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CBSE 12th board 2014 physics paper

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H$moS> Z . Series OSR/C Code No. amob Z . 55/2 narjmWu H$moS >H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Roll No. Candidates must write the Code on the title page of the answer-book. H $n`m Om M H$a b| {H$ Bg Z-n _o _w{ V n > 16 h & Z-n _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Z ~a H$mo N>m C ma -nwp VH$m Ho$ _wI-n > na {bI| & H $n`m Om M H$a b| {H$ Bg Z-n _| >30 Z h & H $n`m Z H$m C ma {bIZm ew $ H$aZo go nhbo, Z H$m H $_m H$ Ad ` {bI| & Bg Z-n H$mo n T>Zo Ho$ {bE 15 {_ZQ >H$m g_` {X`m J`m h & Z-n H$m {dVaU nydm _| 10.15 ~Oo {H$`m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N>m Ho$db Z-n H$mo n T>|Jo Am a Bg Ad{Y Ho$ Xm amZ do C ma-nwp VH$m na H$moB C ma Zht {bI|Jo & Please check that this question paper contains 16 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. Please check that this question paper contains 30 questions. Please write down the Serial Number of the question before attempting it. 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 students will read the question paper only and will not write any answer on the answer-book during this period. ^m {VH$ {dkmZ (g mp VH$) PHYSICS (Theory) {ZYm [aV g_` : 3 K Q>o A{YH$V_ A H$ : 70 Time allowed : 3 hours 55/2 Maximum Marks : 70 1 P.T.O. gm_m ` {ZX}e : (i) g^r Z A{Zdm` h & (ii) Bg Z-n _| Hw$b 30 Z h & Z 1 go 8 VH$ Ho$ Z A{V-bKwC mar` Z h Am a `oH$ EH$ A H$ H$m h & (iii) Z 9 go 18 _| `oH$ Z Xmo A H$ H$m h , Z 19 go 27 _| `oH$ Z VrZ A H$ H$m h Am a Z 28 go 30 _| `oH$ Z nm M A H$ H$m h & (iv) VrZ A H$m| dmbo Zm| _| go EH$ _y `naH$ Z h & (v) Z-n _| g_J na H$moB {dH$ n Zht h & VWm{n, Xmo A H$m| dmbo EH$ Z _|, VrZ A H$m| dmbo EH$ Z _| Am a nm M A H$m| dmbo VrZm| Zm| _| Am V[aH$ M`Z XmZ {H$`m J`m h & Eogo Zm| _| AmnH$mo {XE JE M`Z _| go Ho$db EH$ Z hr H$aZm h & (vi) H $bHw$boQ>a Ho$ Cn`moJ H$s AZw_{V Zht h & VWm{n `{X Amd `H$ hmo Vmo Amn bKwJUH$s` gmaUr H$m `moJ H$a gH$Vo h & (vii) Ohm Amd `H$ hmo Amn {Z Z{b{IV ^m {VH$ {Z`Vm H$m| Ho$ _mZm| H$m Cn`moJ H$a gH$Vo h : c = 3 108 m/s h = 6.63 10 34 Js e = 1.6 10 19 C o = 4 10 7 T mA 1 1 = 9 109 N m2 C 2 4 o me = 9.1 10 31 kg General Instructions : (i) All questions are compulsory. (ii) There are 30 questions in total. Questions No. 1 to 8 are very short answer type questions and carry one mark each. (iii) Questions No. 9 to 18 carry two marks each, questions 19 to 27 carry three marks each and questions 28 to 30 carry five marks each. (iv) One of the questions carrying three marks weightage is value based question. (v) There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all three questions of five marks each weightage. You have to attempt only one of the choices in such questions. (vi) Use of calculators is not permitted. However, you may use log tables if necessary. 55/2 2 (vii) You may use the following values of physical constants wherever necessary : c = 3 108 m/s h = 6.63 10 34 Js e = 1.6 10 19 C o = 4 10 7 T mA 1 1 = 9 109 N m2 C 2 4 o me = 9.1 10 31 kg 1. Vmn-d { Ho$ gmW {H$gr YmVw H$s {VamoYH$Vm _| d { H$s `m `m H $go H$s OmVr h ? How does one explain increase in resistivity of a metal with increase of temperature ? 1 2. Cg eV ( {V~ Y) H$m C oI H$s{OE {OgHo$ A VJ V, H $m {gV {d wV Am a Mw ~H$s` jo m| H$s Cnp W{V _|, H$moB Bbo Q >m Z A{djo{nV J{V H$aVm ahoJm & 1 Write the condition under which an electron will move undeflected in the presence of crossed electric and magnetic fields. 3. 1 g Mma H$s gmaU (~ m S>H$m Q>) {d{Y H$m EH$ CXmhaU Xr{OE & Give one example of broadcast mode of communication. 4. {H$gr C mb b|g na EH$ g_Vb Va J Amn{VV hmoVr h & Bggo {ZJ V Va JmJ Ho$ AmH$ma H$mo Xem BE & 1 Draw the shape of the wavefront coming out of a convex lens when a plane wave is incident on it. 5. 55/2 {X`m h Am J m\$ (AmboI), Xmo g Ym[a m| C1 VWm C2 Ho$ {bE, {d^dm Va V Ho$ gmW Amdoe q Ho$ n[adV Z H$mo Xem Vm h & XmoZm| g Ym[a m| _| n{ >H$mAm| Ho$ ~rM n WH$Z (X ar) g_mZ (~am~a) h , {H$ Vw C2 _| n{ >H$mAm| H$m jo \$b C1 H$s VwbZm _ o A{YH$ h & J m\$ _| H$m Z-gr aoIm (A `m B) C1 Ho$ g JV h ? AnZo C ma Ho$ {bE H$maU {b{IE & 3 1 P.T.O. The given graph shows variation of charge q versus potential difference V for two capacitors C1 and C2. Both the capacitors have same plate separation but plate area of C2 is greater than that of C1. Which line (A or B) corresponds to C1 and why ? 6. {H$gr MmbH$ H$s b ~mB l h & BgHo$ Xmo {gam| Ho$ ~rM V {d^dm Va h & Bg MmbH$ _| Amdoe dmhH$m| Ho$ Andmh doJ Ho$ {bE EH$ ` OH$ {b{IE & 1 Write the expression for the drift velocity of charge carriers in a conductor of length l across which a potential difference V is applied. 7. `{X EH$ Mw ~H$ H$mo AmaoI _| Xem E JE AZwgma, g Ym[a H$s Amoa bo OmE , Vmo boQ (n{ >H$m)> A H$s Yw dVm `m hmoJr ? 1 Predict the polarity of the plate A of the capacitor, when a magnet is moved towards it, as is shown in the figure. 8. g Mma `d Wm _| _m Sw>bZ gyMH$m H$ nX H$mo n[a^m{fV H$s{OE & Define the term modulation index in communication system. 55/2 4 1 9. EH$ Jmobo S1 H$s { `m r1 h Am a Bg_| EH$ ZoQ> Amdoe Q n[a~ h & `{X EH$ A ` g Ho$ r Jmobo S2 H$s { `m r2 (r2 > r1) h , {Og_| 2Q Amdoe n[a~ h , Vmo S1 VWm S2 go Jw OaZo dmbo {d wV b g H$m AZwnmV kmV H$s{OE & `{X S2 Ho$ [a $ WmZ _| dm`w Ho$ WmZ na, K namd wVm H$ dmbm _m `_ ^a {X`m OmE, Vmo S1 Jmobo go Jw OaZo dmbo {d wV b g _| `m n[adV Z hmoJm ? 2 A sphere S1 of radius r1 encloses a net charge Q. If there is another concentric sphere S2 of radius r2 (r2 > r1) enclosing charge 2Q, find the ratio of the electric flux through S1 and S2. How will the electric flux through sphere S1 change if a medium of dielectric constant K is introduced in the space inside S2 in place of air ? 10. Xmo {~ X Amdoe q VWm 2q EH$-X gao go d X ar na p WV h & Amdoe q Ho$ gmnoj, EH$ Eogo {~ X H$s Adp W{V kmV H$s{OE, Ohm na Amdoem| Ho$ Bg {ZH$m` Ho$ H$maU {d^d ey ` hmo & 2 AWdm 55/2 5 P.T.O. EH$ {d wV { Y wd H$mo {H$gr EH$g_mZ {d wV -jo E _| Eogo aIm J`m h {H$ { Y wd H$m { Y wd AmKyU p {d wV -jo Ho$ g_m Va h & kmV H$s{OE (i) { Y wd H$mo BVZm Kw_mZo _| {H$`m J`m H$m` {Oggo CgHo$ { Y wd AmKyU H$s {Xem E H$s {Xem Ho$ {dnarV hmo OmE & (ii) { Y wd H$m dh A{^{d `mg (p W{V) {OgHo$ {bE Cg na bJZo dmbm ~b -AmKyU (Q>m H $) A{YH$V_ hmo OmE & 2 Two point charges q and 2q are kept d distance apart. Find the location of the point relative to charge q at which potential due to this system of charges is zero. OR An electric dipole is placed in a uniform electric field E with its dipole moment p parallel to the field. Find (i) (ii) 11. (a) (b) (a) (b) 12. the work done in turning the dipole till its dipole moment points in the direction opposite to E . the orientation of the dipole for which the torque acting on it becomes maximum. {d wV -Mw ~H$ {H$gr Wm`r Mw ~H$ go {H$g H$ma {^ hmoVm h ? {d wV -Mw ~H$ ~ZmZo Ho$ {bE Cn`w $ nXmW Ho$ Xmo JwUY_ {b{IE & 2 How is an electromagnet different from a permanent magnet ? Write two properties of a material which make it suitable for making electromagnets. EH$ Bbo Q >m Z 2.4 108 m/s H$s p Wa Mmb go Zm{^H$ H$s n[aH $_m H$a ahm h & Bggo g ~ Xo ~ m br Va JX ` H$m _mZ kmV H$s{OE & 2 An electron is revolving around the nucleus with a constant speed of 2.4 108 m/s. Find the de Broglie wavelength associated with it. 13. EH$ gob {OgH$m Am V[aH$ {VamoY r h , Ho$ {d wV -dmhH$ ~b (B .E_.E\$) ( ) VWm Q>{_ Zb dmo Q>Vm (V) Ho$ ~rM A Va (^oX) {b{IE & gob go br JB {d wV Ymam (I) Ho$ gmW CgH$s Q>{_ Zb dmo Q>Vm (V) _| n[adV Z H$mo Xem Zo Ho$ {bE EH$ J m\$ (AmboI) ~ZmBE & Bg J m\$ Ho$ Cn`moJ go, {H$gr gob Ho$ Am V[aH$ {VamoY H$m {ZYm aU H $go {H$`m Om gH$Vm h ? Distinguish between emf ( ) and terminal voltage (V) of a cell having internal resistance r . Draw a plot showing the variation of terminal voltage (V) vs the current (I) drawn from the cell. Using this plot, how does one determine the internal resistance of the cell ? 55/2 6 2 14. (i) (ii) {H$gr I Ymamdmhr A nm e dl go r X ar na, Mw ~H$s` jo Ho$ {bE ~m`mo gmdQ> {Z`_ H$mo g{Xe $n _| {b{IE & EH$ d mmH$ma nme (byn) Ho$ Ho$ na Mw ~H$s` jo Ho$ n[a_mU (_mZ) Ho$ {bE ` OH$ {b{IE, `{X nme (byn) H$s { `m r h Am a Bggo EH$ AMa (p Wa) Ymam I dm{hV hmo ahr h & Bg Ymam-nme Ho$ H$maU C n jo aoImAm| H$mo Xem BE & (i) 15. State Biot Savart law in vector form expressing the magnetic field due to an element dl carrying current I at a distance r from the element. (ii) Write the expression for the magnitude of the magnetic field at the centre of a circular loop of radius r carrying a steady current I. Draw the field lines due to the current loop. (a) {ZamoYr {d^d nX H$s n[a^mfm Xr{OE & Xmo {^ -{^ Amd { m`m| v1 Ed v2 (v2 > v1), {H$ Vw g_mZ Vrd Vm Ho$ Xmo H$me nw Om| Ho$ {bE, EoZmoS> {d^d Ho$ \$bZ Ho$ $n _| H$me-{d wV Ymam Ho$ n[adV Z H$mo Xem Zo Ho$ {bE J m\$ (AmboI) ~ZmBE & (b) (a) Plot a graph showing the variation of photoelectric current as a function of anode potential for two light beams of same intensity but of different frequencies, v1 and v2 (v2 > v1). (a) OR JoQ> (b) 55/2 2 Define the term stopping potential . (b) 16. 2 Ho$ {bE g `_mZ gmaUr VWm BgH$m VH $ VrH$ ~ZmBE & ZrMo Xem E JE {Zdoer Va J- $nm| A VWm B H$m AND JoQ> _| {ZdoeZ {H$`m OmVm h & {ZJ V Va J- $n H$mo kmV H$s{OE & 7 2 P.T.O. (a) (b) 17. Write the truth table for an OR gate and draw its logic symbol. The input waveforms A and B, shown below, are fed to an AND gate. Find the output waveform. B YZwf Ho$ {XImB XoZo ( ojU) Ho$ {bE `m eV o ( {V~ Y) h ? Cn`w $ AmaoIm| H$s ghm`Vm go Xem BE {H$ B YZwf Ho$ ~ZZo H$mo H $go g_Pm Om gH$Vm h & 2 Write the conditions for observing a rainbow. Show, by drawing suitable diagrams, how one understands the formation of a rainbow. 18. AmaoI _| EH$ loUr LCR n[anW Xem `m J`m h Omo 250 V Ho$ EH$ n[adVu Amd { m Ho$ moV go Ow S>m h VWm L = 40 mH, C = 100 F VWm R = 50 h >& {ZYm [aV H$s{OE (i) moV H$s dh Amd { m {Oggo n[anW _| AZwZmX hmo; (ii) n[anW H$m JwUd mm JwUm H$ (Q) & The figure shows a series LCR circuit connected to a variable frequency 250 V source with L = 40 mH, C = 100 F and R = 50 . Determine (i) the source frequency which derives the circuit in resonance; (ii) the quality factor (Q) of the circuit. 55/2 8 2 19. (a) {d^d_mnr (nmoQ>op e`mo_rQ>a) {H$g {g m V na AmYm[aV h , C oI H$s{OE & Bg_|, (i) b ~o Vma H$m, (ii) EH$g_mZ AZw W-H$mQ> jo \$b (_moQ>mB ) Ho$ Vma H$m VWm (iii) mW{_H$ gobmo go A{YH$ {d wV -dmhH$ ~b (B .E_.E\$) Ho$ _mZH$ (MmbH$) gob H$m, Cn`moJ `m| {H$`m OmVm h ? (b) {d^d_mnr (nmoQ>p o e`mo_rQ>a) Ho$ {H$gr `moJ _|, `{X Vma Ho$ AZw W-H$mQ> H$m jo \$b EH$ {gao go X gao {gao H$s Amoa EH$g_mZ $n go ~ T>Vm OmE, Vmo Vma Ho$ EH$ {gao go Bg b ~mB _| d { Ho$ gmW, {d^d dUVm Ho$ n[adV Z H$mo Xem Zo Ho$ {bE EH$ J m\$ ~ZmBE & (a) In a potentiometer experiment, if the area of the cross-section of the wire increases uniformly from one end to the other, draw a graph showing how potential gradient would vary as the length of the wire increases from one end. (a) {H$gr d.c. moV Ho$ {gam| go Ow So EH$ g Ym[a go loUrH $_ _| EH$ Eo_rQ>a H$mo Omo S>m J`m h & g Ym[a H$mo Amdo{eV H$aVo g_` Eo_rQ>a _| j{UH$ {djon `m| hmoVm h ? g Ym[a Ho$ nyU $n go Amdo{eV hmo OmZo na {djon `m hmoJm ?> (b) 20. State the underlying principle of a potentiometer. Why is it necessary to (i) use a long wire, (ii) have uniform area of cross-section of the wire and (iii) use a driving cell whose emf is taken to be greater than the emfs of the primary cells ? (b) {d WmnZ Ymam go g ~ nX H$mo gp _{bV H$aVo h E, Eop n`a Ho$ n[anWr` {Z`_ Ho$ gm_m `rH $V $n H$mo H $go m {H$`m OmVm h ? (a) 3 A capacitor is connected in series to an ammeter across a d.c. source. Why does the ammeter show a momentary deflection during the charging of the capacitor ? What would be the deflection when it is fully charged ? (b) 55/2 3 How is the generalized form of Ampere s circuital law obtained to include the term due to displacement current ? 9 P.T.O. 21. AmaoI _| Xem E JE AZwgma EH$ g_~mh { ^wO ABC Ho$ Xmo erfm o B VWm C na H $_e: Xmo Amdoe + 3q VWm 4q aIo JE h & Bg { ^wO H$s ^wOm a h & BZ Xmo Amdoem| Ho$ H$maU erf A na n[aUm_r {d wV -jo Ho$ (i) n[a_mU (_mZ) VWm (ii) {Xem Ho$ {bE ` OH$ m H$s{OE & 3 Two point charges + 3q and 4q are placed at the vertices B and C of an equilateral triangle ABC of side a as given in the figure. Obtain the expression for (i) the magnitude and (ii) the direction of the resultant electric field at the vertex A due to these two charges. 22. 55/2 AZ ~ AnZo {_ go _mo~mBb na ~h V b ~o g_` VH$ dmVm bmn H$aVm ahm & dmVm bmn g_m hmoZo na, CgH$s ~{hZ A{ZVm Zo CgH$mo am` Xr {H$ BVZo b ~o g_` VH$ dmVm bmn H$aZm hmo, Vmo b S> bmBZ go H$aZm A{YH$ A N>m hmoJm & {Z Zm {H$V Zm| Ho$ C ma Xr{OE : (a) b ~o g_` VH$ _mo~mBb \$moZ H$m Cn`moJ H$aZm hm{ZH$maH$ `m| g_Pm OmVm h ? (b) AZ ~ H$s ~{hZ H$s gbmh {H$Z _y `m| H$m Xe Z H$aVr h ? (c) 10 kHz Amd { m Ho $EH$ g Xoe {g Zb (g Ho$V) H$m A `mamonU, 1 MHz Amd { m H$s dmhH$ Va J H$m _m Sw>bZ Ho$ {bE {H$`m OmVm h & C n nm d -~ S> kmV H$s{OE & 10 3 Arnab was talking on his mobile to his friend for a long time. After his conversation was over, his sister Anita advised him that if his conversation was of such a long duration, it would be better to talk through a land line. Answer the following questions : (a) Why is it considered harmful to use a mobile phone for a long duration ? (b) Which values are reflected in the advice of his sister Anita ? (c) A message signal of frequency 10 kHz is superposed to modulate a carrier wave of frequency 1 MHz. Determine the sidebands produced. 23. (a) Q>moam BS> {H$gr n[aZm{bH$m go {H$g H$ma {^ hmoVm h ? (b) Eop n`a Ho$ n[anWr` {Z`_ Ho$ Cn`moJ mam, {H$gr Q>moam BS> Ho$ A Xa Mw ~H$s` jo H$m _mZ m H$s{OE & (c) Xem BE {H$ EH$ AmXe Q>moam BS> _|, (i) Q>moam BS> Ho$ ^rVa VWm (ii) Q>moam BS> Ho$ ~mha, Iwbo jo _| {H$gr {~ X na, Mw ~H$s` jo ey ` hmoVm h & AWdm Zm{^H$ H$s n[aH $_m H$aVo h E Bbo Q >m Z Ho$ Mw ~H$s` AmKyU ( ) Ho$ {bE, CgHo$ H$moUr` g doJ ( l ) Ho$ nXm| _|, EH$ ` OH$ `w n H$s{OE & Bbo Q >m Z H$s Mw ~H$s` AmKyU H$s {Xem, CgHo$ H$moUr` g doJ Ho$ gmnoj `m h ? (a) (b) (c) 3 3 How is a toroid different from a solenoid ? Use Ampere s circuital law to obtain the magnetic field inside a toroid. Show that in an ideal toroid, the magnetic field (i) inside the toroid and (ii) outside the toroid at any point in the open space is zero. OR Derive an expression for the magnetic moment ( ) of an electron revolving around the nucleus in terms of its angular momentum ( l ). What is the direction of the magnetic moment of the electron with respect to its angular momentum ? 24. (i) (ii) {H$gr ao{S>`moEop Q>d Zm{^H$ H$s Am gV Am`w VWm AY -Am`w Ho$ ~rM g ~ Y H$mo {b{IE & 90 38 Sr H$s AY -Am`w 28 df h & Bg g_ Wm{ZH$ Ho$ H$m n[aH$bZ H$s{OE & {X`m J`m h {H$$ h & 55/2 11 1 J m_ 80 27 Sr 15 _| {_brJ m_ H$s Eop Q>dVm 75 1020 na_mUw hmoVo 3 P.T.O. (i) Write the relation between average life and half-life of a radioactive nucleus. (ii) The half-life of 38 Sr is 28 years. Calculate the activity of 15 mg of 90 80 this isotope. Given that 1 g of 27 Sr contains 75 1020 atoms. 25. (a) Xmo H$bm-g ~ EH$dUu moVm| go {ZJ {_V Va Jm| Ho$ {d WmnZm| H$mo {Z Z H$ma {Z ${nV {H$`m OmVm h : y1 = a cos t VWm y2 = a cos ( t + ), Ohm Xmo {d WmnZm| Ho$ ~rM H$bm Va h & Xem BE {H$ BZ Va Jm| Ho$ A `mamonU Ho$ H$maU {H$gr {~ X na n[aUm_r Vrd Vm H$m _mZ hmoJm, I = 4 Io cos2 /2, Ohm Io = a2. (b) Bggo g nmofr VWm {dZmer `{VH$aU Ho$ {bE eV o m H$s{OE & (a) 3 Two monochromatic waves emanating from two coherent sources have the displacements represented by y1 = a cos t and y2 = a cos ( t + ), where is the phase difference between the two displacements. Show that the resultant intensity at a point due to their superposition is given by I = 4 Io cos2 /2, where Io = a2. (b) 26. 55/2 Hence obtain the conditions for constructive and destructive interference. hmBS >moOZ na_mUw H$s _yb ({Z ZV_) Ad Wm D$Om H$m _mZ 13.6 eV h Am a ~moa { `m = 0.53 h & n[aH$bZ H$s{OE (i) Bbo Q >m Z H$mo _yb Ad Wm go { Vr` C mo{OV Ad Wm VH$ OmZo Ho$ {bE Amd `H$ D$Om & (ii) { Vr` (X gar) C mo{OV Ad Wm _| na_mUw H$s (a) J{VO D$Om Am a (b) H$jr` { `m & 12 3 The value of ground state energy of hydrogen atom is 13.6 eV and Bohr radius is 0.53 . Calculate (i) (ii) (a) the kinetic energy and (b) the orbital radius in the second excited state of the atom. (a) I0 (b) 27. the energy required to move an electron from the ground state to the second excited state. P1 (a) Vrd Vm H$m AY w{dV H$me Xmo nmoboam BS>m| P1 VWm P2 go hmoH$a Jw OaVm h , Am a Bg H$ma P2 H$s nm[aV-Aj P1 H$s nm[aV-Aj go H$moU ~ZmVr h & Bg H$moU ( ) Ho$ ey ` {S>J r go 180 VH$ n[ad{V V hmoZo go, P2 go nmaJ{_V H$me H$s Vrd Vm _| n[adV Z H$mo Xem Zo Ho$ {bE EH$ J m\$ (AmboI) ~ZmBE & Am a P2 Ho$ ~rM _| EH$ Vrgam nmoboam BS> P3 Bg H$ma aIm OmVm h {H$ P3 H$s nm[aV-Aj P1 go H$moU ~ZmVr h & `{X P1, P2 VWm$ P3 go nmaJ{_V ( o{fV) H$me H$s Vrd VmE H $_e: I1, I2 VWm I3 hm|, Vmo H$moU Am a Ho$ Cg _mZ H$mo kmV H$s{OE {OgHo$ {bE I1 = I2 = I3. 3 Unpolarised light of intensity I0 passes through two polaroids P1 and P2 such that pass axis of P2 makes an angle with the pass axis of P1. Plot a graph showing the variation of intensity of light transmitted through P2 as the angle varies from zero to 180 . (b) A third polaroid P3 is placed between P1 and P2 with pass axis of P3 making an angle with that of P1. If I1, I2 and I3 represent the intensities of light transmitted by P1, P2 and P3, determine the values of angle and for which I1 = I2 = I3. 28. (a) {H$gr p-n g {Y S>m`moS> Ho$ V I A{^bjUm| H$m A ``Z H$aZo Ho$ {bE n[anW `d Wm ~ZmBE, `{X S>m`moS> (i) AJ {X{eH$ ~m`g _| hmoo VWm (ii) n M{X{eH$ ~m`g _| hmo & g jon _| n > H$s{OE {H$ {H$gr S>m`moS> Ho$ $nr ({Q>{nH$b) A{^bjU H $go m {H$E OmVo h Am a BZ A{^bjUm| H$mo Xem BE & (b) H$m{eH$ g Ho$Vm| ({g Zbm|) Ho$ g gyMZ ({S>Q>o eZ) Ho$ {bE `w $, \$moQ>mo S>m`moS> H$s H$m` {d{Y H$mo EH$ Amd `H$ n[anW AmaoI mam n Q> H$s{OE & 5 AWdm 55/2 13 P.T.O. (a) EH$ n-p-n Q >m { O Q>a Ho$ {bE n[anW AmaoI ~ZmBE, {Og_| C gO H$-AmYma g {Y AJ {X{eH$ ~m`g _| hmo VWm g J mhH$-AmYma g {Y n M{X{eH$ ~m`g _| h & g jon _| dU Z H$s{OE {H$ Q >m { O Q>a _| Amdoe dmhH$m| H$s J{V go, C gO H$ Ymam (IE), AmYma Ymam (IB) VWm g J mhH$ Ymam (IC) H $go ~ZVr h & Bggo g ~ Y, IE = IB + IC H$mo `w n H$s{OE & (b) EH$ n[anW AmaoI mam n Q> H$s{OE {H$ Q >m { O Q>a, dY H$ H$s ^m {V H $go H$m` H$aVm h & (a) Draw the circuit arrangement for studying the V I characteristics of a p-n junction diode in (i) forward and (ii) reverse bias. Briefly explain how the typical V I characteristics of a diode are obtained and draw these characteristics. (b) 5 With the help of necessary circuit diagram explain the working of a photo diode used for detecting optical signals. OR (a) (b) 29. Draw the circuit diagram of an n-p-n transistor with emitter-base junction forward biased and collector-base junction reverse biased. Describe briefly how the motion of charge carriers in the transistor constitutes the emitter current (IE), the base current (IB) and the collector current (IC). Hence deduce the relation IE = IB + IC. Explain with the help of circuit diagram how a transistor works as an amplifier. (a) {H$gr Q >m g\$m _ a _| mW{_H$ Ed { Vr`H$ Hw $S>{b`m| H$mo bnoQ>Zo H$s `d Wm H$mo EH$ AmaoI go Xem BE O~ Xmo Hw $S>{b`m EH$-X gao Ho$ D$na bnoQ>r JB h & Q >m g\$m _ a H$s H$m` {d{Y Ho$ {g m V H$m C oI H$s{OE Am a { Vr`H$ Hw $S>br _| dmo Q>Vm H$m mW{_H$ Hw $S>br _| dmo Q>Vm Ho$ gmW AZwnmV Ho$ {bE EH$ ` OH$ m H$s{OE : (i) { Vr`H$ Hw $S>br VWm mW{_H$ Hw $S>br _| \o$am o H$s g `m Ho$ nXm| _| (ii) mW{_H$ VWm { Vr`H$ Hw $S>{b`m| _| {d wV Ymam Ho$ nXm| _| & Cn`w $ g ~ Ym| H$mo `w n ( m ) H$aZo Ho$ {bE `w $ _w ` n[aH$ nZm H$m C oI H$s{OE & dm V{dH$ Q >m g\$m _ am| _| D$Om j` Ho$ H$moB Xmo H$maU {b{IE & AWdm (b) (c) (d) 55/2 14 5 YmVw H$s EH$ N> S> H$s b ~mB l h Am a BgH$m {VamoY R h & BgH$m EH$ {gam YmVw Ho$ EH$ d mmH$ma N> o ([a J) Ho$ Ho$ na H$s{bV (qh O) h , Am a X gam N> o H$s n[a{Y na {Q>H$m ahVm h & N> o H$s { `m l h & Bg N> S> H$mo v Amd { m go Kw_m`m OmVm h & N> S> H$s KyU Z Aj, N> o Ho$ Ho$ go Jw OaVr h Am a N> o Ho$ g_Vb Ho$ b ~dV h & EH$ AMa, EH$g_mZ Mw ~H$s` jo B, gd {d _mZ h , {OgH$s {Xem N> S> H$s KyU Z Aj Ho$ g_m Va h & (a) N> S> _| o[aV {d wV -dmhH$ ~b (B .E_.E\$) VWm {d wV Ymam Ho$ {bE EH$ ` OH$ `w n H$s{OE & (b) N> S> _| o[aV {d wV Ymam VWm Cnp WV Mw ~H$s` jo Ho$ H$maU, N> S> na bJZo dmbo ~b Ho$ n[a_mU (_mZ) VWm {Xem Ho$ {bE EH$ ` OH$ m H$s{OE & (c) Bggo N> S> H$mo Kw_mZo Ho$ {bE Amd `H$ e{ $ Ho$ {bE EH$ ` OH$ m H$s{OE & (a) Draw a schematic arrangement for winding of primary and secondary coil in a transformer when the two coils are wound on top of each other. (b) State the underlying principle of a transformer and obtain the expression for the ratio of secondary to primary voltage in terms of the (i) number of secondary and primary windings and (ii) primary and secondary currents. (c) Write the main assumption involved in deriving the above relations. (d) 5 Write any two reasons due to which energy losses may occur in actual transformers. OR A metallic rod of length l and resistance R is rotated with a frequency v, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius l, about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field B parallel to the axis is present everywhere. (a) (b) Due to the presence of the current in the rod and of the magnetic field, find the expression for the magnitude and direction of the force acting on this rod. (c) 55/2 Derive the expression for the induced emf and the current in the rod. Hence obtain the expression for the power required to rotate the rod. 15 P.T.O. 30. (a) (b) EH$ {~ X d Vw H$mo {H$gr C^`mo mb b|g Ho$ gm_Zo aIm J`m h , (b|g H$m dm`w Ho$ gmnoj AndV Zm H$ n = n2/n1) b|g Hoo$ Xmo Jmobr` n R>m| H$s dH $Vm { `mE R1 VWm R2 h & b|g H$s W_ VWm {\$a { Vr` n R> na AndV Z Ho$ H$maU H$me H$s {H$aUm| H$m _mJ Xem Vo h E d Vw H$m EH$ dm V{dH$ {V{~ ~ m H$s{OE & Bggo {H$gr nVbo b|g Ho$ {bE b|g-_oH$a gy m H$s{OE & EH$ C^`mo mb b|g Ho$ XmoZm| n R>m| H$s dH $Vm { `mE Amng _| ~am~a h & b|g Ho$ nXmW H$m AndV Zm H$ 1.55 h & b|g H$s \$moH$g X ar 20 cm hmoZo Ho$ {bE b|g Ho$ n R>m| H$s dH $Vm { `m H$m _mZ kmV H$s{OE & 5 AWdm (a) (b) (a) {H$gr AndVu X aXe H$ mam, X a p WV {H$gr d Vw H$m {V{~ ~ ~ZZm Xem Zo Ho$ {bE EH$ Zm_m {H$V {H$aU AmaoI ~ZmBE & `{X Bg X aXe H$ mam Ap V_ {V{~ ~ AZ V na ~ZVm h , Vmo CgH$s AmdY Z j_Vm Ho$ {bE EH$ ` OH$ `w n H$s{OE & {H$gr AndVu X aXe H$ Ho$ Xmo b|gm| H$s \$moH$g X [a`m| H$m `moJ\$b 105 cm h & EH$ b|g H$s \$moH$g X ar X gao b|g go 20 JwZm h & `{X Ap V_ {V{~ ~ AZ V na ~ZVm h , Vmo X aXe H$ Ho$ H$maU Hw$b AmdY Z kmV H$s{OE & A point object is placed in front of a double convex lens (of refractive index n = n2/n1 with respect to air) with its spherical faces of radii of curvature R1 and R2. Show the path of rays due to refraction at first and subsequently at the second surface to obtain the formation of the real image of the object. Hence obtain the lens-maker s formula for a thin lens. (b) (a) (b) 55/2 A double convex lens having both faces of the same radius of curvature has refractive index 1.55. Find out the radius of curvature of the lens required to get the focal length of 20 cm. OR Draw a labelled ray diagram showing the image formation of a distant object by a refracting telescope. Deduce the expression for its magnifying power when the final image is formed at infinity. The sum of focal lengths of the two lenses of a refracting telescope is 105 cm. The focal length of one lens is 20 times that of the other. Determine the total magnification of the telescope when the final image is formed at infinity. 16 5

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