CBSE Champion Physics Class 12 Past Papers PDF

 CLASS 12 MTG Learning Media (P) Ltd. New Delhi | Gurugram  Price : ` 300 Revised Edition : 2020 Published by : MTG Learning Media (P) Ltd., New Delhi Corporate Office : Plot 99, Sector 44 Institutional Area, Gurugram, Haryana-122 003 Phone : 012...

 CLASS 12 MTG Learning Media (P) Ltd. New Delhi | Gurugram  Price : ` 300 Revised Edition : 2020 Published by : MTG Learning Media (P) Ltd., New Delhi Corporate Office : Plot 99, Sector 44 Institutional Area, Gurugram, Haryana-122 003 Phone : 0124 - 6601200. Web : mtg.in Email : [email protected] Registered Office : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110029 Information contained in this book has been obtained by mtg, from sources believed to be reliable. Every effort has been made to avoid errors or omissions in this book. In spite of this, some errors might have crept in. Any mistakes, error or discrepancy noted may be brought to our notice which shall be taken care of in the next edition. It is notified that neither the publishers nor the author or seller will be responsible for any damage or loss of action to anyone, of any kind, in any manner, therefrom. © MTG Learning Media (P) Ltd. Copyright reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Publisher. All disputes subject to Delhi jurisdiction only. Visit www.mtg.in for buying books online. EVERY GENUINE COPY OF THE BOOK HAS A HOLOGRAM STICKER ON THE COVER Move the book slightly to see the special features of the hologram Kinetic Effect Mirror Effect Micro Text (Genuine) Litho White Emboss Effect Gradient Effect  PREFACE W e feel pleased and delighted in presenting the revised edition of the book “CBSE Champion Chapterwise-Topicwise Physics” as per the CBSE Curriculum for the academic year 2020-21. Special efforts have been put to produce this book in order to equip students with practice material including previous 10 years’ CBSE Board Examination questions. It will give them comprehensive knowledge of subject according to the latest syllabus and pattern of CBSE Board Examination. The book will be helpful in imparting students a clear and vivid understanding of the subject. Salient features Comprehensive and Lucid Theory : Well explained theory with important formulae and tables for quick recap. Topicwise Graphical Analysis : Graphical analysis of previous 10 years’ CBSE Board papers’ questions (1 mark, 2 marks, 3 marks, 5 marks) provided to let students figure out which chapter and which topic is to be revised hard and how much is the weightage of that topic. Chapterwise-Topicwise Questions and Answers : Theory is followed by chapterwise-topicwise questions pulled from previous 10 years’ CBSE-DELHI, ALL INDIA, FOREIGN and COMPARTMENT papers. Answers are given according to the CBSE marking scheme. Strictly Based on NCERT Pattern : In the previous years’ CBSE papers SA, LA I or LA II type questions are generally framed by clubbing together questions from different topics and chapters. These questions are segregated strictly according to NCERT topics. e.g., (1/3, Delhi 2016 ), this question of 1 mark was asked in LA I type category, (1/5, AI 2015), this question of 1 mark was asked in LA II type category, (1/2, Foreign 2016 ), this question of 1 mark was asked in SA type category. Topicwise questions are arranged in descending chronological (2020-2011) order so, that latest years’ questions come first in practice and revision. Key Concepts Highlight : Key concepts have been highlighted for their reinforcement. Practice Papers with Objective Type Questions : 10 Practice Papers strictly based on the latest design and blue print issued by CBSE Board are also incorporated. Various types of questions like MCQs, Fill in the blanks, VSA, SA, LA types are included. Solved CBSE Sample Paper : Solved CBSE sample paper is included with the marking scheme. We are sure that the value addition done in this book will prove helpful to students in achieving success in board examinations. Every possible effort has been made to make this book error free. Useful suggestions by our readers for the rectification and improvement of the book content would be gracefully acknowledged and incorporated in further editions. Readers are welcome to send their suggestions at [email protected]. All The Best MTG Editorial Board CONTENTS 1. Electric Charges and Fields...... 1 2. Electrostatic Potential and Capacitance...... 20 3. Current Electricity...... 45 4. Moving Charges and Magnetism...... 82 5. Magnetism and Matter...... 113 6. Electromagnetic Induction...... 124 7. Alternating Current...... 146 8. Electromagnetic Waves...... 172 9. Ray Optics and Optical Instruments...... 184 10. Wave Optics...... 226 11. Dual Nature of Radiation and Matter...... 261 12. Atoms...... 282 13. Nuclei...... 301 14. Semiconductor Electronics : Materials, Devices and Simple Circuits...... 316 z 10 Practice Papers...... 337 z CBSE Sample Paper...... 401  SYLLABUS Unit No. Title No. of Marks Periods Unit I Electrostatics Chapter-1: Electric Charges and Fields 24 Chapter-2: Electrostatic Potential and Capacitance 16 Unit II Current Electricity 18 Chapter-3: Current Electricity Unit III Magnetic Effects of Current and Magnetism Chapter-4: Moving Charges and Magnetism 22 Chapter-5: Magnetism and Matter 17 Unit IV Electromagnetic Induction and Alternating Currents Chapter-6: Electromagnetic Induction 20 Chapter-7: Alternating Current Unit V Electromagnetic Waves 04 Chapter-8: Electromagnetic Waves Unit VI Optics 18 Chapter-9: Ray Optics and Optical Instruments 27 Chapter-10: Wave Optics Unit VII Dual Nature of Radiation and Matter 08 Chapter-11: Dual Nature of Radiation and Matter Unit VIII Atoms and Nuclei 12 Chapter-12: Atoms 15 Chapter-13: Nuclei Unit IX Electronic Devices Chapter-14: Semiconductor Electronics: Materials, Devices and Simple 12 7 Circuits Total 150 70 Unit I : Electrostatics [24 Periods] Chapter-1: Electric Charges and Fields Electric Charges; Conservation of charge; Coulomb’s law-force between two point charges; forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Chapter-2 : Electrostatic Potential and Capacitance Electric potential; potential difference; electric potential due to a point charge, a dipole and system of charges; equipotential surfaces; electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators; free charges and bound charges inside a conductor. Dielectrics and electric polarisation; capacitors and capacitance ; combination of capacitors in series and in parallel; capacitance of a parallel plate capacitor with and without dielectric medium between the plates; energy stored in a capacitor. Unit II : Current Electricity [18 Periods] Chapter-3: Current Electricity Electric current; flow of electric charges in a metallic conductor; drift velocity; mobility and their relation with electric current; Ohm’s law; electrical resistance; V-I characteristics (linear and non-linear), electrical energy and power; electrical resistivity and conductivity; Carbon resistors; colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell; potential difference and emf of a cell; combination of cells in series and in parallel; Kirchhoff ’s laws and simple applications; Wheatstone bridge, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell. Unit III : Magnetic Effects of Current and Magnetism  [22 Periods] Chapter-4: Moving Charges and Magnetism Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire. Straight and toroidal solenoids (only qualitative treatment); force on a moving charge in uniform magnetic and electric fields; Cyclotron. Force on a current-carrying conductor in a uniform magnetic field; force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter. Chapter-5: Magnetism and Matter Current loop as a magnetic dipole and its magnetic dipole moment; magnetic dipole moment of a revolving electron; magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis; torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid; magnetic field lines; earth’s magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths; permanent magnets. Unit IV : Electromagnetic Induction and Alternating Currents [20 Periods] Chapter-6: Electromagnetic Induction Electromagnetic induction; Faraday’s laws, induced EMF and current; Lenz’s Law, Eddy currents. Self and mutual induction. Chapter-7: Alternating Current Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only); LCR series circuit; resonance; power in AC circuits, power factor; wattless current. AC generator and transformer. Unit V : Electromagnetic waves [04 Periods] Chapter-8: Electromagnetic Waves Basic idea of displacement current, Electromagnetic waves, their characteristics, their Transverse nature (qualitative ideas only). Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses. Unit VI : Optics [27 Periods] Chapter-9: Ray Optics and Optical Instruments Ray Optics: Reflection of light; spherical mirrors; mirror formula; refraction of light; total internal reflection and its applications; optical fibres; refraction at spherical surfaces; lenses; thin lens formula; lensmaker’s formula; magnification, power of a lens; combination of thin lenses in contact; refraction of light through a prism. Scattering of light - blue colour of sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Chapter-10: Wave Optics Wave optics: Wave front and Huygen’s principle; reflection and refraction of plane wave at a plane surface using wavefronts. Proof of laws of reflection and refraction using Huygen’s principle. Interference; Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light; diffraction due to a single slit; width of central maximum; resolving power of microscope and astronomical telescope, polarisation; plane polarised light; Brewster’s law; uses of plane polarised light and Polaroids. Unit VII : Dual Nature of Radiation and Matter [08 Periods ] Chapter-11: Dual Nature of Radiation and Matter Dual nature of radiation; Photoelectric effect; Hertz and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light. Experimental study of photoelectric effect Matter waves-wave nature of particles ; de-Broglie relation; Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained). Unit VIII : Atoms and Nuclei [15 Periods] Chapter-12: Atoms Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Chapter-13: Nuclei Composition and size of nucleus; Radioactivity; alpha, beta and gamma particles/rays and their properties; radioactive decay law, half life and mean life. Mass-energy relation; mass defect; binding energy per nucleon and its variation with mass number; nuclear fission; nuclear fusion. Unit IX : Electronic Devices [12 Periods] Chapter-14: Semiconductor Electronics: Materials, Devices and Simple Circuits Energy bands in conductors; semiconductors and insulators (qualitative ideas only) Semiconductor diode - I-V characteristics in forward and reverse bias; diode as a rectifier; Special purpose p-n junction diodes: LED, photodiode, solar cell and Zener diode and their characteristics; zener diode as a voltage regulator. As per the current syllabus provided by CBSE for class 12, the topics Dispersion by a Prism, Transistors, Logic Gates, and the chapter Communication Systems are no longer a part of the curriculum. The said topics and chapter have now been omitted from the book.  *QUESTION PAPER DESIGN (Class: XII) Maximum marks : 70 Duration : 3 hours S. Approximate Typology of Questions Total Marks No. Percentage 1. Remembering : Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding : Demonstrate understanding of facts and ideas by organizing, 27 38% comparing, translating, interpreting, giving descriptions, and stating main ideas 2. Applying : Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 22 32% 3. Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating : Present and defend opinions by making judgments about 21 30% information, validity of ideas, or quality of work based on a set of criteria. Creating : Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions. TOTAL MARKS 70 100 QUESTIONWISE BREAK UP Type of Question Mark per Question Total No. of Questions Total Marks VSA/ Objective 1 20 20 SA 2 7 14 LA-I 3 7 21 LA-II 5 3 15 Total 37 70 Practical : 30 Marks Note: 1. Internal Choice: There is no overall choice in the paper. However, there will be at least 33% internal choice. 2. The above template is only a sample. Suitable internal variations may be made for generating similar templates keeping the overall weightage to different form of questions and typology of questions same. * For latest details visit www.cbse.nic.in  LATEST 2020-21 PHYSICS PRACTICE PAPERS As per the CBSE Revised Curriculum for the Academic Year 2020-21 issued on 7th July 2020 REVISED SYLLABUS* CLASS XII (THEORY) UNIT I : ELECTROSTATICS (23 Periods) Time : 3 Hours  Max. Marks : 70 Chapter-1 : Electric Charges and Fields No. of Electric Charges; Conservation of charge, Coulomb’s law- Unit Title Marks Periods force between two-point charges, forces between multiple I Electrostatics charges; superposition principle and continuous charge Chapter-1 : Electric Charges and distribution. Fields 23 Electric field, electric field due to a point charge, electric Chapter-2 : Electrostatic Potential 16 field lines, electric dipole, electric field due to a dipole, and Capacitance torque on a dipole in uniform electric field. II Current Electricity Electric flux, statement of Gauss’s theorem and its 15 Chapter-3 : Current Electricity applications to find field due to infinitely long straight wire, III Magnetic Effects of Current uniformly charged infinite plane sheet and Magnetism Chapter-2 : E lectrostatic Potential and Capacitance Chapter-4 : Moving Charges and 16 Electric potential, potential difference, electric potential Magnetism due to a point charge, a dipole and system of charges; Chapter-5 : Magnetism and Matter 17 equipotential surfaces, electrical potential energy of a IV Electromagnetic Induction system of two point charges and of electric dipole in an and Alternating Currents electrostatic field. Chapter-6 : Electromagnetic 19 Conductors and insulators, free charges and bound charges Induction inside a conductor. Dielectrics and electric polarisation, Chapter-7 : Alternating Current capacitors and capacitance, combination of capacitors V Electromagnetic Waves 2 in series and in parallel, capacitance of a parallel plate Chapter-8 : Electromagnetic Waves capacitor with and without dielectric medium between the VI Optics plates, energy stored in a capacitor. 18 Chapter-9 : Ray Optics and Optical 18 UNIT II : CURRENT ELECTRICITY Instruments Chapter-10 : Wave Optics (15 Periods) VII Dual Nature of Radiation and Chapter-3 : Current Electricity Matter Electric current, flow of electric charges in a metallic 7 Chapter-11 : Dual Nature of conductor, drift velocity, mobility and their relation with Radiation and Matter 12 electric current; Ohm’s law, electrical resistance, V - I VIII Atoms and Nuclei characteristics (linear and non-linear), electrical energy and Chapter-12 : Atoms 11 power, electrical resistivity and conductivity; temperature Chapter-13 : Nuclei dependence of resistance. IX Electronic Devices Internal resistance of a cell, potential difference and emf Chapter-14 : Semiconductor 7 7 of a cell, combination of cells in series and in parallel, Electronics : Materials, Devices and Kirchhoff’s laws and simple applications, Wheatstone Simple Circuits bridge, metre bridge(qualitative ideas only) Total 118 70 Potentiometer - principle and its applications to measure *For latest information refer to www.cbse.nic.in potential difference and for comparing EMF of two cells; UNIT VI : OPTICS (18 Periods) measurement of internal resistance of a cell (qualitative Chapter-9 : Ray Optics and Optical Instruments ideas only) Ray Optics : Refraction of light, total internal reflection UNIT III : MAGNETIC EFFECTS OF CURRENT and its applications, optical fibres, refraction at spherical AND MAGNETISM (16 Periods) surfaces, lenses, thin lens formula, lensmaker’s formula, magnification, power of a lens, combination of thin lenses Chapter-4 : Moving Charges and Magnetism in contact, refraction of light through a prism. Concept of magnetic field, Oersted’s experiment. Optical instruments : Microscopes and astronomical Biot - Savart law and its application to current carrying telescopes (reflecting and refracting) and their magnifying circular loop. powers. Ampere’s law and its applications to infinitely long straight wire. Straight and toroidal solenoids (only qualitative Chapter-10 : Wave Optics treatment), force on a moving charge in uniform magnetic Wave optics: Wave front and Huygen’s principle, reflection and electric fields. and refraction of plane wave at a plane surface using Force on a current-carrying conductor in a uniform wave fronts. Proof of laws of reflection and refraction magnetic field, force between two parallel current-carrying using Huygen’s principle. Interference, Young’s double conductors-definition of ampere, torque experienced by slit experiment and expression for fringe width, coherent a current loop in uniform magnetic field; moving coil sources and sustained interference of light, diffraction due galvanometer-its current sensitivity and conversion to to a single slit, width of central maximum ammeter and voltmeter. UNIT VII : DUAL NATURE OF RADIATION Chapter-5 : Magnetism and Matter AND MATTER (7 Periods) Current loop as a magnetic dipole and its magnetic dipole moment, magnetic dipole moment of a revolving electron, Chapter-11 : D  ual Nature of Radiation and Matter bar magnet as an equivalent solenoid, magnetic field lines; Dual nature of radiation, Photoelectric effect, Hertz and earth’s magnetic field and magnetic elements. Lenard’s observations; Einstein’s photoelectric equation- particle nature of light. UNIT IV : ELECTROMAGNETIC INDUCTION Experimental study of photoelectric effect AND ALTERNATING CURRENTS (19 Periods) Matter waves-wave nature of particles, de-Broglie relation Chapter-6 : Electromagnetic Induction UNIT VIII : ATOMS AND NUCLEI (11 Periods) Electromagnetic induction; Faraday’s laws, induced EMF and current; Lenz’s Law, Eddy currents. Self and mutual Chapter-12 : Atoms induction. Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Chapter-7 : Alternating Current Alternating currents, peak and RMS value of Chapter-13 : Nuclei alternating current/voltage; reactance and Composition and size of nucleus impedance; LC oscillations (qualitative treatment Nuclear force only), LCR series circuit, resonance; power in Mass-energy relation, mass defect, nuclear fission, nuclear AC circuits. fusion. AC generator and transformer. UNIT IX : ELECTRONIC DEVICES (7 Periods) UNIT V : ELECTROMAGNETIC WAVES Chapter-14: Semiconductor Electronics : Materials, (2 Periods) Devices and Simple Circuits Chapter-8 : Electromagnetic Waves Energy bands in conductors, semiconductors and insulators Electromagnetic waves, their characteristics, their Transverse (qualitative ideas only). nature (qualitative ideas only). Semiconductor diode - I-V characteristics in forward and Electromagnetic spectrum (radio waves, microwaves, reverse bias, diode as a rectifier; Special purpose p-n infrared, visible, ultraviolet, X-rays, gamma rays) including junction diodes: LED, photodiode, solar cell. elementary facts about their uses. For practicals refer to latest CBSE syllabus   EXAM BITES This Pdf Is Downloaded From www.exambites.in Visit www.exambites.in for More Premium Stuffs,Latest Books,Test Papers,Lectures etc. jeeneetadda jeeneetadda_official jeeneetadda VISIT NOW !!  PRACTICE PAPER (Solved) 1 General Instructions : Read the following instructions very carefully and strictly follow them. (i) This question paper comprises four section – A, B, C and D. (ii) There are 37 questions in the question paper. All questions are compulsory. (iii) Section A – Question no. 1 to 20 are very short answer type questions carrying 1 mark each. (iv) Section B – Question no. 21 to 27 are short answer type questions carrying 2 marks each. (v) Section C – Question no. 28 to 34 are long answer type questions carrying 3 marks each. (vi) Section D – Question no. 35 to 37 are also long answer type questions, carrying 5 marks each. (vii) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of 1 mark, 2 questions of 2 marks, 1 question of 3 marks and all the 3 questions of 5 marks. You have to attempt only one of the choices in such questions. (viii) In addition to this, separate instructions are given with each section and question, wherever necessary. (ix) Use of calculators and log tables is not permitted. (x) You may use the values of physical constants wherever necessary. Time allowed : 3 hours Maximum marks : 70  SECTION - A 5. Spherical wavefronts, emanating from a point source, strike a plane reflecting surface. What Directions (Q. No. 1-10) : Select the most will happen to these wavefronts, immediately appropriate option from those given below after reflection? each question. (a) They will remain spherical with the same 1. Solar radiation is curvature, both in magnitude and sign. (a) transverse electromagnetic wave (b) They will become plane wavefronts. (b) longitudinal electromagnetic waves (c) They will remain spherical, with the (c) both longitudinal and transverse same curvature, but sign of curvature electromagnetic waves reversed. (d) none of these. (d) They will remain spherical, but with different curvature, both in magnitude 2. An element with Z = 33 when added to an and sign. intrinsic semiconductor will give 6. Two protons are kept at a separation of (a) n-type semiconductor 40 Å. Fn is the nuclear force and Fe is the (b) p-type semiconductor electrostatic force between them. Then (c) a superconductor (a) Fn > Fe (d) Fn = Fe 3. The force of interaction between two charges 7. A ray of light enters a rectangular glass q1 = 6 mC and q2 = 2 mC is 12 N. If a charge slab of refractive index 3 at an angle of q = –2 mC is added to each of the charges, incidence 60°. It travels a distance of 5 cm then the new force of interaction is inside the slab and emerges out of the slab. (a) 0 N (b) 8 N The perpendicular distance between the (c) 10 N (d) 12 N incident and the emergent rays is 4. G.P. Thomson experimentally confirmed the 5 (a) 5 3 cm (b) cm existence of matter waves by the phenomena 2 (a) diffraction (b) refraction 3 (c) 5 cm (d) 5 cm (c) polarisation (d) scattering 2 2 CBSE Champion Physics Class 12 8. Whenever there is a relative motion between a 18. Is Huygen’s principle valid for longitudinal coil and a magnet, the magnitude of induced sound waves? emf set up in the coil does not depend upon 19. Why is photoelectric emission not possible the at all frequencies? (a) relative speed between the coil and OR magnet Write the relationship of de-Broglie (b) magnetic moment of the coil wavelength l associated with a particle of (c) resistance of the coil mass m in terms of its kinetic energy E. (d) number of turns in the coil. 20. Can the instantaneous power output of an 9. Which of the following is the correct ac source ever be negative? Can the average Kirchhoff ’s loop rule? power output be negative? (a) The algebraic sum of the currents meeting at a junction is zero. SECTION - B (b) The algebraic sum of potential drops 21. Calculate the value of the resistance needed across all resistors in a circuit is zero. to convert a galvanometer of resistance (c) The algebraic sum of the currents across 100 Ω which gives a full scale deflection all the resistors in a circuit is zero. for a current of 5 mA, into a voltmeter of (d) The algebraic sum of potential drops a 0-10 V range. across all resistors plus those across 22. Explain how electron mobility changes for a sources in a circuit is zero. good conductor, when (a) the temperature 10. The ionization energy required to remove of the conductor is decreased at constant the electron from ground state of hydrogen potential difference and (b) applied potential atom, is difference is doubled at constant temperature. (a) +13.6 eV (b) –13.6 eV OR (c) +13.6 MeV (d) none of these. Two conductors are made of the same material Directions (Q. No. 11-15) : Fill in the blanks and have the same length. Conductor A is a with appropriate answer. solid wire of diameter 1 mm. Conductor B is a hollow tube of outer diameter 2 mm and inner 11. The property of a magnet that interacts diameter 1 mm. Find the ratio of resistance with an applied field to give a mechanical RA to RB. moment is called _________. 23. Two point charges q 1 = +0.2C and 12. The part of electromagnetic spectrum used q2 = +0.4C are placed 0.1 m apart. Calculate in operating a RADAR is __________. the electric field at 13. The fermi level in semiconductors lie midway (a) mid-point between the charges in the gap between _______ and _______. (b) a point on the joining q1 and q2 such 14. Focal length of a convex lens _______ on that it is 0.05 m away from q2 and 0.15 m immersing it in water. away from q1. 15. The equator line corresponding to magnetic 24. Give four basic properties of electromagnetic north and south poles is called ______. waves. OR OR A plane electromagnetic wave travels in The SI unit of permeability is ______. vacuum along z-axis. What can you say about Directions (Q. No. 16-20) : Answer the following. the directions of its electric and magnetic 16. If a charge q revolves around charge Q in field vectors? If the frequency of the wave circle of radius R, then find the amount of is 30 MHz, what is its wavelength? work done. 25. Are the nucleons fundamental particles, or 17. Why are alloys used for making standard do they consist of still smaller parts? One resistance coils? way to find out is to probe a nucleon just Practice Paper - 1 3 as Rutherford probed an atom. What should field of 2 tesla, the field lines being normal to be the kinetic energy of an electron for it the plane of the paper. The loop is connected to be able to probe a nucleon? Assume the to an electrical network of resistors, each of diameter of a nucleon to be approximately resistance 2 W. Calculate the speed of the 10–15 m. loop, for which 2 mA current flows in the loop. 26. Define refractive index of a material. The apparent depth of an object at the bottom of a tank filled with liquid of refractive index 1.3 is 7.7 cm. What is the actual depth of the liquid in the tank? 27. In the following diagrams, indicate which of the diodes are forward biased and which are reverse biased? OR +2 V Obtain an expression +7 V for t h e mutu a l I inductance between a v +5 V a long straight wire r a (i) (ii) and a square loop –12 V of side a as shown –10 V in figure. (iii) (iv) –5 V 32. Consider a two slit interference arrangements such that the distance of the screen from the SECTION - C slits is half the distance between the slits. 28. Two identical spheres A and B, each having Obtain the value of D in terms of λ such a charge of 6 × 10–8 C, are separated by that the first minima on the screen falls at 60 cm. A third uncharged sphere C of the a distance D from the centre O. same size is brought in contact with sphere A, then brought in contact with sphere B S1 T1 OP = x P and finally removed from both. What is the Source O CO = D C new force of repulsion between A and B? S1 C = CS2 = D S2 T2 29. In a series LCR circuit connected to an ac Screen source of variable frequency and voltage 33. If we go on increasing the wavelength of light V = Vm sinwt, draw a plot showing the variation of current (I) with angular incident on a metal surface, what changes frequency (w) for two different values of in the number of electrons and energy take resistance R1 and R2(R1 > R2). Write the place. condition under which the phenomenon of 34. The forbidden energy gap in semiconductors, resonance occurs. For which value of the insulators and metals are E s, Ei and Em resistance out of the two curves, a sharper respectively. Arrange these in descending resonance is produced? Define Q-factor of order. The band gap in silicon is 1.12 eV. the circuit and give its significance. What is the maximum wavelength of light 30. Positronium is just like a H-atom with the that can be emitted by it? proton replaced by the positively charged SECTION - D antiparticle of the electron (called the positron which is as massive as the electron). 35. Three hollow concentric spheres A, B and What would be the ground state energy of C, having radii a, b and c(a < b < c) have positronium? uniform surface charge densities +s, –s and 31. A metallic square loop ABCD of size 15 cm +s respectively. Compute and resistance 1.0 W is moved at a uniform (i) the electric potential at the surface of velocity of v m s–1, in a uniform magnetic each sphere. 4 CBSE Champion Physics Class 12 (ii) the electric field at the surface of each a bar magnet with its north pole is brought sphere. close to it. Explain briefly how the direction OR of the current predicted wrongly results in Obtain an expression for the energy stored the violation of the law of conservation of in a parallel plate capacitor. In the following figure, the energy energy. stored in C4 is 27 37. (a) Draw a ray diagram to show the formation mJ. Calculate the of the image of an object placed on the axis total energy stored of a convex refracting surface of radius of in the system. curvature ‘R’, separating the two media of 36. State Faraday’s law of electromagnetic refractive indices ‘n1’ and ‘n2’ (n2 > n1). induction. Figure shows a rectangular Use this diagram to deduce the relation conductor PQRS in which the conductor PQ n2 n1 n2 − n1 where u and v represent − = , is free to move in a uniform magnetic field B v u R perpendicular to the plane of the paper. respectively the distance of the object and The field extends from x = 0 to x = b and the image formed. is zero for x > b. Assume that only the arm (b) A convex lens of focal length f1 is kept in PQ possesses resistance r. When the arm contact with a concave lens of focal length f2. PQ is pulled outward from x = 0 to x = 2b Find the focal length of the combination. and is then moved backward to x = 0 with constant speed v, obtain the expressions for OR the flux and the induced emf. Sketch the (a) Draw a ray diagram showing the image variations of these quantities with distance formation by an astronomical telescope when 0 ≤ x ≤ 2b. the final image is formed at infinite. (b) (i) A small telescope has an objective S lens of focal length 140 cm and an eyepiece P of focal length 5.0 cm. Find the magnifying power of the telescope for viewing distant R Q objects when the telescope is in normal adjustment and the final image is formed x=0 x=b x = 2b at the least distance of distinct vision. OR (ii) Also find the separation between the State Lenz’s law. Using this law indicate the objective lens and the eye piece in normal direction of the current in a closed loop when adjustment. Detailed Solutions 1. (a) 1 Q1 Q2 2. (a) : The electronic configuration of Z = 33 \ New force of interaction = =0N 4 πε0 r 2 is 2, 8, 18, 5. It is pentavalent, hence will give a 4. (a) : G.P. Thomson experimentally confirmed n-type semiconductor. the existence of matter waves (de Broglie’s 3. (a) : Force between two charges, hypothesis) by demonstrating that electron beams are diffracted when they are scattered by the 1 q1q2 F= regular atomic arrays of crystals. 4 πε0 r 2 5. (c) Initial value of q1 = 6 mC \ Final value of q1 = Q1 = (6 – 2) = 4 mC 6. (a) : Nuclear force is much stronger than Again, initial value of q2 = 2 mC the electrostatic force inside the nucleus, i.e., at \ Final value of q2 = Q2 = (2 – 2) = 0 distances of the order of fermi. At 40 Å, nuclear Practice Paper - 1 5 force is ineffective and only electrostatic force OR h of repulsion is present. This is very high at this λ= distance because nuclear force is not acting 2mE now and the gravitational force is very feeble. 20. Instantaneous power output can be negative Fnuclear R2), (iv) The oscillations of E and B are in the same phase. OR  In electromagnetic wave, the  electric field vector E (A) and magnetic field vector B show their variations perpendicular to the direction of propagation of wave as well as perpendicular to each other. As the electromagnetic wave is travelling along z-axis, (Mrad/s)  hence E and B show their variations in x-y plane. The condition for resonance in the LCR circuit is,   1 1 The direction of E and B are along x-axis and X L = XC ⇒ ω 0 L = ⇒ ω0 = y-axis respectively. ω0C LC 8 −1 c 3 × 10 m s We see that the current amplitude is maximum Wavelength, λ = = = 10 m. υ 30 × 106 s −1 at the resonant frequency. Since im = Vm / R at resonance, the current amplitude for case R2 is 25. Let nucleons are separated by distance d and sharper to that for case R1. the wavelength be l. Quality factor or simply the Q-factor of a resonant To probe nucleons wavelength of signal must be LCR circuit is defined as the ratio of voltage drop less than or equal to d. across the resistance at resonance. As d = 10–15, l ≤ 10–15 m V ωL 1 L hc 6.63 × 10 −34 × 3 × 108 Q= L =. Thus finally, Q = \ K = pc = = J VR R R C λ 10 −15 19.89 × 10 −11 The Q factor determines the sharpness at K= −19 eV ≈ 109 eV resonance as for higher value of Q factor the 1.6 × 10 tuning of the circuit and its sensitivity to accept Real depth Real depth 26. µ = 1.3 and µ = = resonating frequency signals will be much higher. App. depth 7. 7 or Real depth = 1.3 × 7.7 = 10.01 cm −me 4 30. According to Bohr’s formula, = 2 2 2 27. (i) VA – VB = 7 – 5 = + 2 V (Forward biased) 8ε0n h where m is called reduced mass. (ii) VA – VB = 0 – 2 = – 2 V (Reverse biased) In case of hydrogen, m = me = mass of electron. (iii) VA – VB = – 10 – 0 = – 10 V (Reverse biased) For positronium, (iv) VA – VB = – 5 + 12 = + 7 V (Forward biased). m × me me 28. Given, qA = qB = 6 × 10–8 C m= e = me + me 2 When uncharged sphere C is brought in contact m e4 with sphere A, then the charge on A or C is Since for H-atom, E1 = 2e 2 2 = −13.6 eV Charge on A+ Charge on C (6 × 10 −8 + 0) 8ε0n h ′ = qA = −13.6 –8 2 2 So, for positronium E′1 = = − 6.8 eV. = 3 × 10 C 2 Practice Paper - 1 7 31. Here emf induced in the loop e = Blv The first minimum falls at a distance D from the ε Blv center, i.e., x = D. Current in the loop, I = = ...(i) λ R R [D 2 + 4 D 2 ]1/2 − D = Resistance, R = resistance of the loop + resistance 2 of the network, λ ⇒ D(2.236 – 1) = λ D( 5 − 1) = or R = 1.0 + 2 = 3 Ω 2 2 λ (Network is a balanced Wheatstone bridge) \ D= From equation (i), we get 2.472 IR 1 2 hc v= 33. mv = hυ − W0 = − W0 Bl 2 max λ Here, B = 2 T, l = 15 × 10–2 m, I = 2 × 10–3 A, R = 3 W So, on increasing the wavelength of incident 2 × 10 −3 × 3 light, energy of photons decreases whereas \ v= = 2 × 10–2 m s–1 the number of photoelectrons emitted remain −2 2 × 15 × 10 OR same. Consider a rectangular strip of small width dx of 34. Ei > Es > Em the square loop at a distance x from the wire as hc shown in figure. E = hυ = λ Magnetic field due dx −34 hc 6.67 × 10 × 3 × 108 to current carrying I ∴ λ= = E 1.12 × 1.6 × 10 −19 a v wire at a distance x from the wire is l = 1.11 × 10–6 m µ I r a 35. Total charge on B= 0  shell A = 4pa2s = qA x 2πx Area of the strip, x + dx Total charge on dA = adx shell B = 4pb2s = qB Total charge on \ Magnetic flux linked with the strip is shell C = 4pc2s = qC µ I dφ = BdA = 0 (adx ) (i) Potential at surface of outer shell C 2πx Total magnetic flux linked with the square loop is 1  q A qB qC  VC = VCA + VCB + VCC = − + x =r +a x =r +a µ I µ Ia x = r + a dx 4 πε0  c c c  0 ( φ = ∫ dφ = ∫ adx ) = 0 ∫ 4 πσ  a 2 b 2 c  σ  2 2 x =r x = r 2πx 2π x = r x =  − + = a − b2 + c 2  4 πε  c 0 c c ε  0 µ0 Ia µ Ia  r + a  µ0 Ia  a  = | ln x |xx == rr + a = 0 ln   = ln  + 1 Potential at surface of shell B 2π 2π  r  2π  r  VB = VBA + VBB + VBC If M is the mutual inductance between the straight wire and the square loop, then, MI = f 1  q A qB qC  or VB = − + µ a 4 πε0  b b c  or MI = µ0 Ia ln  a + 1 \ M = 0 ln  a + 1 2π  r  2π  r  1  σ × 4 πa2 σ × 4 πb2 σ × 4 πc 2  32. From diagram or VB =  − +  4 πε0  b b c  T1P = T1O – OP = (D – x) T2P = T2O + OP = (D + x) σ  a2  σ 2 2 VB =  − b + c = [a − b + bc] Now S1P = (S1T1 )2 + (T1P )2 = D 2 + (D − x )2 ε0  b  ε0b S2P = (S2T2 )2 + (T2 P )2 = Potential at surface of shell A D 2 + (D + x )2 1  q A qB qC  VA = VAA + VAB + VAC = − + λ Path difference, S2P – S1P = ; for first minimum 4 πε0  a b c  to occur 2 1  σ × 4 πa2 σ × 4 πb2 σ × 4 πc 2  λ VA =  − +  D 2 + (D + x )2 − D 2 + (D − x )2 = 4 πε0  a b c  2 8 CBSE Champion Physics Class 12 σ Q′ = C′V′ = 11 × 10–6 × 3 = 33 mC VA = [a − b + c] ∵ C1 is in series with Cʹ, so charge on them is ε0 same i.e., Q1 = Q′ = 33 mC (ii) Electric field at C 1  q A qB qC  So potential difference across C1 is EC = ECA − ECB + ECC = − + Q 33 µC 4 πε0  c 2 c 2 c 2  V1 = 1 = = 33 V C1 1 µF 4 πσ  a2 b2 c 2  σ  a2 b2  Hence, net capacitance of network is =  2 − 2 + 2 =  2 − 2 + 1 1 1 1 1 1 12 11 4 πε0  c c c  ε0  c c  = + = + = or C = µF Electric field at B C C1 C ′ 1 11 11 12 1  q A qB  Net potential difference across network is EB = EBA − EBB + EBC = − + 0 4 πε0  b2 b2  V = V1 + V′ = 33 + 3 = 36 V \ Net energy stored in the network is 1  4 πa2σ 4 πb2σ  1 EB =  − + 0 U = CV 2 4 πε0  b2 b2  2 [Q electric field due to C is zero] or U = 594 × 10–6 J = 594 mJ 36. Faraday’s law of electromagnetic induction σ  a2  EB =  − 1 states that whenever there is a change in the ε0  b2  magnetic flux linked with a circuit, an induced emf Electric field at A is set up in it, which lasts as long as the magnetic 1  qA  flux linked with it is changing and the magnitude E A = E AA − E AB + E AC =  2 − 0 + 0 4 πε0  a  of induced emf ‘e’ is directly proportional to the 1 4 πa2σ σ rate of change of magnetic flux linked with it i.e., EA = = 4 πε0 a2 ε0 dφ |ε|∝. OR dt Expression for energy stored in a capacitor : According to the data given in question, during If q is the charge and V is the potential difference the motion from x = 0 to x = b, initial flux = 0 and across a capacitor at any instant during its final flux = Blb. charging, then small work done in storing an Motional emf in the arm PQ, e = –Bvl additional small charge dq against the repulsion  dφ  of charge q already stored on it is  Q ε = − dt  dW = V.dq= (q/C)dq So, the total amount of work done in storing the During the motion from x = b to x = 2b, maximum charge Q on capacitor is Flux remains constant which is f = Blb Q Q \ Motional emf, e = 0 q 1  q2  1 Q2 Above values remain same, for the motion of arm W = ∫. dq =   = C C  2  2 C PQ, from x = 2b to b. 0 0 which gets stored in the capacitor in the form During motion from x = b to x = 0, of electrostatic energy. So the energy stored in initial flux f = Blb, final flux = 0 capacitor is dφ \ Motional emf ε = − = + Blv (direction 1 Q2 1 1 dt U= = CV 2 = QV reversed) 2 C 2 2 Variation of these quantities is shown in the 1 following graph. As U4 = 27 mJ, So, C4 (V ′)2 = 27 × 10–6 J 2 Outward Inward 1 or × 6 × 10 −6 (V ′)2 = 27 × 10–6 2 or V′ = 3 V Since C2, C3 and C4 are parallel, so their net capacitance is C′ = C2 + C3 + C4 = 2 + 3 + 6 = 11 mF and hence charge stored in their combination is Practice Paper - 1 9 OR On using them in equation (i), we get Lenz’s law states that the AN AN AN direction of the induced (n2 − n1 ) = n1 + n2 PC PO PI emf and the direction of n2 − n1 n1 n2 induced current are such or = + PC PO PI that they oppose the cause where, PC = + R, radius of curvature which produces them. PO = – u, object distance When the N-pole of a magnet is moved towards PI = + v, image distance a coil, the induced current in the coil flows in n −n n n −n n n n anticlockwise direction on the side of magnet, So 2 1 = 1 + 2 or 2 1 = 2 − 1 so as to acquire north polarity and oppose the R −u v R v u motion of the magnet towards the coil, by applying This gives formula for refraction at spherical repulsive force on it. surface when object is in rarer medium. In order to continue the change in magnetic flux 1 1 1 (b) For convex lens = − ...(i) linked with the circuit, some work is to be done or f1 v ′ u some energy is to be spent against the opposition For concave lens (f2 = –ve) offered by induced emf. This energy spent by the 1 1 1 external source ultimately appears in the circuit in − = − ...(ii) f2 v v ′ the form of electrical energy. Adding equations (i) and (ii) Suppose that the Lenz’s law is not valid. Then 1 1 1 1 v − =− +. v the induced current flows through the coil in a f1 f1 f2 u v direction opposite to one dictated by Lenz’s law. The resulting force on the magnet makes it move 1 1 1 O I I Also, − = faster and faster, i.e., the magnet gains speed v u f u f L1 L2 2 and hence kinetic energy without expending where f = focal length of combination an equivalent amount of energy. This sets up a 1 1 1 f f perpetual motion machine, violating the law of ∴ − =. So, f = 1 2 conservation of energy. Thus Lenz’s law is valid f1 f2 f f2 − f1 and is a consequence of the law of conservation OR of energy. (a) 37. (a) Refraction at convex spherical surface When object is in rarer medium and image formed is real. N n1 i A n2 r    n1 < n 2 O u PN R C I v (b) (i) Given f0 = 140 cm, fe = 5 cm In DOAC, i = a + g and in DAIC, g = r + b or r = g – b When final image is at infinity, magnifying power, sin i i α + γ −f 140 ∴ By Snell’s law, 1n2 = ≈ = m= 0 = − ⇒ m = –28 sin r r γ − β fe 5. 0 n2 α + γ Negative sign shows that the image is inverted. or = or n2 γ − n2β = n1α + n1γ When final image is at the least distance of distinct n1 γ − β or (n2 – n1)g = n1a + n2b...(i) −f  f  vision, magnifying power, m = 0  1 + e  As a, b and g are small and P and N lie close to fe  D each other, −140  5.0  = 1+ = –33.6 AN AN 5.0  25  So, α ≈ tan α = ≈ NO PO (ii) Separation between objective and eye piece AN AN ; γ ≈ tan γ = AN ≈ AN when final image is formed at infinity, β ≈ tan β = ≈ NC PC L = f0 + fe = 140 cm + 5.0 cm = 145 cm NI PI  PRACTICE PAPER (Solved) 2 General Instructions : Read the following instructions very carefully and strictly follow them. (i) This question paper comprises four section – A, B, C and D. (ii) There are 37 questions in the question paper. All questions are compulsory. (iii) Section A – Question no. 1 to 20 are very short answer type questions carrying 1 mark each. (iv) Section B – Question no. 21 to 27 are short answer type questions carrying 2 marks each. (v) Section C – Question no. 28 to 34 are long answer type questions carrying 3 marks each. (vi) Section D – Question no. 35 to 37 are also long answer type questions, carrying 5 marks each. (vii) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of 1 mark, 2 questions of 2 marks, 1 question of 3 marks and all the 3 questions of 5 marks. You have to attempt only one of the choices in such questions. (viii) In addition to this, separate instructions are given with each section and question, wherever necessary. (ix) Use of calculators and log tables is not permitted. (x) You may use the values of physical constants wherever necessary. Time allowed : 3 hours  Maximum marks : 70 SECTION - A 6. The angle of a prism is 42° and refractive index of its material is 3/2. Then angle of Directions (Q. No. 1-10) : Select the most minimum deviation for this prism is appropriate option from those given below each (a) 63° (b) 42° (c) 28° (d) 21° question. –3 7. An electric charge 10 µC is placed at 1. Energy associated with a moving charge is the origin (0, 0) of a (X-Y) co-ordinate due to system. Two points A and B are situated at (a) electric field (b) magnetic field ( 2 , 2 ) and (2,0) respectively. The potential (c) both electric field and magnetic field difference between the points A and B will (d) none of these. be 2. The dielectric constant of air is 1.006. The (a) 4.5 volt (b) 9 volt speed of electromagnetic wave travelling in (c) zero (d) 2 volt air is a × 108 m s–1, where a is about 8. The simple Bohr model cannot be directly (a) 3 (b) 3.88 (c) 2.5 (d) 3.2 applied to calculate the energy levels of an 3. The photoelectric cut-off voltage in a certain atom with many electrons. This is because experiment is 3.5 V. The maximum kinetic (a) of the electrons not being subject to a energy of photoelectrons emitted is central force (a) 2.4 eV (b) 3.5 eV (c) 3.1 eV (d) 4.5 eV (b) of the electrons colliding with each other 4. In n-type semiconductor when all donor (c) of screening effects states are filled, then the net charge density (d) the force between the nucleus and an in the donor states becomes electron will no longer be given by (a) 1 (b) > 1 Coulomb’s law. (c) < 1, but not zero (d) zero 9. The battery of a truck has an emf of 24 V. 5. Electron travels in a direction If the internal resistance of the battery is (a) same to the electric field 0.8 W, then maximum current that can be (b) opposite to the electric field drawn from the battery is (c) independent of the electric field direction (a) 30 A (b) 32 A (d) depends upon the material of conductor. (c) 33 A (d) 34 A Practice Paper - 2 11 10. In a nuclear reactor, moderators slow down SECTION - B the neutrons which come out in a fission 21. With a certain cell, the balance point process. The moderator used have light is obtained at 65 cm from the end of a nuclei. Heavy nuclei will not serve the purpose because potentiometer wire. With another cell whose (a) they will break up. EMF differs from that of first by 0.1 V, the (b) elastic collision of neutrons with heavy balance point is obtained at 60 cm. Find the nuclei will not slow them down. EMF of each cell. (c) the net weight of the reactor would be 22. The following graph depicts the variation of unbearably high. potential difference V between the plates of (d) substances with heavy nuclei do not two capacitors A and B versus charge on the occur in liquid or gaseous state at room capacitors. Which of the two capacitors has temperature. higher capacitance and which has lower? Give Directions (Q. No. 11-15) : Fill in the blanks reason too. V with appropriate answer. B 1 11. The constant of proportionality in A 4 πε 0 coulomb’s law has units ______. 12. The electromagnetic radiations used for studying crystal structure of solids, are O Q ______. OR OR If the total charge enclosed by a surface is The part of electromagnetic spectrum with zero, does it imply that the electric field highest frequency is ______. everywhere on the surface is zero? Conversely, 13. Wavefront is the locus of all points, where if the electric field everywhere on a surface the particles of the medium vibrate with the is zero, does it imply that net charge inside same ______. is zero? 14. The total number of magnetic field lines 23. In an electromagnetic wave, amplitude of passing normally through a given area is electric field is E0 = 60 N/C and its frequency called ______. is υ = 50 MHz. 15. The electric field at the centroid of an (a) Determine B0, ω, k and λ.   equilateral triangle carrying an equal charge (b) Find expressions for E and B. q at each of its vertices is ______. 24. A magician during a show makes a glass lens Directions (Q. No. 16-20) : Answer the following. with m = 1.47 disappear in a trough of liquid. 16. How is the electrical power of an electrical What is the refractive index of the liquid? appliance depends on its resistance. Could the liquid be water? 17. State the path difference between two waves 25. When a capacitor is connected in series with for destructive interference. a series LR circuit, the alternating current OR flowing in the circuit increases. Explain why? How does the magnifying power of a OR telescope change on decreasing the aperture An ordinary moving coil ammeter used in of its objective lens? Justify your answer. d.c. cannot be used to measure an alternating 18. A substance has a critical angle of 45° for current even if its frequency is low. Explain yellow light. What is its refractive index? why? 19. Can the potential barrier across a p-n 26. Three photo diodes D1, D2 and D3 are made junction be measured by simply connecting of semiconductors having band gaps of a voltmeter across the junction? 2.5 eV, 2 eV and 3 eV, respectively. Which 20. What is the equivalent energy of a 10 mg one will be able to detect light of wavelength mass ? 6000 Å? 12 CBSE Champion Physics Class 12 27. An electron in atom revolves around flows through the circuit and is in phase the nucleus in an orbit of radius 0.53 Å. with applied voltage. When the same voltage Calculate the equivalent magnetic moment is applied across another device Y, the same if the frequency of revolution of electron is current again flows through the circuit, but 6.8 × 109 MHz. it leads the applied voltage by π/2 radians (a) Name the devices X and Y. SECTION - C (b) Calculate the current flowing in the circuit 28. A paisa coin is made up of Al-Mg alloy and when same voltage is applied across the weighs 0.75 g. It has a square shape and its series combination of X and Y. diagonal measures 17 mm. It is electrically 33. Explain, with the help of a circuit diagram, neutral and contains equal amounts of the working of a photodiode. Write briefly positive and negative charges. how it is used to detect the optical signals. Treating the paisa coins made up of only 34. The given graph shows the variation of Al, find the magnitude of equal number photoelectric current (I) of positive and negative charges. What versus applied voltage (V) conclusion do you draw from this magnitude? for two different photo- 29. A spherical surface of radius of curvature R sensitive materials and for separates air (refractive index 1.0) from glass two different intensities of (refractive index 1.5). The centre of curvature the incident radiations. is in glass. A point object P placed in air is Identify the pairs of curves found to have a real image Q in glass. The that correspond to different line PQ cuts the surface at a point O and materials but same intensity of incident PO = OQ. Find the distance of the object radiation. from the spherical surface. OR SECTION - D An object of size 3.0 cm is placed 14 cm 35. Using Biot Savart’s law, find an expression in front of a concave lens of focal length for the magnetic field at the centre of a 21 cm. Describe the image produced by the circular coil of N turns and radius R, carrying lens. What happens if the object is moved current I. further away from the lens ? Sketch the magnetic field for a circular loop, 30. A rectangular wire frame, shown below, is clearly indicating the direction of the field. placed in a uniform magnetic field directed OR upward and normal to the plane of the paper. Derive an expression for the force experienced The part AB is connected to a spring. The by a current carrying straight conductor spring is stretched and released when the placed in a magnetic field. Under what wire AB has come to the position AB (t = 0). condition is this force maximum? How would the induced emf vary with time? 36. The first four spectral lines in the Lyman Neglect damping. series of a H-atom are l = 1218 Å, 1028 Å, 974.3 Å and 951.4 Å. If instead of Hydrogen, we consider Deuterium, calculate the shift in the wavelength of these lines. OR If a proton had a radius R and the charge was 31. Two wires made of tinned copper having uniformly distributed, calculate using Bohr identical cross-section (= 10 –6 m 2) and theory, the ground state energy of a H-atom lengths 10 cm and 15 cm are to be used as when (i) R = 0.1 Å, and (ii) R = 10 Å. fuses. Show that the fuses will melt at the 37. (a) Use Huygen’s principle to show how same value of current in each case. a plane wavefront propagates from a 32. When an alternating voltage of 200 V is denser to rarer medium. Hence verify applied across a device X, a current of 0.5 A Snell’s law of refraction. Practice Paper - 2 13 (b) In a single slit diffraction experiment, phase difference between the two waves when a tiny circular obstacle is placed in emanating from the slits does not change the path of light from a distant source, with time, whereas in set B, the phase a bright spot is seen at the centre of the difference between the two waves from shadow of the obstacle. Explain why? the slits changes rapidly with time. What State two points of difference between the difference will be observed in the pattern interference pattern in Young’s double slit obtained on the screen in the two set ups? experiment and diffraction pattern due to (b) Deduce the expression for the resultant a single slit. intensity in both the above mentioned set OR ups (A and B), assuming that the waves (a) There are two sets of apparatus of Young’s emanating from the two slits have the same double slit experiment. In set A, the amplitude A and same wavelength l. Detailed Solutions 1. (c) they have the same mass. Therefore, heavy nuclei 2. (a) : For an electromagnetic wave, will not serve the purpose because elastic collision 1 of neutrons with heavy nuclei will not slow them velocity, c = = 3 × 108 m s −1. down. µ0 ε0 1 Fr 2 N m2 Air acts almost as vacuum. 11. = = 2 = C −2 N m 2 \ a = 3 approximately 4 πε 0 q1 q2 C 3. (b) : Here, V0 = 3.5 V, 12. X-rays are used for studying crystal structure Maximum kinetic energy = eV0 = 3.5 eV of solids. 4. (b) : If all the donor states in n-type 13. Wavefront is the locus of all points, where semiconductor are filled, the number of electrons the particles of the medium vibrate with the same in donor states will increase. Due to it, the charge phase. density in donor states will become more than 14. The total number of magnetic field lines one. passing normally through a given area is called magnetic flux. 5. (b) 15. The electric field at the centroid of an 3  equilateral triangle carrying an equal charge q at 6. (d) : δ m = (µ − 1)A =  − 1 42° = 21° 2  each of its vertices is zero.  ^ ^ 7. (c) : r1 = 2 i + 2 j V2 16. P = for an electrical appliance  R | r1 |= r1 = ( 2 )2 + ( 2 )2 = 2  1 ^ ^ r2 = 2 i + 0 j \ P ∝  R or | r2 | = r2 = 2 λ 17. ∆x = (2n − 1) , where n = 1, 2, 3,... Points A and B are at same 2 potential. OR \ VA – VB = 0 f No change because M = − 0 depends on focal 8. (a) : In atoms with many electrons, electrons fe are not being subjected to one single central length f0 of objective lens and not on its aperture. force. 1 18. µ = = 2 = 1.414 9. (a) sin 45° 10. (b) : During an elastic collision between 19. No, the voltmeter should have a very high two particles, the maximum kinetic energy is resistance as compared to the resistance of p-n transferred from one particle to the other when junction, which is nearly infinite. 14 CBSE Champion Physics Class 12 20. E = mc2 = 10 × 10–6 kg × (3 × 108 m/s)2 1 = 9 × 1011 J \ =0; f = ∞ As, m1 = m2 f 21. For Ist cell, e1 = k × 65...(i) The lens in the liquid will act like a plane sheet For 2nd cell, e2 = k × 60...(ii) of glass. No, the liquid is not water. It could be ε1 65 glycerine. = ε2 60 25. Impedance offered by series LR circuit is As e1 = e2 + 0.1 Z = R 2 + X 2 , but when capacitor is connected in ε1 L 65 So, = series with LR circuit, its impedance decreases to ε1 − 0.1 60 On solving, e1 = 1.3 V and e2 = 1.2 V Z′ = R 2 + ( X L − X C )2 and hence alternating 22. The capacitor A has higher value of capacitance current flowing in the circuit increases. and B has lower capacitance. We know that C = Q/V. OR Hence, slope of V-Q graph represents 1/C. In alternating current, both magnitude and As slope of graph for capacitor A is less, so its direction of current changes with time, which makes the needle of ordinary moving coil ammeter capacitance is more. oscillate with high frequency of A.C. Hence it can OR not be used to measure alternating current.   q According to Gauss’s law  ∫ E ⋅ dS = ε0. If the total 26. We know that, energy of incident photon S hc charge enclosed by the surface is zero i.e., q = 0, E = λ     then ∫ E ⋅ dS = 0 which implies either E= 0 or E l = 6000 Å = 600 nm (given) is perpendicular to the surface. But if E = 0 , then 1242 eV nm q = 0 which implies that the net charge inside the \ E= = 2.07 eV 600 nm surface is zero. D2 will detect these radiations because energy of incident radiation is greater than its band gap. 23. E0 = 60 N/C, υ = 50 MHz E 60 27. Equivalent current in a loop I = ue (a) B0 = 0 = = 2 × 10–7 T I = 6.8 × 109 ×106 × 1.6 × 10–19 c 3 × 108 I = 10.88 × 10–4 A ω = 2πυ = 3.14 × 108 rad s–1 Equivalent dipole moment, c 3 × 108 M = IA = 10.88 × 10–4 × π(0.53 × 10–10)2 λ = = = 6 cm υ 50 × 106 = 9.6 × 10–24 A m2 2 π 2 × 3.14 28. Atomic number of Al, Z = 13. k= = = 1.05 m–1 λ 6 Molar mass of Al, M = 26.9815 g  (b) E = E0 sin (kx – ωt) j Mass of coin, m = 0.75 g As, Number of Al atoms in 1 mole, = 60 sin (1.05x – 3.14 × 108t) j V m–1  NA = 6.023 × 1023 B = B0 sin (kx – ωt) k m \ Number of Al atoms in coin, N = NA = 2 × 10–7 sin (1.05x – 3.14 × 108t) k T M 0.75 24. The refractive index of the liquid must be = × 6.023 × 1023 = 1.67 × 1022 atoms equal to 1.47 in order to make the lens disappear. 26.9815 This means m1 = m2. Magnitude of positive charge in coin = magnitude of negative charge in coin 1 1 1 1  = ( µ 2 − 1)  − = N(Ze) f  R1 R2  = 1.67 × 1022 × 13 × 1.6 × 10–19 C = 3.47 × 104 C 1  µ2  1 1  From this, it can be concluded that ordinary neutral = − 1  − f  µ1   R1 R2  matter, even of small size, contains enormous Practice Paper - 2 15 amount of positive and negative charges. I 2ρl 29. Here, m1 = 1.0, m2 = 1.5 = I 2R = πr 2 Let u = OP = – x, v = OQ = + x where l is the length, r is radius and r is the specific As refraction occurs from rarer to denser medium, resistance of the wire. therefore N Let H = heat lost per second per unit surface area µ1 µ 2 µ 2 − µ1 A of the wire. − + = u v R Neglecting the loss of heat from the end faces of 1 3 (3 / 2) − 1 the wire. − + = P O C Q Heat lost per second by the wire = H × 2prl − x 2x R At steady state temperature, 2+3 1 = u v I 2ρl 2x 2R R H = 2 πrl = 2 2x = 10R, x = 5R πr I 2ρ OR or H = 2 3...(i) Object of size 3 cm is placed 14 cm in front of 2π r concave lens.