Time allowed: 3 hours.                                                                                          Max. Marks: 70

Section-A

1. State the SI unit of the electric polarization vector P

Ans :C/m2

2. Define temperature coefficient of resistivity

Ans: Fractional change in resistivity per unit change in temperature

3. Name the electromagnetic waves that are widely used as a diagnostic tool in medicine.
OR
Name the current which can flow even in the absence of electric charge.

Ans:X-rays
OR
Displacement current

4.A ray of light is incident on a medium with angle of incidence ‘i’ and is refracted into a second
medium with angle of refraction ‘r’. The graph of sin i versus sin r is as shown. Find the ratio
of the velocity of light in the first medium to the velocity of light in the second medium. Ans

5. Two particles have equal momenta. What is the ratio of their de-Broglie wavelengths? 1
OR
Monochromatic light of frequency 6.0x 1014 Hz is produced by a laser. What is the energy of
a photon in the light beam?

Ans:P1= P2
Ratio λ1/ λ2 = 1: 1

OR
Each photon has an energy ,E=h.ν
= ( 6.63 ×10-34 J s) (6.0 ×1014 Hz)
= 3.98 × 10–19 J

Section-B

6. A network of resistors is connected to a 16 V battery with internal resistance of 1., as shown
in the following figure. Compute the equivalent resistance of the network. OR
A 9 V battery is connected in series with a resistor .The terminal voltage is found to be 8 V.
Current through the circuit is measured as 5 A. What is the internal resistance of the battery?

Ans: 7. The diagram below shows a potentiometer set up. On touching the jockey near to the end X
of the potentiometer wire, the galvanometer pointer deflects to left. On touching the jockey
near to end Y of the potentiometer, the galvanometer pointer again deflects to left but now by
a larger amount. Identify the fault in the circuit and explain, using appropriate equations or
otherwise, how it leads to such a one-sided deflection OR

7.Following circuit was set up in a meter bridge experiment to determine the value X of an
unknown resistance. (a) Write the formula to be used for finding X from the observations.
(b) If the resistance R is increased, what will happen to balancing length?

Ans:

The positive of E1 is not connected to terminal X. In loop PGJX, E1 – VG + EXN=0
VG = E1 + EXN
VG = E1 + k ℓ
So, VG (or deflection) will be maximum when ℓ is maximum i.e. when jockey is
touched near end Y. Also, VG (or deflection) will be minimum when ℓ is minimum i.e.
when jockey is touched near end X.

OR
(a) X = (100 - ℓ) R/ℓ
(b) Balancing length will increase on increase of resistance R.

8. The figure shows two sinusoidal curves representing oscillating supply voltage and current
in an ac circuit. Draw a phasor diagram to represent the current and supply voltage appropriately as phasors.
State the phase difference between the two quantities.

Ans:

Phasor diagram Equal length of phasors
phase difference is π/4

9. Compare the following
(i) Wavelengths of the incident solar radiation absorbed by the earth’s surface and the
(ii) Tanning effect produced on the skin by UV radiation incident directly on the skin and
that coming through glass window.

Ans:

(ii)Tanning effect is significant for direct UV radiation; it is negligible for radiation
coming through the glass.

10. A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength λ equals
to 6000 Å and the angular width of the central maxima in the resulting diffraction pattern is
measured. When the slit is next illuminated by light of wavelength λ’, the angular width
decreases by 30%. Calculate the value of the wavelength λ’.

Ans:

Angular width 2ϴ = 2λ/d
Given λ = 6000 Å
In Case of new λ (assumed λ’ here), angular width decreases by 30%
= (􀬵􀬴􀬴􀬿􀬷􀬴
􀬵􀬴􀬴 )2 ϴ
= 0.70 (2 ϴ)
2 λ’/d = 0.70 X (2 λ/d)
∴λ’= 4200 Å

11. What are universal gates? How can AND gate be realized using an appropriate combination
of NOR gates?

Ans:

Universal gates (like the NAND and the NOR gates) are gates that can be
appropriately combined to realize all the three basic gates. 12. A TV transmission tower antenna is at a height of 20 m. How much range can it cover if the
receiving antenna is at a height of 25 m?

Ans;

Range d = √2ℎ􀜴 + 􀶥2ℎ􀯋􀜴
d = 33.9 km

Section-C

13. A particle, having a charge +5 μC, is initially at rest at the point x = 30 cm on the x axis. The
particle begins to move due to the presence of a charge Q that is kept fixed at the origin. Find
the kinetic energy of the particle at the instant it has moved 15 cm from its initial position if
(a) Q =+15μC and (b) Q = -15μC

14. (a) An electric dipole is kept first to the left and then to the right of a negatively charged
infinite plane sheet having a uniform surface charge density. The arrows p1 and p2 show the
directions of its electric dipole moment in the two cases. Identify for each case, whether the dipole is in stable or unstable equilibrium. Justify each

(b) Next, the dipole is kept in a similar way (as shown), near an infinitely long straight wire having
uniform negative linear charge density. Will the dipole be in equilibrium at these two positions? Justify your answer.

Ans:

(a) p1: stable equilibrium
p2: unstable equilibrium
The electric field, on either side, is directed towards the negatively charged sheet and
its magnitude is independent of the distance of the field point from the sheet. For
position p1, dipole moment and electric field are parallel. For position p2, they are
antiparallel.
1/2
1/2+1/2
(b) The dipole will not be in equilibrium in any of the two positions.
The electric field due to an infinite straight charged wire is non- uniform (E α 1/r).
Hence there will be a net non-zero force on the dipole in each case.

15. Two material bars A and B of equal area of cross-section, are connected in series to a DC
supply. A is made of usual resistance wire and B of an n-type semiconductor.
(a) In which bar is drift speed of free electrons greater?
(b) If the same constant current continues to flow for a long time, how will the voltage
drop across A and B be affected?

Ans:

(a) Drift speed in B (n-type semiconductor) is higher
Reason: I = neAvd is same for both
n is much lower in semiconductors.

(b) Voltage drop across A will increase as the resistance of A increases
with increase in temperature.
Voltage drop across B will decrease as resistance of B will decrease with
increase in temperature.

16. Derive an expression for the velocity vC of a positive ions passing undeflected through a
region where crossed and uniform electric field E and magnetic field B are simultaneously
present.
Draw and justify the trajectory of identical positive ions whose velocity has a magnitude less
than IvCI.

Ans:

E = E j and B = B k
Force on positive ion due to electric field FE = qEj
Force due to magnetic field FB = q (vc x B)

For passing undeflected, FE = - FB
qEj = - q (vc x Bk)
This is possible only if qvc x Bk = qvcBj
or vc = (E/B)i

The trajectory would be as shown. Justification: For positive ions with speed v <vc
Force due to electric field = F’E = qE = FE
due to magnetic field F’B = qvB <FB since v <vc
Now forces are unbalanced, and hence, ion will experience an acceleration along E.
Since initial velocity is perpendicular to E, the trajectory would be parabolic

.17. A sinusoidal voltage of peak value 10 V is applied to a series LCR circuit in which resistance,
capacitance and inductance have values of 10 Ω, 1μF and 1H respectively. Find (i) the peak
voltage across the inductor at resonance (ii) quality factor of the circuit.

Ans:

I0 = V0/R = 10/10 = 1 A
ωr = 1/√LC = 1/√ (1 x 1 x 10-6) = 103 rad/s
V0 = I0 XL = I0 ωr L
= 1 x 103 x 1 = 103 V
Q = ωr L/R
= (103 x 1)/10 = 100

18. a) What is the principle of transformer?

b) Explain how laminating the core of a transformer helps to reduce eddy current
losses in it
c) Why the primary and secondary coils of a transformer are preferably wound on the same
core

OR
Show that in the free oscillations of an LC circuit, the sum of energies stored in the capacitor
and the inductor is constant in time.

Ans:

a) Principle of transformer
b) Laminations are thin, making the resistance higher. Eddy currents are confined
within each thin lamination. This reduces the net eddy current.
c) For maximum sharing of magnetic flux and magnetic flux per turn to be the same
in both primary and secondary.

or 18.Draw a labelled ray diagram to show the image formation in a refracting type astronomical
telescope in the normal adjustment position. Write two drawbacks of refracting type
telescopes.

OR
(a)Define resolving power of a telescope. Write the factors on which it depends.
(b) A telescope resolves whereas a microscope magnifies. Justify the statement.

Ans:

Ray diagram: Drawbacks:
(i)Large sized lenses are heavy and difficult to support
(ii) large sized lenses suffer from chromatic and spherical aberration.

OR

(a) Resolving power of a telescope is the reciprocal of the smallest angular separation
between the two objects which can be just distinctly seen.
Factors: diameter of the objective, wavelength of the incident light
(b) a telescope produces image of far objects nearer to our eye. Objects which are not
resolved at far distance, can be resolved by telescope. A microscope, on the other
hand magnifies objects nearer to us and produces their large image.

20. A jar of height h is filled with a transparent liquid of refractive index μ. At the centre of the
jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when it is
placed on the top surface symmetrically about the centre, the dot is invisible Ans: 21. (a) In photoelectric effect, do all the electrons that absorb a photon come out as photoelectrons
irrespective of their location? Explain.
(b) A source of light, of frequency greater than the threshold frequency, is placed at a distance
‘d’ from the cathode of a photocell. The stopping potential is found to be V. If the distance
of the light source is reduced to d/n (where n>1), explain the changes that are likely to be
observed in the (i) photoelectric current and (ii) stopping potential.

Ans:

(a) No, it is not necessary that if the energy supplied to an electron is more than the
work function, it will come out.
The electron after receiving energy, may lose energy to the metal due to collisions
with the atoms of the metal. Therefore, most electrons get scattered into the metal.
Only a few electrons near the surface may come out of the surface of the metal for
whom the incident energy is greater than the work function of the metal.

(b) on reducing the distance, intensity increases.
Photoelectric current increases with the increase in intensity.
Stopping potential is independent of intensity, and therefore remains unchanged.

22. A monochromatic radiation of wavelength 975 Å excites the hydrogen atom from its ground
state to a higher state. How many different spectral lines are possible in the resulting
spectrum? Which transition corresponds to the longest wavelength amongst them?

Ans:

Energy corresponding to the given wavelength:
E (in eV) = 􀬵􀬶􀬸􀬴􀬴
􀮛 ( 􀭧􀭬 Å) = 12. 71 eV
The excited state:
En – E1 = 12. 71
􀬿􀬵􀬷.􀬺
􀭬􀰮 + 13.6 = 12.71
∴ n = 3.9 ≈ 4
Total no. of spectral lines emitted: 􀭬 ( 􀭬􀬿􀬵)
􀬶 = 6
Longest wavelength will correspond to the transition

n = 4 to n = 3

23. Binding energy per nucleon versus mass number curve is as shown.
are four nuclei indicated on the curve. Based on the graph:
(a) Arrange X, W and S in the increasing order of stability.
(b) Write the relation between the relevant A and Z values for the following nuclear
reaction.
S X + W
(c) Explain why binding energy for heavy nuclei is low.

OR
How are protons, which are positively charged, held together inside a nucleus? Explain the
variation of potential energy of a pair of nucleons as a function of their separation. State the
significance of negative potential energy in this region?

Ans:

(a) S,W,X 1

(b) Z = Z1 + Z2
A = A1 + A2
(c) Reason for low binding energy:-
In heavier nuclei, the Coulombian repulsive effects can increase considerably and can
match/ offset the attractive effects of the nuclear forces. This can result in such nuclei
being unstable.
OR
Nuclear force binds the protons inside the nucleus.
For Graph and explanation, refer to NCERT page no 445
Significance of negative potential energy: Force is attractive in nature

24.A sinusoidal carrier wave of amplitude Ac and angular frequency ωc is modulated in
accordance with a sinusoidal information signal of amplitude Am and angular frequency ωm.
Show that the amplitude modulated signal contains three frequencies centered around ωc.
Draw the frequency spectrum of the resulting modulated signal.

Ans: Section-D

25. (a)Write the expression for the equivalent magnetic moment of a planer current loop of area
A, having N turns and carrying a current i. Use the expression to find the magnetic dipole
moment of a revolving electron.
(b) A circular loop of radius r, having N turns and carrying current I, is kept in the XY plane.
It is then subjected to a uniform magnetic field B = Bx i + By j + Bz k. Obtain expression for
the magnetic potential energy of the coil-magnetic field system.

OR
(a) A long solenoid with air core has n turns per unit length and carries a current I. Using
Ampere’s circuital law, derive an expression for the magnetic field B at an interior point on
its axis. Write an expression for magnetic intensity H in the interior of the solenoid.
(b) A (small) bar of material, having magnetic susceptibility χ, is now put along the axis and
near the centre, of the solenoid which is carrying a d.c. current through its coils. After some
time, the bar is taken out and suspended freely with an unspun thread. Will the bar orient
itself in magnetic meridian if (i) χ < 0 (ii) χ ˃ 1000?

Ans:

(a) The equivalent magnetic moment is given by μ = NiA
The direction of μ is perpendicular to the plane of current carrying loop. It is directed
along the direction of advance of a right-handed screw rotated along the direction of
flow of current
derivation of expression for μ of electron revolving around a nucleus

(b) for the loop, μ = N (π r2) i (±k)
Magnetic potential energy = μ.B
= N (π r2) i (±k).( Bx i + By j + Bz k)
= ±π r2 N I Bz

OR
(a) Derivation
H = nI
The direction of H is along the axis of the solenoid, directed along the direction
of advance of a right-handed screw rotated along the direction of flow of current

(b) (i) Not necessarily.
Reason: material is diamagnetic. After removal of magnetising field, no magnetisation
will remain in the material and hence earth’s magnetic field
will not affect it.
(ii) Yes
Reason: The material is ferromagnetic. It will remain magnetised even after removal
from the solenoid and hence align with magnetic meridian.

26. (a)There are two sets of apparatus of Young’s double slit experiment. In set A, the phase
difference between the two waves emanating from the slits does not change with time,
whereas in set B, the phase difference between the two waves from the slits changes rapidly
with time. What difference will be observed in the pattern obtained on the screen in the two
set ups?
(b) Deduce the expression for the resultant intensity in both the above mentioned set ups (A
and B), assuming that the waves emanating from the two slits have the same amplitude A and
same wavelength λ.
OR
(a) The two polaroids, in a given set up, are kept ‘crossed’ with respect to each other. A third
polaroid, now put in between these two polaroids, can be rotated. Find an expression for the
dependence of the intensity of light I, transmitted by the system, on the angle between the
pass axis of first and the third polaroid. Draw a graph showing the dependence of I on ϴ.
(b) When an unpolarized light is incident on a plane glass surface, find the expression for the
angle of incidence so that the reflected and refracted light rays are perpendicular to each other.
What is the state of polarisation, of reflected and refracted light, under this condition?

27. (a) Draw the circuit diagram to determine the characteristics of a pnp transistor in common
emitter configuration.
Explain, using I-V characteristics, how the collector current changes with the base current.
How can (i) output resistance and (ii) current amplification factor be determined from the IV
characteristics?
5
OR
(a) Why are photodiodes preferably operated under reverse bias when the current in the
forward bias is known to be more than that in reverse bias?
The two optoelectronic devices: - Photodiode and solar cell, have the same working principle
but differ in terms of their process of operation. Explain the difference between the two
devices in terms of (i) biasing, (ii) junction area and (iii) I-V characteristics.  OR
(a) The fractional change in majority charge carriers is very less compared to the
fractional change in minority charge carriers on illumination.

(b) The difference in the working of two devices: 