(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 'Mobility' of charge carriers in a conductor. Write its S.I. unit

**Answer :**

Mobility of charge carriers in a conductor is defined as the
magnitude of their drift velocity per unit applied electric
field.

Mobility,

S.I. unit of mobility is

Q2 :

The carrier wave is given by

C(*t*) = 2sin(8π*t*)
volt.

The modulating signal is a square wave as shown. Find modulation
index.

**Answer :**

Modulation index (

The generalised equation of a carrier wave is given
below:

The generalised equation of a modulating wave is given
below:

Here,

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

Amplitude of modulating signal,

Amplitude of carrier wave,

∴

Q3 :

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

**Answer :**

We know that the work done (*W*) in moving a test
charge along an equipotential surface is zero. This is because an
equipotential surface is a surface with a constant value of
potential

at all the points on the surface.

*∴ W* = *Fs* cos*θ* = 0

Here, F is the electric force and s is the magnitude of
displacement of the charge.

For non-zero displacement, this is possible only when cos*θ* is equal to 0.

i.e. cos*θ* *= 0*

*θ* =
90°

Thus, the force acting on the point charge is perpendicular to the
equipotential surface. We know that the lines of force or the
electric field lines indicate the direction of electric force on a
charge. Thus, for any charge configuration, equipotential surface
through a point is normal to the electric field.

Q4 :

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?

**Answer :**

Q5 :

Show variation of resistivity of copper as a function of temperature in a graph.

**Answer :**

Q6 :

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?

**Answer :**

Q7 :

Write the expression, in a vector form, for the Lorentz magnetic
force

**Answer :**

Q8 :

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

**Answer :**

Q9 :

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?

**Answer :**

Q10 :

Given a uniform electric field

**Answer :**

Q11 :

For a single slit of width "a", the first minimum of the
interference pattern of a monochromatic light of wavelength
λ occurs at an angle of

**Answer :**

Q12 :

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.

**Answer :**

Q13 :

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

**Answer :**

Q14 :

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?

**Answer :**

Q15 :

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

**Answer :**

Q16 :

An electric dipole of length 4 cm, when placed with its axis
making an angle of 60° with a uniform electric field,
experiences a torque of

**Answer :**

Q17 :

A proton and a deuteron are accelerated through the same
accelerating potential. Which one of the two has

(a) greater value of de-Broglie wavelength associated with it,
and

(b) less momentum?

Give reasons to justify your answer.

**Answer :**

Q18 :

(i) Monochromatic light of frequency 6.0 × 10^{14} Hz is produced by a laser. The power emitted is 2.0
× 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.

**Answer :**

Q19 :

A 12.5 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 first member of Lyman and first
member of Balmer series.

**Answer :**

Q20 :

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)

**Answer :**

Q21 :

A potentiometer wire of length 1 m has a resistance of 10 Ω. It is connected to a 6 V battery in series with a resistance of 5 Ω. Determine the emf of the primary cell which gives a balance point at 40 cm.

**Answer :**

Q22 :

(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.

**Answer :**

Q23 :

(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.

**Answer :**

Q24 :

(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.

(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 R_{1} and R_{2} when connected by a
conducting wire acquire charges q_{1} and
q_{2} respectively. Find the ratio of their
surface charge densities in terms of their radii.

**Answer :**

Q25 :

(a) State Ampere's circuital law, expressing it in the integral
form.

(b) Two long coaxial insulated solenoids, S_{1}
and S_{2} of equal lengths are wound one over
the other as shown in the figure. A steady current "I" flow
thought the inner solenoid S_{1} to the other
end B, which is connected to the outer solenoid S_{2} through which the same current "I" flows in the
opposite direction so as to come out at end A. If n_{1} and n_{2} 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.

**Answer :**

Q26 :

Answer the following:

(a) Name the em waves which are suitable for radar systems used
in aircraft navigation. Write the range of frequency of these
waves.

(b) If the earth did not have atmosphere, would its average
surface temperature be higher or lower than what it is now?
Explain.

(c) An em wave exerts pressure on the surface on which it is
incident. Justify.

**Answer :**

Q27 :

(a) Deduce the expression, N = N_{0}
e^{−λt}, for the law of radioactive
decay.

(b) (i) Write symbolically the process expressing the
β^{+} decay of

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

**Answer :**

Q28 :

(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 "ω",
emanating from two coherent light sources superpose at a point.
If the displacements due to these waves is given by y_{1} = a cos ωt and y_{2} = a
cos(ωt + ϕ) where ϕ 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 λ, the intensity of light at a point on the
screen where path difference is λ, is K units. Find out
the intensity of light at a point where path difference is
λ/3.

(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 μ = tan i

**Answer :**

Q29 :

(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.

(ii) Induced emf versus dI/dt

(iii) Magnetic potential energy stored versus the current.

(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.

(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?

**Answer :**

Q30 :

(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?

(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.

**Answer :**

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