New Delhi 110 018. Ph. : 9312629035 (1) EINSTEIN CLASSES P R E S E N T S C B S E XIIth Board PRACTICE ASSIGNMENT PHYSICS NOTE THE FOLLOWING POINTS : 1. Einstein Classes is primarily concerned with the preparation of JEE-ADVANCE /JEE-MAIN/BITS/PMT/AIIMS. We also support the School Syllabus & XIIth Board Preparation in the same program. 2. This assignment is meant to help for those students who are appearing for XIIth CBSE Board Examination.
New Delhi 110 018. Ph. : 9312629035 (2) Each question carry 1 mark. SECTION A 1. Does the mass of the neutral body change after charging and how? 2. Three equal and positive charges are placed at the corners of an equilateral triangle. Draw the pattern of electric lines of forces. 3. What is the path of the charge particle in the uniform electric field, if it is projected perpendicular to the field. 4. Draw the pattern of electric lines of forces for infinite non-conducting thin sheet of positive charge. 5. A dipole of dipole moment p is placed in the electric field of infinite non-conducting thin sheet of charge of charge density such that the dipole is inclined at a certain angle with the electric field. What is the force, torque and potential energy of the dipole? 6. Compare equipotential surface and electric lines of forces. 7. Draw the graph for the variation of electric field of spherical charge conductor with distance. 8. What is the ratio of electric field due to dipole along the axis and along the perpendicular bisector at the large distance? 9. Why the lines of forces are not closed? 10. Is the following pattern of lines of forces exists? Give reasons. 11. What is the mininum electric field at a distance of 1 m from a point charge. 12. Draw equipotential surfaces for an electric dipole. 13. Which of the following quantity is a vector quantity : Current and (ii) Curent density. 14. Draw the variation of resistivity with temperature : for copper (ii) for nichrome (iii) for semiconductor. 15. What is the difference between the potential difference across a battery and emf of the battery. 16. On which basic principle Kirchhoff s laws are based? 17. How the drift speed of the electron will vary if a steady state current will flow through a wire of non-uniform cross-section. 18. Why the speed is constant when a charged particle is projected in a magnetic field? 19. Write down the pairs for the physical quantity which are always perpendicular to each other for F q(v B).
New Delhi 110 018. Ph. : 9312629035 (3) 20. Does the time period to complete one revolution by charge particle in a uniform magnetic field for circular motion depends on speed? Give reasons. 21. An electron is moving with constant speed v along a circular path of radius r. Find the magnetic field at the center? 22. A wire of given length is folded into a circular loop of several turns N. Find the dependence of magnetic field at the centre on N? 23. Draw the variation of magnetic field due to current carrying loop along the axis. 24. What is the ratio of magnetic field due to solenoid inside and at the end point? 25. What is the magnetic dipole moment due to circulating electron of charge e in an orbit of radius r? Compare this with the orbital angular momentum of the electron. The speed of the electron is v. 26. What is the gauss law in magnetism? 27. Why the soft iron core is used for electromanget, whereas steel for permanent magnet? 28. Which substance has the behaviour independent of temperature and why? 29. On which basic principle the Lenz law is based? 30. Write down the unit and dimension of inductance. 31. What is the physical meaning of quality factor? 32. Arrange the following in the increasing order of the wavelength : Radiowave, X-rays, UV-rays, -rays. 33. Write down the different conditions for good contrast interference pattern? 34. If Young s double slit experiment is shifted from air to water then what changes will occur? 35. Why the focal length of the lens changes when the wavelength of the light used changed. 36. Why the sky is blue? 37. Draw the variation of kinetic energy of electron in photoelectric effect with frequency of incident light. 38. Why the wave theory of light is not able to explain photoelectric effect? 39. Compare the wavelength associated with electron with kinetic energy 1eV and wavelength associated with photon of the same energy. 40. How the radius of the Bohr orbit depends on quantum number n. 41. Write down the properties of nuiclear force? 42. Compare the radius of the nucleus of hydrogen and oxygen. 43. Which particles are emitted in decay and in + decay. 44. Draw the I-V characteristics for a photo diod and solar cell. 45. What is the frequency band for satellite communication?
New Delhi 110 018. Ph. : 9312629035 (4) 46. An alpha particle is moving vertically downwards in a magnetic field in N-S direction. In which direction will the alpha particle be deflected. 47. Magnetic lines prefer to pass through iron than air, why? 48. What is the rate of work done by a magnetic field on a charge? 49. In the fig. What should be magnitude and direction of electric field so that charge goes undeviated? 50. Why can t tranformer be used to step up d.c. voltage? 51. What is the power factor of an LCR series circuit at resonance? 52. What is the focal length and power of the lens in the figure. The radii of curvature of the two faces are R each. 53. A small piece of stone is dropped into a still water reservoir. What is the shape of wave front formed? 54. What should be the order of size of obstacle or aperature for the light to diffract. 55. A ray of light falls on a transparent slab of µ = 3. If reflected and refracted rays are mutually perpendicular, find out the angle of incidence? 56. A polariser and an analyzer are so oriented that no light is transmitted. The analyzer is then rotated through 60 0. What fraction of the maximum light is transmitted? 57. Law of energy conservation is obeyed in interference pattern. Justify. 58. Give an equation representing the decay of a free neutron. 59. Why are de-broglie waves associates with a moving football not visible? 60. Why is the penetrating power of gamma rays very large? 61. Which have greater ionising power : alpha particles or beta particles? 62. The thickness of base in a transistor is increased. How will the collector current be affected?
New Delhi 110 018. Ph. : 9312629035 (5) 63. In a p-n junction what is the direction of diffusion current? 64. A p-n photodiode is fabricated form a semiconductor with back gap of 2.8eV. Can it detect a wavelength of 6000nm? 65. For the given direction of E and B fields in an em wave, how can one find the direction of proparation of the wave? 66. Which type of em waves are used for telecommunication purpose through artificial satellites? 67. What is ground wave propagation? 68. What is sky wave propagation? Each question carry 2 marks. SECTION B 1. Calculate the Coulomb force between a proton and an electron separated by 0.8 10 15 m and compare with the gravitational force between them. Also calculate the Coulomb force between two -particles separated by a distance 3.2 10 15 m. 2. Define capacitance and its units. Derive an expression for the capacitance of parallel plate capacitor. 3. In a parallel plate capacitor, the capacitance increase from 4 microfarad to 80 microfarad, on introducing a dielectric medium between the plates. What is the dielectric constant of the medium? 4. The capacitor is disconnected from the charging battery, explain how the (ii) (iii) capacitance, p.d. across the plates, and energy stored in the parallel plate capacitor change, when a medium of dielectric constant k is introduced between the plates. 5. An electric dipole of dipole moment p is placed along the direction of the uniform external electric field E. It is disturbed from this position by very small angle. Explain what happens to the dipole on being released. 6. Two point electric charges of unknown magnitude and sign are placed a distance d apart. The electric field intensity is zero at a point, not between the charges but on the line joining them. Write two essential conditions for this to happen. 7. An -particle and a proton are accelerated through the same potential difference. Calculate the ratio of velocities acquired by the two particles. 8. Two point changes +4µC and 6µC are separated by a distance of 20 cm in air. At what point on the line joining the two charges is the electric potential zero?
New Delhi 110 018. Ph. : 9312629035 (6) 9. A proton, placed in a uniform electric field of magnitude 2 10 3 NC 1, moves from a point A to B in the direction of electric field. If AB = 0.05m, calculate the potential difference between A and B, and (ii) work done in moving the proton from A to B. 10. An electric flux of 6 10 3 Nm 2 /C passed normally through a spherical Gaussian surface of radius 10 cm, due to a point charge placed at the centre. What is the charge enclosed by the Gaussian surface? (ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the surface? 11. A metal wire is bent in the shape of a circle of radius 10 cm. It is given a charge of 20µC, which is spread uniformly over it. Calculate electrical potential at the centre of the circle. 12. A 10µF capacitor can withstand a maximum voltage of 100 volts across it whereas another 20µF capacitor can withstand a maximum voltage of only 25 volts. What is the maximum voltage that can be put across their series combination? 13. A dry cell of e.m.f. 1.6 V and internal resistance 0.10 ohm is connected to a resistor of resistance R ohm. If the current drawn from the cell is 2A what is the voltage drop across R? (ii) what is the energy dissipation in the resistor? 14. Write two special characteristics of magnanin due to which it is used in making standard resistances. 15. A carbon resistor of 74 k is to be marked with rings of different colours for its identification. Write the sequence of colours. 16. The current through a wire depends on time as I = i o + At where i o = 5A and A = 2As 1. Find the charge crossing through a section of the wire in 15 seconds. 17. Establish the relation between drift velocity V d of the electrons in a conductor of cross section A carrying current I and concentration of free electrons per unit volume of the conductor being n. 18. Explain the phenomenon of hysterisis in magnetic materials. 19. Derive the expression for the torque on a recrangle lar coil of area A, carrying a current I placed in a magnetic field B. The angle between the direction of B and the vector perpendicular to the plane of the coil is. 20. Give the position of a magnetic dipole held in a magnetic field, where its potential energy is minimum (ii) maximum. Also draw the graph for the variation of potential energy with the angle between the magnetic dipole and the field. 21. How does the intensity of magnetisation of a paramagnetic material vary with increasing applied magnetic field? 22. State and illustrate Curie law in magnetism.
New Delhi 110 018. Ph. : 9312629035 (7) 23. An electron of kinetic energy 25 kev moves perpendicular to the direction of a uniform magnetic field of 0.2 millitesla. Calculate the time period of rotation of the electron in the magnetic field. 24. Give any two factors by which current senstivity of a galvanometry can be increased. 25. Cyclotron is not suitable for accelerating electrons, why? 26. A proton, deutron and an alpha particle with equal K.E s, enter the same magnetic field B perpendicular to it, compare radii of their circular paths. 27. What happens to Pole strength (ii) Magnetic moment. If a bar magnet is cut into two equal pieces transverse to its length (ii) along its length. 28. Find the equivalent magnetic moment. 29. A straight long conductor is carrying current of 5A in east to west direction. Find magnitude and direction of B at point 4cm away northward. 30. Prove that the smallest magnetic moment available with an atom is (eh/4 m). 31. Define the term self-induction. Write two factors which the self-inductance of a coil depends. 32. A coil A is connected to a voltmeter V and the other coil B to an alternating current source D. If a large copper sheet C, is placed between the two coils, how does the induced e.m.f. in the coil A change due to current in coil B? 33. Calculate the current drawn by the primary of a transformer, which steps down 200 V to 20 V to operate a derive of resistance 20. Assume the efficiency of the transformer to be 80%. 34. A rectangular coil of N turns and area of cross-section A, is held in a time-varying magnetic field given by B sin t, with the plane of the coil normal to the magnetic field. Deduce an expression for the e.m.f. induced in the coil. 35. An air-core solenoid is connected to an a.c. source and a bulb. If an iron-core is inserted in the solenoid, how does the brightness of the bulb change? Give reason for your answer. 36. A choke coil and a bulb are connected in series to an a.c. source. The bulb shines brightly. How does its brightness change when an iron core is inserted in the choke coil? 37. Give the direction of induced current (if any) in the metal ring when the magnet is moved away form the rig as shown.
New Delhi 110 018. Ph. : 9312629035 (8) 38. Why do we prefer carbon brushes than copper in an a.c. generator? 39. v-i graph for two series LCR circuit A and B is shown below. Which of the two has larger value of resistance. 40. Why do we prefer a choke coil in place of a resistor in any safety devise? 41. Give the direction of induced current (if any) in metal rings I and II. 42. Explain how will the brightness of bulb be affected if (I) frequency of ac is increased (II) a resistor is put in series. 43. A capacitor blocks d.c., favours a.c. why? 44. What is the role of transformers in long distance transmission of electrical power. Illustrate your answer with an example. 45. In the adjoining figure magnetic field is of strength Band rectangular loop of length l and breadth w. Show graphically 46. Explain briefly the formation of mirage in deserts. 47. Define phase difference and relate this with the path difference. 48. Find the ratio of intensities at two points x and y on a screen in Young s double slit experiment, where waves from S 1 and S 2 have path difference of 0 and (ii) /4. 49. For the same angle of incidence, the angles of refraction in three different media A, B and C are 15 0, 25 0 and 35 0 respectively. In which medium will the velocity of light be minimum? 50. Give two difference between interference and diffraction pattern of light. 51. Calculate the refractive index of the material of an equilateral prism for which the angle of minimum deviation is 60 0.
New Delhi 110 018. Ph. : 9312629035 (9) 52. You are given two convex lenses of focal length 80 mm and 800 mm. Which one will you use as an objective and which one as an eyepiece for constructing an astronomical telescope? 53. The two slits in Young s double sit experiment are separated by a distance of 0.03 mm. An interference pattern is produced on a screen 1.5 m away. The 4th bright fringe is at a distance of 1 cm from the central maximum. Calculate the wavelength of light used. 54. How can one distinguish between an unpolarized light beam and a linearly polarized light beam using a polaroid? 55. Sketch the wave-fronts corresponding to converging rays. 56. Draw a ray diagram to show the formation of the image of an object placed between f and 2f of a thin concave lens. Deduce relation between the object distance, the image distance and the focal length of the lens under this condition. 57. Define lateral displacement. On what factor does it depend? 58. Complete it with correct value of angle of emergence. 59. A fish is situated at the depth h inside a lake. Calculate the radius of circular aperture through which the fish seen the out wide world. 60. A reflecting telescope has a large mirror for its objective with radius of curvature equal to 80 cm. What is the magnifying power of the telescope if the eyepiece used has a focal length of 1.6 cm? 61. Distinguish between Nuclear fission and fusion. 62. Why is the energy distribution of beta rays continuous? 236 63. Name the reaction which takes place when a slow neutron beam strikes 92 U nuclei. Write the nuclear reaction involved. 64. The frequency (v) of incident radiation is greater than threshold frequency (v 0 ) in a photocell. How will the stoping potential vary if frequency (v) is increased, keeping other factors constant? 65. A source of light is placed at a distance of 50 cm from a photocell and the cut-off potential is found to be V 0. If the distance between the light source and photocell is made 25 cm what will be the new cut-off potential? Justify your answer. 66. State with reason why light nuclei usually undergo nuclear fusion.
New Delhi 110 018. Ph. : 9312629035 (10) 67. Radiations of frequency 10 15 Hz are incident on two photosensitive surfaces P and Q. Following observations are made : (ii) Surface P : Photoemission occurs but the photoelctrons have zero kinetic energy, and Surface Q : Photoemission occurs and photoelectrons have some kinetic energy. Which of these has a higher work function? If the incident frequency is slightly reduced, what will happen to photoelectron emission in the two cases. 68. How is the depletion region formed in a p-injuction diode? 69. The output of a 2-input NOR gate is fed to a NOT gate. Write down the truth table for the output of the combination for all inputs. 70. Draw the energy band diagram of a p-type semiconductor. How does the forbidden energy gap of an intrinsic semiconductor vary with increase in temperature? 71. What do you mean by rectification? With the help of a circuit diagram, explain the use of p-n junction diode as a full wave rectifier and half wave rectifier, giving its input and output waveforms. 72. If A = 0, B = 0. Find y for the given combination of tages. 73. Diodes D 1 and D 2 are ideal diodes. Find the current drawn form the battery of emf 5V if the positive terminal is connected to (ii) the point A the point B 74. If the input frequency is 50Hz. What is the output frequency of (ii) Half wave rectifier Full wave rectifier 75. What role does ionosphere play in communication? 76. Why is short wave communication over long distance not possible via ground waves? 77. A certain plane em wave emitted by an antenna has a wavelength of 3.0 cm and a maximum amplitude of the electric field of 3 10 2 Vcm 1. (a) What is the frequency of the wave? What is the magnitude of the maximum magnetic field?
New Delhi 110 018. Ph. : 9312629035 (11) 78. The coverage range of a TV tower is 60 km. Calculate the height of the tower. Take radius of earth to be 6400 km. 79. Why do we need Modulation (Give two reasons) Each question carry 3 marks. SECTION C 1. Derive an expression for the energy stored in a parallel plate capacitor with air as t h e medium between its plates. How does the total energy stored by the capacitor change when the medium of air is replaced by a medium of dielectric constant K? Explain. 1 3 2 Show that electric field E itself is a source of energy with energy density 0E Jm. 2 2. Capacitors P, Q and R have each a capacity C. A battery can charge the capacitor P to a potential difference V. If after charging P, the battery is disconnected from it and the charged capacitor P is connected in following separate instances to Q and R to Q in parallel, and (ii) to R in series, then what will be the potential difference between the plates of P in the two instances? 3. State Gauss s theorem in electrostatics. Apply this to calculate the field intensity at any point inside and outside a hollow and solid charged conducting sphere. (ii) at any point inside and outside of the solid non-conducting charged sphere also draw the variation of electric field with distance. 4. You are given an isolated parallel plate capacitor of capacitance C charged to a potential difference V. What will happen to the following when the separation between the plates is doubled with the help of insulating handles attahced to the plates? (a) (c) (d) charge on the plates potential difference across the plates field between the plates energy stored in the capacitor 5. Two point electric charges of values q and 2q are keep at a distance d apart from each other in air. A third charge Q is to be kept along the same line in such a way that the net force acting on q and 2q is zero. Calculate the position of charge Q in terms of q and d. 6. Calculate the potential and field at the centre of a square of side 2 m, which carries at its four corners charges of +2 nc, + 1nC, 2 nc and 3 nc respectively. Also calculate the work done to carry a charge particle of +10nC from infinity to the center of the square. 7. A parallel plate capacitor has capacitance of 30pF. What will its capacitance become in the two cases shown below when it is half-filled with a dielectric of dielectric constant?
New Delhi 110 018. Ph. : 9312629035 (12) 8. Find the equivalent capacitance of the following network between A and B. 9. Explain the principle of potentiometer, with the help of a circuit diagram, explain how a potentiometer can be used to compare e.m.f. of two primary cells. 10. Find the value of unknown resistance X in the following circuit for which current flows through section AO is zero. Also calculate the current drawn by the circuit from the battery of e.m.f. 6V and negligible internal resistance. 11. Explain, by drawing a labelled diagram, how a positively charged particle is accelerated in a cyclotron. 12. Distinghish between dia, para and ferro magnetic substances. Give one example of each. How does the magnetic property of iron change with increase of temperature? 13. A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields E and B respectively. If the electric field is cut-off, the electron beam moves in a circular path of radius r. Derive the expression for e/m of electrons in terms of r, E and B. 14. A magnet oscillating in a horizontal plane, has a time period of 3 seconds at a place where the angle of dip is 30 0 and 4 seconds at another place, where the dip is 60 0. Compare the resultant magnetic field at the two places. 15. An electron and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. For which of the two particles will the radius of circular path be smaller? Compare the time period to complete one revolution. 16. State Amperes circuital law. Derive expression for magnetic field due to solenoid at a point inside it.
New Delhi 110 018. Ph. : 9312629035 (13) 17. A domain in ferromagnetic iron is in the form of a cube of side of length 1 µm. Estimate number of iron atoms in the domain and maximum possible dipole moment. The molecular mass of iron is 55g/mole and its density is 7.9g/m 3. Assume that each iron atom has a dipole moment of 9.57 10 24 Am 2. 18. A short magnet placed with its axis at 30 0 experiences a torque of 0.16 N.m in an external field of 800G. (a) What is the magnetic moment of magnet. What is the work done by an external torque in turning it from stable equilibrium to unstable equilibrium. 19. (a) What are eddy currents? How are eddy currents produced? Give two application of eddy currents. 20. Draw the graphs to show the variation of X L, and (ii) X C with the frequency of the a.c. source used. A 200 V variable frequency a.c. source is connected to a series combination of L = 5 H, C = 80 µf and R = 40. Calculate angular frequency of the source to get maximum current in the circuit, (ii) the current amplitude at resonance and (iii) the power dissipation in the circuit. 21. Twelve wires of equal lengths are connected in the form of a skeleton-cube which is moving with a velocity v in the direction of a magnetic field B. Find the emf in each arm of the cube. 22. Prove that an ideal inductor does not dissipate power in an a.c. circuit. A bulb of resistance 10, connected to an inductor of inductance L, is in series with an a.c. source marked 100 V, 50 Hz. If the phase angle between the voltage and current is 4 radian, calculate the value of L. 23. A circular copper disc 10 cm in radius rotates at 20 rad/s about an axis through its centre and perpendicular to the disc. A uniform magnetic field of 0.2 T acts perpendicular to the disc. Calculate the potential difference developed between the axis of the disc and the rim. (ii) What is the induced current, if the resistance of the disc is 2 ohm? 24. Define the term root-mean-square (rms) value of a.c. Derive the relation between rms and peak value of a.c. A 1 µf capacitor is connected to a 220 V, 50 Hz a.c., source. Calculate the rms value of the current through the circuit. Also find the peak value of voltage across the capacitor. 25. How does the mutual inductance of a pair of coils change when; the distance between the coils is increased? (ii) the number of turns in each coil is decreased? Justify your answer in each case. 26. Prove that total energy stored in an inductor is ½LI 2, where I is the maximum max max current through the inductor. In which form is this energy store. 27. Define resolving power of a telescope & microscope and give the expression for its resolving power.
New Delhi 110 018. Ph. : 9312629035 (14) 28. What do you understand by polarisation of light? How can the transverse nature of light be demonstrated experimentally? 29. Deduce lens maker s formula for a thin biconves lens. 30. Derive the expression for the fringe width in Young s double slit interference experiment. 31. A double concave lens made of glass of refractive index 1.5 has both radii of curvature of magnitude 40 cm. An object 2 cm high is placed at 10 cm from the lens. Find the position, nature and size of the image. 32. The image of an object formed by a lens on the screen is not in sharp focus. Suggest a method to get clear focusing of the image on the screen without disturbing the position of the object, the lens or the screen. 33. What are coherent source of light? Why is no interence pattern observed when two coherent sources are infinitely close to each other? (ii) far apart from each other? 34. A slit of width d is illuminated by light of wavelength 6,500 Å. For what values of d will the first minimum fall at an angle of diffraction of 30 0? (ii) first maximum fall at an angle of diffraction of 30 0? 35. In the hypothetical fission reaction : 92 X236 a Y 141 + 36 Z b + 3 0 n 1 What are the values of the numbers a and b? Calculate the total energy released per nuclear fission in MeV units when the masses in amu units are of neutron = 1.009 of X-nucleus = 235.891 of Y-nucleus = 140.673 of Z-nucleus = 91.791 36. How does photoelectric current, and (ii) kinetic energy of the photoelectrons emitted in a photocell vary if the intensity of the incident radiation is doubled? When light of wavelength 400 nm is incident on the cathode of a photocell, the stopping potential recorded is 6 V. If the wavelength of the incident light is increases to 600 nm, calculate the new stopping potential. 37. In an experiment of photoelectric effect, the graph between the maximum Kineric energy (E k ) of the emitted photoelectron and the frequency v of the incident light is straight line shown in the fig. Calculate (a) Threshold frequency Work function of cathode metal in electron volt (c) Planck s constant h and (d) Maximum K.E. of electrons emitted by light of frequency v = 30 10 14 s 1.
New Delhi 110 018. Ph. : 9312629035 (15) 38. What is a n-p-n transistor? How dies it differ from p-n-p transistor? Give their sysmbols. Explain transistor action. 39. Draw the logic symbol and truth table for a NAND gate, AND gate, OR gate, NOR gate and Ex-OR gate. 40. In a transistor, the base current is changed by 20 µa. This result in a change of 0.02 V in base to emitter voltage and a change of 2 ma in the collector current. (a) Find the current gains ac and (ii) transconductance g m. If this transistor is used as an amplifier with the load resistance 5 k, calculate the voltage gain of the amplifier. 41. What is a zener diode? How is it symbolically represented? With the help of a circuit diagram, explain the use of zener diode as a voltage stabilizer. 42. A semiconductor has equal electron and hole concentration of 4 10 8 / m 3. On doping with a certain impurity, hole concentration increases to 8 10 12 / m 3 : (ii) Identify the new semiconductor obtained after doping, Calculate the new electron concentration and (iii) How does the energy gap vary with doping? 43. Explain how a transistor works as a Switch? 44. Two signals A and B as shown in figure are used as two input of AND gate (ii) NOR gate (iii) NAND gate (iv) OR gate. Obtain the output in each of the four cases. 45. What is meant by the term modulation? Explain with the help of a block diagram, how the process of modulation is carried out in radio broadcasts. 46. What is 'amplitude modulation' and 'frequency modulation'? Show these process graphically. 47. Explain with the help of input and output waveforms, how a diode can be used for detection of AM waves?
New Delhi 110 018. Ph. : 9312629035 (16) Each question carry 5 marks. SECTION D 1. (a) Define electric dipole moment. Derive an expression for the electric field and potential at any point along the equatorial line (ii) axial line of an electric dipole. Show mathematically that the electric field intensity due to a short dipole at a distance d along its axis is twice the intensity at the same distance along the equatorial axis. Derive an expression for the total work done in rotating the dipole through an angle in uniform electric field E. Also derive the torque acting on the dipole. 2. Explain the construction, basic principle and working of a Van de Graff generator with the help of a diagram. 3. What are the Kirchoff s laws for electric circuit. Apply Kirchoff s laws to obtain the condition of balance in a Wheatstone s bridge. 4. State Biot-Savart s law. Using Biot-Savart s law, derive the expression for magnetic field due to current circular coil, at a point along the axis of the coil (ii) infinite wire. 5. (a) Derive the relation for the force per unit length between two infinity long parallel straight wires carrying currents. Hence define one ampere. Explain why two straight parallel metallic wire carrying current in opposite directions repel each other. 6. (a) Explain with the help of a labelled diagram, the underlying principle, construction and working of a moving coil galvanometer. Define voltage sensitivity and figure of merit of a moving coil galvanometer. Give its S.I. unit. 7. Derive an expression for the impendance of a LCR series AC circuit. A 40 resistor, 3 mh inductor and 2µF capacitor are connected in series to a 110 V, 50 Hz AC source. Calculate the value of the current in the circuit. 8. Draw a labelled diagram of an a.c. generator. Write the principle on which it works. An a.c. generator consists of a coil of 100 turns and cross-sectional area of 3 m 2, rotating at a constant angular speed of 60 radian/sec in a uniform magnetic field of 0.04 T. The resistance of the coil is 500 ohm. Calculate maximum current drawn from the generator and (ii) maximum power dissipation in the coil. 9. Explain the terms reactance and impedance as applied to components of an a.c. circuit. A variable frequency 230 V alternating voltage source is connected across a series combination L = 5.0 H, C = 80 µf and R = 40 Calculate (ii) (iii) the angular frequency of the source which drives the circuit in resonance, the amplitude of the current at resonating frequency and rms potential drop across the inductor at resonating frequency.
New Delhi 110 018. Ph. : 9312629035 (17) 10. When an alternating voltage of 200 V is applied across a device Z, a current of 0.5 A flows through the circuit and is in phase with the applied voltage. When the same voltage is applied across another device Y, the same current again flows through the circuit but it leads the applied voltage by /2 radians. (a) name the devices X and Y. Calculate the current flowing in the circuit when same voltage is applied across the series combination of X and Y. 11. Explain, with the help of a diagram, the principle, construction and working of a step-up transformer. Why is its conlaminated. 12. (a) Draw a labelled diagram of a compound microscope and explain its working. (c) With the help of ray diagram, illustrate the formation of the final image of an object in a compound microscope. Derive an expression for its magnifying power. How can the magnifying power be increased? How will the resolving power of compound microscope be affected when (a) the frequency of light used to illuminate the object is increased, and the focal length of the objective is increased. Justify your answer in each case. 13. (a) State Huygen s Wave theory and its assumptions? Also define coherent source of light Deduce laws of reflection (ii) laws of refraction on the basis of Huygen s principle. 14. (a) Draw a labelled diagram of an astronomical telescope forming the final image at the near point. Write down the formula for its magnifying power. (c) What is the effect of increasing the diameter of the objective of a telescope on its magnifying power and (ii) resolving power? Draw a labelled ray diagram for a refracting type astronomical telescope. How will its magnifying power be affected on increasing for its eye-piece the focal length, and (ii) the aperture? Justify your answer. 15. (a) A slit of width a is illuminated by monochromatic light at normal incidence. Draw the intensity distribution curve observed on the screen, due to diffraction. (c) Determine the angular separation between central maximum and first order maximum of the diffraction pattern due to a single slit of width 0.25 mm. when light of wavelength 5890 Å is incident on it normally. In a single slit diffraction pattern, how is the angular width of central bright maximum changed, when (ii) the slit width is decreased the distance between the slit and the screen is increased
New Delhi 110 018. Ph. : 9312629035 (18) 16. Define interference of light. Two sources of equal amplitude are used to produce interference. Drive an expression for the variation of intensity with phase angle. Hence plot a graph to show this variation. Also derive an expression for the variation of intensity with phase angle for unequal amplitude. 17. Draw a ray diagram to show the formula of real images of a point object due to convex spherical refracting surface, when the ray of light is travelling from rarer medium of Refractive index (µ 1 ), to denser media of Refractive Index (µ 2 ). Using the diagram derive a relation between object distance (u) and image distance (v) radius of curvature R of a convex spherical surface. State the sign conventions and the assumptions made. 18. Draw the graph to show variation of binding energy per nucleon with mass number of different nuclei. Calculate binding energy per nucleon of 40 20 Ca nucleus. 19. Explain what is mean by radioactive decay. A radioactive nucleus is represented by the symbol a b V. How is the new nucleus represented after the emission of an alpha particle, (ii) a beta particle and (iii) a gamma ray? The activity of a source undergoing a single type of decay is I 0 at time t = 0. Obtain an expression in terms of the half-life T ½ for the activity I at any subsequent time t. 20. Draw the experimental arrangement used by Davison and Germer for electron diffraction by crystals. In this experiment what is the maximum accelerating potential applied to the electron to get maximum scattering angle of 500 from the nickel crystal. Using these data verify the wave nature of electron. 21. Explain through a labelled circuit diagram, the working of a transistor as an amplifier (common emitter configuration). Obtain an expression for the voltage gain. 22. What do the following terms stand for? (a) FAX MOD EM (c) PCM (d) LED (e) LASER (f) AM (g) FM