CUET Physics

Cuet (Common University Entrance Test) For Undergraduate Courses Physics (Code: 322) Dr. S. Malhotra Former Director DPS Faridabad   LAXMI PUBLICATIONS (P) LTD (An ISO 9001:2015 Company) BEngalURU  • Chennai • Guwahati • Hyderabad • Jalandhar Kochi  • Kolkata • lucknow • mumbai • Ranchi New Delhi

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Introduction National Testing Agency has been entrusted with the responsibility of conducting the Undergraduate entrance tests for all the Central Universities (CUs) for the academic session 2022–2023. CUET will provide a single window opportunity to students to seek admission in any of the Central Universities (CUs) across the country. The CUET (UG)–2022 will be conducted in Computer Based Test (CBT) Mode. Examination Structure for CUET (UG)–2022: CUET (UG)–2022 will consist of the following four sections:  Section IA – 13 Languages  Section IB – 19 Languages  Section II – 27 Domain Specific Subjects  Section III – General Test Choosing options from each section is not mandatory. Choices should match the requirements of the desired University. Broad features of CUET (UG)–2022: Some features of CUET (UG)–2022 are as follows: Section Subjects/Tests Questions to Question Type Duration be Attempted Section IA– There are 13* different 40 questions to Language to be tested through 45 minutes Languages languages. Any of these be attempted for each languages may be chosen. out of 50 in each Reading Comprehension language language (based on different types of passages–Factual, Literary and Narrative, [Literary Aptitude and Vocabulary] Section IB– There are 19** languages. Languages Any other language apart from those offered in Section I A may be chosen. Section II– There are 27*** Domain 40 questions to • Input text can be used for 45 minutes Domain specific subjects being be attempted for each offered under this section. out of 50 MCQ Based Questions Domain Section III– A candidate may choose specific General a maximum of Six (06) 60 questions to • MCQs based on NCERT subjects Test Domains as desired by be attempted the applicable University/ out of 75 Class XII syllabus only 60 minutes Universities. For any such under- • Input text can be used for graduate programme/ programmes being offered MCQ Based Questions by Universities where a General Test is being used • General Knowledge, Current for admission. Affairs, General Mental Ability, Numerical Ability, Quantitative Reasoning (Simple application of basic mathematical concepts arithmetic/algebra geometry/ mensuration/stat taught till Grade 8), Logical and Analytical Reasoning

* Languages (13): Tamil, Telugu, Kannada, Malayalam, Marathi, Gujarati, Odia, Bengali, Assamese, Punjabi, English, Hindi and Urdu ** Languages (19): French, Spanish, German, Nepali, Persian, Italian, Arabic, Sindhi, Kashmiri, Konkani, Bodo, Dogri, Maithili, Manipuri, Santhali, Tibetan, Japanese, Russian and Chinese. *** DomainSpecificSubjects(27):1.Accountancy/BookKeeping;2.Biology/BiologicalStudies/Biotechnology/ Biochemistry; 3. Business Studies; 4. Chemistry; 5. Computer Science/Informatics Practices; 6. Economics/ Business Economics; 7. Engineering Graphics; 8. Entrepreneurship; 9. Geography/Geology; 10. History; 11. Home Science; 12. Knowledge Tradition and Practices of India; 13. Legal Studies; 14. Environmental Science; 15. Mathematics; 16. Physical Education/NCC/Yoga; 17. Physics; 18. Political Science; 19. Psychology; 20. Sociology; 21. Teaching Aptitude; 22. Agriculture; 23. Mass Media/Mass Communication; 24. Anthropology; 25. Fine Arts/Visual Arts (Sculpture/Painting)/Commercial Arts; 26. Performing Arts– (i) Dance (Kathak/Bharatnatyam/Oddisi/Kathakali/Kuchipudi/Manipuri (ii) Drama-Theatre (iii) Music General (Hindustani/Carnatic/Rabindra Sangeet/Percussion/Non-Percussion); 27. Sanskrit [For all Shastri (Shastri 3 years/4 years Honours) Equivalent to B.A./B.A. Honours courses i.e. Shastri in Veda, Paurohitya (Karmakand), Dharamshastra, Prachin Vyakarana, Navya Vyakarana, Phalit Jyotish, Siddhant Jyotish, Vastushastra, Sahitya, Puranetihas, Prakrit Bhasha,Prachin Nyaya Vaisheshik, Sankhya Yoga, Jain Darshan, Mimansa, AdvaitaVedanta, Vishihstadvaita Vedanta, Sarva Darshan, a candidate may choose Sanskrit as the Domain]. • A candidate can choose a maximum of any 3 languages from Section IA and Section IB taken together. (One of the languages chosen needs to be in lieu of Domain specific subjects). • Section II offers 27 subjects, out of which a candidate may choose a maximum of 6 subjects. • Section III comprises General Test. • For choosing Languages (up to 3) from Section IA and IB and a maximum of 6 subjects from Section II and General Test under Section III, the candidate must refer to the requirements of his/her intended University. Level of questions for CUET (UG)–2022: All questions in various testing areas will be benchmarked at the level of Class XII only. Marking Scheme of Examination For Multiple Choice Questions: To answer a question, the candidates need to choose one option corresponding to the correct answer or the most appropriate answer. However, if any anomaly or discrepancy is found after the process of challenges of the key verification, it shall be addressed in the following manner: (i) Correct answer or the most appropriate answer: Five marks (+ 5) (ii) Any incorrect option marked will be given minus one mark (– 1). (iii) Unanswered/Marked for Review will be given no mark (0). (iv) If more than one option is found to be correct then Five marks (+ 5) will be awarded to only those who have marked any of the correct options. (v) If all options are found to be correct then Five marks (+ 5) will be awarded to all those who have attempted the question. (vi) If none of the options is found correct or a Question is found to be wrong or a Question is dropped then all candidates who have appeared will be given five marks (+ 5). Note: C andidates are advised to visit the NTA CUET (UG)–2022 official website https://cuet.samarth.ac.in/, for latest updates regarding the Examination.

Contents ... 1 ... 21 1. Electrostatics ... 42 2. Current Electricity ... 57 3. Magnetic Effects of Current and Magnetism ... 70 4. Electromagnetic Induction and Alternating Currents ... 79 5. Electromagnetic Waves ... 107 6. Optics ... 119 7. Dual Nature of Matter and Radiation ... 133 8. Atoms and Nuclei ... 144 9. Electronic Devices 10. Communication Systems ... 150–256 Answers Mock Test Papers ... M1–M32

Syllabus (Physics – 322) Note: There will be one Question Paper which will have 50 questions out of which 40 questions need to be attempted. Unit I: Electrostatics Electric charges and their conservation. 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 a 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). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, the electrical potential energy of a system of two point charges, and electric dipoles in an electrostatic field. Conductors and insulators, free charges, and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, the combination of capacitors in series and in parallel, the capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor, Van de Graaff generator. Unit II: Current Electricity Electric current, the flow of electric charges in a metallic conductor, drift velocity and 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. The 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 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 Concept of the 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. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. (vi)

(vii ) Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current‑carrying conductors – definition of ampere. Torque experienced by a current loop in a magnetic field; moving coil galvanometer – its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. The 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 ferromagnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets. Unit IV: Electromagnetic Induction and Alternating Currents Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. 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, wattless current. AC generator and transformer. Unit V: Electromagnetic Waves Need for displacement current. Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses. Unit VI: 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, lens maker’s formula. Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of light–blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Human eye, image formation, and accommodation, correction of eye defects (myopia and hypermetropia) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Wave optics: Wavefront and Huygens’ principle, reflection, and refraction of plane wave at a plane surface using wavefronts. Proof of laws of reflection and refraction using Huygens’ principle. Interference, Young’s double hole experiment and expression for fringe width, coherent sources, and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving the power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids. Unit VII: Dual Nature of Matter and Radiation Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation – particle nature of light. Matter waves – wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only the conclusion should be explained.) Unit VIII: Atoms and Nuclei Alpha – particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones.

(viii) Radioactivity – alpha, beta, and gamma particles/rays, and their properties; radioactive decay law. Mass- energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission and fusion. Unit IX: Electronic Devices Energy bands in solids (qualitative ideas only), conductors, insulators, and semiconductors; semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch. Unit X: Communication Systems Elements of a communication system (block diagram only); bandwidth of signals (speech, TV, and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky, and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave.

ELECTROSTATICS  1 Unit 1 Electrostatics MULTIPLE CHOICE QUESTIONS Tick () the most appropriate choice amongst where ε0 is the permittivity of free space. The the following: SI units of ε0 will be 1. Quantization of charge implies: (a) Nm– 2 C– 2 (b) Nm– 2 C2 (c) N– 1 m– 2 C2 (d) Nm– 2 C– 2 (a) charge does not exits. (b) charge exists on particles. 6. The dimensional representation of ε0 will be (a) [MLT2 A2] (b) [M– 1 L– 3 T4 A2] (c) there is a minimum permissible magnitude of charge. (c) [ML– 2 T2 A– 2] (d) none of these (d) charge can’t be created. 7. When placed in a uniform field, a dipole 2. The minimum amount of charge observed so experiences (a) a net force far is (b) a torque (a) 1 C (b) 4.8 × 10–3 C (c) both a net force and a torque (d) neither a net force nor a torque (c) 1.6 × 10–19 C (d) 1.6 × 1019 C 3. Three charges, each equal to Q, are placed at 8. A parrot comes and sits on a bare high power the corners of an equilateral triangle. If the line. It will (a) experience a mild shock force between any two charges is F, then the net force on the triangle will be (b) experience a strong shock (a) 2F (b) 3F (c) get killed instantaneously (c) 2 F (d) zero (d) not be affected at all 4. A dipole moment →p is kept in a uniform 9. The force between two charges, when placed → →p × →E in free space is 5 N. If they are in a medium electric field E , then represents of relative permittivity 5, the force between (a) torque (b) force them will be (c) capacity (d) charge (a) 1 N (b) 25 N 5. Coulomb’s law in vector form can be written (c) 2.5 N (d) 1/5 N as, 10. 106 electrons are added to a pith ball. The → =  1   q1 q2  r negative charge on the pith ball is  4πε0   r2  (a) 1.6 × 10–13 C (b) 1.6 × 10– 19 C F (c) 1.6 × 10– 25 C (d) none of the above 1

2 PHYSICS 11. When electrons are removed from an 15. Two charges are placed at a certain distance uncharged body, the body apart. If a dielectric slab is placed between them, what happens to the force between the (a) gets negatively charged charges? (b) gets positively charged (c) remains uncharged (a) decreases (d) gets negatively or positively charged (b) increases depending upon its size. 12. Two charges are placed a certain distance (c) remains unchanged apart. A metallic sheet is placed between (d) may increase or decrease depending on them. What will happen to the force between the nature of the dielectric. the charges? (a) increases 16. A positively charged glass rod is brought (b) decreases near the disc of an uncharged gold leaf (c) remains the same electroscope. The leaves diverge. Which of (d) may increase or decrease upon the the following statements is correct? nature of the metal (a) no charge is present on the leaves. 13. The distance (r) between two charges is (b) a positive charge is induced on the varied. Which of the following graphs depicts leaves. the variation between Coulomb’s force (F) between the charges and (r– 2)? (c) a negative charge is induced on the leaves. FF (d) a positive charge is induced on one leaf (a) (b) and a negative charge is induced on the other leaf. 17. Two identical metallic spheres are given equal but opposite charges of +q coulomb and –q coulomb respectively. After charging, O r–2 O r–2 (a) both the spheres still have identical F F masses (c) (d) (b) the positively charged sphere has a smaller mass than the negatively charged sphere O r–2 O r–2 (c) the negatively charged sphere has a smaller mass than the positively charged 14. Which of the graphs in figure below depicts sphere the variation between Colomb’s force (F) between the charges and (r2) in Q. 13? (d) the variation in their masses does not depends on the magnitude of q FF 18. Two charges of 2 µC and 5 µC are placed (a) (b) 2.5 cm apart. The ratio of the Coulomb’s forces experienced by them is (a) 1 : 1 (b) 2 : 5 O r2 O r2 (c) 2 : 5 (d) 4 : 25 F F 19. The ratio of the force between two charges in (c) (d) vacuum kept a certain distance apart to that between the same charges, the same distance apart in a medium of permittivity e is O r2 O r2 (a) e : 1 (b) 1 : e (c) e0 : e (d) none of the above

ELECTROSTATICS  3 20. If Q represents the charge on a particle and V (a) 2 : 1 (b) 2 : 1 the potential difference between two points, (c) 1 : 2 (d) 1 : 2 then QV represents the magnitude of (a) momentum (b) power 27. From where are the electric lines of force assumed to originate? (c) force (d) energy 21. An electron of mass M kg and charge e travels (a) positive charge from rest through a potential difference of (b) negative charge V volts. The final velocity of the electron is (c) both from positive and negative charges (in ms– 1) (d) neither from the positive charge nor (a) 2eV (b) 2MV from the negative charge M e (c) 2eV (d) 2MV 28. The maximum value of the electric intensity M e due to a charged sphere is at (a) its centre (b) its surface 22. As one penetrates a uniformly charged (c) infinity (d) all points sphere, the electric field strength 29. The duration of each lightning flash is about (a) increases (a) 2 × 10–3s (b) 20 s (c) 2 × 10–6s (d) 200 s (b) decreases 30. A charge q is placed at the centre of a line (c) is zero at all points joining two equal charges Q. The system of these three charges will be in equilibrium if (d) remains the same at the surface q equals 23. The ratio of the electric force between two (a) − Q (b) − Q protons to the gravitational force between 2 4 them is of the order of (c) + Q (d) + Q (a) 1042 (b) 1039 4 2 (c) 1036 (d) 1027 31. Two identically charged particles (the charge 24. Two balls carrying charges of + 3 µC and being q for each) are placed at points P and Q – 3 µC attract each other with a force F. between the plates of parallel plate capacitor If a charge of + 3 µC is added to both the balls charged to a potential difference V. The force then the force between them will become on P is (a) F/2 (b) 2F ++++++ (c) F (d) zero r p 25. The capacitance of a parallel plate capacitor Q depends on 2r (a) the type of metal used ––––––––––– (b) the thickness of the plates (a) double of that on Q (c) the potential applied across the plates (b) four times that on Q (c) eight times that on Q (d) the separation between the plates (d) same as that on Q 26. Two identical metal plates, separated by a distance d, form a parallel plate capacitor. A metal sheet of thickness d/2, of the same area as that of either of the plates, is inserted between them. The ratio of the capacitance after the insertion of the sheet to that before insertion is

4 PHYSICS 32. All the 10 capacitors of 1 µF each are to be (a) E2 < E1 (b) E2 > E1 used such that their resultant capacity 1 µF again. Which of the following combination of (c) E2 = E1 (d) E2 = r2 capacitors can be used? r2 E1 (a) 36. In figure, what is the effective capacitance between P and Q? 2 mF 4 mF PQ (b) 2 mF 3 mF 4 mF (a) 6 µF (b) 2 µF 11 11 (c) 24 17 (c) µF (d) none of these (d) None of these 37. What is the effective capacitance between A and B in figure? 33. A hollow aluminium sphere is negatively charged. The electric field at its centre will be (a) zero (b) same as on the surface 2 mF 2 mF (c) more than that on the surface (d) less than that on the surface but not zero 1 mF AB 34. A drop of oil of density d and radius r carries a charge q. When placed in an electric field E, (a) 1 µF (b) 2 µF it moves upwards with a velocity v. If d0 is the density of air, h is the coefficient of viscosity (c) 1.5 µF (d) 2.5 µF of air, then which of the following forces is directed upwards? 38. Two conducting spheres of radii r1 and r2 are at the same potential. The ratio of their (a) 6phrv charges is (b) qE (a) r1 (b) r2 r2 r1 (c) 3 πr 3 (d − d0 )g 4 r12 r22 (d) none of the above (c) r22 (d) r12 35. Figure below shows electric field lines. The 39. If an electric dipole of moment →p is placed in electric field strength at P1 is E1 and that at P2 is E2. If P1 P2 is r, then which of the following → statements is true? an electric field of strength E , then which of P1 r P2 the following gives the potential energy of the dipole? (a) →p ⋅ →E (b) − →p ⋅ →E (c) →p ⋅ →E (d) none of the above

ELECTROSTATICS  5 40. A hollow metal sphere of radius 5 cm is 47. If the radius of a soap bubble is doubled, its capacitance will be charged such that potential on its surface is 20 V. The potential at the centre of the sphere (a) doubled is (b) halved (a) 20 V (c) decreased by 100% (b) zero (d) increased by 50% (c) same as that at a point 5 cm from the surface 48. A number of charged liquid drops coalesce. Which one of the following quantities does (d) same as that at a point 10 cm from the not change? surface 41. Sixty-four drops are joined together to form a (a) potential (b) charge big drop. If each small drop has a capacitance C, a potential V and a charge q, then the (c) capacitance (d) electrostatic energy capacitance of the big drop will be 49. A soap bubble is charged to a potential of (a) C (b) 4C 16 V. Its radius is then doubled. The potential of the bubble will now be (c) 16C (d) 64C (a) 2 V (b) 4 V 42. The equivalent capacitance of the network (c) 8 V (d) 16 V given in figure is 1 µF. The value of C is 50. The capacitance of a conductor in vacuum 1.5 mF is 10 F. If it is put in a medium of relative permittivity 6, the capacitance will be PQ 5 3 3 mF 3 mF (a) unchanged (b) F (c) 60 F C (d) 54 × 1010 F (a) 3 µF (b) 1.5 µF 51. One of the plates of a capacitor is connected to a source of constant negative potential. The (c) 2.5 µF (d) 1 µF number of electrons accumulated on it is 1010. When the other plate is earthed, the number 43. The electric field strength E due to a short dipole is related to the distance r from it as of electrons present on the plate will become (a) E ∝ r– 1 (b) E ∝ r– 2 (a) zero (b) 1010 (c) E ∝ r– 3 (d) E ∝ r– 4 44. The electric field strength due to a circular (c) 106 (d) greater than 1010 loop, of radius r and linear density of charge l, at its centre is proportional to 52. The potentials of the two plates of capacitor are + 10 V and – 10 V. The charge on one of the (a) lr (b) l/r plates is 40 C. The capacitance of the capacitor (c) l/r2 (d) none of the above is 45. What is the angle between an electric dipole (a) 2 F (b) 4 F moment and the electric field strength due to it on its axial line? (c) 0.5 F (d) zero (a) 0° (b) 90° 53. If m drops each of capacitance C, coalesce to form a single drop, the capacitance of the (c) 180° (d) none of the above single drop is 46. On an irregularly shaped charged conductor, the potential is (a) more at the flat parts (a) C (b) mC m (b) more at the sharp edges (c) more at the spherical parts (c) m1/3 C (d) m2/3 C (d) same everywhere

6 PHYSICS 54. If m drops, each charged to a potential V, (a) solid sphere coalesce to form a single drop, then the potential of the coalesced drop is (b) hollow sphere (c) both will have an equal charge (a) m2/3 V (b) V (d) nothing can be decided from the given m information (c) mV (d) m1/3 V 60. The capacitance of a capacitor will decrease if we introduce a slab of 55. Two parallel plates are separated by 2 cm. If (a) copper (b) aluminium the potential difference between them is 20 V, then the electric field between them is (c) zinc (d) none of the above (a) 100 NC–1 (b) 1000 NC–1 61. Two capacitors of capacitance 6 µF and 4 µF are put in series across a 120 V battery. What (c) 2000 NC–1 (d) zero is the potential difference across the 4 µF capacitor? 56. What is the equivalent capacitance of the (a) 72 V (b) 60 V combination shown in figure (c) 48 V (d) zero CC 62. What is the equivalent capacitance of the combination shown in figure? CC C CC (a) C (b) 2C (a) 3 C (c) 4C (d) C (b) C 4 2 57. What is the equivalent capacitance of the (c) C (d) infinity combination shown in figure? 63. A 4 µF capacitor is charged to 200 V and then C its plates are connected by a wire. How much heat will be produced? (a) 0.1 J (b) 0.8 J CC C (c) 0.08 J (d) 8 J C 64. Which of the following factors does not affect the capacitance of a capacitor? C (a) area of the plates 2 (a) C (b) (b) curvature of the plates (c) material of the plates (c) 2C (d) 4C (d) distance between the plates 58. Which of the following is blocked by a 65. One of the plates X of a capacitor is connected capacitor? to a source of + 10 V. The other plate Y is earthed. What is the potential of the plate Y? (a) AC (a) – 10 V (b) 10 V (b) DC (c) zero (d) 20 V (c) both AC and DC 66. One of the plates of a capacitor is given a (d) neither AC nor DC charge of + 20 C. The charge on the other 59. Two copper spheres of the same radius, one plate, which is earthed is solid and the other hollow, are charged to the same potential. Which will have more charge? (a) 20 C (b) – 20 C (c) zero (d) none of the above

ELECTROSTATICS  7 67. What is the effective capacitance between P (a) 90 V (b) 10 V and Q in figure? (c) 100 V (d) 1000 V CC 72. The force acting upon a charged particle kept P 2C Q between the plates of a charged capacitor is F. If one of the plates of the capacitor is removed, the force that acts on the particle becomes CC (a) F (b) F 2 (a) C (b) 3 C (c) 2F (d) zero C 73. An electron initially at rest is accelerated 2 (c) (d) 4 C through a potential difference of one volt. The energy gained by electrons is 68. A insulated copper foil of negligible thickness (a) 1 J (b) 1.6 × 10–19 J is inserted in the middle of a capacitor and (c) 10–19 J (d) none of these parallel to its plates. If the initial capacitance of the capacitor was C, what will be the new 74. A bird sitting on a high power line capacitance? (a) gets killed instantly C (b) gets a mild shock 2 (a) C (b) (c) gets a fatal shock (c) 2 C (d) infinity (d) is not affected practically 69. A certain charge Q is first divided into two 75. A polythene piece rubbed with wool is found parts, q and Q – q. Later on the charges are to have a negative charge of 6.4 × 10–9 C. How placed at a certain distance from each other. many electrons have been transferred during If the force of interaction between them is the process? maximum, then Q/q is equal to (a) 4 × 1012 (b) 4 × 1011 (a) 1 (b) 2 (c) 4 × 1010 (d) none of these 1 1 76. In Q. 75, mass transferred to polythene is 2 4 (c) (d) (a) 3.64 × 10–20 kg (b) 4 × 10–28 kg 70. Q, 2Q, 3Q and 4Q charges are placed at the (c) 4 × 1010 kg (d) none of these four corners A, B, C and D of a square. The 77. A uniform electric field of 10 NC–1 exists in field at the centre O of the square is directed the vertically downward direction. What is the increase in the electric potential as one along goes up through a height of 300 cm? (Q) (2Q) (a) 15 V (b) 30 V AB (c) 45 V (d) none of these O 78. The electrostatic field due to a point charge depends on the distance r as (a) 1 (b) 1 r r2 D C (4Q) (3Q) 1 r3 (c) (d) none of these (a) AB (b) AC 79. Electrostatic potential due to a point charge at (c) BD (d) CB a distance r is proportional to 71. When a charge of 3C is placed in a uniform electric field, it experiences a force of 3000 N. (a) 1 (b) 1 The potential difference between two points r r2 separated by a distance of 1 cm within this field is (c) 1 (d) none of these r3

8 PHYSICS 80. Electrostatic potential at a distance r from the 84. The electric field intensity (E) due to a non- centre of a charged metallic sphere of radius conducting charged solid sphere (radius R) R (r < R) is proportional to with distance (r) is shown by (a) r (b) 1 r E E (c) 1 (d) r0 r2 (a) (b) 81. A sphere S1 of radius r1 encloses a total charge O (r = R) r O (r = R) r Q. If there is another concentric sphere S2 of radius r2 (> r1) and there be no additional E E charges between S1 and S2 what is the ratio of electric flux through S1 and S2? (c) (d) (a) 1 (b) – 1 (c) 2 (d) infinity O (r = R) r O (r = R) r 82. Which of the graphs correctly represents 85. What should be the radius of an isolated the variation of electric intensity (E) with spherical conductor so that if has a capacity perpendicular distance (r) from a thin charged of 1 µF? rod? (a) 1 km (b) 3 km YY (c) 7 km (d) 9 km (a) E (b) E 86. A combination of four identical capacitors is shown in figure. If the resultant capacitance O X O X of the combination between the points P and r r Q is 1 F, what is the capacitance (C) of each capacitor? YY P Q (c) E (d) E C C CC Or XX Or 1 83. The variation of electric field intensity (E) with (a) 4 F (b) 4 F distance (r) from the centre of a uniformly charged spherical shell (radius R) is shown by (c) 2 F (d) 1 F 2 87. The magnitude of a charge q at the centre of E E two equal and like charges Q so that the three (a) (b) charges are in equilibrium is O (r = R) r O (r = R) r (a) Q (b) 1 R2 E E (c) Q (d) − Q 4 4 (c) (d) 88. Figure is a plot of lines of force due to two O (r = R) r O (r = R) r charges Q1 and Q2. Which of the following correctly represents the sign of the charges?

ELECTROSTATICS  9 92. A semi-circular arc of radius r is charged uniformly and the charge per unit length is l. The electric field at the centre is Q1 (a) λ (b) λ Q2 2ε0r2 4ε0r (c) λ (d) none of these 2ε0r (a) both negative 93. Electric field at the centroid of an equilateral (b) both positive triangle (side r) carrying charge Q at each (c) upper positive and lower negative corner is given by (d) upper negative and lower positive 89. A quantity X is given by (a) 2 KQ (b) KQ r 2 r2 2 (c) 3 KQ (d) zero r2 X = ε0 L ∆V , ∆t 94. A capacitor is charged to store an energy U. The charging battery is now disconnected. An where ε0 is permittivity of free space, L is identical capacitor is now connected to the length, DV is potential difference and Dt is first capacitor in parallel. The energy in each time interval. The dimensional formula for X of the capacitor is is same as that of (a) resistance (b) charge UU (a) 4 (b) 2 (c) voltage (d) current 3U 90. A parallel plate capacitor is made by stocking (c) U (d) 2 n equally spaced plates connected alternately. If the capacitance between any two plates is y, 95. One moving a charge of 20 C by 2 cm, 2 J of then the total capacitance is work is done. What is the potential difference between the points under consideration? (a) ny (b) n y (a) 0.5 V (b) 0.1 V (c) y (d) (n – 1)y (c) 2 V (d) 4 V 91. Two identical parallel plate capacitors are 96. A parallel plate capacitor has a capacitance of connected in parallel to a 3 volt battery. The 50 pF in air and 105 pF when immersed in oil. battery is disconnected and the two capacitors The dielectric constant of the oil is are joined in series. What is the potential difference between P and Q? (a) 1 (b) ∞ C (c) 2.1 (d) 0.47 +– 97. A closed surface P is constructed around a C metal wire connected to a battery and a key K. +– On pressing the key, number of free electrons entering P per second is equal to number, 3V of free electrons leaving P per second. The +– electric flux through closed surface +– CC Key P +– +– Q (a) 2 V (b) 3 V P (c) 6 V (d) 9 V

10 PHYSICS (a) is decreased (b) is increased 102. When a capacitor is connected to a battery (c) remains zero (d) none of these 98. ‘Debye’ is the unit of (a) an alternating current flows in the circuit (a) electric flux (b) electric dipole moment (b) no current flows at all (c) electric potential (d) electric field intensity (c) a current flows for some time and finally 99. Four capacitors, each of 25 mF, are connected it decreases to zero as shown in figure. The dc voltmeter reads (d) current keeps on increasing and reaches 200 volts. The charge on each plate of the maximum after some time. capacitors is 103. In the circuit shown below each capacitor has V a capacity of 3 mF. What is the total resistance of the circuit? 4W C D 4W –+ –+ 4W B –+ –+ 1W A 10 V (a) 7 Ω (b) 7 Ω 4 3 (c) 5 Ω (d) none of these (a) ± 2 × 10–3 C (b) ± 5 × 10–3 C 104. In Q. 103, what is the net charge on a charged capacitor? (c) ± 2 × 10–2 C (d) ± 5 × 10–2 C (a) zero (b) 1 µC 100. A large non-conducting sheet S is given a uniform charge density. Two unchanged small (c) 1 C (d) infinity metal rods A and B are held near the sheet as shown in figure. Which of the following is 105. Which of the figure(s) given below can false? correctly represent electrostatic field lines? + +A B + ++ +++ + + +– +– + – + ++ + ++ (a) (b) + + + – S (a) S attracts A (b) S attracts B (c) ++ (d) (c) A attracts B (d) A repels B + ++ 101. A parallel plate capacitor has a capacitance of 50 pF in air and 105 pF when immersed in oil. The dielectric constant of the oil is given by (a) 10/21 (b) 1 (c) 2.1 (d) infinity

ELECTROSTATICS   11 106. Figure below shows tracks of three charged 111. Five balls numbered 1, 2, 3, 4, 5 are suspended particles in a uniform electrostatic field. using a separate threads. The pairs (1, 2), Which particle has the highest charge to mass (2, 4) and (4, 1) show electrostatic attraction, ratio? while pairs (2, 3) and (4, 5) show repulsion. Therefore, ball 1 must be ++ + + 1 2 (a) neutral –– – – (b) positively charged 3 (c) negatively charged (a) 1 (d) metallic (b) 2 112. An electric dipole is kept in a non-uniform electric field. It will experience (c) 3 (a) a force, but not torque (d) nothing can be decided (b) a force and a torque 107. Which of the graphs below shows how charge Q given to a capacitor C varies with (c) a torque but not force the potential difference V? (d) neither a force nor a torque Q Q 113. [ML T–3A–1] is dimensional formula of (a) (b) (a) electric intensity OV OV (b) electric potential Q Q (c) potential difference (c) (d) (d) none of these OV OV 114. Figure given below shows two parallel equipotential surfaces P and Q kept at a small 108. Electric field due to a point charge at its own distance r from each other in an electric field location is E. A point charge – q coulomb is taken from the surface P to Q. Then the amount of net (a) unity (b) zero work done is given by (c) infinity (d) none of these 109. When a condenser is given charge Q so as to r raise its potential to V, then the energy stored PQ in the condenser is (a) QV (b) QV2 (c) 1 QV (d) zero (a) 4π ∈0 − 4πq 2 qr (b) ∈0/ r 110. A body has a negative charge of 1 coulomb. It (c) qEr (d) zero means that 115. Electric field strength at a point varies as 1/r (a) it has lost one electrons for a/an (b) it has gained one electron (a) point charge (c) it has lost 6.25 × 1018 electrons (d) it has acquired 6.25 × 1018 additional (b) electric dipole electrons (c) plane infinite sheet of charge (d) line charge of infinite length

12 PHYSICS 116. Electric flux at a point is an electric field is 124. When a dielectric is introduced between two parallel plates of capacitor, the lines of force (a) zero (b) positive are correctly shown in (c) negative (d) none of these +Q –Q +Q –Q 117. Negative electric flux indicates that the electric lines of force are directed (a) outwards (a) (b) (b) inwards (c) inwards or outwards (d) any one of the above +Q –Q +Q –Q 118. The dimensional formula of electric flux in (c) (d) terms of charge is (a) [ML2 T–2 Q–1] (b) [ML3 T–2 Q–1] (c) [ML3 T–3 Q–1] (d) [ML2 T–2 Q–2] 119. The electric flux over a sphere of radius 2 m is 125. In figure below, the charge on 3 mF capacitor f. If radius of the sphere is doubled without is changing the charge enclosed, then the electric flux is 6mF 3mF 2mF (a) φ (b) 2f 2 (c) φ (d) f 10 V 4 120. A sphere of radius 2 m encloses a charge (a) 3 mC (b) 5 mC of 3 mC. Another charge of – 3 mC is placed inside the sphere. Then the next electric flux (c) 10 mC (d) zero would be 126. A 4 mF capacitor is charged to 400 V and then (a) halved (b) four times its plates are joined through a resistance of 2 kW. The heat produced in the resistance is (c) doubled (d) zero 121. SI unit of potential gradient is (a) 1.28 J (b) 0.64 J (a) V (b) V m–1 (c) 0.32 J (d) 0.16 J (c) V m (d) m 127. The equivalent capacity between points P and Q will be 122. Three capacitors of capacitance 12 mF, 6 mF and 4 mF are joined first in series and then in 2mF parallel. What is the ratio of the equivalent capacitance in two cases? P Q 2mF 2mF (a) 2 : 3 (b) 1 : 11 (c) 1 : 3 (d) 11 : 1 (a) 6 mF (b) mF 123. An electron of charge e coulomb passes (c) 2 m (d) 2 mF 3 through a potential difference of V volt. Its energy in joule will be 128. The capacitance of arrangement of 4 plates of area A at distance d, as shown in figure, is V (a) eV (b) e d P (c) e (d) V V Q

ELECTROSTATICS   13 (a) Aε0 (b) 2ε0 A 135. What is the equivalent capacitance of the d d network between P and Q? A (c) 3Aε0 (d) 4Aε0 2 mF 2 mF d d 1 4 mF 129. A capacitor of capacitance 300 mF is PQ connected to a battery of 300 V and charged. 2 mF 2 mF The the energy stored in the condenser is (a) 3 × 10– 4 J B (b) 6 × 10– 4 J (c) 1.5 × 10– 4 J (a) 2 mF (b) 4 mF (d) none of these (c) 6 mF (d) 8 mF 130. In Question 129 above, the energy supplied 136. What is the equivalent capacitance of the by the battery is network between A and B? (a) 3 × 10– 4 J P (b) 6 × 10– 4 J (c) 1.5 × 10– 4 J 2 mF 2 mF (d) none of these 2 mF AB 131. What is the effective capacitance between P and Q? 2 mF 2 mF Q (a) 2 mF (b) 4 mF (c) 6 mF (d) 8 mF 137. Which of the following is a volt? Given: C2 = 4 mF, C1 = C3 = C4 = C5 = 2 mF (a) erg per cm (b) joule per coulomb C4 PQ (c) erg per ampere (d) newton/(coulomb × metre2) C1 C2 C3 138. Which of the following graphs shows the variation of electric potential V with distance C5 r from the centre of a hollow charged sphere (a) 4 mF (b) 2 mF of radius R? (c) 6 mF (d) 8 mF V V 132. A capacitor works in (a) (b) (a) D.C. circuits OR r V O (b) A.C. circuits V R r (c) both (a) and (b) (d) neither (a) nor (b) (c) (d) 133. Which of the following is best insulator? (a) paper (b) carbon OR r r OR (c) ebonite (d) copper 139. Two charges – 20 C and + 20 C are placed 20 cm apart. Then the potential at the centre 134. What is the dimensional formula for surface of the line joining the two charges is charge density? (a) – 2 V (b) 2 V (a) [M0 L0 T A] (b) [M0 L– 2 T A] (c) [M0 L– 2 T– 2 A] (d) [M L2 T– 2 A] (c) 4 C (d) zero

14 PHYSICS 140. Four dipoles of charges of magnitude q are (a) 2 1 placed inside a cube. The total electric flux (b) 2 coming out of the cube will be 4q 8q (c) 1 (d) 1 4 (a) ε0 (b) ε0 148. The electric potential V is given as a function q (c) 4ε0 (d) zero of distance x (in metre) by, V(x) = (4x2 + 10x – 6) volt. 141. In bringing an electron towards another Then the value of electric field at x = 1 m is electron, the electrostatic potential energy of (a) 18 Vm– 1 (b) – 18 Vm– 1 the system (c) 8 Vm– 1 (d) zero (a) increases (b) decreases (c) remains same (d) becomes zero 149. A charge q mC is placed at the centre of a cube, the flux coming out from any surface will be 142. A parallel plate capacitor is first charged and (in SI units) then a dielectric slab is introduced between the plates. The quantity that remains constant is (a) q × 10− 6 (b) q × 10− 3 6ε0 6ε0 (a) charge (Q) (b) potential (V) (c) capacitance (C) (d) energy (U) q 143. NC– 1 represents SI unit of (c) 24ε0 (d) zero (a) electric intensity 150. Energy per unit volume or a capacitor having (b) electric potential area A and separation d kept at potential (c) electric flux difference V is given by (d) none of these (a) 1 ε0 V2 (b) 1 V2 2 d2 2ε0 d2 144. The dimensional representation of electric charge is (c) 1 CV 2 (d) Q2 2 2C (a) [MLT– 2 A] (b) [M0 L0 AT] (c) [M0 L0 AT–2] (d) [ML2 T– 2 A– 1] 151. A dipole moment is placed in uniform electric field. Then the torque acting on it is given by 145. Electromotive force of a cell represents → →→ → →→ (a) t = p ⋅ E (b) t = p × E (a) force (b) energy →→→ →→→ (c) t= p + E (d) t= p − E (c) force per unit length 152. A straight wire of length L and electric dipole (d) energy per unit charge moment p is bent to form a semicircle. The new dipole moment would be 146. A charge Q is placed at the corner of a cube. p 2p The electric flux through all the six faces of Q 6Q (a) 2 (b) p p (a) 6ε0 (b) ε0 (c) 2p (d) 2p QQ 153. Work done in charging a capacitor is stored in (c) ε0 (d) 3ε0 it in the form of 147. If E1 be the electric field strength of a short (a) magnetic energy dipole at a point on its axial line and E2 that (b) potential energy on an equatorial line at the same distance, (c) kinetic energy then E1 equals E2 (d) electrostatic energy

ELECTROSTATICS   15 154. Which of the following does not represent 161. The dielectric constant of a metal is correct expression for the work done in (a) 0 (b) 1 charging a capacitor? Here symbols have (c) – 1 (d) infinity their usual meanings. 162. The ratio of electric force between two protons (a) E = 1 CV 2 (b) E = 1 QV to the gravitational force between then is of 2 2 the order of (c) E = 1 Q2 (d) E = 1 QCV 2 (a) 1 (b) 1024 2 C 2 (c) 1036 (d) 1042 155. Electric force per unit area on the surface of a 163. A bird sitting on a high power line charged conductor is (s is surface density of charge) (a) gets killed instantly s2 s2 (b) gets a mild shock (a) ∈0 (b) 2 ∈0 s2 2s2 (c) is not affected practically (c) 2∈0 (d) ∈0 (d) gets a fatal shock 156. When a conductor is placed in an external 164. Two electrons are separated by a distance r electric field net electric field in the interior of metre and have a coulomb force F. Two alpha a conductor is particles separated by 2r metre will have a force equal to (a) F (b) 2F (a) infinity (b) unity F 2F (c) 2 (d) (c) very high (d) zero 157. The ratio of charge given to a capacitor and 165. SI unit of electric permittivity is the potential to which it is raised is called its (a) Nm2C– 2 (b) Am– 1 (a) resistance (c) NC– 1 (d) N– 1 m– 2 C2 (b) conductance 166. Each of the two point charges are doubled and their distance is halved. Force of interaction (c) capacitance becomes n times where n is (d) electric intensity 158. Electric field due to a point charge at its own (a) 8 (b) 16 location is 11 (a) unity (b) infinity (c) 16 (d) 8 (c) zero (d) cannot say 167. In the figure, the charge on 3 mF capacitor is 159. Coulomb’s law is valid for only 2 mF 3 mF 6 mF (a) point charges (b) distances greater than 10–15 m (c) big charges (d) both (a) and (b) +– 160. Given that Q1 + Q2 = Q. 10 V For what ratio Q1 will the force between Q1 (a) 5 mC (b) 8 mC Q (c) 10 mC (d) 12 mC 168. Taking earth to be a metallic sphere, its and Q2 be maximum? capacity will approximately be 11 (a) 6.4 × 106 F (b) 700 F (a) 4 (b) 2 (c) 700 mF (d) 700 pF (c) 2 (d) 1

16 PHYSICS 169. The equivalent capacitance between P and Q 173. A thin metal plate M is inserted between the in the given figure is plates of a parallel plate capacitor or shown in figure. The new capacitance in terms of initial 3 mF capacitance C is 6 mF 6 mF P Q M 3 mF (a) C (b) 2C (a) 13.5 mF (b) 2 mF (c) C (d) infinity (c) 4 mF (d) 6 mF 2 170. In the given network, the equivalent 174. In the given figure, the net force on q1, is zero, capacitance of the network between B and q1 D is then the value of q will be B 1 mF 1 mF q1 q 1 mF1 mF A 1 mF C a D q a q1 (a) 1 mF (b) 3 mF (a) 2 (b) 2 2 (c) 2 mF (d) 5 mF 11 (c) 2 2 (d) 2 171. When a dielectric is introduced between two 175. Two point charges + 2 C and + 6 C repel each parallel plates of a capacitor, the lines of force are correctly shown in other with a force of 12 N. If a charge of –4 C is given to each of these charges, the +Q –Q +Q –Q force now is (a) (b) (a) zero (b) 4 N attractive (c) 4 N repulsive (d) 12 N attractive +Q –Q +Q –Q 176. Putting a dielectric substance between two plates of a condenser, the capacity, potential (c) (d) and potential energy respectively (a) increases, decreases, decreases (b) decreases, increases, increases 172. How many capacitors each of 8 mF and 250 V (c) increases, increases, increases are required to form a composite capacitors of 16 mF and 1 kV? (d) decreases, decreases, decreases (a) 32 (b) 24 177. An electron is moving round the nucleus of a hydrogen atom in circular orbit of radius r. (c) 16 (d) 8 → The coulomb force F between the two is

ELECTROSTATICS   17 (a) K e2 rˆ (b) − K e2 → (a) connecting all of them in series r2 r3 r (b) connecting all of them in parallel (c) −K e2 rˆ (d) K e2 → (c) connecting two in series and one in r3 r2 parallel r (d) connecting two in parallel and one in 178. Three capacitors, each of capacity 4 mF are to series be connected in such a way that the effective capacitance is 6 mF. This can be done by CASE BASED QUESTIONS Case Study–1 5. In the above question, the transfer of mass Read the following passage and answer the from wool to polythene is questions that follow: (a) 1.6 × 10–18 kg (b) 1.8 × 10–19 kg Amit was a science teacher. He thought of an interesting science experiment. He combed his dry (c) 1.8 × 10–18 kg (d) 1.6 × 10–19 kg hair with a plastic comb. The comb could now attract small pieces of paper. The children were very surprised Case Study–2 at this. They asked Amit to explain the ability of the Read the following passage and answer the comb to attract pieces of paper. Amit explained that questions that follow: there is no magic in this. Amit explained the concept to frictional electricity. The children were very happy When a physical quantity such as an electric to receive the scientific knowledge. charge exists in discrete “Packets” rather than in 1. What kind of charge is produced when a glass continuous amount, it is said to be quantised. rod is rubbed with silk? The fact that all observable charges are always some integral multiples of elementary charge (a) Negative charge e (= ± 1.6 × 10–19 C) is known as quantisation of charge. (b) Positive charge Any charge q, no matter what is its origin, is given by : (c) Neutral    q = ± ne,     where n = 1, 2, 3, ...... (d) None of these The lowest possible charge e is the magnitude of charge of an electron. It is also equal to the charge of 2. What is the value of charge on a body that a proton. carries 30 excess electrons? A charge q equal to, say, 1.735e or – 507.9e or 2 e is an impossibility. (a) –1.6 × 10–18 C (b) –3.2 × 10–18 C 1. When electrons are added to an uncharged (c) –4.8 × 10–18 C (d) None of these body, then the body 3. Is a charge of 8.4 × 10–18 C possible? (a) gets negatively charged (a) Yes (b) gets positively charged (b) No (c) remains uncharged (c) Can not be decided (d) gets negatively or positively charged depending upon its size. (d) May or may not be 2. Quantisation of charge implies that 4. A polythene piece rubbed with wool is found to have a negative charge of (a) charge does not exist 3.2 × 10–7 C. Estimate the number of electrons transferred from wool to polythene ? (b) charge exists on particles (a) 2 × 1012 (b) 3 × 1012 (c) there is a minimum permissible magnitude of charge (c) 4 × 1012 (d) 5 × 1012 (d) charge can’t be created.

18 PHYSICS 3. How many electronic charges form one 3. Two positively charged ions carrying coulomb of charge ? equal charges repel each other by a force 3.7 × 10–9 N when separated by a distance (a) 6.25 × 1019 (b) 0.625 × 1019 5 Å from each other. How many electrons are missing from each ion ? (c) 1.6 × 1019 (d) none of these 4. Estimate the negative charge possessed by the (a) 1 (b) 2 number of free electrons in 10 g of water. Given: Avogadro’s number = 6.02 × 1023 and molecular (c) 3 (d) 4 weight of water = 18. 4. Force of attraction between two point charges (a) 5.35 × 105 C (b) 5.35 × 106 C placed at a distance d is F. What distance apart should they be kept in the same medium so (c) 3.344 × 104 C (d) none of these F that the force between them is 3 ? 5. If a body gives out 109 electrons every second, how much time is required to get a total charge (a) 1.2 d (b) 1.532 d of 1 C from it ? (c) 1.732 d (d) none of these (a) 189.2 years (b) 180 years 5. A charge of magnitude Q is divided into two (c) 196 years (d) 198.2 years parts q and (Q – q) such that the two parts exert maximum force on each other. The value Case Study–3 Q of ratio q is Read the following passage and answer the questions that follow: Coulomb’s law applies to stationary point (a) 1 (b) 2 charges. (c) 3 (d) 4 In an experiment, two point charges q1 and q2 Case Study–4 separated by a distance r and F be the electrostatic force between these two charges. Read the following passage and answer the questions that follow: According to Coulomb’s law, The given figure shows a single isolated positive (i) F ∝ q1q2    (ii) F ∝ 1 point charge q at the origin O and r is the distance of r2 P from O. The electric potential at P will be equal to the work done in bringing a unit positive charge from Combining, F ∝ q1q2 infinity to P. r2 or    F = k q1q2 q dx q0 r2 + PB A F O ¥ where k is a positive constant of proportionality called r electrostatic force constant or Coulomb constant. x 1. The dimensional representation of e0 will be (a) [MLT2A2] (b) [M–1L–3T4A2] When a test charge q0 is placed at point A and if x be the distance of A from O then by Coulomb’s law, (c) [ML–2T2A–2] (d) none of these the electrostatic force on charge q0 is given by 2. A charge of 2 C is placed at the top of your F = 4π1ε0 qq0 x2 school building and another equal charge at the top of your house. Take the separation between the two charges to be 2 km. How many Also the work done in bringing a unit positive test kilo‑newton of force is exerted by the charges charge from infinity to P gives the electric potential V on each other ? at P is (a) 4 kN (b) 4.8 kN V = 4π1ε0 q r (c) 5.8 kN (d) none of these

ELECTROSTATICS   19 Clearly, V ∝ 1 . The electric potential due to a It positive sign is assign to the electric field r pointing from left to right and negative sign to the electric field pointing from right to left, then point charge is spherically symmetric. In region I, the net electric field is given by 1. The minimum amount of charge observed so far is EI = E1 + E2 = – 1 (s1 + s2) 2ε0 (a) 1 C (b) 4.8 × 10–3 C (c) 1.6 × 10–19 C (d) 1.6 × 10–9 C In region II,   EII = E1 – E2 2. The charge on a particle is q and V is the = 21ε0 (s1 – s2) potential difference between two points, then qV represents the magnitude of In region III,  EIII = E1 + E2 (a) momentum (b) power 1 2ε0 (c) force (d) energy = (s1 + s2) 3. Find the electric potential at the surface of 1. I f s1 = s and s2 = – s, then EI = 0, EIII = 0, then the a gold nucleus. Given : radius of nucleus value of EII will be = 6.6 × 10–15 m and atomic number of gold = 79. (a) 0 (b) 1 (a) 1.6 × 106 V (b) 1.7 × 107 V (c) σ (d) σ (c) 1.5 × 107 V (d) none of these 2ε0 ε0 4. Calculate the potential at a point P due to a 2. The electric field strength at a point varies as 1/r charge of 4 × 10–7 C located 0.09 m away. for a/an: (a) 1.5 × 104 V (b) 2.0 × 104 V (a) point charge (b) electric pole (c) 3.5 × 104 V (d) 4.0 × 104 V (c) plane infinite sheet of charge 5. The electric field at a point due to a point charge is (d) line charge of infinite length 20 N C –1 and the electric potential at that point is 10 J C–1. Calculate the magnitude of the charge. 3. Figure below shows portions of two large sheets (a) 5.56 × 10–9 C (b) 4.56 × 10–10 C of charge with uniform surface charge densities of s+ = + 6.8 mC m–2 and s– = – 4.3 mC m–2. The (c) 5.56 × 10–10 C (d) 4.56 × 10–9 C electric field to the left of the sheets is Case Study–5 s+   s– Read the following passage and answer the +   – questions that follow: +   – In an experiment, two infinite plane parallel sheets of charge A and B are shown in figure below. +   – s1 and s2 be the uniform surface densities of charge on A and B respectively, where s1 > s2. +   – +   – + E2 L +    C   –   R E1 + ++ +   – III ++ E2 E1 + s2 + +   – II ++ E2 + s1 + +   – E1 + + ++ +   – I + B (a) 1.4 × 105 N C–1 towards left ++ + (b) 6.3 × 105 N C–1 towards right A (c) 2.4 × 105 N C–1 towards left (d) none of these

20 PHYSICS 4. In question 3, the electric field between the (c) Because Munish could damage the sheets is capacitor as be was an unexperienced person. (a) 6.3 × 105 NC–1  t owards left (d) none of these (b) 6.8 × 104 NC–1  towards left 3. The combined capacitance of the arrangement (c) 6.3 × 105 NC–1 towards right shown in figure given below in µF, is (d) 1.4 × 105 NC–1 towards right 2 µF 5. In question 3, the electric field to the right of the 6 µF 3 µF sheets is (a) 1 (b) (a) 1.4 × 104 NC–1  towards right (c) 4 (d) 11 (b) 1.4 × 104 NC–1  towards left 4. The capacitance of a parallel plate capacitor (c) 1.4 × 105 NC–1 towards right depends on (d) 1.4 × 105 NC–1 towards left (a) the type of metal used Case Study–6 (b) the thickness of the plates Read the following passage and answer the questions that follow: (c) the potential applied across the plates Munish did not have any practical training of (d) the separation between the plates electricity repair but he always to carry out electricity repair with great enthusiasm. One day the ceiling fan 5. The graph shows the variation of voltage ‘V’ was not working. Munish immediately declared that across the plates of two capacitors Aand B versus the condenser used in the fan has a problem. So he increase of charge ‘Q’ stored on them, Which of decided to check the condenser but his elder brother the two capacitors has higher capacitance ? Neeraj stopped him from touching the condenser. Neeraj told him to wait for at least one hour after the B fan is switched off. Munish argued that the fan is not working and therefore switching off the fan has no VA meaning. Neeraj insisted that he would not touch the condenser immediately after switching off the fan. Q Munish reluctantly agreed. (a) Capacitor A 1. The dimensional formula of capacitance is (b) Capacitor B (c) Both capacitor will have same (a) [ML2T2A–2] (b) [M–1L–2T2A2] capacitance (c) [M–1L–2T4A2] (d) [M–1L2T4A2] (d) None of these 2. Why Neeraj Stopped Munish from touching the condenser ? (a) Because Munish is likely to experience a mild shock. (b) Because Munish is likely to remain unaffected

Unit 4 Electromagnetic Induction and Alternating Currents MULTIPLE CHOICE QUESTIONS Tick (3) the most appropriate choice amongst (a) magnetic flux the following: (b) rate of change of magnetic flux 1. 1 henry is equal to (c) 1 velocity of the rod (a) weber (b) weber ampere volt 1 (d) magnitude of the magnetic field (c) weber ampere (d) none of the above 4. Which of the following is not a part of an AC 2. Two coils are placed closed to each other as generator? shown in figure. When the key is pressed, a current flows in the secondary coil along d a b (a) armature c. What is the direction and magnitude of the current when the key K is removed? (b) field magnet (a) No current flows in the coil S. (c) split ring (commutator) (b) The magnitude of current is lower and (d) brushes the direction is reversed. 5. Which of the following is in accordance with (c) The magnitude of current is greater and the law of conservation of energy? the direction is reversed. (a) Lenz’s law (b) Faraday’s law (d) None of the above. (c) Biot Savart law (d) Ampere’s theorem 3. An aluminium rod is moved in a magnetic field. The charge developed across its ends in 6. A proton and an electron are moving (with proportional to equal velocity) parallel to each other in a magnetic field. The magnetic force acting on the electron is (a) 1/1840 times that on the proton (b) less than that on the proton (c) 1840 times that on the proton (d) same as that on the proton 7. Which of the following is used to determine the direction of the induced current in a generator? 57

58 PHYSICS (a) Fleming’s left-hand rule 14. The average value of AC over a complete cycle is (b) Fleming’s right-hand rule (c) Maxwell’s cork screw rule (a) I0 (b) I0 2 (d) Ampere’s swimming rule 8. In which of the following does the current (c) I0 (d) zero drawn from the device not vary in magnitude? 2 (a) dynamo (b) cell 15. The form factor for AC is about (a) 1.1 (b) (1.1)2 (c) induction coil (d) transformer 9. The magnetic flux (f) linked with a coil is (c) 1 (d) 1 related to the number of turns (N) of the coil as 1.1 (1.1)2 (a) f ∝ N (b) f ∝ N–1 16. In a purely inductive circuit, the current lags behind voltage by (c) f ∝ N2 (d) f ∝ N–2 10. If the magnetic flux linked with a coil through (a) p (b) 2 p which a current of I ampere is set up is f, then the coefficient of self inductance of the coil is, (c) p (d) 3p 2 2 (a) I (b) f 17. If f is the angle of lead or lag, the power factor f I is given by (c) f I (d) none of these R Z 11. Which of the following is independent of the (a) cos f = Z (b) cos f = R direction of the current in a circuit? Z R (a) Electrolysis (c) tan f = R (d) tan f = Z (b) Joule’s heating 18. The effective value of AC in a circuit is 10 A. The peak value of current is (c) Mutual induction (d) all the above (a) 5 A (b) 0.707 A 12. The turn ratio of a transformer is 10 : 1. If (c) 10 A (d) 14.14 A current in the primary is 4 A, what is the current in the secondary? 19. When an electric device X is connected to an AC voltage, the current through it is in the same 4A phase as the applied voltage. What is X? (a) a resistor (b) an inductor Output (c) a capacitor (d) none of these 2V 20. An alternating current is given as I = I0 sin cot. The average value of current over a half cycle is (a) 400 A (b) 1 A (a) zero (b) I0 (c) 100 A 25 2 (d) zero (c) 2I0 (d) I0 p 2 13. In the above questions, what is the emf of the secondary? 21. Eddy currents do not cause (a) 200 V (b) 1 V (a) sparking (b) damping 50 (c) heating (d) loss of energy (c) 20 V (d) zero

Electromagnetic Induction and Alternating Currents   59 22. When the number of turns of a coil is doubled, (a) Ohm (b) Faraday its self inductance (c) Lenz (d) Henry (a) is halved 28. The magnetic flux linked with a coil is (b) becomes eight times inversely proportional to the (c) becomes one quarter (a) magnetic field (d) none of the above (b) area of cross-section 23. A movable wire XY sliding to the right in (c) number of turns the presence of a uniform magnetic field induces an (d) none of the above anticlockwise current as 29. The expression for the induced emf has a shown in figure. Which amongst the following negative sign  E = df  . What does the is a possible direction of  dt  magnetic induction in the region P? negative sign signify? (a) Downward into the paper (a) The induced emf is produced only when the magnetic flux decreases. (b) To the right (b) The induced emf opposes the changes in (c) To the left magnetic flux (d) Upwards perpendicular to the paper (c) The induced emf always decreases (d) none of these 24. A rectangular coil ABCD 30. The induced emf in a coil rotating in a lying flat on a table magnetic field is maximum when the angle moves towards a current between the plane of the coil and the direction carrying conductor PQ, of the field is which is also lying on the table and is parallel to side AD along the (a) 0° (b) 45° direction shown in figure. The direction of the induced current in the coils is (c) 90° (d) 135° 31. Which of the following is a scalar quantity? (a) Electric intensity (a) clockwise (b) anticlockwise (b) Magnetic Lorentz force (c) current will not be induced (c) Magnetic flux density (d) undecided (d) Magnetic flux 25. Whenever the flux linked with a circuit 32. A magnet is allowed to fall through a metal changes, there is an induced emf in the circuit. ring. Its acceleration (a), during the fall is This emf would last in the circuit. (a) a < g (b) a > g (a) for a very short time (c) a = g (d) a = 0 (b) for a very long time (c) for a moderate time 33. The north pole of a bar magnet is rapidly (d) none of these introduced into a solenoid from its end P. 26. What generates the restoring tendency in the Which of the following statements correctly depicts the phenomenon taking place? LC circuit? (a) No induced emf is set up (a) capacitor (b) inductor (c) battery (d) none of these (b) The end P of the solenoid behaves like a north pole. 27. Which one of the following scientist is not connected with the theory of electromagnetic (c) The end P of the solenoid behaves like a induction? south pole. (d) none of the above

60 PHYSICS 34. Which of the following instruments does not (a) (b) make use of eddy currents? (c) (d) (a) electrical brakes (b) induction motor 40. The dimensional formula of induced emf is (c) transformer (a) [ML2 T–2 A–1] (b) [ML2 T–3 A–1] (d) dead beat galvanometer (c) [ML2 T–3 A–2] (d) [ML2 T–2 A–2] 35. The induction furnace makes use of 41. The motional emf produced across a wire (a) self-induction (b) mutual induction moving through a magnetic field does not (c) eddy currents (d) all of the above depend on its 36. For long distance transmission, the AC is (a) length (b) composition stepped up because transmission at high (c) orientation (d) diameter voltage is 42. Which of the following helps in the operation (a) economical (b) faster of a choke coil? (a) eddy currents (c) not damped (d) not dangerous (b) self-induction (c) mutual induction 37. The current in the armature of a DC motor is (d) none of the above maximum when the motor is 43. The instantaneous current in a circuit is given (a) switched on by I = 2 sin (100 pt + p/4) ampere (b) switched off (c) running at full speed What is the rms current? (d) all the above 38. In the circuit shown in figure, the key K is plugged at time t = 0. Which one of the graphs shown in the figure represents variation of current I in the circuit with time t? (a) 1 A (b) 2 A (a) (b) (c) 1 A (d) zero 2 44. Which of the following increases the efficiency of a transformer? (a) high voltage (b) sinusoidal nature of AC (c) (d) (c) absence of moving parts (d) none of these 39. Which one of the graphs shown in the figure 45. The magnetic flux linked with a coil varies represents the variation of voltage V across with time, given by f = (2t2 + t + 5) weber the inductor L with time t? What is the induced emf at t = 1s? (a) 5 V (b) 4 V (c) 3 V (d) zero

Electromagnetic Induction and Alternating Currents   61 46. The average power dissipated in a choke coil for a complete cycle is (a) zero (b) nearly zero (a) S (b) N (c) I02wL (d) I2rms wL (c) P (d) Q 47. The Q factor of an LCR circuit at resonance is 52. An electron moves on a straight line path PQ as (a) R2 + w2L2 (b) R2 +  Lw − 1 2 shown in figure, the coil a b c d is kept adjacent to  Cw  the path of the electron. What will be the direction of current, if any, induced in the coil? (c) wr L (d) R2 + 1 R C 2 w2 48. An inductor L and a resistance R are connected in series to an AC emf source. The admittance of the circuit is (a) R2 + w2L2 (b) 1 R2 + w2L2 wL (a) along a b c d R (c) (d) w LR (b) along a d c b 49. An AC source of frequency f is connected to an (c) no current LCR circuit. Which graph in figure represents the variation of current I with frequency f? (d) nothing can be decided (a) (b) 53. A bulb and an inductor are connected in series to a steady voltage in a circuit. When the key in the circuit is switched off, the intensity of light of the bulb will become (a) gradually zero (b) immediately zero (c) very high before becoming zero (d) undecided (c) (d) 54. A coil and a bulb are connected in series with a 3 V battery. When a soft iron core is inserted in the coil, the intensity of the bulb (a) increases 50. For perfect coupling of two coils of inductances (b) decreases L1 and L2, their mutual inductance M should (c) remains the same be (d) undecided L1 (a) L1 L2 (b) L2 55. The dimensional formula L/R is similar to that of (c) L2 (d) L1 L2 (a) frequency (b) time L1 (c) length (d) none of these 51. Figure shows a straight thick wire placed 56. A conducting square loop PQRS of side l and between the pole pieces of a magnet. An resistance r moves in a plane with a uniform induced emf will be set up across the ends of velocity v perpendicular to one of its sides. the wire, when it is moved towards A magnetic field B, constant in time and

62 PHYSICS space, pointing perpendicular and into the 63. The hot wire instruments measure plane of the square loop exists everywhere. Then the current induced in the square (a) peak voltage (b) average voltage loop is (c) rms voltage (d) none of the above 64. The reading of an AC voltmeter is 200 V. What is the peak voltage. (a) 200 V (b) 200 V 2 (a) Blv clockwise (b) Blv anticlockwise (c) 2 × 200 V (d) none of these r r 65. A hot wire ammeter reads 5 A in an AC circuit. The peak value of current is (c) zero (d) infinite (a) 5 2 A (b) 5 A 2 57. If R, C and L denote resistance, capacitance (c) 5 A (d) none of these and inductance respectively, then which of the following does not have the dimensions 66. If the frequency of AC is 50 Hz, how many of frequency? times in one second does the voltage in the circuit become zero? (a) R (b) 1 (a) 25 (b) 50 L RC (c) 100 (d) 150 (c) 1 (d) R 67. Which of the following converts AC to DC? LC CL (a) rectifier (b) transformer 58. An iron core decreases the loss in energy due (c) generator (d) none of the above to 68. In an AC circuit, the capacitive reactance (a) flux leakage (b) eddy currents equals the inductive reactance. The phase difference between the current and the (c) heating (d) hysteresis voltage will be 59. The power factor varies between (a) 0° (b) 45° (a) 0 and 0.5 (b) 0 and 1 (c) 90° (d) 135° (c) 1 and 1.5 (d) 0.5 and 1 69. The core of the transformer is laminated to avoid loss in energy due to 60. What is the average power dissipated in an inductance L when the current through it is I? (a) heating (b) flux leakage (a) 1 LI 2 (b) LI2 (c) eddy currents (d) all of the above 2 70. The transformer varies 1 (c) zero (d) 2 LI (a) current (b) power (c) energy (d) frequency 61. The alternating current in an LCR circuit is 71. Which of the following is independent of the maximum when frequency of AC? (a) XL = 0 (b) XC = 0 (a) resistance (c) XL = XC (d) XL2 + XC2 =1 (b) impedance (c) inductive reactance 62. How wire ammeters can measure (d) capacitive reactance (a) only AC 72. The choke coil of resistance R and inductance L is connected across a battery of emf E. The (b) only DC final current in the choke depends on (c) both AC and DC (a) R and L (b) L and E (d) neither AC nor DC (c) E and R (d) R, L and E

Electromagnetic Induction and Alternating Currents   63 73. Which one of the following represents the 76. Which of the following does not cause any variation between XL and frequency (f) of an loss of energy in a transformer. AC? (a) heating (a) (b) (b) eddy current (c) (d) (c) mechanical motion 74. Which one of the following represents the variation between XC and frequency (f) of an (d) hysteresis AC? 77. How does the current in an RC circuit vary when the charge on the capacitor builds up? (a) decreases linearly (b) increases linearly (c) decreases exponentially (d) increases exponentially 78. For the circuit in figure, the growth of charge with time is shown. Which of the graphs below, represents the corresponding variation of current with time? (a) (b) (c) (d) (i) (ii) (a) (b) 75. For the circuit in figure, the growth and decay of current with time are best depicted by (c) (d) 79. For high frequency, a capacitor offers (a) (b) (a) infinite resistance (c) (d) (b) more resistance (c) zero resistance (d) lesser resistance 80. A transformer is used to light a 100 W, 110 V lamp from a 220 V supply. If the supply current is 0.5 A, the efficiency of the transformer is (a) 30% (b) 50% (c) 80% (d) 90%

64 PHYSICS 81. A pair of slip rings is used in Which of the following graphs gives the variation of voltage with time? (a) AC generator (b) AC motor (c) DC motor (d) DC generator (a) (b) 82. A DC circuit contains 10 W resistance in series with 10 H coil. The impedance of the circuit is (a) 10 W (b) 20 W (c) 1 W (d) zero (c) (d) 83. A motor starter is a (a) fixed resistance (b) variable resistance (c) fixed capacitor 87. When the frequency of AC is doubled, the impedance of an LCR circuit. (d) variable capacitor 84. The current I flows through a coil of N turns. (a) is halved The magnetic flux linked with the coil (of inductance L) is (b) is doubled (c) increases (a) LI (b) NLI (d) first decreases then increases (c) N2 LI (d) NI 88. Alternating voltage V = 400 sin (500 pt) is L applied across the resistance 0.2 kW. The r.m.s. value of current is equal to 85. In figure below, the final value of current in 10 W resistor, when plug of key K is inserted (a) 14.14 A (b) 1.414 A will be (c) 0.1414 A (d) 2.0 A 89. Power factor is unity for a/an (a) pure inductor (b) pure capacitor (c) pure resistor (d) inductor and a capacitor 90. The average value of current in AC over a (a) 3 A (b) 3 A complete cycle is (I0 is max. value of current) 10 11 (a) I0 (b) 2I0 3 p 20 (c) A (d) zero (c) I0 (d) zero 2 86. The alternating current I in an inductance coil varies with time according to the graph in 91. The resonant frequency of a circuit is f. If the figure below. capacitance is made four times the initial value, then the resonant frequency will becomes (a) f (b) 2f 2 (c) 3f (d) f 4

Electromagnetic Induction and Alternating Currents   65 92. Weber/m2 is equal to 100. A copper ring having a cut such as not to form a complete loop is held horizontally and a bar (a) volt (b) henry magnet is dropped through the ring with its length along the axis (c) tesla (d) none of these of the ring. The acceleration of the falling magnet is (in terms of 93. One tesla equals X gauss. Then the value of X is acceleration due to gravity g) (a) 104 (b) 10–4 (a) g (b) < g (c) 107 (d) 10–7 (c) > g (d) zero 94. Len’s law is a consequence of law of 101. The current from P to Q is increasing in magnitude. What is the direction of induced conservation of current, if any, in the loop shown as follows? (a) energy (b) mass (a) clockwise current (b) anticlockwise current (c) charge (d) momentum (c) no current is induced (d) alternating current 95. The ratio of SI units to CGS units of magnetic 102. The direction of induced emf in a coil is given by field strength is (a) Faraday’s laws (b) Lenz’s law (a) 107 (b) 105 (c) Fleming’s left hand rule (c) 104 (d) 10–7 (d) Newton’s 3rd law of motion 103. An inductor may store energy in a/an 96. A capacitor of capacity C has reactance X. If (a) electric field (b) magnetic field (c) both (a) and (b) (d) neither (a)nor (b) frequency and capacitance become double, 104. When the rate of change of current passing then reactance will be through a circuit is unity, then induced e.m.f. is equal to (a) X (b) X (a) thickness of a coil 4 2 (b) number of turns in a coil (c) coefficient of self induction (c) 2X (d) 4X (d) total flux linked with a coil 105. If N is number of turns in a coil, the value of 97. For a coil having L = 2 mH, current flows at self inductance varies as the rate of 1 mA s–1. The magnitude of e.m.f. (a) N–2 (b) N2 (c) N (d) N0 induced is 106. The total charge induced in a conducting loop when it is moved in a magnetic field depends on (a) 1 V (b) 2 µV (a) rate of change of magnetic flux (b) initial magnetic flux only (c) 3 V (d) zero (c) total change in magnetic flux and 98. The power factor of an AC circuit having resistance (d) final magnetic flux only resistance R and inductance L connected in series to an AC source of angular frequency w is (a) wL (b) R R wL (c) R (d) none of these R2 + wL 99. The inductance between P and Q is (a) 6 H (b) 2 H 3 (c) 3 H (d) zero 2

66 PHYSICS 107. Who discovered that electric field is produced 115. The equivalent quantity of mass in electricity is in a conductor when magnetic lines of force intercepting it change? (a) charge (b) current (a) Maxwell (b) Oersted (c) coefficient of self inductance (c) Lenz (d) Faraday (d) potential 108. The current passing through a choke coil of 116. In an oscillating system, a restoring force is a 5 H is decreasing at the rate of 2 As–1. The must. But in an LC circuit, restoring force is provide by a/an e.m.f. developed across the coil is (a) + 10 V (b) – 10 V (a) capacitance (b) inductance (c) – 2.5 V (d) + 2.5 V (c) resistance (d) impedance 109. Two pure inductors, each of self inductance L, 117. What is the ratio of inductive and capacitive are connected in parallel. The total (effective) reactances in an AC circuit? inductance is (a) 1 (b) zero L (c) w2L (d) w2LC 2 (a) L (b) 118. Power dissipation in R-L-C circuit is directly proportional to L (c) 2L (d) 4 (a) Z (b) R (c) L (d) C 110. Self induction can be compared to 119. The natural frequency of an L-C circuit is equal to (a) energy (b) force (c) inertia (d) power (a) 1 (b) LC 2π LC 2π 111. If R is resistance and L is coefficient of self induction, then R has the dimensions of (c) C (d) L L (a) time (b) mass 2π L 2π C (c) length (d) frequency 120. The potential difference V and current I flowing through an instrument in an AC 112. A choke coil is used with an arc lamp circuit are given by (a) to increase the voltage (b) to increase the current V = 4 cos wt (volt) (c) to limit the current without much power I = 3 sin wt (ampere) loss The power dissipated in the instrument is (d) to limit the resistance without power (a) 215 W (b) 10 W loss (c) 5 W (d) zero 113. The equivalent quantity of force in electricity is (a) charge 121. An AC series circuit contains 8 W of resistance and 6 W of inductive reactance. Then the (b) potential impedance of the circuit is (c) inductance (a) 2 W (b) 10 W (d) current 114. The momentum in mechanics is expressed as (c) 14 W (d) 18 W mv. The analogous expression in electricity is (symbols have their usual meanings) 122. Which of the following effects can’t be shown by alternating current? (a) IV (b) IQ (a) chemical effect (b) heating effect (c) IL (d) LQ (c) magnetic effect (d) all of these

Electromagnetic Induction and Alternating Currents   67 123. The power factor is unity for 130. The power loss in a transformer working on (a) pure resistor 220 V AC supply is 30%. The ratio of primary (b) pure inductor to secondary current when output voltage is (c) pure capacitor 110 V will be (d) an inductor and a capacitor (a) 1 : 2 (b) 2 : 1 124. The average value of AC over a complete (c) 3 : 5 (d) 5 : 7 cycle is (symbols have their usual meanings) 131. The ratio of number of turns is primary and secondary coils of transformer is 1 : 10. Then (a) zero (b) 2I0 the ratio of currents in primary and secondary π coils will be (c) 2 I0 (d) r0 (a) 1 : 10 (b) 10 : 1 π (c) 1 : 100 (d) 100 : 1 125. An increase in the resonant frequency can be brought about by 132. In a circuit containing an inductance of zero resistance, the current leads the applied AC (a) decreasing R voltage by a phase angle of (b) increasing R (a) 0° (b) 90° (c) decreasing L (c) – 90° (d) – 180° (d) increasing L 133. The dimensions of coefficient of mutual inductance is 126. An A.C. circuit contains 4 W resistance in series with an inductance coil of reactance (a) [MLT–2 A–1] (b) [ML2T–2A–1] 3 W. Then the impedance of the circuit is (c) [ML2 T–2A–2] (d) [M0L0T0A0] 1 (a) 5 W (b) 3 Ω 134. The average power dissipation in a pure capacitive AC circuit is (c) 7 W (d) 1 W (a) 1 CV2 (b) CV2 127. An AC ammeter connected in series in an 2 AC circuit reads 5 A. Then the peak value of current is (c) 2 CV2 (d) zero (a) 5 A (b) 5 A 135. A series LCR circuit is tuned to resonance. 2 The impedance of the circuit now is 10  2 1/ 2 π R2   (c) 5 2 A (d) A (a)  +  ωL − 1   Cω 128. The reactance of a capacitor of 1 farad at  1 1/2 π  (ωC  (b) R2 + (ωL)2 +  50 Hz is )2  (a) 10 W (b) 10–1 W (c) 10–2 W (d) 100 W (c)  R + ωL − 1 2  ωC  129. In an LCR circuit, the inductance is changed from L to L . In order to keep the same (d) R 2 136. If a half wave rectifier is used to convert resonance frequency, C should be changed to 50 Hz AC into DC, then the number of pulses present in rectified voltage is (a) 2 C (b) C 2 (a) 25 (b) 50 (c) 4 C (d) C (c) 75 (d) 100 4

68 PHYSICS 137. The power factor of a series LCR circuit at 144. A transformer works on the principle of resonance is (a) inverter (b) rectifier (a) 1 (b) 1 (c) mutual induction (c) 2 2 (d) zero (d) self induction 138. What will be the phase difference between 145. The best material for the core of a transformer virtual voltage and virtual current, when the is current in the circuit is wattless? (a) soft iron (b) hard steel (a) 45° (b) 90° (c) stainless steel (d) none of these (c) 120° (d) 180° 146. The phase difference between the current and 139. In a choke coil, the reactance XL and resistance voltage at resonance is R are such that (a) 0° (b) 90° (a) XL = R (b) XL >> R (c) XL << R (d) XL = ∞ (c) 180° (d) – 90° 140. In the circuit shown in figure, what will be the 147. The quantity that remains unchanged in a reading of the voltmeter? transformer is (a) 200 V (b) 300 V (a) frequency (b) current (c) 400 V (d) 900 V (c) voltage (d) all the above 148. Which of the following quantities is increased in a step-down transformer? (a) frequency (b) current (c) voltage (d) power 141. Which of the following graphs correctly 149. In instantaneous magnetic flux (f) in a circuit represents the variation of capacitative is given by, reactance (XC) with frequency (f)? f = 4t2 – 4t + 3 The total resistance of circuit is 20 W. At t = 0.5 s, the induced current in the circuit is (a) (b) (a) 0.2 A (b) 0.4 A (c) 0.6 A (d) zero 150. In the given LR circuit, if frequency is 100 Hz, the phase angle is π (c) (d) 142. The quantity that remains unchanged in a (a) 30° (b) 45° transformer is (c) 60° (d) 90° (a) voltage (b) current 151. The self inductance of the motor of an electric (c) frequency (d) none of these fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a 143. Which quantity is increased in a step-down capacitance of transformer? (a) current (b) voltage (a) 1 µF (b) 2 µF (c) power (d) frequency (c) 4 µF (d) 8 µF

Electromagnetic Induction and Alternating Currents   69 CASE BASED QUESTIONS Case Study–1 Case Study–2 Read the following passage and answer the Read the following passage and answer the questions that follow: questions that follow: Faraday Cage: Alternating current (ac) is generated in the hilly regions by employing natural falls of water flowing A Faraday cage or in the rivers. In this way, electricity is quite cheaply Faraday shield is an generated at hydroelectric power houses. In the hilly enclosure made of a regions, requirements of electric consumption are less conducting material. The than the cities on the plains where industries are set fields within a conductor up on a large scale. Thus, the electricity is generated cancel out with any external at one place and it is to be consumed at another place fields, so the electric field several hundred kilometre away. within the enclosure is zero. These Faraday cages act as big hollow conductors you can put things in The transmission of electricity is always done at to shield them from electrical fields. Any electrical shocks the cage receives, pass harmlessly around the the highest possible voltage. For small distance, it may outside of the cage. be 11 kV. When the distance is large, the transmission is done at 132 kV. Since this voltage transformation 1. Which of the following material can be used can only be done with transformers, we have to use to make a Faraday cage ? alternating current only. [A transformer is essentially (a) Plastic (b) Glass an ac device]. Thus, all household electricity is (c) Copper (d) Wood 220 volt alternating current. 2. Example of a real-world Faraday cage is 1. An electric bulb is designed to operate at 12 volt dc. If this bulb is connected to an ac (a) car (b) plastic box source and gives normal brightness, what would be the peak value of the source ? (c) lightening rod (d) metal rod 3. What is the electrical force inside a Faraday (a) 15.289 volt (b) 16.832 volt cage when it is struck by lightning ? (c) 16.968 volt (d) none of these (a) The same as the lightning 2. The ac cannot be used for (b) Half that of the lightning (a) heating (b) lighting (c) Zero (c) electrolysis (d) production of mechanical energy (d) A quarter of the lightning 3. If the supply frequency of a transformer 4. An isolated point charge +q is placed inside increases, the secondary output voltage of the the Faraday cage. Its surface must have charge equal to transformers (a) increases (b) decreases (a) zero (b) +q (c) remains the same (d) any of these (c) –q (d) +2q 4. Transformer core are laminated in order to 5. A point charge of 2 µC is placed at centre (a) reduce hysteresis loss of Faraday cage in the shape of cube with surface of 9 cm edge. The number of electric (b) reduce hysteresis and eddy current loss field lines passing through the cube normally will be (c) minimize eddy current loss (d) copper loss (a) 1.96 × 105 Nm2/C entering the surface 5. A power transmission line feeds input power at 2200 V to a step-down transformer with its (b) 1.96 × 105 Nm2/C leaving the surface primary windings having 3000 turns. Find the number of turns in the secondary to get (c) 2.26 × 105 Nm2/C leaving the surface the power output at 220 V. (d) 2.26 × 105 Nm2/C entering the surface (a) 150 (b) 200 (c) 250 (d) 300

Unit 6 Optics MULTIPLE CHOICE QUESTIONS Tick (3) the most appropriate choice amongst (a) p (b) 2p the following: p 1. On reflection from a denser medium, a light (c) 2 (d) zero wave suffers a phase difference of 5. A ray of light travelling in air, is incident (a) p (b) p on a glass slab. The ray gets partly reflected 2 and partly refracted. The phase difference between the reflected and the refracted waves (c) p (d) 2p is 4 (a) p/2 (b) p/4 2. The branch of optics dealing with the formation of images using the concept of (c) p (d) zero straight line propagation of light is called 6. Which of the following is a correct relation (a) geometrical optics between a wave front and a ray of light? A ray of light (b) physical optics (a) is normal to the wavefront (c) corpuscular optics (b) is tangential to the wavefront (d) quantum optics (c) can be inclined at any angle with the 3. Which of the following is not a property of wavefront light? (d) none of these (a) It can travel through vacuum. 7. Which of the following forms a part of the (b) It has a finite speed. electromagnetic spectrum? (c) It involves transportation of energy. (a) alpha rays (b) beta rays (c) gamma rays (d) all the above (d) It requires a material medium for its 8. If q is the polarizing angle, then the refractive propagation. index of the material is 4. Two points P and Q are situated at the same (a) sin q (b) cos q. distance from a source of light but on opposite (c) tan q (d) cot q sides. The phase difference between the light waves passing through P and Q will be 79

80 PHYSICS 9. The angle between the plane of polarization (c) The two sources emit light waves of and the plane of oscillations is different amplitudes. (a) zero (b) p (d) There is no constant phase difference between the waves emitted by the two (c) 2p (d) π 2 sources. 10. What is the nature of the wavefront associated 16. A single slit diffraction pattern is obtained with a parallel beam of light? using a beam of red light. What happens if the red light is replaced by a blue light? (a) plane (b) spherical (a) There is no change in the diffraction pattern. (c) elliptical (d) none of these 11. When light is incident at the polarizing angle, (b) Diffraction fringes become narrower then which of the following is completely and crowded. polarized? (c) Diffraction fringes become broader and (a) refracted light farther apart. (b) reflected light (d) The diffraction pattern disappears. (c) both reflected and refracted light 17. When a polaroid is rotated, the intensity of light does not vary. The incident light may be (d) neither reflected nor refracted light 12. Which of the following generates a plane (a) unpolarised wavefront at very large distance from the source? (b) completely polarized (a) point source (c) partially plane polarized (b) extended source (d) none of the above (c) monochromatic source 18. Out of the following colours, from which can a monochromatic beam not be obtained? (d) none of these (a) green (b) red 13. Which of the following is an absolute constant? (c) blue (d) white (a) refractive index 19. Huygen’s concept of secondary waves is useful in (b) velocity of light in vacuum (a) explaining polarization (c) intensity of light (b) determining the focal length of a lens (d) focal length of a lens (c) geometrical reconstruction of a wave- 14. How is the interference pattern in Young’s front double slit experiment affected if one of the slits, say S1, is covered with a black opaque (d) none of the above paper? 20. A ray of light is incident on a glass slab at (a) The bright fringes become fainter. 60°. The reflected and the refracted rays are found to be mutually perpendicular. Then the (b) The fringe width decreases. refractive index of the glass is (c) There is non-uniform illumination all (a) 1.73 (b) 1.50 over the screen. (d) There is a bright slit but no interference (c) 2.00 (d) 1.64 pattern is obtained. 21. After reflection from a denser medium, the 15. What is the reason for your answer to Q. 14? path difference introduced in a wave is (a) The two sources do not emit light of the (a) zero (b) l same wavelength. (c) λ (d) 2l (b) The two sources emit waves that travel 2 with different speeds.

Optics   81 22. Which of the following is essential for 30. The intensity of the light emerging from the observing diffraction? two slits in Young’s experiment is in the ratio 1 : 4. The ratio of the intensity of the minimum (a) a narrow slit (b) white light to that of the consecutive maximum will be (c) a screen (d) two coherent sources 23. A bright spot at the centre of the geometrical (a) 1 : 4 (b) 1 : 9 shadow of a small circular disc placed in the path of light is due to the phenomenon of (c) 1 : 16 (d) 2 : 3 (a) diffraction (b) interference 31. The interference fringes formed by a thin oil film on water, when seen in the yellow light (c) dispersion (d) polarization of sodium lamp will be 24. If the amplitude ratio of two sources (a) coloured (b) yellow and black producing interference is 3 : 5, the ratio of intensities at the maxima and the minima is (c) green (d) red 32. Interference differs from diffraction in that (a) 16 : 25 (b) 5 : 3 (a) interference minima are perfectly dark while that of diffraction may not be dark (c) 16 : 1 (d) 9 : 25 25. Indicate the colour of light that travels slowest (b) it cannot be observed with white light through glass: (c) unlike diffraction the interference fringes (a) red (b) green are of varying intensity (c) violet (d) yellow (d) all of the above 26. What is the frequency of radio waves 33. If Young’s experiment is performed in water instead of air, then fringe width will corresponding to a 10 m wavelength? (a) 3 × 109 Hz (b) 3.3 × 10–8 Hz (a) shrink (b) enlarge (c) 3 × 107 Hz (d) 3.4 × 10–7 Hz (c) disappear (d) remain the same 27. Approximate limits of the visible spectrum 34. Which of the following is conserved when are: light waves interfere? (a) 1000 to 4000 Å (b) 7000 to 10,000 Å (a) phase (b) intensity (c) 4000 to 7000 Å (d) 20 to 20,000 Å (c) amplitude (d) none of these 28. In Young’s double slit experiment, a maximum 35. In Young’s double slit experiment, a minimum is obtained when the path difference between is obtained when the phase difference of the the interfering waves is (n ∈ I): superposting waves is (n ∈ I): (a) nl (b) nλ (a) np (b)  n + 1  π 2  2  (c) (2n + 1) λ (d) (2n − 1) λ (c) (2n + 1)p (d) zero 2 4 36. The minimum value of the refractive index is (a) zero 29. Two sources of light are said to be coherent (b) 1 when both give out light waves of the same (c) less than 1 but not zero (d) more than 1 (a) amplitude and phase 37. In vacuum, the speed of light depends upon (a) frequency (b) velocity (b) intensity and wavelength (c) wavelength (d) none of the above (c) speed (d) wavelength and a constant phase difference

82 PHYSICS 38. Coherence is a measure of 47. If the sodium light in Young’s double slit experiment is replaced by a red light, the (a) waves being diffracted fringe width will (b) Capability of producing interference by waves (a) decrease (b) increase (c) waves being reflected (c) remain unaffected (d) waves being refracted (d) first increase and then decrease 39. What should be the refractive index of a 48. If Young’s double slit experiment performed completely transparent medium for it to be with an ordinary filament lamp, the fringes visible in vacuum? obtained are (a) 1 (b) less than (a) black and white (c) greater than 1 (d) none of the above (b) no fringe 40. The geometrical path of a ray of light in a (c) coloured with a black central fringe medium of refractive index 2 is 8 units of length. Then the optical path (in units of (d) coloured with a white central fringe length) is 49. In Young’s double slit experiment, the (a) 4 (b) 8 radiations from two coherent sources of intensity I and 4I superpose. The ratio of (c) 16 (d) none of these the intensity at the minimum to that at the maximum is 41. The time taken by light to travel a distance of (a) 1 : 9 (b) 4 : 1 3 × 10–2 m in air is (c) 1 : 4 (d) 2 : 3 (a) 10–8 s (b) 108 s 50. What should be the order of the thickness of (c) 10–10 s (d) 1010 s an oil film on the water surface to enable one to see colours in it? 42. The absolute refractive indices of water and glass are 1.3 and 1.5 respectively. The (a) 1 nm (b) 1 mm refractive index of water w.r.t. glass is (c) 1 mm (d) 1 m (a) 1.3 (b) 1.5 51. The fringe width b of a diffraction pattern and 1.5 1.3 the slit width d are related as (c) 1.5 × 1.3 (d) none of these (a) b ∝ d (b) b ∝ 1 d 43. A beam of light passes from air to glass. How does the speed of light vary? (c) b ∝ d (d) b ∝ 1 d2 (a) decreases (b) increases 52. CV Raman was awarded the Nobel prize for his work associated with which of the (c) remains unchanged following phenomenon of radiations? (d) it may increase or decrease depending (a) scattering (b) diffraction upon the colour (c) interference (d) polarization 44. The velocity of light in vacuum is 3 × 1010 cm s–1. The velocity of light in a medium of m = 1.5 is 53. Light takes 10–10 s to cross a glass slab. What is the thickness of the glass slab? (a) 2 × 1010 cms–1 (b) 4.5 × 1010 cms–1 (a) 2 cm (b) 3 cm (c) 1.5 × 1010 cms–1 (d) none of these 45. The wave theory of light was proposed by (c) 2.5 cm (d) 3.5 cm (a) Huygen (b) Maxwell 54. In Young’s double slit experiment, the central point on the screen is (c) Planck (d) Doppler 46. 1 Å equals (a) bright (a) 10–13 m (c) 1010 km (b) 10–13 km (b) dark (d) 1010 m

Optics   83 (c) first bright and then dark 61. The refractive index of diamond is 2.0, then the velocity of light in diamond is (cms–1) (d) first dark and then bright approximately 55. A phase difference of 5p corresponds to a (a) 6 × 1010 (b) 3 × 1010 path difference (in terms of l) of (c) 2 × 1010 (d) 1.5 × 1010 (a) 5l (b) 10l 62. In the set-up shown in figure, the two slits S1 and S2 are not equidistant from the slits S. (c) 5l/2 (d) 2l Then the central fringe at O is 56. A polaroid produces a strong beam of light which is (a) circularly polarized (b) elliptically polarized S1 S (c) plane polarized O S2 (d) unpolarized 57. A white light is used to illuminate the two (a) always dark slits in Young’s double slit experiment. The (b) always bright separation between the slits is b and the (c) either bright or dark depending on the screen is at a distance d(> b) from the slits. At a point on the screen directly in front of one of position of S the slits, certain wavelengths are missing. The (d) neither dark nor bright missing wavelengths are 63. A beam of light AO is incident on a glass slab (a) b2 , b2 (b) b2 , b2 (m = 1.54) in a direction as shown in figure. d 3d 2d 4d The reflected ray OB is passed through a Nicol prism (N). On rotating the Nicol prism, (c) 2b2 , 4b2 (d) b2 , b2 we find that dd 2d 3d A NB 58. In Young’s double slit experiment, the 7th 33° 33° maximum with wavelength l1 is at a distance d1 and that with wavelength l2 is at a distance O d2. Then d1/d2 is equal to (a) λ2 (b) l1l2 (a) there is no change in intensity λ1 (b) the intensity decreases somewhat but (c) λ1 (d) λ1 rises again λ2 λ2 (c) the intensity is reduced to zero and 59. In Young’s double slit experiment, one slit remains zero is covered with red filter and another slit is covered by green filter, then the interference (d) the intensity gradually reduces to zero pattern will be and then again increases (a) yellow (b) red 64. The variation between fringe width (b) and distance between the slits (d) is correctly shown by (c) green (d) invisible 60. Light of wavelength 7200 Å in air has a b b wavelength in glass (m = 1.5) equal to (a) (b) (a) 7200 Å (b) 4800 Å (c) 10800 Å (d) none of these dd

84 PHYSICS b b 69. What will be the Brewster angle for an airwater interface for yellow light? Given (c) (d) refractive index of water for yellow light = 13.3. d d (a) tan–1 (1.33) 65. Figure below represents the intensity distribution curve for (b) cot–1 (1.33) (c) tan − 1  1   1.33  O (d) sin–1 (1.33) (a) Young’s double slit experiment 70. A man runs towards a plane mirror with (b) diffraction due to a single slit a speed of 3 ms–1. The relative speed of his (c) dispersion of light through a prism image w.r.t. him will be (d) none of these 66. If f is the phase difference between two (a) 3 ms−1 (b) 3 ms–1 2 interfering waves, then the resultant intensity I at any point on the screen due to two coherent (c) 6 ms–1 (d) zero sources in Young’s double slit experiment is (I0 is maximum intensity) 71. The critical angle for water w.r.t. air is q. The (a) I = 4I0 cos2 (f/2) (b) I = I0 cos f angular range in which a fish just below the (c) I = I0 cos2 f (d) I = I0 cos (f/2) water surface can see the objects outside is 67. Figure below represents the intensity distribution curve for (a) q (b) θ 2 O (c) 2q (d) 3θ (a) Young’s double slit experiment 2 (b) single slit diffraction (c) dispersion of white light 72. The maximum intensity produced by two (d) none of these coherent sources of intensity I1 and I2 will be 68. Figure below represents the intensity (a) I1 + I2 distribution curve for (b) I21 + I22 O (c) I1 + I2 + 2 I1 I2 (a) Young’s double slit experiment (d) zero (b) single slit diffraction 73. A ray of light enters from a denser medium (c) diffraction grating (d) none of these into a rarer medium. The speed of light in the rarer medium is twice that in the denser medium. For total internal reflection, the critical angle will be (a) 30° (b) 45° (c) 60° (d) 90° 74. A ray of light is incident from a denser medium on the surface of separation of a rarer medium. The reflected and refracted rays are inclined to each other at 90°. If r is the angle of reflection and r′ be the angle of refraction, then the critical angle is

Optics   85 N (a) 2 m (b) 1 m B A (c) 1 m (d) 4 m X Denser 2 i r medium 79. The critical angle for a medium is 60°. Then 90° Y the refractive index of the medium will be O Rarer (a) 3 (b) 2 r¢ medium (c) 1 (d) 2 C 33 N¢ 80. Which of the following graphs represents the variation of the angle of deviation (D) with (a) sin–1 (tan r) (b) sin–1 (tan r′) the angle of incidence (i)? (c) tan–1 (sin r) (d) tan–1 (sin r′) 75. The correct curve between refractive index (m) D D and wavelength (l) will be (a) (b) mm (a) (b) ii ll D D mm (c) (d) (c) (d) ii ll 81. If dm is the angle of minimum deviation, A is the angle of the prism, then the refractive 76. While finding the focal length of a convex index n of the material of the prism is given lens, a graph was plotted taking l/v along the by y-axis and 1/u along the x-axis. Which of the following graphs correctly represents this (a) n= sin (δm / 2) variation? sin (A / 2) (a) (b) (b) n= sin (A + δm ) / 2 sin (A / 2) (c) n= sin (A + δm ) / 2 cos (A / 2) (c) (d) (d) none of these 82. The focal length of a glass slab is (a) 0 (b) 1 77. The time taken by a ray of light to travel (c) – 1 (d) infinity through a slab of glass of thickness 2 m and 83. The wavelength of a monochromatic light is m = 1.5 will be 5000 Å. Then its wave number (in m–1) is (a) 10–8 s (b) 108 s (a) 2 × 106 (b) 2 × 10–6 (c) 10–8 min (d) infinite (c) 2 × 107 (d) 2 × 104 78. Two lenses of power + 6D and – 4D are placed in contact with each other. The focal length of the combination is

86 PHYSICS 84. The angle of minimum deviation for a prism are then put in contact as shown in figure (c). of m = 1.5 is equal to the angle of the prism. What is the focal length of the combination? Then the angle of the prism is (take cos 40° = 0.75) (a) 80° (b) 62° (c) 41° (d) 18° 85. An equilateral prism is placed on the prism (a) (b) (c) table of a spectrometer in the position of minimum deviation. If the angle of incidence (a) zero (b) 5 cm is 60°, then the angle of deviation of the ray is (a) 30° (b) 45° (c) 10 cm (d) 20 cm (c) 60° (d) 90° 92. A double convex lens of focal length 20 cm is cut into two parts as shown in figure (b). The 86. The focal length of the objective of a telescope two parts are then put in contact as shown is 60 cm. To obtain a magnification of 20, the in figure (c). What is the focal length of the focal length of the eyepiece should be combination? (a) 2 cm (b) 3 cm (c) 4 cm (d) 5 cm 87. A person cannot see objects clearly beyond 50 cm. The power of the lens to correct his vision is (a) + 0.5 dioptre (b) – 0.5 dioptre (a) (b) (c) (c) – 2 dioptre (d) + 2 dioptre (a) zero (b) 10 cm 88. When a telescope is in normal adjustment, the (c) 20 cm (d) 40 cm distance of the objective from the eye-piece is found to be 100 cm. If the magnifying power 93. A plano-convex lens of focal length (f) 20 cm of the telescope at normal adjustment is 24, is silvered at plane surface. The new f will be the focal lengths of the lenses are (a) 96 cm, 4 cm (b) 80 cm, 20 cm (c) 60 cm, 40 cm (d) 50 cm, 50 cm 89. A monochromatic light is refracted from air (a) 40 cm (b) 30 cm into a glass of refractive index m. The ratio of the wavelengths of the incident and the (c) 20 cm (d) 10 cm refracted waves is (a) 1 : m (b) 1 : m2 94. The refractive indices of violet and red light are 1.54 and 1.52 respectively. If the angle of (c) m : 1 (d) m2 : 1 the prism is 10°, the angular dispersion is 90. The focal length of a lens is 50 cm. The power (a) 0.2° (b) 0.02° of the lens is (c) 3.06° (d) 30.6° (a) + 2D (b) + 1D 95. Two lenses having powers + 6 D and (c) – 2D (d) – 1D – 4 D are placed in contact. The power of the combination is 91. A convex lens of focal length 20 cm is cut into two equal parts to form, two plano-convex (a) – 2 D (b) – 4 D lenses as shown in figure (b). The two parts (c) + 4 D (d) + 2 D