# 12th Physics Paper Solutions Set 3 : CBSE Abroad Previous Year 2014

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.
Q1 :

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.

The electric potential at a point distant r due to the field created by a positive charge Q is given by
v=14πÎµ0qrv=14πÎµ0qr
Since rQ > rP, we have:
VQ < VP
∴ The potential energy difference VP - VQ is positive between Q and P.

Q2 :

In both Î² and Î²+ decay processes, the mass number of a nucleus remains same whereas the atomic number Z increases by one in Î² decay and decreases by one in Î²+ decay. Explain, giving reason.

In Î²- decay, a Î² particle of zero mass and -1 charge is emitted. The decay process is shown below:
XzAâ†’YZ+1A+Î²-10+Î½XzAâ†’YZ+1A+Î²-10+Î½
Since the mass of Î²- particle is negligibly small, the mass number of the nucleus remains the same and the atomic number increases by 1 due to the loss of 1 negative charge.
Similarly, for a Î²+ decay, a Î² particle of negligibly small and +1 charge is emitted. The decay process is shown below:
XzAâ†’YZ+1A+Î²+10+Î½XzAâ†’YZ+1A+Î²+10+Î½
The mass number remains the same, but here, the atomic number decreases by 1 due to the loss of 1 positive charge.

Q3 :

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

Electric field is defined to be the gradient of potential and the surface of a conductor has a constant potential. Therefore, there is no field along the surface of the conductor and, hence, the electrostatic field at the surface of a charged conductor should be normal to the surface at every point.

Q4 :

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.

Q5 :

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.

Q6 :

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 refractive index of the material of the sphere is 3âˆš.

Q7 :

Arrange the following electromagnetic waves in decreasing order of wavelength:

Î³-rays, infrared rays, X-rays and microwaves.

Q8 :

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.

Q9 :

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

Q10 :

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, Dm = 2i − A.

Q11 :

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.

Q12 :

Show that the current leads the voltage in phase by Ï€/2 in an AC circuit containing an ideal capacitor.

Q13 :

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.

Q14 :

(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.

Q15 :

Give two points to distinguish between a paramagnetic and a diamagnetic substance.

Q16 :

Identify the gate equivalent to the circuit shown in the figure. Write its truth table.

Q17 :

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

Q18 :

A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 â„¦ and a capacitor of reactance 200 â„¦ in series. An alternating emf of 1502âˆš, V, 500/π Hz is applies across this series combination. Calculate the power dissipated in the resistor.

Q19 :

(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.

Q20 :

(a) Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib 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.

Q21 :

(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.

Q22 :

(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 Ïƒ1 and Ïƒ2 (Ïƒ1 > Ïƒ2) are shown in the figure. Write the magnitudes and directions of the net fields in the regions marked II and III.

Q23 :

When Puja, a student of 10th 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.

Q24 :

Three concentric metallic shells A, B and C or radii a, b and c (a < b < c) have surface charge densities + Ïƒ,  −Ïƒ and + Ïƒ, 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.

Q25 :

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.

Q26 :

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.

Q27 :

(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.

Q28 :

(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.

Q29 :

(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 (Ï„). Find out their relationships with the decay constant (Î»).

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

Q30 :

(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 Îµ1 and Îµ2 connected in the manner shown are obtained at a distance of l1 = 120 cm and l2 = 300 cm from the end A. Determine (i) Îµ1/Îµ2 and (ii) position of null point for the cell Îµ1 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 Î© resistor is 200 W, determine the power dissipated in the 5 Î© resistor.