-Answer all Questions from Part I and six questions from Part II, choosing two questions from each of the Section A, B and C.
-All working, including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer.
-The intended marks for questions or parts of questions are given in brackets ( ).
-Material to be supplied: Log tables including Trigonometric functions
-A list of useful physical constants is given at the end of this paper.

Q 1Answer all questions briefly and to the point:-  (Marks 20)
(i) State Gauss's theorem of electrostatics.
(ii) An alpha particle is accelerated through a potential difference of 2000 volt. What will be the increase in its energy in electron volt?
(iii) Assuming the earth as an isolated spherical conductor of radius 6400 km, calculate its electrical capacitance in farad.
(iv) If the potential difference applied across a variable resistor is constant, draw a graph between the current in the resistor and the resistance.
(v) Find the equivalent resistance between the point 'a' and 'c' of the given network of resistors (See Fig. 1).

(vi) Show with a labelled graph how thermo-emf varies with the temperature of the hot junction of a thermocouple.
(vii) What is the function of shunt in an ammeter?
(viii) What is meant by 'Wattless' current?
(ix) Name the physical principle and one advantage in the use of optical fibers.
(x) Can two independent monochromatic source of light be coherent? Explain very briefly.
(xi) What is the relation between the refractive indices n₁ and n₂ if the behaviour of light rays is as shown in the following Fig. 2?

Here n₁ and n₂ are the refractive indices of the surrounding medium and the lens respectively.
(xii) What is the principle of global communication by satellites?
(xiii) State Brewster's law for polarisation of light.
(xiv) Two thin lenses-one convex and the other concave - of focal lengths 15 cm and 20 cm respectively are put in contact. Find the focal length of the doublet lens.
(xv) Two stars three and four light years away from the earth have same luminous intensity. Find the ration of the illuminance (intensity of illumination) on the surface of the earth, normal to the starlight, produced by each star.
(xvi) The historic experiment on the diffraction of electron confirmed a new nature of electron. What is this new nature of electron? Who had proposed it?
(xvii) Explain briefly why there is a maximum frequency for the X-rays produced by an X-ray tube operating at a certain voltage.
(xviii) Draw circuit diagrams to illustrate forward biasing and reverse biasing of a diode.
(xix) Name two alternative sources of energy and mention where they can be used.
(xx) The half-life period of a radioactive substance is 16 hours. After how much time will 6.25% of the material remain undecayed?

PART II

Answer six question in this part, choosing two questions each from the Sections A, B and C.

SECTION A
Answer two questions

Q 2 (a) Derive an expression for the electric potential at a point due to a point charge. (Marks 4)

Q 2 (b) An electric flash lamp has 20 capacitors each of capacitance 5F connected in parallel. The lamp is operated at 100 volt. Calculate how much energy will be radiated in a flash. (Marks 3)

Q 2 (c) Name one material whose resistivity decreases with rise in temperature. Explain briefly on the basis of free electron theory why the resistivity decreases. (Marks 2)

Q 3 (a) State and explain Kirchoff's laws for electric circuits. What are the conservation laws implied in each law? State the sign convention for current and emf. Use the Fig. 3 given below for your explanation. (Marks 4)

Q 3 (b) An electron is moving vertically upwards in the uniform magnetic field of the earth. The velocity of the electron is 2.0 x 10⁶ m/s and the horizontal component of earth's magnetic field is 0.32 x 10^-4 tesla. Obtain the magnitude and direction of the force on the electron. (Marks 3)

Q 3 (c) Permanent magnets are made of special alloy while the core of temporary magnets are made of soft iron. Why? (Marks 2)

Q 4 (a) Define self inductance. Obtain the expression for the self inductance of a solenoid, explaining steps with the help of a diagram. (Marks 3)

Q 4 (b) What is meant by back emf in a dc motor? The back emf in a dc motor, delivering 3 kilowatts of mechanical power, is 180 volts when operating on 220 volt line. Determine the armature current and the motor resistance. (Marks 3)

Q 4 (c) In an LCR circuit with all components connected in series, the emf and the current flowing in the circuit are given by the following equations:-
= 200 sin (314t + /6) volts
I = 5 sin 314 t ampere
Obtain:
(i) the peak values of current and emf.
(ii) the frequency of the ac source.
(iii) the phase difference between current and emf. (Marks 3)

SECTION B
Answer two questions.

Q 5 (a) State Huygens' principle. Explain with the help of a diagram the phenomenon of refraction of waves on the basis of this principle. (Marks 3)


Q 5 (b) What is chromatic aberration in lenses? State the necessary condition for an achromatic doublet. How are these conditions practically achieved? (Marks 3)

Q 5 (c) Fraunhofer diffraction from a single slit of width 1.0 m is observed with light of wavelength 500 nm. Calculate the half angular width of the central maximum. (Marks 2)

Q 6 (a) Draw a neat ray diagram of a simple microscope. Deduce the formula for its angular magnification when the image is formed at the least distance of distinct vision. (Marks 3)

Q 6 (b) A beam of monochromatic light of wavelength 500 nm falls on two parallel slits. The distance between the slits is 0.15 mm. Determine the width of the interference fringes on a screen placed at a distance of 1.5 m from the slits. (Marks 3)

Q 6 (c) Draw a sketch of electromagnetic spectrum, showing relative positions of UV, IR, X-rays and microwaves with respect to visible light. State approximate wavelengths of any two. (Marks 2)

Q 7 (a) With the help of neat diagram describe with theory, Michelson's method for the determination of the speed of light. What is the presently accepted nine digit value of the speed of light? (Marks 4)

Q 7 (b) What is meant by pure and impure spectrum? Explain briefly how you will set up a spectrometer to obtain pure spectrum. Draw a diagram of a spectrometer and describe its parts. (Marks 4)

SECTION C
Answer two questions.

Q 8 (a) The ionisation potential of hydrogen atom is 13.6 volt. Draw the energy level diagram showing four levels. Calculate
(i) the energy of the photon emitted when an electron falls from the third orbit to the second orbit.
(ii) the wavelength of this photon. (Marks 4)

Q 8 (b) Described briefly with a diagram and theory an experiment to determine e/m of electron. (Marks 4)

Q 9 (a) What is Compton scattering? State briefly its importance. (Marks 2)

Q 9 (b) When ultraviolet light of wavelength 300 nm is incident on a metal plate, a negative potential of 0.54 volt is required to stop the emission of photo electrons. Calculate the energy of the incident photon and the work function for the metal in eV. (Marks 4)

Q 9 (c) Draw the circuit diagram of a half wave rectifier using a semi-conductor diode. Explain briefly the function of each component. (Marks 2)

Q 10 (a) Heavy water is suitable moderator in a nuclear reactor. Explain briefly why? (Marks 2)

Q 10 (b) Draw labelled diagrams to illustrate
(i) energy bands of a conductor, semiconductor and insulator.
(ii) npn and pnp transistors.
(iii) transistor as an amplifier (common emitter). (Marks 4)

Q 10 (c) What do you mean by AND gate? How will you realise AND gate with junction diodes? (Marks 2)