Physics · Sample Paper 3

General instructions

Section A · Objective

1. Question 11 mark

   Electric field lines start on

   1. A.negative charges
   2. B.positive charges
   3. C.neutral bodies
   4. D.magnets
2. Question 21 mark

   Three capacitors of 3 μF each are connected in parallel. The equivalent capacitance is

   1. A.1 μF
   2. B.3 μF
   3. C.9 μF
   4. D.6 μF
3. Question 31 mark

   The drift velocity of electrons in a conductor is of the order of

   1. A.10⁸ m/s
   2. B.10⁻⁴ m/s
   3. C.10³ m/s
   4. D.1 m/s
4. Question 41 mark

   The force on a current-carrying wire in a magnetic field is maximum when the angle between them is

   1. A.0°
   2. B.45°
   3. C.90°
   4. D.180°
5. Question 51 mark

   The magnetic field lines of a bar magnet inside the magnet run from

   1. A.N to S
   2. B.S to N
   3. C.nowhere
   4. D.east to west
6. Question 61 mark

   Eddy currents are reduced in transformer cores by using

   1. A.a solid iron core
   2. B.laminated cores
   3. C.copper cores
   4. D.air cores
7. Question 71 mark

   The reactance of a capacitor is

   1. A.directly proportional to frequency
   2. B.inversely proportional to frequency
   3. C.independent of frequency
   4. D.zero
8. Question 81 mark

   The speed of electromagnetic waves in vacuum is

   1. A.3 × 10⁸ m/s
   2. B.3 × 10⁶ m/s
   3. C.340 m/s
   4. D.it depends on frequency
9. Question 91 mark

   A concave mirror forms a real image of the same size when the object is at

   1. A.F
   2. B.C (2F)
   3. C.infinity
   4. D.between F and P
10. Question 101 mark

    Coherent sources must have

    1. A.the same amplitude only
    2. B.a constant phase difference and the same frequency
    3. C.different frequencies
    4. D.different colours
11. Question 111 mark

    The particle nature of light is shown by

    1. A.interference
    2. B.diffraction
    3. C.the photoelectric effect
    4. D.polarisation
12. Question 121 mark

    Which element is added to silicon to make a p-type semiconductor?

    1. A.phosphorus
    2. B.arsenic
    3. C.boron
    4. D.antimony
13. Question 131 mark

    Assertion (A): The resistance of a metal increases with temperature.

    Reason (R): Increased thermal vibrations of ions cause more frequent collisions with electrons.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.
14. Question 141 mark

    Assertion (A): Microwaves are used in radar.

    Reason (R): Microwaves have short wavelengths and travel in straight lines, allowing precise detection.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.
15. Question 151 mark

    Assertion (A): Hydrogen atoms emit line spectra.

    Reason (R): Electrons in atoms can have only certain discrete energy levels.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.
16. Question 161 mark

    Assertion (A): The photoelectric current increases with frequency of incident light at constant intensity.

    Reason (R): The kinetic energy of photoelectrons increases with frequency.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.

Section B · Very short answer

1. Question 172 marks

   Two charges of $+4\mu$C and $-4\mu$C are 2 mm apart. Find the dipole moment and the torque on it in a field of $10^5$ N/C at $30^{\circ }$.

2. Question 182 marks

   A wire of resistance 12 Ω is bent into a circle. Find the resistance between two diametrically opposite points.

3. Question 192 marks

   State Lenz's law. Show that it follows from conservation of energy.

4. OR

   Question 192 marks

   Why is AC preferred over DC for long-distance transmission?

5. Question 202 marks

   An object is placed 10 cm in front of a convex lens of focal length 15 cm. Find the position and nature of the image.

6. Question 212 marks

   Distinguish between nuclear fission and nuclear fusion with one example each.

Section C · Short answer

1. Question 223 marks

   Derive an expression for the potential energy of a system of two point charges. Find it for $+3\mu$C and $-2\mu$C placed 30 cm apart.

2. Question 233 marks

   State Kirchhoff's rules. In a circuit, a 6 V battery (internal resistance 1 Ω) is connected across 5 Ω. Find the current and the power dissipated in the 5 Ω resistor.

3. Question 243 marks

   State the Biot–Savart law. Use it to find the magnetic field at the centre of a circular loop of radius R carrying current I.

4. Question 253 marks

   A 220 V, 50 Hz supply is connected across a 100 μF capacitor. Find the capacitive reactance and the rms current.

5. OR

   Question 253 marks

   Name the parts of the electromagnetic spectrum used for (a) mobile communication (b) seeing broken bones (c) night-vision cameras. Arrange them in increasing wavelength.

6. Question 263 marks

   What is the difference between interference and diffraction? Give two points.

7. Question 273 marks

   Find the de Broglie wavelength of a proton moving at $3\times 10^5{\text{m s}}^{-1}$. ($m_p=1.67\times 10^{-27}$ kg)

8. Question 283 marks

   Draw (describe) the V–I characteristics of a p-n junction diode in forward and reverse bias. What is the knee voltage?

Section D · Case-based

1. Question 294 marks

   Case study — Camera flash. A camera flash uses a capacitor of 100 μF charged to 300 V by a battery circuit. When the button is pressed, the capacitor discharges through the flash tube in about 1 ms.

   (i) Find the charge on the capacitor. (1 mark)

   (ii) Find the energy stored in it. (1 mark)

   (iii) Find the average power delivered during the flash. (2 marks)

   OR

   (iii) If a dielectric of constant 2 is inserted while it is still connected to the 300 V source, find the new energy stored. (2 marks)

2. Question 304 marks

   Case study — Optical fibres. Optical fibres carry internet signals across oceans. Light travels through a glass core (refractive index 1.5) surrounded by cladding of lower refractive index (1.4). Light hitting the core–cladding boundary at angles greater than the critical angle is totally reflected.

   (i) Name the phenomenon that keeps light inside the fibre. (1 mark)

   (ii) State the two conditions for this phenomenon. (1 mark)

   (iii) Find the critical angle at the core–cladding boundary. (2 marks)

   OR

   (iii) Give two advantages of optical fibres over copper cables. (2 marks)

Section E · Long answer

1. Question 315 marks

   State Gauss's law. Use it to derive the electric field (a) due to an infinite plane sheet of charge, and (b) outside a uniformly charged thin spherical shell.

2. OR

   Question 315 marks

   Derive the expression for the equivalent capacitance of capacitors in series and in parallel. Find the equivalent capacitance of 2 μF and 4 μF in series, connected in parallel with 6 μF.

3. Question 325 marks

   Describe the construction and working of a transformer. Derive the relation between the voltages and turns. State two sources of energy loss.

4. OR

   Question 325 marks

   What is the principle of an AC generator? Describe its working and derive the expression for the induced emf.

5. Question 335 marks

   Using Young's double-slit experiment, derive the expression for fringe width. What happens to the fringe width if (a) the separation between the slits is halved (b) the experiment is done in water?

6. OR

   Question 335 marks

   State Bohr's postulates. Derive the expression for the radius of the nth orbit of the hydrogen atom and show that it is proportional to $n^2$.