Board Paper of Class 12-Science 2014 Physics (SET 3) - Solutions

General Instructions:
(i) All questions are compulsory.
(ii) There are 30 questions in total. Question Nos. 1 to 8 are very short answer type questions and carry one mark each.
(iii) Questions Nos. 9 to 18 carry two marks each. Questions Nos. 19 to 27 carry three marks each and questions Nos. 28 to 30 carry five marks each.
(iv) 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 three questions of five marks each. You have to attempt only one of the choices in such questions.
(v) Use of calculators is not permitted. However, you may use log tables if necessary.

Question 1
Figure shows the field lines due to a positive point charge. Give the sign of potential energy difference of a small negative charge between the points Q and P.
VIEW SOLUTION

Question 2
In both β⁻ and β⁺ decay processes, the mass number of a nucleus remains the same, whereas the atomic number Z increases by one in β⁻ decay and decreases by one in β⁺ decay. Explain giving reason. VIEW SOLUTION

Question 3
Why must electrostatic field at the surface of a charged conductor be normal to the surface at every point? Give reason. VIEW SOLUTION

Question 4
A triangular loop of wire placed at abc is moved completely inside a magnetic field which is directed normal to the plane of the loop away from the reader to a new position a'b'c'. What is the direction of the current induced in the loop? Give reason.
VIEW SOLUTION

Question 5
An electron in an atom revolves round the nucleus in an orbit of radius r with frequency v. Write the expression for the magnetic moment of the electron. VIEW SOLUTION

Question 6
A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if the refractive index of the material of the sphere is $\sqrt{3}$ .

VIEW SOLUTION

Question 7
Arrange the following electromagnetic waves in decreasing order of wavelength:
γ-rays, infrared rays, X-rays and microwaves.
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Question 8
Plot a graph showing the variation of photoelectric current with collector plate potential at a given frequency but for two different intensities I₁ and I₂, where I₂ > I₁. VIEW SOLUTION

Question 9
In the circuit shown in the figure, find the total resistance of the circuit and the current in the arm AD.
VIEW SOLUTION

Question 10
Figure shows a ray of light passing through a prism. If the refracted ray QR is parallel to the base BC, show that (i) r₁ = r₂ = A/2 and (ii) angle of minimum deviation, D_m = 2i − A.

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Question 11
Draw energy band diagrams of an n-type and p-type semiconductor at temperature T > 0 K. Mark the donor and acceptor energy levels with their energies.

OR

Distinguish between a metal and an insulator on the basis of energy band diagrams. VIEW SOLUTION

Question 12
Show that the current leads the voltage in phase by π/2 in an AC circuit containing an ideal capacitor. VIEW SOLUTION

Question 13
Two very small identical circular loops, (1) and (2), carrying equal currents I are placed vertically (with respect to the plane of the paper) with their geometrical axes perpendicular to each other as shown in the figure. Find the magnitude and direction of the net magnetic field produced at the point O.
VIEW SOLUTION

Question 14
(a) How does oscillating charge produce electromagnetic waves?
(b) Sketch a schematic diagram depicting oscillating electric and magnetic fields of an em wave propagating along + z-direction. VIEW SOLUTION

Question 15
Give two points to distinguish between a paramagnetic and a diamagnetic substance. VIEW SOLUTION

Question 16
Identify the gate equivalent to the circuit shown in the figure. Write its truth table.
VIEW SOLUTION

Question 17
Define the term modulation. Draw a block diagram of a simple modulator for obtaining AM signal. VIEW SOLUTION

Question 18
A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 Ω and a capacitor of reactance 200 Ω in series. An alternating emf of $150 \sqrt{2}$ , V, 500/π Hz is applies across this series combination. Calculate the power dissipated in the resistor. VIEW SOLUTION

Question 19
(a) Why is zener diode fabricated by heavily doping both p- and n-sides of the junction?
(b) Draw the circuit diagram of zener diode as a voltage regulator and briefly explains its working.
OR

(a) How is a photodiode fabricated?
(b) Briefly explain its working. Draw its V - I characteristics for two different intensities of illumination. VIEW SOLUTION

Question 20
(a) Two long straight parallel conductors 'a' and 'b', carrying steady currents I_a and I_b are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?

(b) Show with the help of a diagram how the force between the two conductors would change when the currents in them flow in the opposite directions. VIEW SOLUTION

Question 21
(a) Describe briefly how the Davisson-Germer experiment demonstrated the wave nature of electrons.

(b) An electron is accelerated from rest through a potential V. Obtain the expression for the de-Broglie wavelength associated with it. VIEW SOLUTION

Question 22
(a) A point charge (+Q) is kept in the vicinity of an uncharged conducting plate. Sketch the electric field lines between the charge and the plate.
(b) Two infinitely large plane thin parallel sheets having surface charge densities σ₁ and σ₂ (σ₁ > σ₂) are shown in the figure. Write the magnitudes and directions of the net fields in the regions marked II and III.
VIEW SOLUTION

Question 23
When Puja, a student of 10^th class, watched her mother washing clothes in the open, she observed coloured soap bubbles and was curious to know why the soap bubbles appear coloured. In the evening when her father, an engineer by profession, came home, she asked him this question. Her father explained to her the basic phenomenon of physics due to which the soap bubbles appear coloured.
(a) What according to you are the values displayed by Puja and her father?

(b) State the phenomenon of light involved in the formation of coloured soap bubbles. VIEW SOLUTION

Question 24
Three concentric metallic shells A, B and C or radii a, b and c (a < b < c) have surface charge densities + σ, −σ and + σ, respectively as shown in the figure

If shells A and C are at the same potential, then obtain the relation between the radii a, b and c. VIEW SOLUTION

Question 25
A toroidal solenoid with air core has an average radius of 15 cm, area of cross-section 12 cm² and has 1200 turns. Calculate the self-inductance of the toroid. Assume the field to be uniform across the cross-section of the toroid. VIEW SOLUTION

Question 26
Explain, with the help of a suitable diagram, the space wave mode of propagation. Give two examples in communication systems where this mode is used. What is the frequency range of these waves? Give reason for using this range of frequency. VIEW SOLUTION

Question 27
(a) Distinguish between unpolarised and linearly polarised light.

(b) A partially plane polarised beam of light is passed through a polaroid. Show graphically the variation of the transmitted light intensity with angle of rotation of the polaroid.

(c) Explain with the help of a diagram how sunlight is polarised by scattering through atmospheric particles. VIEW SOLUTION

Question 28
(a) Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main considerations required in selecting the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope.

(b) A compound microscope has an objective of focal length 1.25 cm and eyepiece of focal length 5 cm. A small object is kept at 2.5 cm from the objective. If the final image formed is at infinity, find the distance between the objective and the eyepiece.

OR

(a) Write three characteristic features to distinguish between the interference fringes in Young's double slit experiment and the diffraction pattern obtained due to a narrow single slit.

(b) A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is a distance of 2.5 mm away from the centre. Find the width of the slit. VIEW SOLUTION

Question 29
(a) Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom.

(b) Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.

OR

(a) Define the terms (i) half-life (T₁_/2) and (ii) average life (τ). Find out their relationships with the decay constant (λ).

(b) A radioactive nucleus has a decay constant λ = 0.3465 (day)^–1. How long would it take the nucleus to decay to 75% of its initial amount? VIEW SOLUTION

Question 30
(a) State the principle of a potentiometer. Define potential gradient. Obtain an expression for potential gradient in terms of resistivity of the potentiometer wire.

(b) Figure shows a long potentiometer wire AB having a constant potential gradient. The null points for the two primary cells of emfs ε₁ and ε₂ connected in the manner shown are obtained at a distance of l₁ = 120 cm and l₂ = 300 cm from the end A. Determine (i) $\frac{ε_{1}}{ε_{2}}$ and (ii) position of null point for the cell ε₁ only.

OR

(a) Define the term 'drift velocity' of charge carriers in a conductor. Obtain the expression for the current density in terms of relaxation time.

(b) A 100 V battery is connected to the electric network as shown. If the power consumed in the 2 Ω resistor is 200 W, determine the power dissipated in the 5 Ω resistor.

VIEW SOLUTION

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