Sample Paper I

Question 1. Two positive charges q2 and q3 fixed along the y axis, exert a net electric force in the + x direction on a charge q1 fixed along the x axis as shown. If a positive charge Q is added at (x, 0), the force on q1

(a) shall increase along the positive x-axis.

(b) shall decrease along the positive x-axis.

(c) shall point along the negative x-axis.

(d) shall increase but the direction changes because of the intersection of Q with q2 and q3.

Question 2. Two batteries of emf $\epsilon_1$ and $\epsilon_2$ ($\epsilon_2 > \epsilon_1$) and internal resistances $r_1$ and $r_2$ respectively are connected in parallel as shown.

(a) The equivalent emf $\epsilon_{eq}$ of the two cells is between $\epsilon_1$ and $\epsilon_2$, i.e. $\epsilon_1 < \epsilon_{eq} < \epsilon_2$.

(b) The equivalent emf $\epsilon_{eq}$ is smaller than $\epsilon_1$.

(c) The $\epsilon_{eq}$ is given by $\epsilon_{eq} = \epsilon_1 + \epsilon_2$ always.

(d) $\epsilon_{eq}$ is independent of internal resistances $r_1$ and $r_2$.

Question 3. A proton has spin and magnetic moment just like an electron. Why then its effect is neglected in magnetism of materials?

Question 4. If a LC circuit is considered analogous to a harmonically oscillating spring-block system, which energy of the LC circuit would be analogous to potential energy and which one analogous to kinetic energy?

Question 5. A variable frequency ac source is connected to a capacitor. How will the displacement current change with decrease in frequency?

Question 6. In pair annihilation, an electron and a positron destroy each other to produce gamma radiation. How is the momentum conserved?

Question 7. Can the potential barrier across a p-n junction be measured by simply connecting a voltmeter across the junction?

Question 8. The conductivity of a semiconductor increases with increase in temperature because

(a) number density of free current carriers increases.

(b) relaxation time increases.

(c) both number density of carriers and relaxation time increase.

(d) number density of current carriers increases, relaxation time decreases but effect of decrease in relaxation time is much less than increase in number density.

Question 9. Two charges q and –3q are placed fixed on x-axis separated by distance ‘d’. Where should a third charge 2q be placed such that it will not experience any force?

Question 10. The battery remains connected to a parallel plate capacitor and a dielectric slab is inserted between the plates. What will be effect on its (i) potential difference, (ii) capacity, (iii) electric field, and (iv) energy stored?

Question 11. Obtain an expression for the magnetic dipole moment of a revolving electron in a Bohr model.

Question 12. A wire in the form of a tightly wound solenoid is connected to a DC source, and carries a current. If the coil is stretched so that there are gaps between successive elements of the spiral coil, will the current increase or decrease? Explain.

Question 13. You are given a 2$\mu$F parallel plate capacitor. How would you establish an instantaneous displacement current of 1mA in the space between its plates?

Question 14. There are two sources of light, each emitting with a power of 100 W. One emits X-rays of wavelength 1nm and the other visible light at 500 nm. Find the ratio of number of photons of X-rays to the photons of visible light of the given wavelength?

Question 15. A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is $1.813 \times 10^{-4}$. Calculate the particle’s mass and indentify the particle.

Question 16. Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

Question 17. What do the terms ‘depletion region’ and ‘barrier potential’ mean for a p-n junction?

Question 18. If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earth’s radius?

Question 19. Derive an expression (in vector form) for electric field of a dipole at a point on the equitorial plane of the dipole. How does the field vary at large distances?

Question 20. What is relaxation time? Derive an expression for resistivity of a wire in terms of member density of free electrons and relaxation time.

Question 21. First a set of n equal resistors of R each is connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current becomes 10 times. What is ‘n’?

Question 22. An equiconvex lens (of refractive index 1.50) is placed in contact with a liquid layer on top of a plane mirror as shown. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Question 23. Obtain an expression for focal length of a combination of thin lenses in contact.

Question 24. Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $h/3$. A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.

Question 25. Define ‘half -life’ and ‘average-life’ of a radioactive substance. What is the relation between the two?

Question 26. Using a suitable combination from a NOR, an OR and a NOT gate, draw circuits to obtain the truth tables given below:

Question 27. Define the terms ‘modulation index’ for an AM wave. What would be the modulation index for an AM wave for which the maximum amplitude is ‘a’ and the minimum amplitude is ‘b’?

Question 28. (i) Derive an expression for the magnetic field at a point on the axis of a current carrying circular loop.

(ii) A coil of 100 turns (tighty bound) and radius 10 cm. carries a current of 1A. What is the magnitude of the magnetic field at the centre of the coil?

State Ampere’s circuital law. Consider a long straight wire of a circular cross section (radius a) carrying steady current I. The current I is uniformly distributed across this cross section. Using Ampere’s circuital law, find the magnetic field in the region $r < a$ and $r > a$.

Question 29. An ac voltage $v = v_m \sin \omega t$ is applied to a series LCR circuit. Obtain the expression for current in the circuit and the phase angle between current and voltage. What is the resonance frequency?

An ac voltage $v = v_m \sin \omega t$ is applied to a pure inductor L. Obtain an expression for the current in the circuit. Prove that the average power supplied to an inductor over one complete cycle is zero.

Question 30. (i) State and explain Huygens Principle. Using it, obtain Snell’s law of refraction.

(ii) When light travels from a rarer to a denser medium, the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave?

With the help of a labelled ray diagram show the image formation by a compound microscope. Derive an expression for its magnifying power. How can the magnifying power be increased?