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Half yearly Examination : September:2018 PHYSICS (Class 12 ) PAPER 1 (THEORY) (Maximum Marks: 70) (Time allowed: Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) All questions are compulsory. This question paper is divided in 4 Sections A, B, C and D as follows. Section A Question number 1 is of twelve marks. All parts of this question are compulsory. Section B Question numbers 2 to 12 carry 2 marks each with two questions having internal choice. Section C Question numbers 13 to 19 carry 3 marks each with two questions having internal choice. Section D Question numbers 20 to 22 are long-answer type questions and carry 5 marks each. Each question has an internal choice. Section A Question : 1(a) Objective type questions: 1. A constant current of 2.82 A flows in a resistor. The rms current is : (a) 2.82 A (b) 2.0 A (c) 1.41 A (d) undefined 2. Two thin lenses of optical powers of -10 D and + 6 D are placed in contact to each other. The focal length of the combination is : (a) + 0.25 cm (b) - 0.25 cm (c) + 0.25 m (d) -0.25 m 3. Point out the wrong statement : Electromagnetic waves (a) Are transverse (b) are produced by accelerating charges ( c ) travel with same speed in all media (d) travel with speed of light in free space. 4. A moving electric charge produces : (a) Both electric and magnetic fields. (b) Electric field only (c) Magnetic field only (d) Neither of these two fields. 5. The reactance of a capacitor in an AC circuit is 10 ohm. If the frequency is doubled the reactance will become: (a) 5 (b) 10 (c) 15 (d) 20 Question 1 (b): Answer all questions briefly and to the point: 1. An ideal inductor in an AC circuit consumes no power, though both V and I are non-zero. Why? 2. Arrange in ascending order of wavelength: microwaves, rays, radio waves, ultraviolet light. 3. Give the expression for the power factor in an C R circuit in terms of the resistance R and capacitive reactance . 4. The magnetic flux threading a coil changes from 12 10 Wb to 6.0 10 Wb in 0.01 sec. calculate the induced emf. 5. State Ampere s circuital law. 6. A 900pF capacitor is charged by a 100 V battery. How much energy is stored by the capacitor? 7. State three basic properties of charge. Section B Question 2: (a) Find the value of resistance X in the given circuit so that the junctions M and N are at the same potential. Or (b) Calculate the energy stored in the capacitor included in the given circuit. Question 3: Define the terms magnetization (M) and magnetic susceptibility . Question 4: Name two conservation laws implied in Kirchhoff s law of electric circuits. Question 5: What is meant by drift velocity and relaxation time? Question 6 (a) Obtain the relation = for a wheat stone bridge. The symbols have their usual meanings. Or (b) Two large metal plates of area 1m2 face each other .They are 5 cm apart and have equal but opposite charges on their inner surfaces. If the electric fields between the plates, ignoring edge effects, is 55 NC-1,Find the charges on plates. Question 7: Two particles A and B having charges 8 10 C and - 2 10 C respectively are held fixed with a sepration of 20 cm. Where should a third charge be placed so that it does not experience a net electric force. Question 8: Prove that for a concave mirror, the radius of curvature is twice the focal length. Question 9: Derive, using Gauss theorem, an expression for the electric field intensity at any point due to an infinite line charge of uniform linear charge density coulomb/meter. Question 10: A galvanometer with a coil of resistance 100 and a scale having 100 divisions has a current sensitivity of 25 / divison. How will you convert it into an ammeter of range 0 to 5 A. Question 11: Obtain an expression for an equivalent capacitance C,when three capacitors having capacitance , and are connected in parallel. Question 12: Calculate the critical angle for glass water pair? Given refractive index of glass is 1.62 and that of water 1.33. Section C Question 13 (a) What are the elements of the earth s magnetism? Write relations among these elements. Or (b) Draw a neat labeled diagram of refraction through a combination of parallel multiple media and prove that Question14: In the given diagram and are two cells of emfs 4 V and 6 V respectively, having negligible internal resistances.applying Kirchhoff;s laws of electrical networks,find the values of and . Question 15 (a) With the help of a neatly labeled diagram,prove that the magnitude of motional emf e is given by e = B l v, where l is the length of metallic rod and v is velocity with which it is pulledin a transverse magnetic field B. Or (b) Write an expression for Biot Savart law in vector form. Derive an expression for magnetic field at the centre of a circular current carrying coil of radius r,with N turns. Question 16: The figure shows a right angled isosceles triangle PQR of base equal to a metre.A current of I ampere is flowing downwards along a thin straight wire cutting the plane of the paper normally at Q .A similar wire carries an equal current flowing upwards at R .Find the magnitude and direction of the magnetic induction at P . Assume the wires to be infinitely long. Given : = 4 10 TmA-1 Question 17: Derive the lens makers formula : = (n 1)( - ), symbols have their usual meaning. Question 18:A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm.What is the area of the surface of water through which light of bulb can emerge out? Refractive index of water is 1.33.Consider the bulb to be point source. Question 19: What is the relation between the refractive indices n,n1 and n2,if the behavior of light rays is as shown in the figures? Section D Question 20 a) In the given L-C-R series circuit fed by 220 V 50 Hz A.C.mains, find (1) current in the circuit,(2) value of inductor L, (3) value of capacitor C and (4) value of C ( for the same L) required to produce resonance.The voltmeter readings across R,L and C are as shown. b) In which part of the electromagnetic spectrum do the following radiation lie : I. Having wavelength of 20 nm. II. Having frequency of 10 MHz. Or Obtain the relation I = sin( + ) and = for a pure capacitor across which an alternating emf E = sin is applied. Draw a phasor diagram showing emf e ,current I and their phase difference . d) In an A C circuit ,R = 40 ,Z = 50 , = 200 V .Calculate the average power consumed over a full cycle. Question 21: a) Using Ampere s Circuital Law and with the help of a labelled diagram, show that magnetic flux density B at a distance r from a long straight conductor is given by : B = , where the terms have their usual meaning. b) A cyclotron s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons ? If the radius of its dees is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator Or c) Figure shows a uniform managing wire XY of length 100cm and resistance 9 , connected to an accumulator D of emf 4V and internal resistance 1 through a variable resistance R. E is a cell of emf 1.8Vconnected to the wire XY via a jockey J and a central zero galvanometer G .It is found that the galvanometer shows no deflection when XJ = 80cm.Find the value of R. c) d) A concave mirror produces a real image of half the size of an object at 60 cm infront of it.Where should the object be placed to obtain a virtual imageof double the size of the object? Question 22: a) Two point charges + 3q and 4q are placed at the vertices B and C of an equilateral triangle ABC of side a as given in the figure. Obtain the expression for (i) the magnitude and (ii) the direction of the resultant electric field at the vertex A due to these two charges. b) Draw a labelled diagram of a potentiometer circuit used to measure internal resistance of cell. Or c) In the following diagram, an object O is placed 15 cm in front of a convex lens of focal length 20 cm and the final image is fomed at I at a distance of 80 cm from the second lens . Find the focal length of the lens . d) Depict the equipotential surfaces due to (i) an electric dipole, (ii) two identical positive charges separated by a distance.
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