­General Instructions:

1. All questions are compulsory. There are 27 questions in all.
2. This question paper has four sections: Section A, Section B, Section C and Section D.
3. Section A contains five questions of one mark each, Section B contains seven questions of two marks each, Section C contains twelve questions of three marks each, Section D contains three questions of five marks each.
4. There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all the three questions of five marks weightage. You have to attempt only one of the choices in such questions.
5. You may use the following values of physical constants wherever necessary:

Mass of neutron = 1.675 × 10⁻²⁷ kg

Mass of proton = 1.673 × 10²⁷ kg

Avogadro’s number = 6.023 × 10²³ per gram mole

Boltzmann constant = 1.38 × 10⁻²³ JK^-1

 

Section A

 

Question 1:

Draw equipotential surfaces for an electric dipole.

 

Question 2:

A proton is accelerated through a potential difference V, subjected to a uniform magnetic field acting normal to the velocity of the proton. If the potential difference is doubled, how will the circular path described by the proton in the magnetic field change?

 

Question 3:

The magnetic susceptibility of magnesium at 300 K is 1.2 × 10⁵. At what temperature will its magnetic susceptibility become 1.44 × 10⁵?

                                                                     OR

The magnetic susceptibility χ of a given material is –0.5. Identify the magnetic material.

 

Question 4:

Identify the semiconductor diode whose V-I characteristics are as shown.

 

Question 5:

Which part of the electromagnetic spectrum is used in RADAR? Give its frequency range.

                                                  OR

How are electromagnetic waves produced by accelerating charges?

 

Section B

 

Question 6:

A capacitor made of two parallel plates, each of area ‘A’ and separation ‘d’ is charged by an external dc source. Show that during charging, the displacement current inside the capacitor is the same as the current charging the capacitor.

 

Question 7:

A photon and a proton have the same de-Broglie wavelength l. Prove that the energy of the photon is  times the kinetic energy of the proton.

 

Question 8:

A photon emitted during the de-excitation of electron from a state n to the first excited state in a hydrogen atom, irradiates a metallic cathode of work function 2 eV, in a photo cell, with a stopping potential of 0.55 V. Obtain the value of the quantum number of the state n.

                                                                                                   OR

A hydrogen atom in the ground state is excited by an electron beam of 12.5 eV energy. Find out the maximum number of lines emitted by the atom from its excited state.

 

Question 9:

Draw the ray diagram of an astronomical telescope showing image formation in the normal adjustment position. Write the expression for its magnifying power.

                                                                                                  OR

Draw a labelled ray diagram to show image formation by a compound microscope and write the expression for its resolving power.

 

Question 10:

Write the relation between the height of a TV antenna and the maximum range up to which signals transmitted by the antenna can be received. How is this expression modified in the case of line of sight communication by space waves? In which range of frequencies, is this mode of communication used?

 

Question 11:

Under which conditions can a rainbow be observed? Distinguish between a primary and a secondary rainbow.

 

Question 12:

Explain the following:

(a) Sky appears blue.

(b) The Sun appears reddish at (i) sunset, (ii) sunrise.

 

Section-C

 

Question 13:

A capacitor (C) and resistor (R) are connected in series with an ac source of voltage of frequency 50 Hz. The potential difference across C and Rare respectively 120 V, 90 V, and the current in the circuit is 3 A. Calculate (i) the impedance of the circuit (ii) the value of the inductance, which when connected in series with C and R will make the power factor of the circuit unity.

                                                                                                                        OR

The figure shows a series LCR circuit connected to a variable frequency 230 V source.

                                                             

(a) Determine the source frequency which drives the circuit in resonance.

(b) Calculate the impedance of the circuit and amplitude of current at resonance.

(c) Show that potential drop across LC combination is zero at resonating frequency.

 

Question 14:

Give reason to explain why n and p regions of a Zener diode are heavily doped.

Find the current through the Zener diode in the circuit given below: (Zener breakdown voltage is 15 V)

                                    

 

Question 15:

Draw a labelled diagram of cyclotron. Explain its working principle. Show that cyclotron frequency is independent of the speed and radius of the orbit.

                                                                                                             OR

(a) Derive, with the help of a diagram, the expression for the magnetic field inside a very long solenoid having n turns per unit length carrying a current I.

(b) How is a toroid different from a solenoid?

 

Question 16:

Prove that the magnetic moment of the electron revolving around a nucleus in an orbit of radius r with orbital speed v is equal to  Hence using Bohr’s postulate of quantization of angular momentum, deduce the expression for the magnetic moment of hydrogen atom in the ground state

 

Question 17:

Two large charged plane sheets of charge densities s and  are arranged vertically with a separation of d between them. Deduce expressions for the electric field at points (i) to the left of the first sheet, (ii) to the right of the second sheet, and (iii) between the two sheets.

                                                                                                                        OR

A spherical conducting shell of inner radius r₁ and outer radius r₂ has a charge Q.

(a) A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surfaces of the shell.

(b) Is the electric field inside a cavity (with no charge) zero; independent of the fact whether the shell is spherical or not? Explain.

 

Question 18:

A signal of low frequency f_m is to be transmitted using a carrier wave of frequency f_c. Derive the expression for the amplitude modulated wave and deduce expressions for the lower and upper sidebands produced. Hence, obtain the expression for modulation index.

 

Question 19:

Draw a plot of  scattering by a thin foil of gold to show the variation of the number of the scattered particles with scattering angle. Describe briefly how the large angle scattering explains the existence of the nucleus inside the atom. Explain with the help of impact parameter picture, how Rutherford scattering serves a powerful way to determine an upper limit on the size of the nucleus.

 

Question 20:

A  parallel plate capacitor having plate separation of 5 mm is charged by a 100 V dc source. It remains connected to the source. Using an insulated handle, the distance between the plates is doubled and a dielectric slab of thickness 5 mm and dielectric constant 10 is introduced between the plates. Explain with reason, how the (i) capacitance, (ii) electric field between the plates, (iii) energy density of the capacitor will change?

 

Question 21:

Why is it difficult to detect the presence of an anti-neutrino during  Define the term decay constant of a radioactive nucleus and derive the expression for its mean life in terms of the decay constant.

                                                                                                          OR

(a) State two distinguishing features of nuclear force.

(b) Draw a plot showing the variation of potential energy of a pair of nucleons as a function of their separation. Mark the regions on the graph where the force is (i) attractive, and (ii) repulsive

 

Question 22:

A triangular prism of refracting angle 60° is made of a transparent material of refractive index  A ray of light is incident normally on the face KL as shown in the figure. Trace the path of the ray as it passes through the prism and calculate the angle of emergence and angle of deviation.

 

Question 23:

Prove that in a common-emitter amplifier, the output and input differ in phase by 180°. In a transistor, the change of base current by  produces change of 0·02 V in the base-emitter voltage and a change of 4 mA in the collector current. Calculate the current amplification factor and the load resistance used, if the voltage gain of the amplifier is 400.

 

Question 24:

Show, on a plot, variation of resistivity of (i) a conductor, and (ii) a typical semiconductor as a function of temperature. Using the expression for the resistivity in terms of number density and relaxation time between the collisions, explain how resistivity in the case of a conductor increases while it decreases in a semiconductor, with the rise of temperature.

 

Section-D

 

Question 25:

(A) Derive an expression for the induced emf developed when a coil of N turns, and area of cross-section A, is rotated at a constant angular speed w in a uniform magnetic field B.

(B) A wheel with 100 metallic spokes each 0·5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth’s magnetic field. If the resultant magnetic field at that place is 4 * 10 ^–4 T and the angle of dip at the place is 30°, find the emf induced between the axle and the rim of the wheel.

                                                                                                                         OR

(a) Derive the expression for the magnetic energy stored in an inductor when a current I develop in it. Hence, obtain the expression for the magnetic energy density.

(b) A square loop of sides 5 cm carrying a current of 0·2 A in the clockwise direction is placed at a distance of 10 cm from an infinitely long wire carrying a current of 1 A as shown. Calculate (i) the resultant magnetic force, and (ii) the torque, if any, acting on the loop.

                                                                                                 

 

Question 26:

Explain, with the help of a diagram, how plane polarized light can be produced by scattering of light from the Sun. Two polaroid’s P₁ and P₂ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity I is incident on P₁. A third polaroid P₃ is kept between P₁ and P₂ such that its pass axis makes an angle of 45° with that of P₁. Calculate the intensity of light transmitted through P₁, P₂ and P₃.

                                                                                                OR

(a) Why cannot the phenomenon of interference be observed by illuminating two pin holes with two sodium lamps? 

(b) Two monochromatic waves having displacements y₁ = a cos wt and y₂ = a cos(wt + f) from two coherent sources interfere to produce an interference pattern. Derive the expression for the resultant intensity and obtain the conditions for constructive and destructive interference.

(c) Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 * 10^–6 m. If the distance between the slit and the screen is 1·5 m, calculate the separation between the positions of the second maxima of diffraction pattern obtained in the two cases.

 

Question 27:

(a) Describe briefly, with the help of a circuit diagram, the method of measuring the internal resistance of a cell.

(b) Give reason why a potentiometer is preferred over a voltmeter for the measurement of emf of a cell.

(c) In the potentiometer circuit given below, calculate the balancing length l. Give reason, whether the circuit will work, if the driver cell of emf 5 V is replaced with a cell of 2 V, keeping all other factors constant.

                                                                                             OR

(a) State the working principle of a meter bridge used to measure an unknown resistance.

(b) Give reason:

(i) why the connections between the resistors in a metre bridge are made of thick copper strips.

(ii) why is it generally preferred to obtain the balance length near the mid-point of the bridge wire.

(c) Calculate the potential difference across the 4 Ω resistors in the given electrical circuit, using Kirchhoff’s rules.

 

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