Code No.55/1/1

· Please check that this question paper contains 11 printed pages.

· Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate.

· Please check that this question paper contains 27 questions.

· Please write down the serial number of the question before attempting it.

PHYSICS (Theory)
Time allowed : 3 hours Maximum Marks : 70

(i) All questions are compulsory.

(ii) There is no overall choice. However, an internal choice has been provided in one

question of two marks, one question of three marks and one question of five marks.

You have to attempt only one of the choices in such questions.

(iii) Question numbers 1 to 5 are very short answer type questions, carrying one mark each.

(iv) Question numbers 6 to 12 are short answer type questions, carrying two marks each.

(v) Question numbers 13 to 24 are also short answer type questions, carrying three marks each.

(vi) Question numbers 25 to 27 are long answer type questions, carrying five marks each.

(vii) Use of calculators is not permitted. However, you may use log tables, if necessary.

(viii) You may use the following values of physical constants wherever necessary :

c = 3 × 10⁸ ms^-1

h = 6.6 × 10^-34 Js

e = 1.6 × 10^-19 C

m_e = 9.1 × 10^-31 kg

μ₀ = 4π × 10^-7 T m A^-1

1/4πε₀ = 9×109 N-m² / C²

Mass of neutron m_n=1.6 × 27^-27 kg

Boltzmann's constant k = 1.38 × 10^-23 J K^-1

Avogadro's number N_A = 6.023 × 10²³ / mole

1. An electric dipole of dipole moment 20 × 10^-6 C.m is enclosed by a closed surface. What is the net flux coming out of the surface ? 1

2. An electron beam projected along + X-axis, experiences a force due to a magnetic field along the + Y-axis. What is the direction of the magnetic field ? 1

3. The power factor of an a.c. circuit is 0.5. What will be the phase difference between voltage and current in this circuit ? 1

4. Electrons are emitted from a photosensitive surface when it is illuminated by green light but electron emission does not take place by yellow light. Will the electrons be emitted when the surface is illuminated by (i) red light, and (ii) blue light ? 1

5. What should be the length of the dipole antenna for a carrier wave of frequency 3 × 10⁸ Hz ? 1

6. Define 'electric line of force' and give its two important properties. 2

7. (a) Why does the electric field inside a dielectric decrease when it is placed in an external electric field ?

(b) A parallel plate capacitor with air between the plates has a capacitance of 8 pF. What will be the capacitance if the distance between the plates be reduced by half and the space between them is filled with a substance of dielectric constant K = 6 ? 2

8. Draw V—I graph for ohmic and non-ohmic materials. Give one example for each. 2

9. Define the terms 'Magnetic Dip' and 'Magnetic Declination' with the help of relevant diagrams. 2

10. (i) Draw the graphs showing variation of inductive reactance and capacitive reactance with frequency of applied a.c. source.

(ii) Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied voltage of the a.c. source ? Justify your answar. 2

11. The image of a candle is formed by a convex lens on a screen. The lower half of the lens is painted black to make it completely opaque. Draw the ray diagram to show the image formation. How will this image be different from the one obtained when the lens is not painted black ? 2

12. An electric dipole is held in a uniform electric field. (i) Using suitable diagram, show that it does not undergo any translatory motion, and (ii) derive an expression for the torque acting on it and specify its direction. 3

13. A galvanometer with a coil of resistance 120 ohm shows full scale deflection for a current of 2.5 mA. How will you convert the galvanometer into an ammeter of range 0 to 7.5 A ? Determine the net resistance of the ammeter. When an ammeter is put in a circuit, does it read slightly less or more than the actual current in the original circuit ? Justify your answer. 3

14. Define the term 'resistivity' and write its S.I. unit. Derive the expression for the resistivity of a conductor in terms of number density of free electrons and  relaxation time. 3

State the principle of potentiometer. Draw a circuit diagram used to compare the e.m.f. of two primary cells. Write the formula used. How can the sensitivity of a potentiometer be increased ?

15. Explain, with the help of diagram, the principle and working of an a.c. generator. Write the expression for the e.m.f. generated in the coil in terms of its speed of rotation. 3

16. Give reasons for the following : 3

(i) Long distance radio broadcasts use short-wave bands.

(ii) The small ozone layer on top of the stratosphere is crucial for human survival.

(iii) Satellites are used for long distance TV transmission.

17. A figure divided into squares, each of size 1 mm², is being viewed at a distance of 9 cm through a magnifying lens of focal length 10 cm, held close to the eye.

(a) Draw a ray diagram showing the formation of the image.

(b) What is the magnification produced by the lens ? How much is the area of each square in the virtual image ?

(c) What is the angular magnification of the lens ? 3

18. Ultraviolet light of wavelength 2271 Å from a 100 W mercury source radiates a photo cell made of molybdenum metal. If the stopping potential is 1.3 V, estimate the work function of the metal. How would the photo cell respond to high intensity (10⁵ Wm^-2) red light of wavelength 6328 Å produced by a He - Ne laser ? Plot a graph showing the variation of photoelectric current with anode potential for two light beams of same wavelength but different intensity. 3

19. (a) Draw a graph showing the variation of potential energy of a pair of nucleons as a function of their separation. Indicate the regions in which nuclear force is (i) attractive, and (ii) repulsive.

(b) Write two characteristic features of nuclear force which distinguish it from the coluomb force. 3

20. (a) Show that the decay rato 'R' of a sample of a radionuclide is related to the number of radioactive nuclei 'N' at the same instant by the expression R = λN.

(b) The half life of ₉₂U²³⁸ against α-decay is 1.5 × 10¹⁷ s. What is the activity of a sample of ₉₂U²³⁸ having 25 × 10²⁰ atoms ? 3

21. Distinguish between analog and digital communication. Write any two modulation techniques employed for the digital data. Describe briefly one of the techniques used. 3

22. Draw a schematic diagram of a single optical fibre structure. Explain briefly how an optical fibre is fabricated. Describe in brief, the mechanism of propagation of light signal through an optical fibre.

23. (a) With the help of a labelled diagram, explain the principle and working, of a moving coil galvanometer.

(b) Two parallel coaxial circular coils of equal radius ‘R’ and equal number of turns ‘N’, carry equal currents 'I' in the same direction and are separated by a distance ‘2R’. Find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres. 5

24. (a) How is a wave front different from a ray ? Draw the geometrical shape of the wave fronts when (i) light diverges from a point source, and (ii) light emerges out of a convex lens when a point source is placed at its focus.

(b) State Huygens’ principle. With the help of a suitable diagram, prove Snell’s law of refraction using Huygens’ principle. 5

(a) In Young’s double slit experiment, deduce the conditions for (i) constructive, and (ii) destructive interference at a point on the screen. Draw a graph showing

variation of the resultant intensity in the interference pattern against position ‘x’ on the screen.

(b) Compare and contrast the pattern which is seen with two coherently, illuminated narrow slits in Young’s experiment with that seen for a coherently illuminated single slit producing diffraction.

25. (a) Distinguish between metals, insulators and semiconductors on the basis of their energy bands.

(b) Why are photodiodes used preferably in reverse bias condition ? A photodiode is fabricated from a semiconductor with band gap of 2.8 eV. Can it detect a wavelength of 6000 nm ? Justify. 8

(a) Explain briefly, with the help of circuit diagram, how V—I characteristics of a p-n junction diode are obtained in (i) forward bias, and (ii) reverse bias. Draw the shape of the curves obtained.

(b) A semiconductor has equal electron and hole concentration of 6×108/m3 . On doping with certain impurity, electron concentration increases to  9×1012/m3.

(i) Identify the new semiconductor obtained after doping.

(ii) Calculate the new hole concentration.