AHSEC HS 2nd Year Question Paper 2019 Physics

Total number of pages – 12
29T PHYS

2019

PHYSICS
( Theory )

Full Marks : 70
Pass Marks : 21

Time : Three hours

The figures in the margin indicate full marks
for the questions.

Q. No. 1 carries 1 mark each 1×8 = 8

Q. No. 2 carries 2 marks each 2×10 = 20

Q. No. 3 carries 3 marks each 3×9 = 27

Q. No. 4 carries 5 marks each 5×3 = 15

Total = 70

Contd.

1. (a) What did Meissner actually observe which is known as Meissner
effect ? 1
Œ˜˝◊ ڱÀ1 √õ∂fl‘¬Ó¬ÀÓ¬ øfl¬ ¬Û˚«À¬ıé¬Ì fl¬ø1ø¢ ø˚ÀȬ±fl¬ Œ˜˝◊ ڱ1 øSê˚˛± ¬ı≈ø˘ Œfl¬±ª± ˝˚˛∑
(b) A very interesting fact regarding electromagnetic waves can be seen
with the help of a portable AM radio. What is it ? 1

¤È¬± ¬Ûí1ÀȬ¬ı˘ AM Œ1øά’í1 ¸˝±˚˛Ó¬ ø¬ı≈…» ‰≈¬•§fl¬œ˚˛ Ó¬1—· ¸•Ûfl«¬œ˚˛ ¤È¬± ¬ı1
’±À˜±ÊÚfl¬ ‚Ȭڱ Œø‡¬ıÕ˘ Œ¬Û±ª± ˚±˚˛º ‚ȬڱÀȬ± øfl¬∑
(c) Mention one similarity between Coulomb force and gravitational force
acting between two stationary charges. 1
ø¶ö1 ’ª¶ö±Ó¬ Ôfl¬± ≈Ȭ± ’±Ò±Ú1 ˜±ÊÓ¬ øSê˚˛± fl¬1± fl≈¬˘•§ ¬ı˘ ’±1n∏ ˜±Ò…±fl¬¯∏«øÌfl¬ ¬ı˘1
˜±ÊÓ¬ Ôfl¬± ¤È¬± ¸±‘˙… Î◊¬À~‡ fl¬1±º
(d) Define mutual inductance of 1 Henry. 1
1 Œ˝Ú1œ ¬Û±1¶Ûø1fl¬ ’±Àª˙1 ¸—:± ø˚˛±º
(e) If the radius of the first orbit of hydrogen atom is 5  3  10 11 m ,
what is the radius of the third orbit ? 1
˝±˝◊EíÀÊÚ ¬Û1˜±Ì≈1 √õ∂Ô˜ fl¬é¬¬ÛÔ1 ¬ı…±¸±X«√ 5  3  10 11 m ˝íÀ˘ Ó‘¬Ó¬œ˚˛ fl¬é¬¬ÛÔ1
¬ı…±¸±X«√ øfl¬˜±Ú∑
(f) If the work function of two metals X and Y are 4  17eV and
8  24  1019 J respectively, then for which metal lesser amount of
energy will be required to emit an electron ? 1

˚ø X ’±1n∏ Y Ò±Ó≈¬ ≈ø¬ıÒ1 ¬ı±À¬ı fl¬±˚«Ù¬˘Ú1 ˜±Ú SêÀ˜ 4  17eV ’±1n∏ 8  24  1019 J
˝˚˛ ŒÓ¬ÀôL Œfl¬±Úø¬ıÒ Ò±Ó≈¬1¬Û1± ˝◊À˘fl¬È¬™Ú øÚ·«˜Ú1 ¬ı±À¬ı fl¬˜ ˙øMê1 √õ∂À˚˛±ÊÚ ˝í¬ı∑
(g) Arrange the following communication methods / modes in
descending order on the basis of their operating frequency. 1
¸—À˚±· ¬ı…ª¶ö± ¸•Ûfl«¬œ˚˛ Ó¬˘Ó¬ ø˚˛± ¬ÛX√√øÓ¬¸˜”˝, ø¸˝“ÀÓ¬ ¬ı…ª˝±1 fl¬1± fl¬•ÛÚ±—fl¬1
’±Ò±1Ó¬ ’ªÓ¬ø1Ó¬ Sê˜Ó¬ ¸Àʱª±º
(i) AM Radio transmission
¤í¤˜ Œ¬ıÓ“¬±1 ¸•x‰¬±1Ì
29T PHYS [2]

(ii) Cellular communication
Œfl¬±¯∏œ˚˛ ”1-¸—À˚±· ¬ı…ª¶ö±
(iii) Sky wave propagation
’±fl¬±˙œ Ó¬1—· ø¬ıô¶±1Ì
(iv) Satellite communication
Î◊¬¬Û·Ë˝ ”1-¸—À˚±· ¬ı…ª¶ö±º
(h) The sparkle of a diamond can be explained by which phenomenon of
light ? 1
˝œ1± ¤Àά±‡11 øÊø˘fl¬øÚ, Œ¬Û±˝11 Œfl¬±Úø¬ıÒ ¬Ûø1‚Ȭڱ1 ¸˝±À˚˛À1 ¬ı…±‡…± fl¬ø1¬ı ¬Û±ø1∑

2. (Attempt any ten of the following questions)
[ø˚Àfl¬±ÀÚ± ˝È¬± √õ∂ùü1 Î◊¬M1 ø˘‡±]
(a) A magnetic dipole is oscillating in a magnetic field obeying the
following expression.
d 2 mB
2
 
dt I
What is the time period of oscillation and mention the nature of
oscillation ? 1½+½=2

¤È¬± Œ‰¬Ãø•§fl¬ ø ZÀ˜1n∏ ¤‡Ú Œ‰¬Ãø•§fl¬ Œé¬SÓ¬ ≈ø˘ ’±Àº Œ±˘Ú¸˜”À˝ øÚ•ßø˘ø‡Ó¬ √õ∂fl¬±˙1±ø˙
˜±øÚ ‰¬ø˘Àº
d 2 mB
2
 
dt I
Œ±˘Ú1 Œ±˘Úfl¬±˘ øÚÌ«˚˛ fl¬1± ’±1n∏ Î◊¬Mê Œ±˘Ú1 √õ∂fl‘¬øÓ¬› Î◊¬À~‡ fl¬1±º
(b) You know that Ampere’s circuital law is mathematically expressed
as given below.

Š B .dl  0 i
Also you know that this law was corrected by Maxwell and which is
known as Ampere-Maxwell law. Write the general form of the law
and name the additional term. 1+1=2

29T PHYS [3] Contd.

Ó≈¬ø˜ ʱڱ Œ˚ ·±øÌøÓ¬fl¬ˆ¬±Àª ¤ø•Û˚˛±11 ¬ıÓ«¬Úœ ¸”SÀȬ± Ó¬˘Ó¬ ø˚˛± Ò1ÀÌ √õ∂fl¬±˙ fl¬1± ˝˚˛º

Š B .dl  0 i
Ó≈¬ø˜ Œ¸˝◊ÀȬ±› ʱڱ Œ˚ ¸”SÀȬ± Œ˜'ÀªÀ˘ qX√√ fl¬ø1ø¢ ’±1n∏ ø˚ÀȬ± ¤ø•Û˚˛±1-Œ˜'Àª˘1
¸”S ¬ı≈ø˘ ÊÚ± ˚±˚˛º ¸±Ò±1Ìœfl¬1Ì fl¬1± ¸”SÀȬ±1 ¬·±øÌøÓ¬fl¬ 1+¬Û ’±1n∏ qX√√ 1+¬ÛÀȬ±Ó¬ Ôfl¬±
’øÓ¬ø1Mê ¬ÛÀȬ±1 Ú±˜ ø˘‡±º

(c) Explain in brief — “Infrared waves are sometimes referred to as heat
waves.” 2
‰¬˜≈Õfl¬ ¬ı…±‡…± fl¬1± ñ ëë’ªÀ˘±ø˝Ó¬ Ó¬1—·À¬ı±1fl¬ Œfl¬øÓ¬˚˛±¬ı± Ó¬±¬Û Ó¬1—· ¬ı≈ø˘› Œfl¬±ª±
˝˚˛ºíí

(d) Under what conditions Doppler effect is called (i) red shift and (ii) blue
shift ? 1+1=2
øfl¬ ‰¬Ó«¬Ó¬ ά¬Ûv±1 ¬Ûø1‚Ȭڱfl¬ (i) 1„± ¸1Ì ’±1n∏ (ii) Úœ˘± ¸1Ì ¬ı≈ø˘ Œfl¬±ª± ˝˚˛∑

(e) Draw a neat diagram to show lateral shift of a ray refracted through
a parallel-sided slab. Indicate the lateral shift in the diagram by a
double-headed arrow. 1½+½=2

≈˝◊ ¸˜±ôL 1±˘ ¬Û‘á¬˚≈Mê fl“¡±‰¬1 È≈¬fl≈¬1± ¤È¬±1 ˜±ÀÊø √õ∂øÓ¬¸ø1Ó¬ 1øù¨ ¤È¬±1 ¬Û±ù´«œ˚˛ ¸1Ì
Œ‡≈ª±¬ıÕ˘ ¤È¬± ¬Ûø1©®±1 ø‰¬S ’±“fl¬±º ø‰¬SÀȬ±Ó¬ ≈˝◊ ˜”1˚≈Mê ¤Î¬±˘ fl¬±“άˇ1 Z±1± ¬Û±ù´«œ˚˛ ¸1Ì
ø‰¬ø˝êÓ¬ fl¬1±º

(f) Define one coulomb charge. Two point charges at a distance r in air
exert a force F on each other. At what distance will these charges
experience the same force F in a medium of dielectric constant k ?
1+1=2

¤fl¬ fl≈¬˘•§ ’±Ò±Ú1 ¸—:± ø˚˛±º ¬ı±˚˛≈Ó¬ r ”1QÓ¬ Ôfl¬± ≈Ȭ± ø¬ıμ≈ ’±Ò±Ú1 ˜±Ê1 ¬ı˘ F,
k ø¬ı≈…» ˜±Ò…˜±—fl¬1 ˜±Ò…˜Ó¬ øfl¬˜±Ú ”1QÓ¬ Ô±øfl¬À˘ ø¸˝“Ó¬1 ˜±Ê1 ¬ı˘ F ¤Àfl¬ Ô±øfl¬¬ı∑

29T PHYS [4]

(g) Find the value of current I flowing from A to B in the following
circuit. 2

Ó¬˘Ó¬ ø˚˛± ¬ıÓ«¬ÚœÀȬ±Ó¬ A 1¬Û1± B Δ˘ ‰¬±ø˘Ó¬ Œ˝±ª± √õ∂ª±˝ I 1 ˜±Ú øÚÌ«˚˛ fl¬1±º
4

4
A B
4
4

4V 1 6

(h) Explain Lenz’s law from the principle of conservation of energy.
2
˙øMê1 ¸—1é¬Ì˙œ˘Ó¬±1 ¸”S1¬Û1± Œ˘?1 ¸”SÀȬ± ¬ı…±‡…± fl¬1±º
(i) What is modulation index ? If the maximum amplitude of an
amplitude modulated wave is 10V and the minimum amplitude is
2V, what is the value of modulation index ? 1+1=2

fl¬˘Ú ¸”‰¬fl¬ øfl¬∑ ø¬ıô¶±1 fl¬ø˘Ó¬ Ó¬1—· ¤È¬±1 ¸À¬ı«±2‰¬ ø¬ıô¶±1 10V ’±1n∏ ¸¬ı«øÚ•ß ø¬ıô¶±1
2V ˝íÀ˘ fl¬˘Ú ¸”‰¬fl¬1 ˜±Ú øfl¬˜±Ú ˝í¬ı∑

(j) Obtain an expression for drift velocity of an electron in a conductor.
2

Œfl¬±ÀÚ± ¬Ûø1¬ı±˝œ1 ¬ı±À¬ı ˝◊À˘fl¬È¬™Ú1 ’¬Û¬ı±˝√√ Œ¬ı·1 √õ∂fl¬±˙ 1±ø˙ Î◊¬ø˘›ª±º

(k) Establish the relation between the focal length  f  and radius of
curvature  R  for a spherical mirror. 2

Œ·±˘±fl¬±1 ±À¬Û±Ì ¤‡Ú1 ¬ı±À¬ı Ù¬ífl¬±Â Δ‚«…  f  ’±1n∏ ˆ¬±“Ê ¬ı…±¸±X«√  R  1 ˜±Ê1
¸•Ûfl«¬ÀȬ± ¶ö±¬ÛÚ fl¬1±º

29T PHYS [5] Contd.

3. (Attempt any nine of the following questions)
[ø˚Àfl¬±ÀÚ± ÚȬ± √õ∂ùü1 Î◊¬M1 ø˘‡±]
(a) There is an electric dipole on the x  y plane. Its dipole moment is
9
4  10 Cm . On the same plane there is also a uniform electric field
of magnitude 5  10 4 NC 1 . If the axis of the dipole makes an angle
30 with the electric field, calculate the magnitude of the torque
acting on the dipole and also mention the direction of torque.
2+1=3

x  y Ó¬˘Ó¬ ¤È¬± Δ¬ı≈…øÓ¬fl¬ ø ZÀ˜1n∏ ’±Àº ˝◊˚˛±1 ø ZÀ˜1n∏ w±˜fl¬ ˝í˘ 4  10 Cm º
9

¤Àfl¬‡Ú Ó¬˘Ó¬ 5  10 4 NC 1 ˜±Ú1 ¤‡Ú ¸≈¯∏˜ Δ¬ı≈…øÓ¬fl¬ Œé¬S› ’±Àº ˚ø ø ZÀ˜1n∏1
’鬽◊ Δ¬ı≈…øÓ¬fl¬ Œé¬S‡ÚÀ1 Δ¸ÀÓ¬ 30 Œfl¬±Ì fl¬À1, ŒÓ¬ÀôL ø ZÀ˜1n∏ÀȬ±1 ›¬Û1Ó¬ øSê˚˛±˙œ˘
Ȭfl«¬1 ¬Ûø1˜±Ì øÚÌ«˚˛ fl¬1± ’±1n∏ ˘·ÀÓ¬ Î◊¬Mê Ȭfl«¬1 øÀ˙± Î◊¬À~‡ fl¬ø1¬ı±º
(b) The capacity of a parallel plate capacitor with air is 18 pF . When a
dielectric material is inserted in the space between the plates, its
capacity becomes 108 pF . Calculate the permittivity of the material.
What is the material ? 2+1=3
¬ı±˚˛≈ ˜±Ò…˜Ó¬ ¤È¬± Ò±1fl¬1 Ò±1fl¬Q Δ˝À 18 pF º Œ˚øÓ¬˚˛± Ò±1fl¬ÀȬ±1 ¬Û±Ó¬ ≈‡Ú1 ˜±ÊÓ¬
¤È¬± ¬Û±Ô« ¸≈˜≈ª±˝◊ ø˚˛± ˝˚˛, Ò±1fl¬Q ˝˚˛Õ· 108 pF º ¬Û±Ô«ÀȬ±1 ¬Û1± ø¬ı≈…» ÒËn∏ ıfl¬
øÚÌ«˚˛ fl¬1±º ¬Û±Ô« ø¬ıÒ øfl¬∑
(c) A current carrying solenoid is shown below. Show that the magnetic
field intensity at point P be
 2m
B 0 3 ,
4 r
where the symbols have their usual meaning. 3
x
dx

a P
O

l l
r
›¬Û1Ó¬ ø‰¬SÓ¬ ø¬ı≈…» √õ∂¬ı±ø˝Ó¬ ¤È¬± ÂÀ˘Ú˚˛Î¬ Œ‡≈›ª± Δ˝Àº Œ‡≈ª± Œ˚ P ø¬ıμ≈Ó¬
Œ‰¬Ã•§fl¬Àé¬S1 √õ∂±ª˘… ˝í¬ı
0 2m
B ,
4 r 3
˚íÓ¬ ¬ı…ª˝+Ó¬ ¸—Àfl¬Ó¬À¬ı±À1 ¸‰¬1±‰¬1 ’Ô« ¬ı˝Ú fl¬ø1Àº
29T PHYS [6]

(d) Consider that the electric field amplitude of an electromagnetic wave
is E 0  120NC 1 and its frequency is   50Hz . Determine B 0 , 
and k . 3
¤È¬± ø¬ı≈…» ‰≈¬•§fl¬œ˚˛ Ó¬1—·1 ø¬ı≈…» Œé¬S1 ø¬ıô¶±1 E 0  120NC 1 ’±1n∏ fl¡•ÛÚ±—fl¡
  50Hz ¬ı≈ø˘ Òø1À˘ B 0 ,  ’±1n∏ k øÚÌ«˚˛ fl¬1±º
(e) Show that the total energy of an electron in an atom is negative and
it is
e2 .
E 
8 0
What is the significance of the negative energy. 2+1=3
Œ‡≈›ª± Œ˚ ¬Û1˜±Ì≈ ¤È¬±Ó¬ Ôfl¬± ˝◊À˘fl¬È¬™Ú ¤È¬±1 ˜≈ͬ ˙øMê Ÿ¡Ì±Rfl¬ ’±1n∏ ˝◊ ˝í˘
e2
E  º
8 0
Ÿ¡Ì±Rfl¬ ˙øMê1 Ó¬±»¬Û˚« øfl¬∑
(f) Name the only gate which is used in the following circuit. Write the
truth table for each of the circuits. Identify the logic operation
(i.e. OR, AND, NOT etc.) performed by the circuits. ½+(½+1½)+½=3

A

A Y Y

B

a  b 
¬›¬Û11 ¬ıÓ«¬Úœ ≈Ȭ±Ó¬ ¬ı…ª˝+Ó¬ ¤fl¬˜±S Œ·íȬ‡Ú øfl¬∑ √õ∂ÀÓ¬…fl¬ÀȬ± ¬¬ıÓ«¬Úœ1 ¬ı±À¬ı Ȭ™≈Ô ŒÈ¬¬ı≈˘
ø˘‡± ’±1n∏ ≈À˚˛±È¬± ¬ıÓ«¬ÚœÓ¬ ¸•Û±Ú Œ˝±ª± ˘øÊfl¬ øSê˚˛± [’Ô«±» OR, AND, NOT
˝◊Ó¬…±ø] ø‰¬Ú±Mê fl¬1±º
(g) Two long straight thin conductors carrying currents I1 and I 2
respectively along the same direction are placed parallel to each other
at distance d in air. Find the force per unit length acting on any one
of the conductors. Hence define one ampere. 2+1=3
d ”1QÓ¬ ¬Û1¶Û1 ¸˜±ôL1±˘Õfl¬ Ôfl¬± ≈ά±˘ œ‚˘ Œ¬Û±Ú ¬Ûø1¬ı±˝œÓ¬ SêÀ˜ I1 ’±1n∏ I 2
√õ∂ª±˝ ¤Àfl¬ ø˙Ó¬ ‰¬±ø˘Ó¬ Δ˝Àº ø˚Àfl¬±ÀÚ± ¤È¬± ¬Ûø1¬ı±˝œ1 ¤fl¬fl¬ Δ‚«…Ó¬ øSê˚˛± fl¬1± ¬ı˘
øÚÌ«˚˛ fl¬1± ’±1n∏ ˝◊˚˛±1¬Û1± ¤fl¬ ¤ø•ÛÀ˚˛11 ¸—:± ø˚˛±º
29T PHYS [7] Contd.

(h) Draw a ray diagram to show the correction of a myopic eye. The near
point of a person with defective eye is 75cm from the eye. Find the
power of lens required to see clearly at 25cm from the eye.
1+2=3

鬜Ì‘ø©Ü1 ¸—À˙±ÒÚœ Œ‡≈ª±˝◊ ¤È¬± 1øù¨ ø‰¬S ’“±fl¬±º ø¬ıfl¬±1·Ëô¶ ‰¬fl≈¬1 ˜±Ú≈˝ ¤ÊÚ1 øÚfl¬È¬
ø¬ıμ≈ ‰¬fl≈¬1¬Û1± 75cm ”1QÓ¬ ’ªø¶öÓ¬º 25cm ”1QÓ¬ ¶Û©Ü Œø‡¬ıÕ˘ √õ∂À˚˛±ÊÚœ˚˛ Œ˘k1
鬘Ӭ± øÚÌ«˚˛ fl¬1±º
(i) What are coherent sources ? In a Young’s double slit experiment the
intensity of light at a point on the screen where path difference  is
k units. Find the intensity at a point where the path difference is  3 .
1+2=3
¬˙± ¸—¬ıX√√ Î◊¬»¸ øfl¬∑ ˝◊˚˛„1 ø ZøÂ^ ¬Û1œé¬±Ó¬ ¬Û«±1 Œfl¬±ÀÚ± ¤È¬± ø¬ıμ≈Ó¬ ¸˜±À1±¬ÛÌ ‚Ȭ±
Ó¬1—· ≈Ȭ±1 ¬ÛÔ ¬Û±Ô«fl¬…  º Œ¸˝◊ ø¬ıμ≈Ó¬ ˘t √õ∂±¬ı˘… k ¤fl¬fl¬º ’±Ú ¤È¬± ø¬ıμ≈Ó¬ ¬ÛÔ
¬Û±Ô«fl¬…  3 ˝íÀ˘ Œ¸˝◊ ø¬ıμ≈Ó¬ ˘t Ó¬œ¬ıËÓ¬± øfl¬˜±Ú ˝í¬ı∑
(j) Explain the source of solar energy with the help of proton-proton
cycle. What is the role of cadmium rods in a nuclear reactor ?
2+1=3
√õ∂ȬÚ-√õ∂È¬Ú ‰¬Sê1 ¸˝±˚˛Ó¬ Œ¸Ã1 ˙øMê1 Î◊¬»¸ ¬ı…±‡…± fl¬1±º øÚÎ◊¬flv¬œ˚˛ ø1À˚˛"√1 ¤È¬±Ó¬
Œfl¬Îƒ¬ø˜˚˛±˜ G1 fl¬±˜ øfl¬∑

4. (Attempt any three of the following questions)
[ø˚Àfl¬±ÀÚ± øÓ¬øÚȬ± √õ∂ùü1 Î◊¬M1 ø˘‡±]
(a) “The phenomenon of electro-magnetic induction has been
technologically important application in the generation of alternating
currents.” Name the device which can generate alternating currents.

Draw a neat diagram of it. A rectangular coil having area vector A

and number of turns N is rotating in a magnetic field B with angular

speed  . If  be the angle made by the area vector A with the field

B at time t , derive an expression for alternating emf  starting
directly from Faraday’s law. Draw a graph to show the generated emf
at time 0, T 4 , T 2 , 3T 4 and T. ½+1½+2+1=5

29T PHYS [8]

ëëø¬ı≈…»-Œ‰¬Ã•§fl¬ ’±Àª˙ ¬Ûø1‚ȬڱÀȬ± √õ∂˚≈øMêø¬ı…±Ó¬ ø¬ıøˆ¬iß Ò1ÀÌ ¬ı…ª˝+Ó¬ Δ˝ ’±ø˝Àº
˝◊˚˛±1 ¤È¬± ’±ª˙…fl¬œ˚˛ ¬ı…ª˝±1 ˝í˘ ¬Ûø1ªÓ«¬œ √õ∂¬ı±˝ Î◊¬»¬Û±Ú fl¬1±ºíí ¬Ûø1ªÓ«¬œ √õ∂¬ı±˝
Î◊¬»¬Û±Ú fl¬1± ’±ø˝˘±ø¬ıÒ1 Ú±˜ ø˘‡± ’±1n∏ ˝◊˚˛±1 ¤È¬± ¬Ûø1©®±1 ø‰¬S ’“±fl¬±º ¬N Û±fl¬˚≈Mê
 
’±1n∏ A Œé¬SÙ¬˘ Œˆ¬"√11 ¤È¬± ’±˚˛Ó¬±fl¬±1 fl≈¬G˘œ  Œfl¬ÃøÌfl¬ ^n∏øÓ¬À1 B Œ‰¬Ãø•§fl¬
 
Œé¬SÓ¬ ‚”ø1 ’±Àº ˚ø Œfl¬±ÀÚ± ¤fl¬ ¸˜˚˛ t Ó¬ A ’±1n∏ B 1 ˜±Ê1 Œfl¬±Ì  ˝˚˛, ŒÓ¬ÀôL
ŒÙ¬1±Àά1 ¸”S ¬ı…ª˝±1 fl¬ø1 ¬Ûø1ªÓ«¬œ ø¬ı≈…»‰¬±˘fl¬ ¬ı˘1 ¤È¬± √õ∂fl¬±˙1±ø˙ øÚÌ«˚˛ fl¬1±º
0, T 4 , T 2 , 3T 4 ’±1n∏ T ¸˜˚˛Ó¬ Î◊¬»¬Ûiß Œ˝±ª± ø¬ı≈…» ‰¬±˘fl¬ ¬ı˘1 ¤È¬± Œ˘‡
’—fl¬Ú fl¬1±º
(b) State Kirchhoff’s (i) Junction rule and (ii) Loop rule. Determine the
equivalent resistance of the network given below and the total current
going out of the battery. Given, each resistor has resistance of 1 .
1+1+2+1=5

D I
I C
2
I I I
2 2 I
A B
C
I D I
I 2 I I
2 2
I
3I A B

E  10V

¬fl¬±‰«¬Ù¬1 (i) ¸—À˚±· ø¬ıμ≈1 ¸”S ’±1n∏ (ii) ¬ıg ¬ıÓ«¬Úœ1 ¸”S ≈Ȭ± ø˘‡±º ›¬Û1Ó¬ ø˚˛±
¸7¬¬¬±ÀȬ±1 ¸˜Ó≈¬˘… Œ1±Ò ’±1n∏ Œ¬ıȬ±1œ1¬Û1± √õ∂¬ı±ø˝Ó¬ Œ˝±ª± ø¬ı≈…» øÚÌ«˚˛ fl¬1±º ø˚˛± ’±ÀÂ
¸7¬¬¬±ÀȬ±1 √õ∂øÓ¬ÀȬ± ¬ı±UÓ¬ Ôfl¬± √õ∂øÓ¬ÀȬ± Œ1±Òfl¬1 ˜±Ú 1 º

29T PHYS [9] Contd.

(c) You know that the modulated signal in amplitude modulation (AM)
is expressed as given below

Ac Ac
Cm t   A c sin  c t  cos  c  m  t  cos  c  m  t .
2 2

Plot the frequency spectrum of the signal i.e. a plot of amplitude

versus  . Write what will happen if the modulation index   1 .

What are sidebands ? Write the full forms of PAM, PDM, PWM and

PPM. 1+1+1+(4×½)

Ó≈¬ø˜ ʱڱ Œ˚ ø¬ıô¶±1 fl¬˘ÚÓ¬ fl¬ø˘Ó¬ ¸—Àfl¬Ó¬fl¬ Ó¬˘Ó¬ ø˚˛±1 À1 √õ∂fl¬±˙ fl¬1± ˝˚˛º
Ac Ac
Cm t   A c sin  c t  cos  c  m  t  cos  c  m  t
2 2

 1 ø¬ı¬Û1œÀÓ¬ ¸—Àfl¬Ó¬ fl¬•ÛÚ±—fl¬1 ¬ıÌ«±˘œ1 Œ˘‡ ’—fl¬Ú fl¬1±, ’Ô«±»  1 ø¬ı¬Û1œÀÓ¬
ø¬ıô¶±11 Œ˘‡º fl¬˘Ú ¸”‰¬fl¬   1 ˝íÀ˘ øfl¬ ˝í¬ı ø˘‡±º ¬Û±ù´«¬ÛøȬ¸˜”˝ÀÚ± øfl¬∑ PAM,
PDM, PWM ’±1n∏ PPM 1 ¸•Û”Ì« 1+¬Û ø˘‡±º

(d) A source of emf , Vm sin t is connected in series with an inductor L,

capacitor C and resistor R. Calculate the impedance and resonant

frequency of the circuit. Also write an application of the resonant

circuit. 3+1+1=5

Vm sin t ø¬ı≈…»‰¬±˘fl¬ ¬ı˘1 Î◊¬»¸ ¤È¬± ’±Àª˙fl¬ L , Ò±1fl¬ C ’±1n∏ Œ1±Òfl¬ R 1 Δ¸ÀÓ¬

Œ|ÌœªX√√ˆ¬±Àª ¸—À˚±· fl¬1± Δ˝Àº ¬ıÓ«¬ÚœÀȬ±1 √õ∂øÓ¬¬ı±Ò± ’±1n∏ ’Ú≈Ú± fl¬•ÛÚ±—fl¬ øÚÌ«˚˛
fl¬1±º ˘·ÀÓ¬ ’Ú≈Ú±œ ¬ıÓ«¬Úœ1 ¤È¬± ¬ı…ª˝±1 ø˘‡±º

29T PHYS [ 10 ]

(e) For refraction at a convex spherical surface of radius of curvature R
from a medium of refractive index n1 to a medium of refractive
index n 2  n 2  n1  , establish the relation
n2 n1 n 2  n1
  .
v u R
What will be the behaviour of a convex lens of refractive index 1 47
when it is immersed in a liquid of refractive index 1 47 ?
4+1=5

R ˆ¬“±Ê ¬ı…±¸±X«√1 ¤‡Ú Î◊¬M˘ Œ·±˘±fl¬±1 ¬Û‘á¬Ó¬ n1 √õ∂øÓ¬¸1̱—fl¬1 ˜±Ò…˜1¬Û1± n 2
õ∂øÓ¬¸1̱—fl¬1 ˜±Ò…˜Õ˘  n 2  n1  √õ∂øÓ¬¸1Ì ‚Ȭ±1 Œé¬SÓ¬ Œ‡≈›ª± Œ˚
n2 n1 n 2  n1
 
v u R

1 47 √õ∂øÓ¬¸1̱—fl¬1 Î◊¬M˘ Œ˘k ¤‡Ú 1 47 √õ∂øÓ¬¸1̱—fl¬1 Œfl¬±ÀÚ± Ó¬1˘Ó¬ Î≈¬¬ı±˝◊
øÀ˘ Œ˘k‡Ú1 ’±‰¬1Ì Œfl¬ÀÚ ˝í¬ı∑

———— ×————

29T PHYS [ 11 ]

29T PHYS [ 12 ] 43+