*General
Instructions:*

*(i) There
are 26 questions in all.
All questions are compulsory.*

*(ii) This
question paper has five sections : Section
A, Section B, Section
C, Section D and Section
E.*

*(iii)
Section A contains five questions
of one mark each, Section B
contains five questions of two
marks each, Section C contains
twelve questions of three
marks each, Section D contains
one value based question of four
marks and Section E contains
three question*

Q1 :

Define capacitor reactance. Write its S.I units.

**Answer :**

Capacitor reactance is the resistance offered by a capacitor when
it is connected to an electric circuit. It is given by

where

Ï‰ = Angular frequency of the source

* C *= Capacitance of the capacitor

The SI unit of capacitor reactance is ohm (Î©).

Q2 :

What is the electric flux through a cube of side 1 cm which encloses an electric dipole?

**Answer :**

As per the Gauss's law of electrostatics, electric flux
through a closed surface is given by

where

*E =* Electrostatic field

*Q* = Total charge enclosed by the surface

In the given case, cube encloses an electric dipole. Therefore, the
total charge enclosed by the cube is zero, i.e. *Q* = 0.

Therefore, from (i), we have

Q3 :

A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens?

**Answer :**

A concave lens made up of certain material behaves as a diverging
lens when it is placed in a medium of refractive index less than
the refractive index of the material of the lens, and behaves as a
converging lens when it is placed in a medium of refractive index
greater than the refractive index of the material of the lens, then
it behaves as a diverging lens.

In the given case, concave lens is immersed in the medium having
refractive index greater then the refractive index of the material
of the lens. Therefore, it will behave as a diverging lens.

Q4 :

How are side bands produced?

**Answer :**

Q5 :

Graph showing the variation of current versus voltage for a
material Ga As is shown in the figure. Identify the region of

(i) negative resistance

(ii) where Ohm's law is obeyed.

**Answer :**

Q6 :

A proton and an Î±-particle have the same de-Broglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds.

**Answer :**

Q7 :

Show that the radius of the orbit in hydrogen atom varies as
*n*^{2}, where *n* is the principal quantum
number of the atom.

**Answer :**

Q8 :

Distinguish between 'intrinsic' and 'extrinsic' semiconductors.

**Answer :**

Q9 :

Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?

**Answer :**

Q10 :

Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge.

**Answer :**

Q11 :

Name the parts of the electromagnetic spectrum which is

(a) suitable for radar systems used in aircraft navigation.

(b) used to treat muscular strain.

(c) used as a diagnostic tool in medicine.

Write in brief, how these waves can be produced.

**Answer :**

Q12 :

(i) A giant refracting telescope has an objective lens of focal
length 15 m. If an eye piece of focal length 1.0 cm is used, what
is the angular magnification of the telescope ?

(ii) If this telescope is used to view the moon, what is the
diameter of the image of the moon formed by the objective lens ?
the diameter of the moon is 3.48 Ã— 10^{6} m
and the radius of lunar orbit is 3.8 Ã—
10^{8} m.

**Answer :**

Q13 :

Write Einstein's photoelectric equation and mention which
important features in photoelectric effect can be explained with
the help of this equation.

The maximum kinetic energy of the photoelectrons gets doubled
when the wavelength of light incident on the surface changes from
*Î»*_{1} to
*Î»*_{2}. Derive the expressions for
the threshold wavelength *Î»*_{0} and
work function for the metal surface.

**Answer :**

Q14 :

In the study of Geiger-Marsdon experiment on scattering of
Î± particles by a thin foil of gold, draw the
trajectory of Î±-particles in the coulomb field of
target nucleus. Explain briefly how one gets the information on
the size of the nucleus from this study.

From the relation *R* = *R*_{0}
*A*^{1}^{/3}, where *R*_{0}
is constant and *A* is the mass number of the nucleus,
show that nuclear matter density is independent of
*A*.

Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.

Calculate the energy release in MeV in the deuterium-tritium fusion reaction :

**Answer :**

Q15 :

Draw a block diagram of a detector for AM signal and show, using necessary processes and the waveforms, how the original message signal is detected from the input AM wave.

**Answer :**

Q16 :

A cell of emf '*E*' and internal resistance '*r*'
is connected across a variable load resistor R. Draw the plots of
the terminal voltage *V* versus (i) *R* and (ii)
the current *I*.

It is found that when *R* = 4 â„¦, the
current is 1 A and when R is increased to 9
â„¦, the current reduces to 0.5 A. Find the
values of the emf *E* and internal resistance r.

**Answer :**

Q17 :

Two capacitors of unknown capacitances C_{1} and
C_{2} are connected first in series and then in parallel
across a battery of 100 V. If the energy stored in the two
combinations is 0.045 J and 0.25 J respectively, determine the
value of C_{1} and C_{2}. Also calculate the
charge on each capacitor in parallel combination.

**Answer :**

Q18 :

State the principle of working of a galvanometer.

A galvanometer of resistance *G* is converted into a
voltmeter to measure upto *V* volts by connecting a
resistance *R*_{1} in series with the coil. If a
resistance *R*_{2} is connected in series with it,
then it can measures upto *V*/2 volts. Find the
resistance, in terms of *R*_{1} and
*R*_{2}, required to be connected to convert it
into a voltmeter that can read upto 2 V. Also find the resistance
*G* of the galvanometer in terms of *R*_{1}
and *R*_{2}.

**Answer :**

Q19 :

With what considerations in view, a photodiode is fabricated?
State its working with the help of a suitable diagram.

Even though the current in the forward bias is known to be more
than in the reverse bias, yet the photodiode works in reverse
bias. What is the reason?

**Answer :**

Q20 :

Draw a circuit diagram of a transistor amplifier in CE
configuration.

Define the terms : (i) Input resistance and (ii) Current
amplification factor. How are these determined using typical
input and output characteristics?

**Answer :**

Q21 :

Answer the following questions :

(a) In a double slit experiment using light of wavelength 600 nm,
the angular width of the fringe formed on a distant screen is
0.1Â°. Find the spacing between the two slits.

(b) Light of wavelength 5000 Ã… propagating in air
gets partly reflected from the surface of water. How will the
wavelengths and frequencies of the reflected and refracted light
be affected?

**Answer :**

Q22 :

An inductor *L* of inductance *X _{L}* is
connected in series with a bulb B and an ac source. How would
brightness of the bulb change when (i) number of turn in the
inductor is reduced, (ii) an iron rod is inserted in the inductor
and (iii) a capacitor of reactance

**Answer :**

Q23 :

A group of students while coming from the school noticed a box
marked "Danger H.T. 2200 V" at a substation in the main street.
They did not understand the utility of a such a high voltage,
while they argued, the supply was only 220 V. They asked their
teacher this question the next day. The teacher thought it to be
an important question and therefore explained to the whole
class.

Answer the following questions:

(i) What device is used to bring the high voltage down to low
voltage of a.c. current and what is the principle of its working
?

(ii) Is it possible to use this device for bringing down the high
dc voltage to the low voltage? Explain

(iii) Write the values displayed by the students and the teacher.

**Answer :**

Q24 :

(a) State Ampere's circuital law. Use this law to obtain the
expression for the magnetic field inside an air cored toroid of
average radius '*r*', having '*n*' turns per unit
length and carrying a steady current *I*.

(b) An observer to the left of a solenoid of N turns each of
cross section area 'A' observes that a steady current I in it
flows in the clockwise direction. Depict the magnetic field lines
due to the solenoid specifying its polarity and show that it acts
as a bar magnet of magnetic moment *m* = NIA.

(a) Define mutual inductance and write its S.I. units.

(b) Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other,

(c) In an experiment, two coils c

**Answer :**

Q25 :

(a) Using Huygens's construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.

(b) Show that the angular width of the first diffraction fringe is half that of the central fringe.

(c) Explain why the maxima at *n*.

**OR**

(a) A point object 'O' is kept in a medium of refractive index *n*_{1} in front of a convex spherical surface of radius of curvature *R* which separates the second medium of refractive index *n*_{2}_{ }from the first one, as shown in the figure.

Draw the ray diagram showing the image formation and deduce the relationship between the object distance and the image distance in terms of *n*_{1}, *n*_{2} and *R*.

**(b) When the image formed above acts as a virtual object for a concave spherical surface separatig the medium n_{2} from n_{1} (n_{2} > n_{1} **

**Answer :**

Q26 :

(a) An electric dipole of dipole moment *q *and Ã¢ˆ’*q** *separated by a distance 2*a* apart. Deduce the expression for the electric field *x* from the centre of the dipole on its axial line in terms of the dipole moment

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