ii wr qRsda€tdrt ?

g. An electron does not suffer any deflection while passing through a

region of uniform magneticfield. What is the direction of the magnetic

freld ?

+1.$raqia ffi q+qqmgE-dq Qr qla p1q fr 1-$Gwq frfrfr-d€ fr-ortqq-*tqdr 4i fqrTrwT t ?

55t2

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^'dQ-'

''4. 'Namethe EM waves used for

What is its frequency range ?

studying crystal structure of solids.

t .

8.

9.

ahii q1 ffi'q {€iT 6T epqqq olt fr wq}T di qm fqgq-grc+iq rcii or

iTq frfuq r gp61qTTRqR-q{Hr t ?

Two thin lenses of power + 4D and - 2D are in contact. What is the

focal length of the combination ? o'!

A q-d-Aifu, ga6] qTrdr(+4Dderr -2Dt, €q-t ii {d t | {qfs{ ut qt*T

Efrert ?

Give the logic symbol of NAND gate.

NANDi.a or n4 q-d-sdfuq r

Two nuclei have mass numbers in the ratio 8

of their nuclear radii ?

A iTFeii qi rqqn {sreil Hr srgqn 8 : 125t

The maximum kinetic energy of a photoelectron is 3 eV. What is its

s topp ingpo ten t ia l?3Vffi rsmr ffq dr 3Tfi{sffi 'rftffi g.qf g eV d | {FsT FflT$ f+rq f+?rqTt ?

(i) State the principle on which the working of an optical fiber is

based.

(ii) What are the necessary conditions for this phenomenon to

occur ?

(i) {6 fuqr< fdnsqlqs qt fuqi TfirRrsil{

(ii) {s qRqe{r* sq* A} t ftre 3rqrq6 {rt

eTqTRdt r

: 125. What is the ratio

I ii*'

q1 q,rffi

Hrt ?

4

\ \

55t2

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Rs=2s)

Rr=1Q

R+=2 s l

Rz=5Q Re=4f )

10. Calculate the current drawn from the battery in the given network. 2

4Y

^ \ c \ . \ - _ + + _ _ +Rq {q T&NCF q q.{ q qfl T$ fqgq qnr qR*Ftrddrfuq

Rs=2Q

4V

11. Draw 3 equipotential surfaces corresponding to a field that uniformly

increases in magnitude but remains constant along Z-direction. How

are these surfaces different from that of a constant electric field along

Z-direction? 2

cq t{ t aqsq nt{ qqh,r+Yts'dfqq ffi qRqTUTii qs'Hurqgk E}-fiA,!1E Z-fur Ar3n-iffiTF'+oraart r i Ys s{ Ydt t f+q F6Rga t S ffi

t{qdfrgE-frt z-Fq{Tr+ ruR{Tt ?

R l = 1 Q

55t2 P.T .O.

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L2. Define electric flux. Write its S.I. unit.

A charge q is enclosed by a spherical surface of radius R. Ifradius is reduced to half, how would the electric flux throughsurface change ?

fu wqq +1qRr{TqT{fqq | {srr s.I. qrs fdnsqIdi qTarTq ffit R t*q *'ffiq yu fr {< t I qR frwr +} qrqr6-rRqqK, d] y$ t 1-wtiqra dgd rrcir*rii wr qFE-&ArT ?

the

the

2

13. Answer the following questions :

(a) Opticat and radio telescopesare built on the ground

astronomy is possible only from satellites orbitingwhv ?

(b) The small ozone layer on top of the stratosphere ishuman sunival. \\:tr1'?

2

rvhile X-ray

the Earth.

crucial for

Frqfufudq*ii * s+t qIR( :

(a) nffi{fr"q nsn tBA B-qqfi yrd

u'to-ngn 6r sTtzrfigQEjtsT+ 1cFil !

qr Frfrd-fsqqRffiOT q,{ G sqrd ERTA €,rq t I

(b) qqdTq{sf, * sqfr eh .n +E-Fi effi-{ qfd qr+Eqtqq +m

Aqh-*

drF i i ?

14. Write the function of (i) Transducer and (ii) Repeater in the context of

communication svstem. 2

OR

Write two factors justifying the need of modulation for transmission

of a signal.

{q-q q-{*p{r+ +qrf fr tit grqqsq dqT(ii) g{irfiis t qTd ff,fuq IsTsrerT

* fdq qgqq ql enqr+-o-frr<tlii qTAq) o,Rq ldfuq C{

2

ffi fu"i-f, * €q{uT

sr"i gtr dfrq t

655t2

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I

A wire of 15 f) resistance is gradually stretched to double its original

length. It is then cut into two equal parts. These parts are then

connectedin parallel across a 3'0 volt battery. Find the current drawn

from the battery. 0. )

ffi dR,fuffsTxfrtq 15o t, q] frt-qii dd qt ss+1Eqr$eTrfi{f, dErieig$taqrfr t | $furAq{1-qqqrr i ff roraqrdTAI F{qr, fdfur8.0+€aqi ffi * tu{i t qrr{ffi.Tfr sq}fudfuqrqrart r*an t ffi T$RgqerRr{kT*1Fq r

Define the term 'linearly polarised light'.

When does the intensity of transmitted light becomemaximum, whena polaroid sheet is rotated between two crossedpolaroids ?'fufr-er gfe-ar+rw' qi qRrTM

{tqqr

q-qA fikd qjarFr t Et-qfr qii errqq)frrns {fre 4i gqrqTqrdTi, n} qrcTR-drqm +1atqmenq+-cqq.q *oi d ?

(a ) The mass e f a t t i re l t ' us i r i i t s g round s ta te i s a ln-a- r - - .less than thetotai ruass oi rts con-qfituents - neutrons and protons. Explain.

rbr Plot a graph showing the variation of potential energy of a pair ofnrrleons as a function of their sepgration.

(a) fuql qTFrsq.r r{r+1f+ndq sFR{rTi rqqiq seq Bq+ 3rqrqj - *inneil*d-ii - t gffi rarrrn t qq Etdrt I rqs 6ifqq I

o) aksr+ * grn qi turfrqc.qifr qMq q) qFm$m+* yq+-qt q-n{t sq fr qvrit+ tdq qTsdfu |

18. Define current sensitivity and voltage sensitivity of a galvanometer.

Increasing the current sensitivity may not necessarily increase thevoltage sensitivity of a galvanometer. Justify.

a , , i i ) \ ) ^ ^ktrqr rriq.{|rrETSt qr{I gqTtrdTdqT+€f,r wTRRT+1 qRtTqTqlfqq r

ffir ffidlqiar q1 eTKrgntrdTfr gk t}} w q6 sTl-+q-{s€ t fu BF*1+"TdTWTR-dTfr oi gFdA I qq-m15E qifqq I

15.

16.

17.

755t2 P.T .O.

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19. Draw a schematic arrangement of the Geiger- Marsden experiment.

How did the scattering of cx-particlesby a thin foil of gold provide an

important way to determine an upper limit on the size of the nucleus ?

Explain briefly. 3

rrr5rR- qTCsqqqtrr aT qq{qrflrrn frFqrT dfqq I Fuf qT q-f,di qfr gm cr-qoii

qr x+ffiq ffi yfi-q 4Fffi t qrfe ai s€ q"lqr fl-a qai qI qmqut eTq{q;rT ? qsor {i*q fr qufq dRq I

20. Give a circuit diagram of a common emitter amplifier using an n-p-n

transistor. Draw the input and output waveforms of the signal. Write

the expressionfor its voltage gain.c--; -+_- , ,-' -"'qne g?q-f6 gsrffi 6f qliqql+* l l n-p-n t l ls l td{

chl sHqlr l ch( f t .J}1

fqr{f, + f++qTa'erfrIh n.r'rsq {fr'fqq I ge-eildR-iT df"T + tgq

(i ) State the larv that gives the polaritl' of the induced emf.

(i i ) A 15.0 pF capacitor is connectedto 220 \I. 50 Hz source. Find the

capacitir-ereactance and the rms clrrrent. 3

(i) Td fqq fdfisq^ffi Eq mF iqgi1t1= 1.:*1;-

z-- i t

(iil 15.0 prFqT qTi €ETIf{d220v,50 Hz drd + +'ffiH-mnwrt r*F*i*'**.-

qTR-drsfrqlf, dqT{q-ii q-{rtrd e,i-r'rea-1r (rms) tIRl flfi dfrq I

(a) In a single slit diffraction experiment, a slit of width 'd' is

illuminated by red light of wavelength 650 nm. For what.value of'd ' wili

(i) the first minimum fall at an angle of diffraction of 30", and

(ii) the first maximum fall at an angle of diffraction of 30' ?

(b) Why does the intensity of the secondaryma-''cimumbecomeless as

compared to the central maximum 7 3

(a) q,*-otr-frffiq n+T fr 'd'N df f.rt +i OSOnm d\irdd t ,fio r+rqr

t TAR fu-qr.TqT

t r

'd'+

fs-sqTq+ frq

(i) qEqfrFe' 30'+ ffiq qloTqr Rqd'Et'r, aelT

(ii) qqqsHs 30"t ffi{ qtoTq{ ft{d Etr ?

(b) +dq sfffi +1gon C ffizm sftr 4i fi-dnT6q d A qrfr d ?

3

sili€ ffi tr - , n, , . ,

cqqch tg i l € ( I

2L .

855t2

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2g. Use Gauss'slaw to derive the expressionfor the electrlc field betweentwo uniformly charged large parallel sheets with surface chargedensitieso and -o respectiveiy. S

OR

(a) A charge +Q is placed on a large spherical conducting shell of

radius R. Another small conducting sphere of radius r carryingcharge 'q' is introduced inside the large shell and is placed at itscentre. Find the potential difference between two points, oneIying on the sphere and the other on the shell.

(b) How would the charge between the two flow if they are connectedby a conducting wire ? Name the device which works on this fact.

'nss fr-qq *,r sq+q 6$ A wi q6qqn qT+RTdq'rt<R q-Et, fq{+ ydq 3ilaTrqqci *.qfl: o cTelr- o €, + dT-qfrgq-qi + lf,q aiqs E3-dr{qifqq r

sTsrqtRF-qT+ ffi q,9'idq q?r+dre q{ 6rqqTaTT+e fr+oi r r frq1 qfuqfrerq d) qp66rft-fr,fus qt 'q' qftsJ$, d q-e€]e + Sd{ 3q+*'q q{ {GI qfflI d r q} fu€si, fuafr q-onl}d w derTqslr re}-ow Rern*\ --5- c--- -6 dra rq!|Tar=ry 5rF --r--r: '

€ g qqi ri ffi m dRt $.............-qlfffd t,' fr, st +q 3n+vrfus xqn*il i'r z Ts gfu -il qH fdfuqq} Esr?Fzrq{ +r4q,rfi t r

21. Distinguish between sky wave and space wave propagation. Give a

brief description with the help of suitable diagrams indicating howthese waves are propagated.

6q)q d-{,T$q{uT d?il 3Tt.FrfldtT €q'{uTfr qE dfqq I sqgffi 3nU q1 vorqflr t,qEfrRE +G gq rs i drii |qq trFR€q'RnE)-frt, qqff €Ri-drq-q{uT{fqq r

(a)

br

25. (i)

(i i)

with the help of circuit diagrams, distinguish between forwardbiasing and reversebiasing of a p-n junction diode.

Draw v - I characteristics of a p-n junction diode in (a) forward

bias,(b)

reversebias.(i) .qRqq3rrtdi s] s6Tq-drt ffi p-n *ifrT sTqts+ eqmrm qrqs delr

q-rqfqRr*qmq fr t( qifqq I

(ii) (a) elqRRr-mqTq{T,6y qsqftffi qrqs fr ftrfr p-n {rq srqt-s* v - tsTfiroqTFffidRq I

955t2 P.T .O.

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26. (i)

(ii)

State the principle of working of a meter bridge.

In a meter bridge balance point is found at aresistancesR and S as shown in the figure.

X

distance /, with

when an unknown resistanceX is connectedin parallel withresistances, the balance point shifts to a dist ance lo. Findexpressionfor X in terms of /1 , /2 and _S.

frer+Em 6rffi 6r lvqrn-lafuqr

the

the

3

(i)

(ii) ffi qlz{ t-E fr w frQqRrft, fqr fr q{Ttq3rgqR,R dens qfr-tq*HTq(fr /1vt qrq *-fr t r

qq qfrTtqS + qnd*q fr

r1a frfu ftvfrqfrz,wqqi t aiqs {16 +ifuu r

qli ewroqftTtq

TqTqrdRdEi qrfrx {i?ifdd q-t t{qr qrdT€, dr

d r xt fuq/1, lzdqrs+

55t2 10

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27, Draw a plot showing the variation of binding energy per nucleon

versus the mass number A. Expiain with the help of this plot the

release of enerry in the processesof nuclear fission and fusion.

rqqn {qr A i qffi{ * qrq tiffi sqf yfr Aks-{ fr qRg-drd qqfi +

fre ns dfqq | {s Trs q1 vorqort nFffiiq {f,'fi nqyqftffiq fuar qt

Yhqrci q u.qf t-m d{'r Hs qltrq I

28. (a) ( i )

( i i)

Draw a labelled ray diagram to show the formation ofimage in an astronomical telescopefor a distant object.

Write three distinct advantages of a reflecting typetelescopeover a refracting type telescope.

(b) A convex lens of focal length 10 cm is placed coaxially 5 cm away

from a concave lens of focal length 10 cm. If an object is placed

30 cm r-n front of the convex lens, finfl_the position of the final

inage formed by the consbined system. 5

(a)

OR

with the help of a suitable ray diagram, derive the mirrorformula for a concavemirror.

(b) The near point of a hypermetropic person is b0 cm from the eye.

what is the power of the lens required to enable the person to

read clearly a book held at 25 cm from the eye ?

(a) (i) ffi qrw frq + ffl q'ilmq (rErfssnrqfrTFqcqiTErfi t fdq

qTqiffrdrqrqrfu$ryertrs dFq r

(ii) s{qqfi}rq.n* $E{H +1gearfi q{Ttr TfrRt $Effi * fr+ ws

m'qfrfuq r

o

115512 P.T .O.

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(b) 10cmqtsq {fr + FnSsre AH t fs+ qqTqT5 cmEfi vr *$ to .*++-q qtr w stftrmt'q {cT t r qR ffi kq s} cre frq * qrqt

B0 cm Er rd, A {iT.F ftsrq srurq} BTFilqqfrfuq +1 ftqft uaqifqq I

ewlEtt

(a) srgr rqrvr futq 3lrtq +i vdr{rdrt ffi siqcrcTEq"r* leq EqrTqt--a-c,-

%-ffi sneq ;

(b) iidqtr *q t gm ffi qtu + rd-dzr{€ ei tr t {ft 50cmt I sq'

d€ Ei'qrff,r

*il t fq€qi sdpfdTq

Ez aufuq"sil6

d) iT t zs cm (frq"{ {Gf,{ HE qE sani i ?

2g.Drawaschemat icsketchofacycIot ron.B"p i l i ' fu"* .

and how it is used to accelerate the charged particles.

(i) Show that time period of ions in a cyclotron is independent of

both the speed and radius of circular path.

(ii) What is resonancecondition ? How is it used to accelerate the

charged particles ?

OR

(a) Two straight long parallel conductors carry currents I, and I, h

the same direction. Deduce the expression for the force per unitlength between them.

Depict the pattern of magnetic field lines around them.

1255t2

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(b) A rectangular current carrying loop.EFGH is kept in a uniformmagnetic field as shown in the figure.

E;F

WeticWhat is the direction of the magn

current loop ?

When is the torque acting on the(B)

zero ?

(i )

(ii)

eTKrET + 3'q+tq .fl{.f qi l<vr €T t ?qq qt sTftd q-m-3TITIf6q (A) 3rftIfdq,

moment of the

loop (A) maximum,

P.T .O.

5qF@ir sTquruqT-3rrts dfuq I vg-s]ffi nqr eTrlRtd6"il q) dRd srifr {s* w+{ +}TiSqfr ws qituqr(i) Td wf{q r* eFdqh d em++qr a+r+dqmoerTqq}q1 qrd apnr*q qq

S1 fr'qT *q) q{ foJr a-* qr-r?r r

-; '=-E Envd +ryi 7 fr 6uil t dfu E{i fr gr*r wql"rfuq Fs.nfurvol r

A qE ed vqrar

1rm$it *#*A* fr $rRigr1

den12rEr6d.d rfit r r+t qtqqfr q-6isdqri qr qe + ldq *-" €", qifuqr5+*qr-freir gq-drqtr turcil+ H +)q{kq r

f J sUsq)ger<-ar+nqR*rf'ETEFGHfosl q-sqqr{gq+iqqHq rqr qrord r

(a )

(b)

HW( i)

(ii)(B)Ytqd ?

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30. (a) what are eddy currents ? write their two apprications.

(b) Figure shows a rectangular conducting loop pesR in which armRS of rength 'r ' is movabre. The roop is kept in a uniformmagnetic field 'B'

directed downward perpendicularto the piane

- of the loop. The arm RS is moved with a uniform speed.,r-,.

PX X X XRX X

ax XS X

Deduce an expression for -.i.. - ar=.+,

(i ) the emf induced across the arm

(ii; the external force required to move the arm, and(iii) the power dissipated as heat.

t:I

l:.RS"

D

(a)

(b)

(a )

OR

state Lenz's law. Give one exampre to illustrate this raw. *The

Lenz's law is a consequenceof the principle of consen-ation ofenerg1r."Justify this statement.

Deduce an expression for the mutual inductanceof tlvo longcoaxial solenoidsbut having different radii and different number

of turns.

$iqrqnrqwr t ? F+ * qg.+,TFofuqr

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(b) fr-{ ii qs 3{FldlrFRslcf.FE{ eQSRRfqT 'rqTt Gqfi TqTnS q1dwri'/' t der qa 'ft qr sofi t r qo qv ffi qq,-sqngqdq tr 'B'il rqr

d qi W * ae * dq{-{ e&rtgcifu t I gqr ns +} qssqn qn{ 'v'

q 'rfr q'rrqi q-,fr,t I

PX

X X XRX X

AX X X XSX

Frqfufudt ldq aiws€sd dfqq :

(i) Uqr'RS'+ ffii qr iRo f+gqe6* q-o,

(ii) gw d qfr srr} + frq 3lr+{q_sq@ EE,

::1,, 5q i5 S,f q ffr fr{t f

iIlGrT

fr-e a f{qq fdfuq r g*rd ar€!fi fii * ieq q* Fffirq €tqq | "ds 6'rtrqq $qt €ren'T.FrqqqTqs qfiqq'

tr"

Fsqwr q1

5Eqifqq I

qi atqi qqq+rqnmFemrgii,ffi M npTrtt +1M frd-fl,rdt, +siq)=Th.r + fuq aiqs 1-dr +1Fqqr

1'lx

IX

Il*

i a )

(b)

97100

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