# 12th Physics Paper Solutions Set 3 : CBSE Delhi 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 :

Define the term 'drift velocity' of charge carriers in a conductor and write its relationship with the current flowing through it.

In a current-carrying conductor, a charged particle is accelerated by an electric field. It also undergoes frequent collisions with the stationary ions of the wire material. These two effects result in a very slow net motion (drift) of moving charged particles in the direction of the electric force. This motion is described by the drift velocity(vd).

The relationship of drift velocity with current is given by
vd = IneA

Here:
I is the current following through the conductor.
n is the number density of an electron.
A is the area of the conductor.
e is the charge of the electron.

Q2 :

The carrier wave of a signal is given by C(t) = 3 sin (8Ï€t) volt. The modulating signal is a square wave as shown. Find its modulation index. Modulation index (Î¼) is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

The generalised equation of a carrier wave is given below:
c(t) =AcsinÏ‰ct

The generalised equation of a modulating wave is given below:

cm(t)=AcsinÏ‰ct+Î¼AcsinÏ‰mtsinÏ‰ct

Here, Î¼ is defined as AmAc.

On comparing this with the equations of carrier wave and modulating wave, we get:

Amplitude of a modulating signal, Am = 1.5 V

Amplitude of a carrier wave, Ac = 3 V

∴  Î¼=AmAc=1.53=12=0.5

Q3 :

Write the expression, in a vector form, for the Lorentz magnetic force Fâƒ—  due to a charge moving with velocity Vâƒ—  in a magnetic field Bâƒ— . What is the direction of the magnetic force?

The Lorentz magnetic force is given by the following relation:
Fâƒ— =q(Vâƒ— xBâƒ— )
Here, q is the magnitude of the moving charge.
The direction of the magnetic force is perpendicular to the plane containing the velocity vector (Vâƒ— ) and the magnetic field vector (Bâƒ— ).

Q4 :

Plot a graph showing variation of current versus voltage for the material GaAs.

Q5 :

A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

Q6 :

The figure given below shows the block diagram of a generalized communication system. Identify the element labelled 'X' and write its function. Q7 :

Two spherical bobs, one metallic and the other of glass, of the same size are allowed to fall freely from the same height above the ground. Which of the two would reach earlier and why?

Q8 :

"For any charge configuration, equipotential surface through a point is normal to the electric field." Justify.

Q9 :

An electric dipole of length 1 cm, which placed with its axis making an angle of 60Â° with uniform electric field, experience a torque of 63âˆš Nm. Calculate the potential energy of the dipole if it has charge Â±2 nC.

Q10 :

State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies.

Q11 :

A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance? Q12 :

A deuteron and an alpha particle are accelerated with the same accelerating potential.
Which one of the two has
(1) greater value of de-Broglie wavelength, associated with it and
(2) less kinetic energy? Explain.

Q13 :

Out of the two magnetic materials, 'A' has relative permeability slightly greater than unity while 'B' has less than unity. Identify the nature of the materials 'A' and 'B'. Will their susceptibilities be positive or negative?

Q14 :

State Kirchhoff's rules. Explain briefly how these rules are justified.

Q15 :

Given a uniform electric filed Eâƒ— =4x103 iË† N/C. Find the flux of this field through a square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 30Â° angle with the x-axis?

Q16 :

(i) Monochromatic light of frequency 5.0 Ã— 1014 Hz is produced by a laser. The power emitted is 3.0 Ã— 10–3 W. Estimate the number of photons emitted per second on an average by the source.

(ii) Draw a plot showing the variation of photoelectric current versus the intensity of incident radiation on a given photosensitive surface.

Q17 :

Write the truth table for the combination of the gates shown. Name the gates used. OR

Identify the logic gates marked 'P' and 'Q' in the given circuit. Write the truth table for the combination. Q18 :

For a single slit of width "a", the first minimum of the interference pattern of a monochromatic light of wavelength Î» occurs at an angle of Î»a. At the same angle of Î»a, we get a maximum for two narrow slits separated by a distance "a". Explain.

Q19 :

(a) State Ampere's circuital law, expressing it in the integral form.
(b) Two long coaxial insulated solenoids, S1 and S2 of equal lengths are wound one over the other as shown in the figure. A steady current "I" flow thought the inner solenoid S1 to the other end B, which is connected to the outer solenoid S2 through which the same current "I" flows in the opposite direction so as to come out at end A. If n1 and n2 are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point (i) inside on the axis and (ii) outside the combined system. Q20 :

A 12.3 eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy level the hydrogen atoms would be excited?
Calculate the wavelengths of the second member of Lyman series and second member of Balmer series.

Q21 :

(a) Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.

(b) The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a. OR

(a) Derive the expression for the capacitance of a parallel plate capacitor having plate area A and plate separation d.

(b) Two charged spherical conductors of radii R1 and R2 when connected by a conducting wire acquire charges q1 and q2 respectively.

Find the ratio of their surface charge densities in terms of their radii.

Q22 :

(a) A mobile phone lies along the principal axis of a concave mirror. Show, with the help of a suitable diagram, the formation of its image. Explain why magnification is not uniform.

(b) Suppose the lower half of the concave mirror's reflecting surface is covered with an opaque material. What effect this will have on the image of the object? Explain.

Q23 :

(a) Draw a labelled ray diagram showing the formation of a final image by a compound microscope at least distance of distinct vision.

(b) The total magnification produced by a compound microscope is 20. The magnification produced by the eye piece is 5. The microscope is focussed on a certain object. The distance between the objective and eyepiece is observed to be 14 cm. If least distance of distinct vision is 20 cm, calculate the focal length of the objective and the eye piece.

Q24 :

Answer the following the questions:
(a) Name the em waves which are produced during radioactive decay of a nucleus. Write their frequency range.
(b) Welders wear special glass goggles while working. Why? Explain.
(c) Why are infrared waves often called as heat waves? Given their one application.

Q25 :

A potentiometer wire of length 1 m has a resistance of 5 Î©. It is connected to a 8 V battery in series with a resistance of 15 Î©. Determine the emf of the primary cell which gives a balance point at 60 cm.

Q26 :

(a) Deduce the expression, N = N0 e-Î»t, for the law of radioactive decay.

(b) (i) Write symbolically the process expressing the Î²+ decay of Na1122. Also write the basic nuclear process underlying this decay.

(ii) Is the nucleus formed in the decay of the nucleus Na1122, an isotope or isobar?

Q27 :

When Sunita, a class XII student, came to know that her parents are planning to rent out the top floor of their house to a mobile company she protested. She tried hard to convince her parents that this move would be a health hazard.
Ultimately her parents agreed :
(1) In what way can the setting up of transmission tower by a mobile company in a residential colony prove to be injurious to health?
(2) By objecting to this move of her parents, what value did Sunita display?
(3) Estimate the range of e.m. waves which can be transmitted by an antenna of height 20 m. (Given radius of the earth = 6400 km)

Q28 :

(a) State briefly the processes involved in the formation of p-n junction explaining clearly how the depletion region is formed.

(b) Using the necessary circuit diagrams, show how the V-I characteristics of a p-n junction are obtained in

(i) Forward biasing
(ii) Reverse biasing

How are these characteristics made use of in rectification?

OR

(a) Differentiate between three segments of a transistor on the basis of their size and level of doping.

(b) How is a transistor biased to be in active state?

(c) With the help of necessary circuit diagram, describe briefly how n-p-n transistor in CE configuration amplifies a small sinusoidal input voltage. Write the expression for the ac current gain.

Q29 :

(a)
(i) 'Two independent monochromatic sources of light cannot produce a sustained interference pattern'. Give reason.
(ii) Light waves each of amplitude "a" and frequency "Ï‰", emanating from two coherent light sources superpose at a point. If the displacements due to these waves is given by y1 = a cos Ï‰t and y2 = a cos(Ï‰t + Ï•) where Ï• is the phase difference between the two, obtain the expression for the resultant intensity at the point.

(b) In Young's double slit experiment, using monochromatic light of wavelength Î», the intensity of light at a point on the screen where path difference is Î», is K units. Find out the intensity of light at a point where path difference is Î»/3.

OR

(a) How does one demonstrate, using a suitable diagram, that unpolarised light when passed through a Polaroid gets polarised?

(b) A beam of unpolarised light is incident on a glass-air interface. Show, using a suitable ray diagram, that light reflected from the interface is totally polarised, when Î¼ = tan iB, where Î¼ is the refractive index of glass with respect to air and iB is the Brewster's angle.

Q30 :

(a) Describe a simple experiment (or activity) to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it.

(b) The current flowing through an inductor of self inductance L is continuously increasing. Plot a graph showing the variation of

(i) Magnetic flux versus the current
(ii) Induced emf versus dI/dt
(iii) Magnetic potential energy stored versus the current.
OR​

(a) Draw a schematic sketch of an ac generator describing its basic elements. State briefly its working principle. Show a plot of variation of

(i) Magnetic flux and
(ii) Alternating emf versus time generated by a loop of wire rotating in a magnetic field.

(b) Why is choke coil needed in the use of fluorescent tubes with ac mains?