Sample Paper 1 Solutions
Class XIE 2023-24
Physics
‘Time: $ Hours
General Instructions:
1. There are $3 questions in all. All questions are compulsory
2. This question paper has mn A, Section B, Section C, Section D and Section B,
3. All the sections are compulsory.
4. Section A contains sixteen questions, twelve MCQ and four assertion reasoning based of 1 mark each, Section B contains
five questions of 2 marks each, Section C contains Seven questions of 3 marks each, Section D contains two ease study based
Max. Marks: 70
  
questious of 4 marks each aud Section E contains three loug questious of 5 marks each,
choices in such questions
6. Use of ealeulators is not allowed
5. There is no overall choice. However, an internal choice has been provided in one question in Section B, one questi
Section C, one question in each CBQ in Section D andl all three qu
 
cone of the
   
stions in Section E. You have to attempt
7. You may use the following values of physical constants where ever necessary
i.e =3x 10'm/s
fim 91% Wg
fil, © = 16x WC
iv. py = 4x 107 Ta
G68 x 10s
8851 1 EN
Avogadro's mmber = 6.423 x 10" per gram mole
vk
 
  
 
 
SECTION-A
Tn Huygen’s wave theory, the loeus of all points oscillating
in the same phase is called &
(a)ray (b) vibrator
(c) wavefront (4) half period zone
 
Ans : (¢) wavefront
We know from the Huygen’s wave theory that the locns of
all points oscillating in the same phase is called a wavefront
In other words, a wavefront is defined as a surface of constant
phase
If a glass rod is immersed in a liquid of the same refractive
index, then it will
(a) disappear
(€) look longer
(b) look bent
(4) look shorter
Ans : (a) disappear
We know that if a glass rod is will immersod in a liquid
of the same refractive index as that of the rod, then no
rufraction will take place
Therefore, the glass rod will disappear.
 
 
Most of the substance show which of the following magnetic
property?
(b) paramagnetism
(@) both b and €
 
Ans : (a) disnaguetism
We know that all substances show diamagnotism, as itis
niversal. Since hoth the paramagnetism and ferromagnetisin
substances have diamagnetism in weak, therefore they are
hard to deteet.
 
When two charged capacitors having capacitance and
potential G, Vj and C;, Vs respectively, are joined with the
help of a wire, the common potential will be
(G+ (o) GM AG
 
 
+O
SHE Gu ( GYLG
ree Vi+Vi
Ans: ) SHES
Given,
Capacitance of first capacitor = C,
 
Potential of first capacitor = Vi
Capacitance of second eapacitor = C;
 
and Potential of second eapacitor =
We know that when two charged capacitors are joined with
the help of a wire, then the eommon potential,
YtGu
CHG
o
Oa
In photoelectric effect the maximum kinetic energy of
‘emitted electron depends on
(a) wavelength (b) frequency
(c) intensity (4) work function
    
 
Ans: (a,b)
' plotoclectric equation is given by,
K,
where, y= work function
 
   
Hence,
  
© y and Ku, © 4
Hence, Ky 2 1 ad Kus 5.
Hence maximnm kinetic energy depends on the wavelength,
and frequency
 
The number of Photons of frequency 10 Ha in radiation of
6.624 will he
(a) 10” (b) 10!
(c) 10” (a) 10
Ans (c) 10”
 
Given:Page 2
 
E=602)
vy = 10H
Energy
 
Frequency,
We know that,
‘Nuuuber of Photons = Energy
‘Energy of one Photon
= 6.02 6.62,
Ww Gx 10 XO
1 What the estas of a AOW lap tel
fal rine by ncuren of EAP
(a) 200 (o) 2000
(©) 3600 (a) 4809
Ans : (c) 3600
Given,
Power of lam, P =40W
Current
 
A
We know that resistance of lamp,
P_4
Rate = Hy ~ s000
4 Which of the following doe
smutual induetion’?
(a) dynamo
(6) induction coil
Ans  (d)clectre heater
We know that phenomenon according to which an opposing
E.ME. is prodhiced in col as «result of ehonge in enrrent
or maguotic ux linked with a neighbouring coil, is called
suutual induction
Since electric heater is based on heating effect of current.
therefore it does not obey the phenomenon of mutual
induetion.
And dynamo, transformer and induction coils are based on
the phionomenon ofthe mutual induetion
NEET 45 YEARS PAPERS
Downdload Free PDF From NODIA App
Search Play Store by NODIA
For more details vist : www.nodia injec
‘Add 86058 29866 in Your Class Whatsapp Group Got POF
 
not obey the phenomen
 
(b) transformer
(@) electric heater
& In a series combination, R= 3009, L
= 1000 rad — 5". The impedance of th
 
9H, C=20F,
LCReeireut is,
 
 
(a) 4000 (b) 5009
(e) 9000 (a) 13000
Ans: (b) 5008
Given,
Resistance,
Inductance,
Capacitance, C= 2nP = 2x 104P
Angular velocity 1000 rad — s"
     
We know that reactance of inductor,
  
Xi, =wL = 1000 x09 = 9009
and reactance of eapacitor,
Mla 1
Xe = So = i000 (2x10)
 
500
 
Sample Paper 1 Solutions
CBSE Physics Class 12
Therefore, impedance of LCR-cireuit
2=/R+(%- Xe
+/(300)* + (900 = 500)"
= ¥'90000 + 760000
/ 250000 = 5000
 
 
 
1. An electric dipole consists of positive and negative charge
‘of 4yC cach placed at a distance of 5 mm, The dipole
moment is
(2x 10°C
() 6x 10°C m
Ans: (a) 2x 10%C-m
(b)4x Wm
(a) 8x W*Cm
 
  
Magnitude of each charge on dipole
q=4yC =4x 10°C
and distance betwoen the charges,
x 10%m
 
2
We know that,
   
 
Dipole moment,p = 4x 20
=x 9 x 6x09)
=2x10°Cm
ML Two solenoids of the same length having number of turns
in the ratio of 2:3 are connectod in series, The ratio of
magnetic fields at their centres is
 
 
(a) 2:1 (b) 3:1
(a) 3:2
No, of tums in first solenoid, XN
No. of tums in second solenoid, —N
We know that no. of turns per unit le
 
 
 
where, = length of solenoid
We also know that maguetic field at the centre of solenoid,
B= pont = mol Bree N
Therfore
BuBs
 
1, Assertion : In Young’s experiment, the fringe width for dark
fringes is different from that for white fringes.
Reason : In Young's double slit experiment the fringes are
performed with a source of white ligt, then only black ancl
bright fringes are observed.
(a) Both Assertion and Reason are correct and Reason is the
correct explanation of Asserti
(b) Both Assertion and Reason are correct, but Reason is
not the correct explanation of Assertion,
(} Assertion is correct but Reason is incorrect.
 
 
 
(a) Assertion is incorrect but Reason is correct.
Ans : (il) Both the Assertion and Reason are incorrect.
Tn Young's experiment, fringe width of dark and white
fringes are equal. IF white light is used as source, coloured
fringes axe observed representing bright band of different
colours.Page 3 Sample Paper 1 Solutions
1 Assertion We cannot think of magnet ikl configuration
with thre poles
Reason : A bar magnet docs exert ator
its own fil,
(#) Both Assertion and Reason are correct aud Reason isthe
correct explanation of Assertion.
(b)Both Assertion and Reason aro coreet, but Reason is
not the correct explanation of Assertion,
(6) Asertion is comoct but Reason is incorrect
(4) Asertion is incorrect hut Reason is correct.
on itself due to
 
Ans : (d) Assertion is incorrect but Reason is correct
Magnet field may be formed with the help of three poles. A.
bar magnet does not exert a torque on itself due to its own,
field
 
M. Assertion (A) : Diamond behaves like an insulator,
Reason (R) : There is a large energy gap between valence
band and conduetion band of diamond
(a) Both Assertion and Reason are correct and Reason is the
correct explanation of Assertion.
(b)Both Assertion and Reason are eorreet, but Reason is
not the correct explanation of Assertion
(c) Assertion is correct but Reason is incorrect,
(a) Assertion is incorrect but Reason is correct.
 
‘Ans : (a) Both Assertion and Reason are correct and Reason,
is the correct explanation of Assertion
Ta insulator, the forbidden energy gap is quite large. When
‘leetrie field is applied to such a solid, the electron find it
difficult to acquire such a large amount of energy. Thus no
electron flow ovens.
 
18 Assertion : In sories LOR cirenit resonance ean take place.
Reason : Resonance takes place if inductance and capacitive
resistances are equal and opposite
(a) Both Assertion and Reason are correct and Reason is the
correct explanation of Assertion.
(b)Both Assertion and Reason are correet, but Reason is
not the correct explanation of Assertion
(c) Assertion is correct but Reason is incorrect,
(a) Assertion is incorrect but Reason is correct.
Aus : (a) Both Assertion and Reasou are correct and Reason,
is the correct explanation of Assertion
In series resonance cireuit, current becomes maximum,
Decanse total impeslance becomes zero. In case of LC circuit,
 
 
 
 
‘Total imptance
  
W® Assertion (A) : Capacity of a parallel plate capacitor
increases whan distance between the plates is doereased
Reason (R) : Capacitance of capacitor is inversely
proportional to distance between them.
(9) Both Assertion and Reason are correct andl Reason isthe
correet explanation of Assertion,
(b)Both Assertion and Reason are correct, but Reason is
not the correct explanation of Assertion.
(¢) Assertion is correct but Reason is incorrect,
(4) Assertion is incorrect but Reason is correct
Aus : (c) Assertion is correct but Reason is incorrect,
Barth is a good conductor of very large size. When some
CBSE Physics Class 12
small charge is given to earth, its potential does not change.
Hence potential of earth is assumed to be zero, It is just
like sen level which does not alter materially when water is
added to it or removed from it. Thus, the potential of all,
‘other bodies are measured with reference to the earth, For
this if the connection of a charged body to the ground by a.
metallic conductor would cause electrons to flow to that body
from ground, the body is at positive potential. Conversely,
is also true. In either ease the conductor is neutralized and
brought to zero potential. In fact the atmosphere does
possess significant electric field,
T-JEE 45 YEARS 120 PAPERS
Downdload Free PDF From NODIA App.
Search Play Store by NODIA
For more details visit: www.nodia inijee
‘Add 86056 209609 in Your Class Nhasepp Group to Got POF
   
 
 
SECTION-B
In which sitmation is there a displacement current bnt no
‘conduction current ?
Ans :
During charging or discharging thereisadisplacement current
but no conduction eurrent betwoen plates of eapacitor.
Define conductivity of a material. Give its ST unit.
Ans :
The reciprocal of the resistivity of a material is called its
coutnctivity and is denoted by a. Thus,
Rar
Conductivity = aaa
  
or =}
SI unit of conductivity is ohm-'m or ohm m™ or
 
How does a cirenlar loop carrying current behaves as a.
magnet?
Ans:
The eurrent round in the face of the coll isin anti-clockwise
direction, then this behaves like a North pole, whereas when
it viewed from other seale, then current round ia it isin
clockwise direction necessarily forming South pole of magnet.
OY
Hence, current loop have both magnetic poles and therefore,
behaves like a magnetic dipole
The current flowing through @ pure inductance 2 mt is
(15 c0s3004) A, What is the (i) rans. and (i) average
value of current for a complete cycle
 
 
Ans:
Current flowing through the inductor,
I = 15c0s300¢
Comparing withPage
T= hsinut
Here, peak value of curren,
1=15A
() For compete cyclo, rms valus of current
a
v2 V2
(ii) For complete eycle average value of current is zero
fie Io =0
11 State the criteria for the phenomenon of total internal
reflection of light to take place,
or
‘What is the difference between Magnification and Magnifying
power?
Ans :
 
Following are the criteria for total internal reflection
(i), Light must pass from a denser to @ rarer medi,
(ii) Angle of incidence must be greater than critical angle.
‘The difference between Magnification and Magnifying power:
Magnification ‘Magnifying Power
1. | Magnification is the ratio| Magnifying power is,
‘of image size to object | the ratio of visual angle
am sta hy th ge
(3) and visual angle
bn th
(a).
Tie wl of maging
poner es toner 2
au (I+ 3)
CUET 30 SAMPLE PAPERS
Downdload Free PDF From NODIA App
Search Play Store by NODIA
For more details visit: www.nodia.in/cuet
‘Add 88056 280609 n Your Class Whatsaop Group to Get POF
 
 
 
2, | Therangeofmagnification
ix 0 to 400
 
 
 
 
 
SECTION-C
‘2 In the Rutherford scattering experiment, the distance of
ile is
 
closest approach for an a-particle i dk. Mapa
replaced by a proton, then how much kinetic energy in
comparison to a-particle will be tequted to have the same
distance of closest approach d
Aus
Distance of closest approach
= 2kee
Ke
Since, forgiven distance of cat appronch
Knot energy 27 (atomic aber)
 
ere, k=
Where, k= =
 
% Draw energy band diagram of n-typed and p-typed
semiconduetor at temperature T> 0K. Mark the donar
 
Sample Paper 1 Solutions
CBSE Physics Class 12
and acceptor encrgy level with their energies
Ans:
The required energy band diagram is shown below.
 
‘Condaction band
 
Acorptorenegy vel
eet oe
 
 
 
 
mot ev
Valence band
(0) pve
Condation bane
in04 ev
eee
Donor ene lve
 
Valence band
 
 
 
(0) mtype
2A Two equal balls having equal positive charge q caulombs are
suspended by two insulating strings of equal length. What
would be the effect on the force when a plastic sheet is,
inserted between the two?
   
 
Ans:
Form Coulomb's law, electri force between the two charged
bodies, in a medium,
 
where, K = dielectric coustant of the medium,
K=1
For plastic, K >1
Therefore, after insertion of plastic sheet, the force between
the two balls wll reduce
For vacuum,
% State the Bio-Savart law for the magnetic field due to a
‘current carrying element. Use this law to obtain a formula
for maguetic field at the eoutre of a eiccular loop of radius
R carrying a steady current 1. Indicate the dircetion of the
magnetic field.
   
    
 
Ans:
According to Bio-Savart's law, the magnctie field due to
a current element di carrying current I at a point P at
distance r from itis given by,
a = fe. Hind
where, is permeability of free space and 9, is the angle
betwoen di’ and 7.
Magnetic field at the centre of a circular eurrent carrying
coil: Consider a circular loop of wire of radius r carrying &
‘current J. Consider a current clement a of the loop.
The direction of df is along the tangent, so dL 7. From
Bio-Savart law, magnetic field at the centre Q due to thisPage 5 Sample Paper 1 Solutions
[Magnet Fed atthe Centre of Cirelar Current Loop
‘The magnetic field due to all such current elements wil point
into the plane of paper at coutze O as shown by encireled
cross ©, Hon the total magnetic field at the centre 0 is,
fan = [tel dl = ool
ae fanm fie Gee fa
dol,
a
sul
 
 
28, When does snell’s law fail in reftaction?
Ans
Snell's law fails, ff ray of light in a denser medium incident
‘on a rarer medium at an angle more than the eritieal angle
for that pair of media, then the ray of light is totally reflected,
back into the denser medium instead of going to the rarer
smeodiuta as predicted by Suell’s law. Hence in this situation,
Snell's law fails in refraction,
1. How the size of @ ancleus is experimentally determined?
Write the relation between the radius and mass nmmber of
tle melons. Show that the density of nucleus is independent
of its mass mnmiber.
  
 
     
 
Ans
‘Tho size of the nuclous is experimentally determined using
Rutherford's a-scattering experiment and the distance of
closest approach ancl impact parameter.
Tho relation betwoon radius and mass number of nucleus is,
R= RAM
1.2Fm
A= mass mmnber
 
 
 
where, R,
 
radius of nucleus
Nuclear density,p = Masso nucleus_ ___md___
P= Volmmeof uncleus ~ Tz(R, A")
amass of each meleon
Hence, P= aa
 
 
where, m
 
From the above forumila, itis clear that p does not depend
‘on the mass number.
2. Explain why do we need coherent sources to produce
Interference of light.
jonable mass. Give its
  
Define multiplicat
CBSE Physics Class 12
plisical significance.
Ans:
When two monochromatic waves of intensity , fe ancl
phase difference 6 meet at a point, the resultant inte
is given by,
 
 
=Hhth+Whhoso
‘The last term 2y I, /, cos is called interference term. There
ae «wo posites
Le Hew rem c total intensity
at any point ill bo constant, The intensity will be
maximum (vf +yh)* at points where cosd is +1.
aus sininnn (/,~ (/B)? at points where con =— 1
“The sures in this ease are coherent
2. If cong vats contiamosly with tne, thea the inter
ference term averages to ner, The
tensity, = 1, +h at every point ie., there will be
eral illumination on the obnervation sereen. The two
foeos inthe case are Incoherent
Hence to observe interference, we need to have two sours
withthe sume frequency aud with sable phase diference
Sich a pir of sources are called ecierent sourees,
ins constant with time, t
 
 
 
  
  
 
‘The multiplication factor of a fssionable mass is defined as
th ber of neutrous present at the beginning
‘ofa particular generation to the munber of neutrons present
at the beginning of the previous generation,
ratio of the
 
 
 
‘Ser of en pret he basing of pes et
ure of the growth
 
Thos,
 
 
The multiplication factor k gives a me:
rate of the neutrons in a fissionable mass
If k> 1, the chain reaction grows.
If k= 1, the chain reaction remains steady.
If < 1, the chain reaction gradually dies out.
 
 
SECTION-D
Consider the situation shown in figure, The two sits s, and s,
placed symmetrically around the central line are illuminated,
by monochromatic light of wavelength a. The separation
betwen the slits iso The ligt transmitted hy the sits falls
‘oa screen §; place at a distance D frou the slits. The slits
‘is at the contral line and the slit 5, is ta distance fr
S Another sereen S., is placed a further distanee D away’
from 5,
   
 
 
(i) Find the path difference if 2=42
(aa oan
(haya (a
Ams :(b) 4/2
As sai
At s:AZasPage 6
 
NO NEED TO PURCHASE SAMPLE PAPERS
Download India’s Best 20 Sample Papers
“DOWNLOAD NODIA APP
Every School conduct Pre-Board
From These Sample Papers
(ii) Find the ratio of the maximum to minimum intensity
observed on §,, if == 42
(a)
(©
Aus (c)
 
@t
wD
7
 
s:42~ ADS.
Ag at S:az=4Pd oy
Hence, maxima at Sas well as S,
Resultant intensity at §,
  
(iil) Two coherent point sources s, and S, are separated by
a suall distance das shown in figure. The fringes ob-
tained on the sereen will be
1.
SSN sercen
D
(a) concentric cireles _(b) points
(6) straight lines (a) semi-cireles
 
Ans : (a) concentric eizeles
When the screen is placed perpendicular to the line joining
the sources, the fringes will be concentric circles.
(iv) Tn the case of light waves from two colierent sources
5\ and 5, there will be constructive interference at an
arbitrary point P, ifthe path difference 5,P~ 5? is
   
 
 
 
(b)m
(a) 19
Ans : (b) 0
Constructive interference occurs when the path difference
 
(S,P— ,P) is an integral multiple of».
or §P- SP = nd, where n= 0, 1,2, 8,
 
(©) Two monochromatic light waves of amplitudes 34 and
2A interfering at a point have a phase difference of 60°.
The intensity at that point will be proportional to
(0) sa (bist
(ou (die
Ans : (@) 194
Hore, 4)=34, 4, =24 and 6 =00
 
The resultant amplitude at @ point is
ab Ay 2AA,
Veayy ear
oa aay oa
As, Intensity = (Amplitude)®
‘Thorefore, intensity at the same point is
 
2K GA KA X cost"
 
0
   
 
Sample Paper 1 Solutions
CBSE Physics Class 12
Tee 194
CO
3 Gauss’s law and Coulomb's law, although expressed in
different forms, are equivalent ways of deseribing the relat
betwoen charge and cleetric field in statie conditions.
Gans law is when gay is the net charge inside an
imaginary closed ‘ure called Gaussian surfce. 9 = $B di
sive the electri fus through the Ga face, The two
‘equations hold only when the net charge i in vacuum or ai.
   
 
 
 
 
 
Gaussian
spherical sitfaces
(i) there is only one type of charge in the miverse, then
(B+ Electric field, dé + Area vector)
(of surface
(b) f 8 ai could not be defined
(6) f B+ i= if charge is inside
(l) f= de=0 if charge is ow
O Nee wine
+ i#0 on an
   
   
fee
 
Ans: (d) fB+ d=0 if charge is outside, fE+ dF
dase ;
If there is only one type of charge in the universe then it will
produce electric field somehow. Hence Ganss's lar is valid
(i) What is the nature of Ganssian surface involved in
Gans lnw of electrostatic ?
(a) Magnetic (b) Scalar
(6) Vector (4) Electrical
Ans + (¢) Vector
(ii) A charge 10 uC is plied at the centre of a hemisphere
of radius f= 10 em as shown. The electric lux through,
the hemisphere (in MKS units) is
H10pe
 
 
 
(0) 20x 10°
(6x 10
Ans: (0) 6 x 10°
According to Ganss’s theorem,
Blectrie flax through the sphere = 2
Flectrc fx throngh the hemisphere =
(b)10 x 10°
(a2 x16
 
10x10
SSH
06x W°Nm?Ct = 6x 10°NmeC
(iv) ‘The clectrie fx through a closed surface area S enclos-
ing charge Q is 9. Ifthe surface area is doubled, then
the flux is
(a) 26 (yee
0.56 x 10NmeePage 7 Sample Paper 1 Solutions
(©) of (oe
Ams: (a) 6
‘As fue is the total number of lines passing thongh the
surface, for a given charge, it is always the charge enclosed.
Qlén- If area is doubled, the flux remains the same.
(0) A Gaus surface endosesadpale The ltr through
this surface is
@e (yt
(ot (A) zero
Ans : () zero
As net charge on a dipole is
Card=o
Thns, when a ganssian surface encloses a dipole, as per
Ganss’s theorem, electric fux through the surface,
 
 
 
NEET 45 YEARS PAPERS
Downdload Free PDF From NODIN?
Search Play Store by NODI
For more details vist : www. en injjee
‘Ad 89056 29966 in Your Class Watsapp Group to Got POF
SECTION-E
31 Define mutual inductance between a pair of evils, Derive
‘an expression for the mutual inductance of two long coaxial,
solenoids of same length round one over the other.
In a closed cirenit of resistance 109, the linked flux varies
with time according to relation 6 = 6 — 5t+1. At t= 0.25
second, What is the eurrent (in Ampere) flowing through
the cirenit?
 
Ans
Mutual Inductance : Let » current of jj ampere flow in the
primary coil. Let, due to this eurrent, the magnetic flux,
Tinked with each turn of the sceondary evil be 6. If Ny be
the umber of turns in the secondary coil, then the nmmber
of flux-linkages im the coil will be Nags, This nmmber is
proportional to the current j flowing in the primary col,
iil TRE
a
1b: iy or Nib: = Mig
Where, Mis constant, called! the coefficient of mutual
induetion or mmtual inductance of the two coils. From the
‘equation, we have,
 
 
    
 
 
Ii =1, then M = Nad
Mutual Inductance of Two Long Coaxial Solenoids
Consider two loug solenoids $, and S$) of same length (J,
CBSE Physics Class 12
such that solenoid (S,) surrounds solenoid (.) incompletely.
5
Let m, be the number of turus per unit ls
he the number of turus per unit length of $1, be eurrent
passed throngh solenoid $; and ga be fax linked with Sy
due to current fowing through S,
64 [oF 6x = Mah
Where MG isthe coefficient of nmtual induetion ofthe two
solenoids
when current is passed through solenoid ($) an emf is
induced in solenoid ().
Magnetic fell produeed inside solenoid (Si) on passing
current through it
Bi = torch
Magnetic flux linked with each turn of solenoid (%) will be
‘qual to By times the area of cross-section of solenoid (S))
Magnetic fax linked. with each turn ofthe solenoid
(5) = BA.
Therefore, total magnetic Oh: Knked with the solenaid ($3)
BAX tal
pomh x AX nal
portal
hommAL (1)
Similaely, the unt inductances between the two solenoids,
when current is passed through solenoid (S;) and induced
{is produced in solenoid (8) and is given by
Ma =ommal
M. M (say)
Hence, cooficient of mutual induction hetwoen the two long
solenoids
   
 
 
 
  
 
 
   
 
 
 
 
M = poonmAl.
Wo can rewrit oq. (1) as
Mamet
 
Given,
We know that,
 
 
 
  
Hee,
12x 0.2545
345=2Volt
‘Now, Current -£
Here, R=09Page 8 Sample Paper 1 Solutions
3-02
T-JEE 45 YEARS 120 PAPERS
Downdload Free PDF From NODIA App
Search Play Store by NODIA
For more details visit : www.nodia.in/jee
‘Add 89056 708689 n Your Class Whatsapp Grup to Get POF
 
 
 
 
 
the inconsistency in Ampere’s cireuital law. What
modification was made my Maxwell in this law?
A parallel plate capacitor is charged to 60uC. Due to a
radioactive souree, the plate loses charge at the rate of
18x 10°Cs"', What is the magnitude of displacement
current?
 
Ans :
 
According to Ampere’
aagneti field Bt nlong any closed loop Cis proportional to
the current 1 passing through the closed loop, ie
SP bmn ()
16K = +) 0=
i 4 |_| —4
Battery Battery
 
 
 
 
 
A parallel plite capacitor being charged hy a battery
Tn 1864, Maxwell showed that the Eq. (1) is logically
inconsistent, Consider a parallel plate capacitor being charged
by a battery, as shown in figure (a). As the charging current
T flows, a magnetie field is set up around the eapacitor.
Now, the current I flows across the area honnded by loop
G. Therefore
 
 
(2)
But the are bounded by C; lies in the region between the
capacitor plates, so no current flows across it,
Hence, f5-d=o (3)
Imagine the loops C; ane Cs to be infinitesimally close to
‘each other, as shown in figure (b). Then we must have,
f Bedi f Be dl
‘This result is inconsistent with the Eq, (2) anu (8). ‘There
inst be sonne missing term in this law.
Maxwell's Modification of Ampere’s Law
Maxwell argued that a changing electric field between the
capacitor plates must induce a magnetic field. As currents
tare the usual sources of magnetic fields, a changing electric
field amist be associated with a current, Maxwell called this
current as the displacement current:
If, A be the arva ofthe eapacitor plates and g be the charge
on the plates at any’ instant £ during the charging process,
ten the electric field in the gap will be,
B=2
 
 
 
 
 
 
CBSE Physics Class 12
Fox,
 
 
Hence,
4/9) _ 1d
= ale) = coat
But dg/dt is the rate of change of charge on the capacitor
plates. It is called displacement current and is given by,
&
a
This isthe missing term in Ampere’ circuit law, The total
arnt rast be the sum of the conduction current, and
the displacement current [,. Thus
Lth=
at
  
 
   
 
 
  
‘Hence, the modified form of the Ampere's law is,
f8-d = pf ecMte
  
Given,
 
Charge on capacitor, q = 60uC = 60 x 10°C
‘and rate of losses of charge,
Mt 
rs
 
 
 
 
charging capacitor C, a time varying current I(0)
flows through the conducting wire, so on applying Ampere’s
cireuital law (for loop A)
B+ di = jol() (1)
f
 
 
 
4
 
i
 
 
 
Now, we cousider a pot like surface enclosing the positively
charged plate and nowhere touches the conducting wire
(2)
 
 
 
 
 
If surface A and B forms a tiffin box and electric field B is
passing through the surface (B); constitute an electric flux.
o=8/4|=2]4]
Hank @)
If the charge on the plate in the tiffin box is changing with
time, there mst be a current between the plates.
From equation (8), we got
Sample Paper 1 Solutions
CBSE Physics Class 12
1Q_ do,
1= B= 4Fe00) =o
his is the missing term in Ampere’s cireuital la.
‘The inconsistency may disappear if displacement current is
included betwoon the plates,
So, generalised! Ampere’s cirenital law can be given as
fia
  
 
o@l(t) + o6de
= oll + noo
1. By considering straight line of V-I characteristic
curve between 10 mA to 20:mA; and assuming passing
through the origin, draw horizontal and vertical lines
from 10mA and 20 mA, we have
1 =10mA,
iv
mA,
osv
resistance in forward biasing can be given as,
 
 
Dynami
 
av
Roar
(8-0.7)V _ o1v
~(20-T0)mA ~ 10mA
  
O19 =
$2 x 10'9 =100
2, At -10V. The V-J characteristic graph is a straight
line parallel to the voltage axis and not showing any
‘variation. So, the statie resistance ean be given as,
wv