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CBSE Class 12 Board Exam 2019 : Physics (Series 2)

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SET-1 H$moS> Z . Series BVM/2 Code No. amob Z . 55/2/1 narjmWu H$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 > 19 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 _| >27 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 19 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 27 questions. Please write down the Serial Number of the question before attempting it. 15 minute 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 55/2/1 Maximum Marks : 70 1 P.T.O. gm_m ` {ZX}e : (i) g^r Z A{Zdm` h & Bg Z-n _| Hw$b 27 Z h & (ii) Bg Z-n Ho$ Mma ^mJ h : I S> A, I S> ~, I S> g Am a I S> X & (iii) I S> A _| nm M Z h , `oH$ H$m EH$ A H$ h & I S> ~ _| gmV Z h , `oH$ Ho$ Xmo A H$ h & I S> g _| ~mah Z h , `oH$ Ho$ VrZ A H$ h Am a I S> X _| VrZ Z h , `oH$ Ho$ nm M A H$ h & (iv) Z-n _| g_J na H$moB {dH$ n Zht h & VWm{n, EH$ A H$ dmbo Xmo Zm| _|, Xmo A H$m| dmbo Xmo Zm| _|, VrZ A H$m| dmbo Mma Zm| _| 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$aZm h & (v) Ohm Amd `H$ hmo, Amn {Z Z{b{IV ^m {VH$ {Z`Vm H$m| Ho$ _mZm| H$m Cn`moJ H$a gH$Vo h : c = 3 108 m/s h = 6.63 10 34 Js e = 1.6 10 19 C 0 = 4 10 7 T m A 1 0 = 8.854 10 12 C2 N 1 m 2 1 4 = 9 109 N m2 C 2 0 Bbo Q >m Z H$m `_mZ (me) = 9.1 10 31 kg `yQ >m Z H$m `_mZ = 1.675 10 27 kg moQ>m Z H$m `_mZ = 1.673 10 27 kg AmdmoJm mo g `m = 6.023 1023 {V J m_ _mob ~mo Q > O_mZ {Z`Vm H$ = 1.38 10 23 JK 1 General Instructions : (i) All questions are compulsory. There are 27 questions in all. (ii) This question paper has four sections : Section A, Section B, Section C and Section D. (iii) 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. 55/2/1 2 (iv) There is no overall choice. However, an internal choice(s) has been provided in two questions of one mark, 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. (v) 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 0 = 4 10 7 T m A 1 0 = 8.854 10 12 C2 N 1 m 2 1 = 9 109 N m2 C 2 4 0 Mass of electron (me) = 9.1 10 31 kg Mass of neutron = 1.675 10 27 kg Mass of proton = 1.673 10 27 kg Avogadro s number = 6.023 1023 per gram mole Boltzmann constant = 1.38 10 23 JK 1 I S> A SECTION A 1. 1 {H$gr d wV { Y wd Ho$ {bE g_{d^d n R> It{ME & Draw equipotential surfaces for an electric dipole. 2. {H$gr moQ>m Z H$mo CgHo$ doJ H$s {Xem Ho$ A{^b ~dV EH$g_mZ Mw ~H$s` jo _| doe H$amZo go nyd {d^dm Va V VH$ d[aV {H$`m J`m & `{X {d^dm Va H$mo X JwZm H$a {X`m OmE, Vmo Mw ~H$s` jo _| moQ>m Z mam Mbo JE d mmH$ma nW H$s { `m {H$g H$ma n[ad{V V hmoJr ? 1 A proton is accelerated through a potential difference V, subjected to a uniform magnetic field acting normal to the velocity of the proton. If the potential difference is doubled, how will the radius of the circular path described by the proton in the magnetic field change ? 55/2/1 3 P.T.O. 3. 300 K Vmn na _ Zr{e`_ H$s Mw ~H$s` d { m Mw ~H$s` d { m 1 44 105 hmo OmEJr ? AWdm {H$gr {XE JE nXmW H$s Mw ~H$s` d { m 0 5 h 1 2 105 h & {H$g Vmn na BgH$s 1 & Bg Mw ~H$s` nXmW H$mo nhMm{ZE & 1 The magnetic susceptibility of magnesium at 300 K is 1 2 105. At what temperature will its magnetic susceptibility become 1 44 105 ? OR The magnetic susceptibility of a given material is 0 5. Identify the magnetic material. 4. Cg AY MmbH$ S>m`moS> H$mo nhMm{ZE {OgHo$ V-I A{^bmj{UH$ AmaoI _| Xem E AZwgma h & Identify the semiconductor diode whose V-I characteristics are as shown. 55/2/1 4 1 5. aoS>ma _| {d wV -Mw ~H$s` no Q >_ Ho$ {H$g ^mJ H$m Cn`moJ {H$`m OmVm h Amd { m-n[aga {b{IE & AWdm d[aV hmoVo Amdoem| mam {d wV -Mw ~H$s` Va J| {H$g H$ma C n H$s OmVr h ? BgH$m 1 ? 1 Which part of the electromagnetic spectrum is used in RADAR ? Give its frequency range. OR How are electromagnetic waves produced by accelerating charges ? I S> ~ SECTION B 6. jo \$b A H$s n{ >H$mAm| go ~Zo Xmo g_m Va n{ >H$m g Ym[a , {OZHo$ ~rM n WH$Z d h , H$mo {H$gr ~m dc moV mam Amdo{eV {H$`m J`m h & `h Xem BE {H$ Amdo{eV H$aVo g_` g Ym[a Ho$ ^rVa {d WmnZ Ymam, g Ym[a H$mo Amdo{eV H$aZo dmbr Ymam Ho$ g_mZ hr hmoVr h & 2 A capacitor made of two parallel plates, each of area A and separation d is charged by an external dc source. Show that during charging, the displacement current inside the capacitor is the same as the current charging the capacitor. 7. {H$gr \$moQ>m Z Am a {H$gr moQ>m Z H$s Xo-~ m br Va JX ` g_mZ h & {g H$s{OE {H$ \$moQ>m Z H$s D$Om moQ>m Z H$s J{VO D$Om H$s (2m c/h) JwZr h & 2 A photon and a proton have the same de-Broglie wavelength . Prove that the energy of the photon is (2m c/h) times the kinetic energy of the proton. 55/2/1 5 P.T.O. 8. {H$gr hmBS >moOZ na_mUw _| {H$gr Bbo Q >m Z H$mo Ad Wm n go nhbr C mo{OV Ad Wm VH$ `w mo{OV H$aVo g_` C g{O V H$moB \$moQ>m Z 0 55 V Ho$ {ZamoYr {d^d dmbo H$me {d wV gob _| 2 eV H$m` \$bZ Ho$ Ymp dH$ H $WmoS> H$mo {H$a{UV H$aVm h & Ad Wm n H$s dm Q>_ g `m H$m _mZ m V H$s{OE & AWdm 12 5 eV D$Om Ho$ {H$gr Bbo Q >m Z nw O mam {H$gr hmBS >moOZ na_mUw H$mo CgH$s {Z ZV_ Ad Wm go C mo{OV {H$`m J`m h & Bg C mo{OV Ad Wm go na_mUw mam C g{O V bmBZm| H$s A{YH$V_ g `m kmV H$s{OE & 2 2 A photon emitted during the de-excitation of electron from a state n to the first excited state in a hydrogen atom, irradiates a metallic cathode of work function 2 eV, in a photo cell, with a stopping potential of 0 55 V. Obtain the value of the quantum number of the state n. OR A hydrogen atom in the ground state is excited by an electron beam of 12 5 eV energy. Find out the maximum number of lines emitted by the atom from its excited state. 9. gm_m ` g_m`moOZ H$s p W{V _| {H$gr IJmobr` X a~rZ (X aXe H$) mam {V{~ ~ ~ZZm Xem Zo Ho$ {bE {H$aU AmaoI It{ME & BgH$s AmdY Z j_Vm Ho$ {bE ` OH$ {b{IE & AWdm {H$gr g `w $ gy _Xeu mam {V{~ ~ ~ZZm Xem Zo Ho$ {bE Zm_m {H$V {H$aU AmaoI It{ME Am a BgH$s {d^oXZ j_Vm Ho$ {bE ` OH$ {b{IE & Draw the ray diagram of an astronomical telescope showing image formation in the normal adjustment position. Write the expression for its magnifying power. OR Draw a labelled ray diagram to show image formation by a compound microscope and write the expression for its resolving power. 55/2/1 6 2 2 10. {H$gr TV E Q>rZm H$s D $MmB Am a Cg E Q>rZm mam o{fV {g Zbm| Ho$ A{YH$V_ n[aga {Og_| Cg {g Zb H$mo m V {H$`m Om gH$Vm h , Ho$ ~rM g ~ Y {b{IE & Q>aoIr` g Mma Ho$ H$aU _| `mo_ Va Jm| Ho$ {bE Bg ` OH$ H$mo {H$g H$ma g emo{YV {H$`m OmVm h ? Amd { m`m| Ho$ {H$g n[aga _| g Mma H$s Bg {dYm H$m Cn`moJ {H$`m OmVm h ? 2 Write the relation between the height of a TV antenna and the maximum range up to which signals transmitted by the antenna can be received. How is this expression modified in the case of line of sight communication by space waves ? In which range of frequencies, is this mode of communication used ? 11. {H$Z n[ap W{V`m| _| B YZwf H$m ojU {H$`m Om gH$Vm h B YZwfm| Ho$ ~rM {d^oXZ H$s{OE & $ ? mW{_H$ Ed { Vr`H$ 2 Under which conditions can a rainbow be observed ? Distinguish between a primary and a secondary rainbow. 12. 2 {Z Z{b{IV H$s `m `m H$s{OE : (a) AmH$me H$m Zrbm VrV hmoZm & (b) (i) gy`m V Ed (ii) gy`m}X` Ho$ g_` gy` H$m a $m^ VrV hmoZm & Explain the following : (a) Sky appears blue. (b) The Sun appears reddish at (i) sunset, (ii) sunrise. 55/2/1 7 P.T.O. I S> g SECTION C 13. 50 Hz Amd { m Ho$ {H$gr ac dmo Q>Vm moV Ho$ gmW loUr _| H$moB g Ym[a (C) Am a {VamoYH$ (R) g `mo{OV h & C Am a R Ho$ {gam| na {d^dm Va H $_e: 120 V Am a 90 V h , VWm n[anW _| dm{hV Ymam 3 A h & (i) n[anW H$s {V~mYm VWm (ii) oaH$ d H$m dh _mZ n[aH${bV H$s{OE {Ogo C Am a R Ho$ gmW loUr _| g `mo{OV H$aZo na n[anW H$m e{ $ JwUm H$ EH$ hmo OmVm h & AWdm AmaoI _| n[adVu Amd { m Ho$ 230 V Ho$ moV Ho$ gmW loUr LCR n[anW Xem `m J`m h & (a) n[anW H$mo AZwZmX _| Mm{bV H$aZo dmbr moV Amd { m {ZYm [aV H$s{OE & (b) AZwZmX H$s p W{V _| n[anW H$s {V~mYm Am a Ymam H$m Am`m_ n[aH${bV H$s{OE & (c) `h Xem BE {H$ AZwZmX Amd { m na h & LC g `moOZ Ho$ {gam| na {d^d nmV ey ` hmoVm A capacitor (C) and resistor (R) are connected in series with an ac source of voltage of frequency 50 Hz. The potential difference across C and R are respectively 120 V, 90 V, and the current in the circuit is 3 A. Calculate (i) the impedance of the circuit (ii) the value of the inductance, which when connected in series with C and R will make the power factor of the circuit unity. 55/2/1 OR 8 3 3 The figure shows a series LCR circuit connected to a variable frequency 230 V source. (a) Determine the source frequency which drives the circuit in resonance. (b) Calculate the impedance of the circuit and amplitude of current at resonance. (c) Show that potential drop across LC combination is zero at resonating frequency. 14. OoZa S>m`moS> Ho$ n Am a p jo m| H$mo A `{YH$ _m{XV {H$E OmZo H$s `m `m H$aZo Ho$ {bE H$maU Xr{OE & ZrMo {XE JE n[anW _| OoZa S>m`moS> go dm{hV Ymam kmV H$s{OE : ( OoZa ^ OZ dmo Q>Vm 15 V h ) 3 Give reason to explain why n and p regions of a Zener diode are heavily doped. Find the current through the Zener diode in the circuit given below : (Zener breakdown voltage is 15 V) 55/2/1 9 P.T.O. 15. gmB bmoQ >m Z H$m Zm_m {H$V AmaoI It{ME & BgHo$ H$m` H$mar {g m V H$s `m `m H$s{OE & `h Xem BE {H$ gmB bmoQ >m Z Amd { m Mmb Am a H$jm H$s { `m na {Z^ a Zht H$aVr & 3 AWdm AmaoI H$s ghm`Vm go {H$gr A `{YH$ b ~r Ymamdmhr n[aZm{bH$m, {Og_| \o$am| H$s g `m n \o$ao {V EH$m H$ b ~mB h VWm Ymam I dm{hV hmo ahr h , Ho$ ^rVa Mw ~H$s` jo Ho$ {bE ` OH$ `w n H$s{OE & Q>moam BS> n[aZm{bH$m go {H$g H$ma {^ hmoVm h ? 3 (a) (b) Draw a labelled diagram of cyclotron. Explain its working principle. Show that cyclotron frequency is independent of the speed and radius of the orbit. OR 16. (a) Derive, with the help of a diagram, the expression for the magnetic field inside a very long solenoid having n turns per unit length carrying a current I. (b) How is a toroid different from a solenoid ? {g H$s{OE {H$ { `m r H$s H$jm _| H$jr` Mmb v go {H$gr Zm{^H$ H$s n[aH $_m H$aVo h E {H$gr Bbo Q >m Z H$m Mw ~H$s` AmKyU evr/2 hmoVm h & Bg H$ma ~moa Ho$ H$moUr` g doJ Ho$ dm Q>_rH$aU Ho$ A{^J hrV H$m Cn`moJ H$aVo h E hmBS >moOZ na_mUw Ho$, {Z ZV_ Ad Wm _|, Mw ~H$s` AmKyU Ho$ {bE ` OH$ `w n H$s{OE & 3 Prove that the magnetic moment of the electron revolving around a nucleus in an orbit of radius r with orbital speed v is equal to evr/2. Hence using Bohr s postulate of quantization of angular momentum, deduce the expression for the magnetic moment of hydrogen atom in the ground state. 17. Am a 2 C/m2 Amdoe KZ d H$s Xmo ~ hV Amdo{eV g_Vb MmXa| EH$-X gao Ho$ ~rM n WH$Z d Ho$ gmW D$ dm Ya `dp WV H$s J`r h & Cg {~ X na {d wV -jo Ho$ {bE ` OH$ `w n H$s{OE Omo p WV h (i) nhbr MmXa Ho$ ~m`t Amoa, (ii) X gar MmXa Ho$ Xm`t Amoa, VWm (iii) XmoZm| MmXam| Ho$ ~rM & AWdm 55/2/1 10 3 ^rVar { `m Q h & r1 Am a ~mhar { `m r2 Ho$ {H$gr Jmobr` MmbH$ Imob na Amdoe H$s _m m (a) Bg Imob Ho$ Ho$ na H$moB Amdoe q p WV h & Bg Imob Ho$ ^rVar n R> Am a ~mhar n R> na n R>r` Amdoe KZ d kmV H$s{OE & (b) `m {H$gr {dda ({~Zm {H$gr Amdoe Ho$) Ho$ ^rVa {d wV -jo ey ` hmoVm h ; `h Bg V ` na {Z^ a Zht H$aVm {H$ Imob Jmobr` h AWdm Zht ? `m `m H$s{OE & 3 Two large charged plane sheets of charge densities and 2 C/m2 are arranged vertically with a separation of d between them. Deduce expressions for the electric field at points (i) to the left of the first sheet, (ii) to the right of the second sheet, and (iii) between the two sheets. OR A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. (a) A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surfaces of the shell. (b) Is the electric field inside a cavity (with no charge) zero; independent of the fact whether the shell is spherical or not ? Explain. 18. {Z Z Amd { m fm Ho$ {H$gr {g Zb H$mo Amd { m fc H$s dmhH$ Va J H$m Cn`moJ H$aHo$ o{fV {H$`m OmZm h & Am`m_ _m Sw> {bV Va J Ho$ {bE ` OH$ `w n H$s{OE VWm C n {Z Z Am a C nm d ~ S>m| Ho$ {bE ` OH$ `w n H$s{OE & Bg H$ma _m Sw> bZ gyMH$m H$ Ho$ {bE ` OH$ m V H$s{OE & 3 A signal of low frequency fm is to be transmitted using a carrier wave of frequency fc. Derive the expression for the amplitude modulated wave and deduce expressions for the lower and upper sidebands produced. Hence, obtain the expression for modulation index. 55/2/1 11 P.T.O. 19. H$sU Z H$moU Ho$ gmW H$s{U V H$Um| H$s g `m H$m {dMaU Xem Zo Ho $ {bE Jmo S> H$s nVbr n r mam -H$Um| Ho$ H$sU Z H$m J m\$ It{ME & g jon _| dU Z H$s{OE {H$ {H$g H$ma H$sU Z H$m ~ hV H$moU hmoZm na_mUw _| Zm{^H$ Ho$ Ap V d H$s `m `m H$aVm h & g K >> mMb {M U H$s ghm`Vm go `m `m H$s{OE {H$ aXa\$moS> H$sU Z {H$g H$ma Zm{^H$ Ho$ gmB O H$s Cn[a-gr_m {ZYm [aV H$aZo Ho$ EH$ e{ $embr T> J Ho$ $n _| H$m_ AmVm h & 3 Draw a plot of -particle scattering by a thin foil of gold to show the variation of the number of the scattered particles with scattering angle. Describe briefly how the large angle scattering explains the existence of the nucleus inside the atom. Explain with the help of impact parameter picture, how Rutherford scattering serves a powerful way to determine an upper limit on the size of the nucleus. 20. n WH$Z dmbo 200 F Ym[aVm Ho$ {H$gr g_m Va n{ >H$m g Ym[a H$mo 100 V Ho$ dc moV mam Amdo{eV {H$`m J`m Am a moV H$mo g `mo{OV aIm J`m & {H$gr {d wV amoYr h {S>b mam n{ >H$mAm| Ho$ ~rM H$s X ar X JwZr H$a Xr J`r Am a CZHo$ ~rM namd wVm H$ 10 H$s 5 mm _moQ>r namd wV n{ >H$m aI Xr J`r & H$maU g{hV `m `m H$s{OE {H$ {Z Z{b{IV _| `m n[adV Z hm|Jo : (i) g Ym[a H$s Ym[aVm, (ii) n{ >H$mAm| Ho$ ~rM {d wV -jo , (iii) g Ym[a H$m D$Om KZ d ? 5 mm 3 A 200 F parallel plate capacitor having plate separation of 5 mm is charged by a 100 V dc source. It remains connected to the source. Using an insulated handle, the distance between the plates is doubled and a dielectric slab of thickness 5 mm and dielectric constant 10 is introduced between the plates. Explain with reason, how the (i) capacitance, (ii) electric field between the plates, (iii) energy density of the capacitor will change ? 21. -j` H$s Ad{Y _| {V `y{Q >Zmo H$s Cnp W{V H$m g gyMZ H${R>Z `m| h ? {H$gr ao{S>`moEop Q>d Zm{^H$ Ho$ j`m H$ nX H$s n[a^mfm {b{IE VWm j`m H$ Ho$ nXm| _| Bg Zm{^H$ H$s _m ` Am`w Ho$ {bE ` OH$ `w n H$s{OE & AWdm (a) Zm{^H$s` ~b Ho$ Xmo {d^oXZH$mar bjU {b{IE & (b) `yp bAm Zm| Ho$ ~rM n WH$Z H$mo \$bZ _mZH$a `yp bAm Zm| Ho$ {H$gr `wJb H$s p W{VO D$Om Ho$ {dMaU H$mo Xem Zo Ho$ {bE J m\$ It{ME & J m\$ na Cg jo H$mo A {H$V H$s{OE Ohm na Zm{^H$s` ~b (i) AmH$fu, VWm (ii) {VH$fu h & 55/2/1 12 3 3 Why is it difficult to detect the presence of an anti-neutrino during -decay ? Define the term decay constant of a radioactive nucleus and derive the expression for its mean life in terms of the decay constant. OR (a) State two distinguishing features of nuclear force. (b) Draw a plot showing the variation of potential energy of a pair of nucleons as a function of their separation. Mark the regions on the graph where the force is (i) attractive, and (ii) repulsive. 22. 2 / 3 AndV Zm H$ Ho$ nmaXeu H$moU 60 h & AmaoI _| Xem E _m `_ go ~Zo {H$gr { ^wOmH$ma { _ H$m AndV Z AZwgma H$moB H$me {H$aU Bg { _ Ho$ \$bH$ KL na A{^b ~dV AmnVZ H$aVr h & { _ _| Bg {H$aU H$m nW Amao{IV H$s{OE VWm {ZJ V H$moU d {dMbZ H$moU n[aH${bV H$s{OE & 3 A triangular prism of refracting angle 60 is made of a transparent material of refractive index 2 / 3 . A ray of light is incident normally on the face KL as shown in the figure. Trace the path of the ray as it passes through the prism and calculate the angle of emergence and angle of deviation. 55/2/1 13 P.T.O. 23. {g H$s{OE {H$ {H$gr C^`{Z R>-C gO H$ dY H$ _| {ZJ V Am a {Zdoe Ho$ ~rM 180 H$bm Va hmoVm h & {H$gr Q >m { O Q>a _| AmYma-Ymam _| 30 A H$m n[adV Z H$aZo na AmYma-C gO H$ dmo Q>Vm _| 0 02 V Am a g Jm hH$ Ymam _| 4 mA H$m n[adV Z C n hmoVm h & `{X dY H$ H$s dmo Q>Vm bp Y 400 h , Vmo Ymam dY Z JwUm H$ Am a Cn`moJ {H$`m J`m bmoS> {VamoY n[aH${bV H$s{OE & 3 Prove that in a common-emitter amplifier, the output and input differ in phase by 180 . In a transistor, the change of base current by 30 A produces change of 0 02 V in the base-emitter voltage and a change of 4 mA in the collector current. Calculate the current amplification factor and the load resistance used, if the voltage gain of the amplifier is 400. 24. Vmn Ho$ \$bZ Ho$ $n _| (i) {H$gr MmbH$, Am a (ii) {H$gr $nr AY MmbH$ H$s {VamoYH$Vm Ho$ {dMaU H$mo Xem Zo Ho$ {bE J m\$ It{ME & g `m KZ d Am a g K >m| Ho$ ~rM {dlm {V-H$mb Ho$ nXm| _| {VamoYH$Vm Ho$ {bE ` OH$ H$m Cn`moJ H$aHo$ `m `m H$s{OE {H$ Vmn _| d { Ho$ gmW {H$g H$ma MmbH$ Ho$ H$aU _| {VamoYH$Vm _| d { hmoVr h , O~{H$ AY MmbH$ _| H$_r hmoVr h & Show, on a plot, variation of resistivity of (i) a conductor, and (ii) a typical semiconductor as a function of temperature. Using the expression for the resistivity in terms of number density and relaxation time between the collisions, explain how resistivity in the case of a conductor increases while it decreases in a semiconductor, with the rise of temperature. 55/2/1 14 3 I S> X SECTION D 25. (a) (b) (a) (b) {H$gr EH$g_mZ Mw ~H$s` jo B _| AMa H$moUr` Mmb go KyU Z H$aVr, \o$am| H$s g `m N Am a AZw W-H$mQ> jo \$b A H$s, {H$gr Hw$ S>br _| C n o[aV {d.dm. ~b (emf ) Ho$ {bE ` OH$ `w n H$s{OE & YmVw Ho$ 100 Aam|, {OZ_| `oH$ H$s b ~mB 0 5 m h , dmbm H$moB n{h`m, n dr Ho$ Mw ~H$s` jo Ho$ j {VO KQ>H$ Ho$ A{^b ~dV Vb _|, 120 n[aH $_U {V {_ZQ> go KyU Z H$a ahm h & `{X Cg WmZ na n[aUm_r Mw ~H$s` jo 4 10 4 T VWm Z{V H$moU 30 h , Vmo n{hE H$s Ywar Am a Zo{_ Ho$ ~rM o[aV {d.dm. ~b (emf ) kmV H$s{OE & AWdm {H$gr oaH$ _| Ymam I C n hmoZo na Cg_| g {MV Mw ~H$s` D$Om Ho$ {bE ` OH$ `w n H$s{OE & Bg H$ma Mw ~H$s` D$Om KZ d Ho$ {bE ` OH$ m V H$s{OE & 5 cm ^wOm H$m H$moB dJ nme, {Oggo X{jUmdVu {Xem _| 0 2 A Ymam dm{hV hmo ahr h , AmaoI _| Xem E AZwgma {H$gr AZ V b ~mB Ho$ Vma, {Oggo 1 A Ymam dm{hV hmo ahr h , go 10 cm X ar na aIm h & nme na H$m` aV (i) n[aUm_r Mw ~H$s` ~b, VWm (ii) ~b AmKyU , `{X h , n[aH${bV H$s{OE & (a) Derive an expression for the induced emf developed when a coil of N turns, and area of cross-section A, is rotated at a constant angular speed in a uniform magnetic field B. (b) A wheel with 100 metallic spokes each 0 5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth s magnetic field. If the resultant magnetic field at that place is 4 10 4 T and the angle of dip at the place is 30 , find the emf induced between the axle and the rim of the wheel. OR 55/2/1 15 5 5 P.T.O. 26. (a) Derive the expression for the magnetic energy stored in an inductor when a current I develops in it. Hence, obtain the expression for the magnetic energy density. (b) A square loop of sides 5 cm carrying a current of 0 2 A in the clockwise direction is placed at a distance of 10 cm from an infinitely long wire carrying a current of 1 A as shown. Calculate (i) the resultant magnetic force, and (ii) the torque, if any, acting on the loop. AmaoI H$s ghm`Vm go `m `m H$s{OE {H$ H$sU Z mam gy` Ho$ H$me go g_Vb Yw {dV H$me {H$g H$ma C n {H$`m Om gH$Vm h & Xmo nmoboam BS>m| P1 Am a P2 H$mo EH$-X gao Ho$ nmg-Ajm| H$mo b ~dV aIm J`m h & Vrd Vm I H$m AYw {dV H$me P1 na AmnVZ H$aVm h & P1 Am a P2 Ho$ ~rM EH$ Vrgao nmoboam BS> P3 H$mo Bg H$ma aIm J`m h {H$ BgH$m nmg-Aj P1 Ho$ nmg-Aj go 45 H$m H$moU ~ZmVm h & P1, P2 Am a P3 go nmaJ{_V H$me H$s Vrd Vm n[aH${bV H$s{OE & AWdm (a) Xmo gwB {N> m| H$mo Xmo gmo{S>`_ b nm| mam Xr V H$aHo$ `{VH$aU H$s n[aKQ>Zm H$m ojU `m| Zht {H$`m Om gH$Vm ? (b) Xmo H$bm-g ~ moVm| go C g{O V Xmo EH$dUu Va J|, {OZHo$ {d WmnZ y1 = a cos t Am a y2 = a cos ( t + ) h , `{VH$aU H$aHo$ `{VH$aU n Q>Z C n H$aVr h & n[aUm_r Vrd Vm Ho$ {bE ` OH$ `w n H$s{OE VWm g nmofr Am a {dZmer `{VH$aU Ho$ {bE {V~ Y m V H$s{OE & (c) 590 nm Am a 596 nm Va JX ` Ho$ gmo{S>`_ H$me ~mar-~mar go 2 10 6 m maH$ H$s {H$gr EH$b {Par 55/2/1 H$s Xmo Va Jm| H$m Cn`moJ mam {ddV Z H$m A ``Z H$aZo Ho$ {bE {H$`m J`m h & `{X {Par Am a nX} Ho$ ~rM H$s X ar 1 5 m h , Vmo XmoZm| H$aUm| _| nX} na m V {ddV Z n Q>Zm] Ho$ { Vr` C{ R>m| H$s p W{V Ho$ ~rM n WH$Z n[aH${bV H$s{OE & 16 5 5 Explain, with the help of a diagram, how plane polarized light can be produced by scattering of light from the Sun. Two polaroids P1 and P2 are placed with their pass axes perpendicular to each other. Unpolarised light of intensity I is incident on P1. A third polaroid P3 is kept between P1 and P2 such that its pass axis makes an angle of 45 with that of P1. Calculate the intensity of light transmitted through P1, P2 and P3. OR (a) Why cannot the phenomenon of interference be observed by illuminating two pin holes with two sodium lamps ? (b) Two monochromatic waves having displacements y1 = a cos t and y2 = a cos ( t + ) from two coherent sources interfere to produce an interference pattern. Derive the expression for the resultant intensity and obtain the conditions for constructive and destructive interference. (c) Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 10 6 m. If the distance between the slit and the screen is 1 5 m, calculate the separation between the positions of the second maxima of diffraction pattern obtained in the two cases. 27. (a) (b) (c) n[anW AmaoI H$s ghm`Vm go {H$gr gob Ho$ Am V[aH$ {VamoY H$mo _mnZo H$s {d{Y H$m g jon _| dU Z H$s{OE & H$maU Xr{OE {H$ {H$gr gob Ho$ {d.dm. ~b (emf ) H$s _mn Ho$ {bE dmo Q>_rQ>a H$s VwbZm _| nmoQ> p e`mo_rQ>a Ho$ Cn`moJ H$mo dar`Vm `m| Xr OmVr h & ZrMo {XE JE nmoQ> p e`mo_rQ>a n[anW _| g VwbZ b ~mB l n[aH${bV H$s{OE & H$maU XoH$a n Q> H$s{OE {H$ `{X g^r A ` H$maH$m| H$mo An[ad{V V aIVo h E 5 V {d.dm. ~b (emf ) Ho$ n[aMmbH$ gob H$mo 2 V Ho$ gob mam {V Wm{nV H$a {X`m OmE, Vmo `h n[anW H$m` H$aoJm AWdm Zht & 5 AWdm 55/2/1 17 P.T.O. (a) (b) (c) (a) (b) (c) _rQ>a goVw mam {H$gr AkmV {VamoY H$mo _mnZo Ho$ H$m` H$mar {g m V H$m C boI H$s{OE & H$maU Xr{OE (i) {H$gr _rQ>a goVw _| {VamoYH$m| Ho$ ~rM Ho$ g `moOZm| H$mo _moQ>o Vm ~o H$s n{ >`m| H$m `m| ~Zm`m OmVm h , (ii) gm_m `V: g VwbZ b ~mB H$mo goVw Vma Ho$ _ `-{~ X Ho$ {ZH$Q> aIZo H$mo dar`Vm `m| Xr OmVr h & {H$aImo \$ Ho$ {Z`_ H$m Cn`moJ H$aHo$ {XE JE {d wV n[anW _| 4 {VamoYH$ Ho$ {gam| Ho$ ~rM {d^dm Va n[aH${bV H$s{OE & Describe briefly, with the help of a circuit diagram, the method of measuring the internal resistance of a cell. Give reason why a potentiometer is preferred over a voltmeter for the measurement of emf of a cell. In the potentiometer circuit given below, calculate the balancing length l. Give reason, whether the circuit will work, if the driver cell of emf 5 V is replaced with a cell of 2 V, keeping all other factors constant. OR 55/2/1 18 5 (a) (b) (c) 55/2/1 State the working principle of a meter bridge used to measure an unknown resistance. Give reason (i) why the connections between the resistors in a metre bridge are made of thick copper strips, (ii) why is it generally preferred to obtain the balance length near the mid-point of the bridge wire. Calculate the potential difference across the 4 resistor in the given electrical circuit, using Kirchhoff s rules. 19 P.T.O.

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