1
1) Define the term 'Mobility' of charge carriers in a conductor. Write its S.I. unit.
SOL: Mobility: Mobility of a charge carrier is defined as the drift velocity of the charge carrier per
unit electric field.
It is generally denoted by μ
The SI unit of mobility is m2 V–1 s–1 . It is 104 of the mobility in practical units (cm2 V–1 s–1).
2) The carrier wave is given by
C(t) = 2 sin (8  t) volt.
The modulating signal is a square wave as shown. Find modulation index.
SOL: It can be observed from the given modulating signal that the amplitude of the modulating signal
is Am= 1 V.
The carrier wave is given by c(t)  2sin8 t . Amplitude of the carrier wave is AC = 2 V.
Modulation index is  
Am 1
  0.5 .
AC 2
3) "For any charge configuration, equipotential surface through a point is normal to the
electric field." Justify.
SOL: On an equipotential surface VB – VA = 0 = 
E.dl  0

E.dl .
hence E  dl
2
4) 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 ?
SOL: Glass bob would reach earlier on ground as a= g
No induced current is develop in it due earth’s magnetic field.
5) Show variation of resistivity of copper as a function of temperature in a graph.
SOL:
6) 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 ?
SOL: Fig. shows a convex lens placed in contact with a plane mirror. An axial point object is placed
at O at a distance OC = 20 cm.
As the image I of the object coincides with O, the rays
refracted first from the lens and then reflected by the
plane mirror must be retracing their path. This would
happen when rays refracted by the convex lens fall
normally on the mirror i.e., the refracted rays form a beam
parallel to principal axis of the lens. Hence the object O
must be at the focus of the convex lens.
f = CO = 20 cm.
3
7) Write the expression, in a vector form, for the Lorentz magnetic force F due to a charge
moving with velocity V in a magnetic field B . What is the direction of the magnetic force ?
SOL: F  q(v  B) where F is  to the plane containing v and B .
8) The figure given below shows the block diagram of a generalized communication system.
Identify the element labelled 'X' and write its function.
SOL:
Block diagram of a generalised communication system
X is channel
Function : The channel is the physical medium that connects the transmitter and the receiver. The
signal from the transmitter is carried to the receiver by the communication channel.
9) 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 ?
SOL: A is paramagnetic  m  ve , B is diamagnetic  m  ve .
10) Given a uniform electric field E = 5 ×103 i N/C, find the flux of this field through a square
of 10 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 30° angle with the x-axis ?
4
SOL: E = 5 ×103 i , A = (0.1)2 = 0.01 m2 in Y –Z plane
E is  to surface
  EA  5 103  0.01  50 Nm2 / C
If
= 600 ,   EA cos   5 
1
 25 Nm2 / C
2
11) For a single slit of width "a", the first minimum of the interference pattern of a
monochromatic light of wavelength  . occurs at an angle of


. At the same angle of
we
a
a
get a maximum for two narrow slits separated by a distance "a". Explain.
SOL: In diffraction angular position  
Hence  
x
for first minima x   .
a

a
In interference given d = a and angular position  
Angular position of first Maxima ( x   )  

a
x
d
.
12) Write the truth table for the combination of the gates shown. Name the gates used.
SOL: R is OR and S is AND
A
0
0
1
1
B
0
1
0
1
Y’= (A+B)
0
1
1
1
Y= A.(A+B)
0
0
1
1
OR
5
Identify the logic gates marked 'P' and `Q' in the given circuit. Write the truth table for the
combination.
SOL: P is NAND and OR
A
B
A.B
A.B
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
X = B+ A.B
1
1
1
1
13) State Kirchhoff s rules. Explain briefly how these rules are justified.
SOL: Kirchhoff's first rule ( Kirchhoff's Current Law or Junction Rule )
It is stated as follows : "The sum of the currents flowing towards a junction is equal to the sum of
currents leaving the junction."
This is in accordance with the conservation of charge which is the basis of Kirchhoff's current rule.
I1+ I2 – I3 – I4 – I5 = 0
"In any electrical network, the algebraic sum of currents meeting at a junction is always zero."
I  0
Kirchhoff 's second rule ( Loop rule ) :
"The algebraic sum of all the potential drops and emfs along any closed path in a network is zero."
Or
the algebraic sums of the emfs in any loop of a circuit is equal to the algebraic sum of the products of
currents and resistances in it.
Mathematically, the loop rule may be expressed as
 E   IR
Kirchhoff 's second law expresses the conservation of energy:
14) 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
6
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 ?
SOL: (i) Due to dielectric C increases X C 
I rms 
1
2
2
decreases Z  R  X C decreases.
C
Vrms
increases Brightness of bulb increases.
Z
(b) R increases Z increases Irms decreases brightness decreases.
15) State the underlying principle of a cyclotron. Write briefly how this machine is used to
accelerate charged particles to high energies.
SOL:
16) 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 4 3 Nm. Calculate the potential energy of
the dipole, if it has charge ±8 nC.
SOL: 2a = 4×1–2 m , θ = 60o ,   4 2 ,
  q(2 a) Esin   q(2 a)  E 
E
q = 8 109 C .
3
4 2
2
8 2
q(2 a) 3
Potential Energy   PE cos   q(2a) Ecos   q(2a) 
8 2
1 4 2
J
 
q(2a) 3 2
3
7
17) 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.
SOL:  
h
1

2mV0 q
m
V0 and q same for both
m is more for proton so  is more.

h
p
 p
h

hence both have same momentum.
18) (i) Monochromatic light of frequency 6.0 × 1014 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.
SOL: (a)
energy nh

second sec.
Power
2 103
n / sec. 

 0.05 1017
34
14
h
6.6 10  6 10
Power 
(b)
8
19) 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.
SOL: E1  13.6eV , E2  3.4eV , E3  1.51eV , E4  0.85eV
E3  E1  12.09eV , E4  E1  12.75eV
1 
2
(10.2)
1 
3
(12.09)
1 
4
(12.75)
1 
5
(13.06)
1 
6
(13.12)
(None of the given values in paper does not matches with the given data.)
First member of lyman
1 1 
 RH (1)2  2  2 
1
1 2 
First member of Balmer
1 1
 RH (1)2  2  2 
12
2 3 
1
1
20) 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
i)
In what way can the setting up of transmission tower by a mobile company in a
residential colony prove to be injurious to health ?
ii) By objecting to this move of her parents, what value did Sunita display ?
iii) 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)
SOL:
21) A potentiometer wire of length 1 m has a resistance of 10Ω. It is connected to a 6 V battery
in series with a resistance of 5Ω. Determine the emf of the primary cell which gives a
balance point at 40 cm.
9
SOL: l = 1 m = 100 cm , R = 10 Ω , E0 = 6 Volt , R1 = 5 Ω
I
E0
6
6
A


R  R ' 10  5 15
VAB  IR 
6
60
10 
 4 Volt
15
15
VAB
4

 0.04 ,
l
100
Eo 
VAB
 x  0.04  40  1.6Volt
l
22) (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.
SOL: m  m0 .me
20 = m0  5
m0  4
 v0
 4  v0  4u0
u0

1
1
1


u0 4v 0 70
u  1 5
1


4u0
4u0 f 0
10
me  1 
4
D
20
 5  1
fe
fe
20
 fe  5
fe
Using
1
1 1 1  4
1
  

ue
20 5
20
4
ue  4
L = v0 + | ue |

14 = v0 + u
Hence f o  
v0 = 10  u0 
v0
 2.5
4
uv0
4
   (2.5)  2cm
5
5
23) (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.
SOL:
u will be different for different points on object.
(b) Intensity ×
1
, complete image is formed.
2
11
24) (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 rectangular loop abed a.
SOL: (a) U 
1
1 0 A
CV 2 
(Ed)2
2
2 d
U
1
 Energy density =  0 E 2 .
Ad
2
(b) Cyclic path , conservative field , net work done = 0.
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.
SOL: (b) V1 = V2
K
q1
q
q
R
K 2  1  1
R1
R2
q2 R2
2
 1 q1 / 4 R12 q1  R2  R2

   
 2 q2 / 4 R22 q2  R1 
R1
25) (a)State Ampere's circuital law, expressing it in the integral form.
12
(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 through the inner solenoid S 1 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.
SOL: (a)
(b) Inside Bnet = B1 –B2 = 0 n1I  0 n2 I
B to A
Out side Bnet = 0 .
26) 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.
SOL: (a) Microwaves
(b) Temperature would decreases (No green house effect)
13
(c) em Waves carry momentum =
energy
hence exerts pressure.
C
27) Deduce the expression, N = No e  t , for the law of radioactive decay.
(b) (i) Write symbolically the process expressing the β+ decay of
11Na
22
. Also write the basic
nuclear process underlying this decay.
(ii) Is the nucleus formed in the decay of the nucleus 11Na12, an isotope or isobar ?
SOL:
11
Na 22 
10 Y 22 10 e   Q
V is an Isobar.
28) (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 y1 = a cos ωt
and y2 = a cos(ωt+  ) where  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  , the intensity
of light at a point on the screen where path difference is  , is  units. Find out the intensity of
light at a point where path difference is ,  /3.
SOL: y1  a cos t, y2  a cos(t   )
R  a 2  b2  2ab cos  using parallogram law
R  a 2  a 2  2a 2 cos   2a 2  2a 2 cos   2a 2 (1  cos  )
 2a 2  2  cos 2

2
 2 cos

2
14
I1  a 2 , I 2  a 2
I net  R 2
I net  R  

     2 cos 
I
2
2 
2
I net  4 I cos 2
2

2
2
(b) Intensity I  4 I 0 cos

2
Path difference of  , is equivalent to phase difference of 2 π.
I  4I 0 cos2   4I 0 = K (given)
When path difference, x 
'
2

 x 
 I  4 I 0 cos 2
2



3


3

3
, the phase difference,
2
Radian
3
;
 I  K cos 2

2
1 1
K   K
3
4
2
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 μ= tan iB, where ) μ is
the refractive index of glass with respect to air and iB is the Brewster's angle.
29) (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 einf versus dI/dt
15
(iii)Magnetic potential energy stored versus the current.
SOL: (a)
e   L.
dI
dt
dI
 ve
dt
U
1 2
LI  U  I 2
2
Hence e is –ve and constant.
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 ?
SOL:   BNA cos t
e = BNA sin t
(b) choke coil is used to control current in LCR circuit. Without much wastage of power.
30) (a) State briefly the processes involved in the formation of p-n junction explaining clearly
how the depletion region is formed.
16
(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.
17
18
1) Define the term 'drift velocity' of charge carriers in a conductor and write its relationship
with the current flowing through it.
SOL: The average velocity acquired by the free electrons along the length of a metallic conductor
under a p.d. applied across the conductor is called 'drift velocity' of the electrons.
vd 
I
.
neA
2) The carrier wave of a signal is given by C(t) = 3 sin (8πt) volt. The modulating signal is a
square wave as shown. Find its modulation index.
SOL: It can be observed from the given modulating signal that the amplitude of the modulating signal
is Am= 1.5 V.
The carrier wave is given by c(t)  3sin8 t . Amplitude of the carrier wave is AC =3 V.
Modulation index is  
Am 1.5

 0.5 .
AC
3
4) Plot a graph showing variation of current versus voltage for the material GaAs.
SOL:
(Variation of current versus voltage for GaAs.)
19
12) 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.
SOL: (1)  
h
1
; 
2mV0 q
mq
1/ 2me
d

e 1/ 4m.2e
d 2

e 1
(2)
KEd
V e 1
 0

KEe V0  2e 2
24) 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 ? Give their one application.
SOL: (a) gamma rays
(b) Protect from UV rays
(c) Produces heating
27) 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 :
20
(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)
SOL: d  2Rh  2  6.4 106  20  16 103 m
21
22
All questions are similar to SET-1 and SET -3
23