# physics

```PREVIOUS YEAR QUESTION ASKED IN CBSE,BOARD EXAM.
CHAPTER-1, ELECTRIC CHARGE AND FIELD
2006
Q. What is electric flux? Write its S. I. Units.Using Gauss’s theorem, deduce an expression for the electric field at a
point due to a uniformly charged infinite plane sheet.(5)
ANS: The electric flux through a given surface area is the total number of electric lines of force passing normally this
area. It is given by φE =E.dS .
The SI unit of electric flux = Nm2C-1.
According to Gauss’s theorem, the total flux through a closed surface is1/Ɛ0times the total charge enclosed by the
closed surface.
Derivation: Consider a non-conducting sheet of charge with surface charge density .Consider a cylinder of length 2r
and cross - sectional area A as Gaussian surface.referncert book,page38,fig:1.30.
From symmetry electric field E points at right angle to the end caps and away from the sheet.
There is no contribution from the curved surface because angle between E and dS is 900.
At the end faces, angle between E and dsis zero.
From Gauss’s law,Φ=∫E.ds=q/ε0=EA+EA=σ A/ε0 ,So, E=A/2ε0
-----------------------------------------------------------------------------------------------------------------------------------------2007
Q. The electric field due to a point charge at any point near it is defined as E&amp;E =limtF/q
q 0
where q is the test charge and F is the force acting on it. What is the physical significance of
lim
q 0in this expression? Draw the electric filed lines of a point charge Q when (i) Q &gt; 0and (ii)
Q &lt;0 .(2)
lim
ANS:Thelim.
q 0 indicates that the test charge is so small that its presence does not disturb the distribution of source charge and
hence its electric field.
The electric fields of the point charge Q are shown in figure 1.11(a)&amp;(b),page-18,NCERT,book.
OR
Define electric flux. Write its S.I. Units. A spherical rubber balloon carries a charge that is uniformity distributed over
its surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface
change? Give reason.(2)
ANS:The electric flux through a given surface area is the total number of electric lines of force passing normally
through that area. It is given by.
φE =E.dS
SI unit of electric flux is Nm2C-1.
As the balloon is blown up, the total charge on the balloon surface remains unchanged, so the total electric flux
coming out of its surface remains unchanged.
Q.Deduce an expression for the electric potential due to an electric dipole at any point on its axis. Mention one
contrasting feature of electric potential of a dipole at a point as compared to that due to single charge.(3)
ANS:
13.Let P be an axial point at distance r from the centre of the dipole of length2a.
-q
+q
P
2a
Electric potential at point P will be,V=V1+V2
=1/4∏Ɛ0(-q/r+a + q/r-a )
On simplification we get,
=1/4∏Ɛ0(p/r2-a2 ) where p=2aq
For a far away point, r &gt;&gt; a, V =1/4∏Ɛ0(p/r2 )
At large distances, dipole potential falls off as1/r2whereas the potential due to a singlecharge falls off as 1/r.
Q.A parallel plate capacitor, each with plate area A and separation d is charged to a potential difference V. The battery
used to charge it is then disconnected. A dielectricslab of thickness d and dielectric (3)
constant K is now placed between the plates. Whatchange, if any, will take place in
(i) charge on the plates(ii) electric field intensity between the plates(iii) capacitance of the capacitor
ANS:
(i)The charge on the capacitor plates remains same.
(ii)The electric field intensity between the capacitor plates decreases due to the introduction of a dielectric.
Introduction of dielectric field creates an intrinsic electric field directed opposite to the original electric field. That is
why the electric field intensity decreases.
(iii)The capacitance of the capacitor increases due to the introduction of a dielectric. Electric field decreases,
therefore, the capacitor can get more charge to bring back the electric field to its original value. This increases the
capacity of holding the charge and hence the capacitance increases.
2008
Q.A 500 micro-coulomb charge is at the centre of a square of side 10 cm. Find the work done in moving a charge of 10
micro-coulomb between two diagonally opposite points on the square.(1)
ANS: The 500&micro;Ccharge is at the same distance from all the corners of the square. The opposite corners, say A and C,
will have the same potential VA=Vc.
Work done in moving a charge q between points A and C is given as: W = q(VC − VA) = q &times; 0 = 0.
Hence, no work is done in moving the charge between two diagonally opposite points on the square.
--------------------------------------------------------------------------------------------------------------------------------------Q.(a) Using Gauss' law, derive an expression for the electric field intensity at any point outside a uniformly charged
thin spherical shell of radius R and charge density σC/m2.Draw the field lines when the charge density of the sphere is
(I) positive,(ii) negative.(b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of
100&micro;C/m2. Calculate the(i) Charge on the sphere(ii) Total electric flux passing through the sphere.(5)
ANS: (a) Electric field intensity at any point outside a uniformly charged spherical shell.
Figure1.31 (a)&amp;(b),Page:39,NCERT, TEXT BOOK.
Consider a thin spherical shell of radius R and with centre O. Let charge + q be uniformly distributed over the surface
of the shell.Let P be any point on the Gaussian sphere S1 with centre O and radius r, as shown in the following figure.
According to Gauss’s law, we can write the flux through ds as:Φ=∫E.ds=q/ε0
Or, E (4πr2)=q/ε0
Or, E=1/4πε0(q/r2)
At any point on the surface of the shell, r = R,E=1/4πε0(q/R2)
For charge density σ, q=4πR2σ, Substituing,we get E=σ/ε0 .
(b) Diameter of the sphere = 2.5 m So, Radius of the sphere, R=2.5/2=1.25
Charge density,σ=100 micro coulomb per square meter =10-4C/m2
Total charge, q=4πR2σ=1.96 *10-3C. Total electric Flux, φE =q/ε0=2.21*108Nm2C-1
-----------
2009
Q.A positive point charge (+q) is kept in the vicinity of an uncharged conducting plate. Sketch electric filed lines
originating from the point on the surface of the plate.Derive the expression for the electric field at the surface of a
charged conductor.(3)
ANS: Take a charged conductor of any arbitrary shape with charge density 2 σC / m .The total flux through a small
cylindrical Gaussian surface will be given by Gauss’slaw as follows: EA = σA/ε0So, E=σ/ε0n.
The electric field will be normal to the surface at all points of the conductor.
2010
Q.Figure shows three points charges, +2q, -q and +3q. Two charges +2q and –q are enclosed within a surface ‘S’. What
is the electric flux due to this configuration through the surface ‘S’? (1)
+3q
+2q
-q
ANS: Electric flux through the surface S will be as per Gauss law:
φE= net charge/ε0=(2q-q)/ ε0 =q/ε0.
2011
Q.A point charge Q is place at point O as shown in the figure. Is the potential difference
VA – VB positive, negative or zero, if Q is (i) positive (ii) negative?
Q
A
(2)
B
O
Ans: Potential at a point: V = kQ/r
For any Q, VA-VB = kQ( 1/rA-1/rB)
Where, rA&lt;rB , So 1/rA&gt;1/rB
And So 1/rA-1/rB&gt; 0.
If Q at O is positive, VA-VB will be positive.
If Q at O is negative, VA-VB will be negative.
-----------------------------------------------------------------------------------------------------------------------------------------Q. Using Gauss’s law to obtain the expression for the electric field due to a uniformly charged thin spherical shell of
radius R at a point outside the shell. Draw a graph showing the variation of electric field with r, for r &gt; R and r&lt; R.
Q
ANS:
EdS
R
o.
r
Consider a spherical Gaussian surface of radius r (›R), concentric with given shell. If Eis electric field outside the shell,
then by symmetry, electric field strength hassame magnitude Eon the Gaussian surface and is directed radially
outward. Alsothe directions of normal at each point is radially outward, so angle between E0 and dS is zeroat each
point. Hence, electric flux through Gaussian surface = Φ=∫E.ds
=∫Eds= E*4πr2
Now, Gaussian surface is outside the given charged shell,so charge enclosed by the Gaussian surface
is Q.Hence, by Gauss’s theorem
E*4πr2 = c.
E =Q/4πr2 ε0
Thus, electric field outside a charged thin spherical shell is same as if the wholecharge Q is concentrated at the centre.
Graphically,
Y
Emax
EEα 1/r2
X
r=Rr
For r ‹ R, there is no strength of electric field inside a charged spherical shell.
For r › R, electric field outside a charged thin spherical shell is same as if the wholecharge Q is concentrated at the
centre.
-----------------------------------------------------------------------------------------------------------------------------------------2012
Q.Why should electrostatic field be zero inside a conductor? (1)
Ans: If the electric field inside the conductor is not zero, the electrons will accelerate due to the electric field and for
the electrostatic condition the net field becomes zero due to the redistribution of the charge carries and electrons
come at rest (electrostatics).
-----------------------------------------------------------------------------------------------------------------------------------------2013
Q.What is the geometrical shape of equipotential surfaces due to a single isolated charge? (1)
ANS: The equipotential surfaces due to a single isolated charge are concentric spherical surfaces. As the distance
from the charge increases the electric field strength will decrease and the distance between the spherical surfaces
will increase.
DIAGRAM:figure-2.9(a),page=60,ncert book,class-xii.
2014
Q.Why do the electric field lines never cross each other? (1)
Ans: Electric field line is a curve drawn in such a way that the tangent to it at each point is in the direction of the net
field at that point. Two fields can never cross each other. If they did,it means the field at the point of intersection will
not have a unique direction, which is meaningless).
---------------------------------------------------------------------------------------------------------------------------------------------------
CHAPTER-2,ELECTROSTATIC POTENTIAL AND CAPACITANCE
2006
Q.Define the term 'dielectric constant' of a medium in terms of capacitance of a capacitor.(1)
ANS:Dielectric constant of a medium is defined as the ratio of the capacitance of a capacitor with the dielectric as the
medium to its capacitance with vacuum between its plates.
Q. The electric field and electric potential at any point due to a point charge kept in air is 20NC-1 and 10JC-1
respectively. Compute the magnitude of this charge.
(2)
ANS: E=1/4πε0(q/r2)=20NC-1
V=1/4πε0(q/r)=10NC-1
And R=V/E=10/20=1/2=0.5
So, q=4πε0rV=10*0.5/9*109
=0.55* 10-9
-------------------------------------------------------------------------------------------------------------------------------------Q.11.The given graph shows the variation of charge q versus potential difference V for twocapacitors C1 and C2. The
two capacitors have same plate separation but the plate areaof C2 is double than that of C1. Which of the lines in the
graph correspond to C1 and C2and why? (2)
ANS:
q
A
B
V
As q =CV so, C=q/Vand graph A has a larger slope than B, so the graph A represents acapacitor of larger
capacitance.Also, C= ε0A/d, hence: C αA.
As the plate area of C2is double of that of C1, so C2 has a larger capacitance. Hence theline A of the graph corresponds
to C2.
---------2008
Q. Derive the expression for the electric potential at any point along the axial line of an electricdipole? (2)
ANS: FIGURE:
A
B
P
Let P be an axial point at distance r from the centre of the dipole. Electric potential at point P is given asV= V1+ V2, V1
and V2are the potentials at point P due to charges +q and -q respectively.
V=1/4πε0 (q/r-a +-q/r+a)
=q/4πε0( 2a/r2-a2)=1/4πε0( p/r2-a2)
------------------------------------------------------------------------------------------------------------------------------------------
Q.(a) Derive an expression for the torque experienced by an electric dipole kept in auniform electric field.
(b) Calculate the work done to dissociate the system of three charges placed on the vertices of an equilateral triangle
of side 10 cms.as shown.Here, q = 1.6*10-10C.(5)
q
-4q+2q
ANS:
(a) The figure given below shows an electric dipole of charges +q and –q which are separated by distance 2a.
Refer,Figure :NCERT BOOK Fig no-2.16,Page-66.
A NS: Expression for the torque: The above arrangement forms a couple. The couple exerts a torque which is
given by, τ=Force x Perpendicular distance between the two forces
=qE x 2a.sinθ
=pEsinθ(p=2aq,dipole moment)
Since the direction of torque is perpendicular to p and Ewe can rewrite the above equation as,
τ =pX E.
(b) The work done will be equal to the potential energy of the system
U= 1/4πε0[ (q*2q)/0.1+(q*-4q)/0.1+(2q*-4q)/0.1]
=9*109*10(-10q2)
=9*109*10*(-10)*1.6*10-10*1.6*10-10
=-23.04*10-9J.
2009
Q. Draw 3 equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant
along Z – direction. How are these surfaces different from that of a constant electric field along Z- direction? (2)
ANS: Planes parallel to the x-y plane. If the field increases and equi-potential surfaces are drawn for the same
difference in potential then as the field increases the surfaces will become closer to each other.
F IGURE:
X
Z
Q.A parallel plate capacitor is charged by a battery. After some time the battery is dis-connected and a dielectric slab
of dielectric constant K is inserted between the plates.
How would (i) the capacitance (ii) the electric field between the plates and (iii) the energystored in the capacitor be
_
_
_
+
+
+
ANS: (i) On inserting a slab of dielectric constant K between the plates, the capacitance of the capacitor is K times.
New capacitance, C =KCo.
(ii) The electric field between the plates of the capacitor decreases. It becomes E = Eo/k
(iii) The energy stored by a capacitor is Q2/2C0 which becomes Q2/2C =Q2/2kC0
So the energy stored becomes 1/K times its original value.
-----------------------------------------------------------------------------------------------------------------------------------------2010
Q.In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii)un-stable equilibrium?(1)
ANS:Stable position of the dipole: parallel to electric field.
Un-stableposition: perpendicular to the electricfield.
Q.A parallel plate capacitor is charged by a battery. After sometime the battery isdisconnected and a dielectric slabs its
thickness equal to the plate separation is inserted between the plates. How will (i) the capacitance of the capacitor. (ii)
Potential difference between the plates and (iii) the energy stored in the capacitor be affected?Justify your answer in
each case.(3)
ANS: (i) Capacitance of the capacitor increases by a factor K, i.e., it becomes KC.
(ii) Net electric field will get reduced. As potential difference V=-Ed, as E is reduced,potentialdifference between the capacitor plates also reduces.
(iii) Energy of the capacitor:As the charge Q is fixed on plates,Energy stored in the capacitor,
U =q2/2C=1/k*(energy without di-electric)
So, Uα 1/k ,it goes down.
Q. (a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance ’d’
apart.(b) Deduce the expression for the potential energy of a system of two point charges q1 and q2 brought from
infinity to the points r1 and r2 respectively in the presence of external electric field E.
(3)
ANS: a) An equipotential surface is a surface with a constant value of potential at all points on the surface. The
Equipotential surfaces for two identical positive charges.Refer figure, Ncert book,Fig.no:2.11(b),page-60.
First, we calculate the work done in bringing the charge q1 from infinity to r1. Work done in this step is q1 V (r1).
Next, we consider the work done in bringing q2 to r2. In this step, work is done not only against the external field E but
also against the field due to q1.
Work done on q2 against the external field = q2 V (r2)
Work done on q2 against the field due to q1 = q1q2/4πε0r12
Where r12 is the distance between q1 and q2. By the superposition principle for fields, we add up the work done on
q2 against the two fields (E and that due to q1):
Work done in bringing q2 to r2 = q2Vr2+q1q2/4πε0r12
Thus, Potential energy of the system= the total work done in assembling the configuration=
q1 V (r1)+q2 V (r2)+ q1q2/4πε0r12.
-----------------------------------------------------------------------------------------------------------------------------------------2011
Q.Two uniformly large parallel thin plates having charge densities + δ and – δ are kept in the X-Z plane at a distance’d’
apart. Sketch an equi-potential surface due to electric field between the plates. If a particle of mass m and charge '-q'
remains stationary between the plates, what is the magnitude and direction of the field?
(3)
OR
Two small identical electrical diploes AB and CD, each of dipole moment 'p' are kept an angle of 120o as shown in the
figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field E directed
along +X direction, what will be the magnitude and direction of the torque acting on this?(3)
Y
D+q
1200
X
X’
C
-q
Y’
Ans:
+
+
-
+
-
+
-
+
-
+
-
-
Here the darkarrowsrepresent the parallel equi-potential surfaces along X-Z plane.
If a charge q has to be held stationary between the two plates, it will have to be balanced by two forces.
Gravitational force: mg, downwards
Electrostatic force= 2qE, acting upwards.
This implies, that in X-Z plane, the upper plate is + charged plate &amp; lower plate is –charged plate.
So, E field lines have to be directed along –y axis.
OR
Resultant dipole moment,pres =p1+p2
=(p12 +p22+2 p1p2cos1200 )1/2
=p
Direction of resultant dipole moment:
tanθ =psin1200/p+pCos1200 =(3)1/2
So, θ =600
That is, 30 degrees with +x axis.
Given applied E is along +x axis,So torque on resultant dipole will be ζ=pESin300=pE/2.
Direction will be along -z axis.
---------------------------------------------------------------------------------------------------------------------------------------
. Q.Figure shows to identical capacitors, C1 and C2, each of 1 F capacitance connected to a battery of 6V.Initially switch
‘S’ is closed. After sometimes ‘S’ is left open and dielectric slabs of dielectric constant K =3 are inserted to fill
completely the space between the plates of the two capacitors. How will the (i) charge and (ii) potential difference
between the plates of the capacitors be affected after the slabs are inserted?
ANS: In C2: Charge QD = CDVD will not change. Where CD = K C= increases K times
VD = V/K = decreases K times.
In C1: Charge QD = CDV Potential V remains the same as 6V.
Charge QD =KCV= KQ, increases K times.
2012
Q.Draw a plot showing the variation of (i) electric field Eand (ii) electric potential V with distance r due to a point
charge Q.
(2)
Ans: E at a point varies inversely as the square of its distance from Q.
V at a point varies inversely as its distance from Q.
Figure 2.4, NCERT Book, Page No- 55.
-----------------------------------------------------------------------------------------------------------------------------------------2013
Q. What is the geometrical shape of equi-potential surfaces due to a single isolated charge?
ANS: 1. Theequi-potential surfaces due to a single isolated charge are concentric spherical surfaces. As the distance
from the charge increases the electric field strength will decrease and the distance between the spherical surfaces will
increase.
+q
+
q
-q
.A capacitor has been charged by a dc source. What are the magnitudes of conduction and displacement currents,
when it is fully charged?
(2)
ANS:Electric flux through the plates of the capacitor, ɸ =q/ Ɛ𝟎. As q is constant after the capacitor is fully charged,
ɸwill also be a constant.So displacement current, Id = Ɛ𝟎 𝒅ɸ/dt =0 .Conduction current = Ic =C dV/dt =0 as V is
constant.
Ic = Id when the capacitor will be fully charged.
-----------------------------------------------------------------------------------------------------------------------------------------Q.A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 300 &micro;C.When
potential across the capacitor is reduced by 100 V, the charge stored in it becomes 100 &micro;C.Calculate the potential V
and the unknown capacitance. What will be the charge stored in the
capacitor if the voltage applied had increased by 100 V? (3)
OR
A hollow cylindrical box of length 0.5 m and area of cross-section 20 cm2 is placed in a three dimensional coordinate
system as shown in the figure. The electric field in the region is given byE=20xi, where Eis inNC-1&amp; x is in metres.Find:
(i) Net flux through the cylinder.
(ii) Charge enclosed in the cylinder.
Y
O
X
0.5m
Z
ANS: We know :Q= CV
in case1 : 300x10-6= CV........(i)
in case2 :100 x10-6=C(V-100)…….(ii)
from(i) &amp; (ii) : V =150 V.
If voltage applied have increased by 100 V:
Charge stored will be=Q= CV
in this case: Q=2*10-6*250=500*10-6C.
OR
E=20xi
E1=at the left circular face=10i(putting the value of x)
E2=at the right circular face=20i(putting the value of x)
(i)
ɸnet =∫E.ds=∫E1.ds+∫E2.ds+∫E.ds(curve surface)
=-10*20/100*100+-20*20/100*100=0.02Nm2C-1
(ii)Charge enclosed in the cylinder=q/ Ɛ𝟎. = 𝟎. 𝟎𝟐
So,q= Ɛ0 ∗ 0.02
=0.177*10-12 (on simplification,putting the value ofƐ𝟎 ).
----------------------------------------------------------------------------------------------------------------------------------------Q.A capacitor has been charged by a dc source. What are the magnitudes of conduction and displacement
currents, when it is fully charged?
ANS: 3. Electric flux through the plates of the capacitor, ɸ =q/ Ɛ𝟎.
As q is constant after the capacitor is fully charged, ɸwill also be a constant.
So displacement current,Id = Ɛ𝟎 𝒅ɸ/dt =0.
Conduction current = Ic =C dV/dt =0 as V is constant.
Ic = Id when the capacitor will be fully charged.
Q.While travelling back to his residence in the car, Dr. Pathak was caught up in a thunderstorm. It became very dark.
He stopped driving the car and waited for thunderstorm to stop? Suddenly he noticed a child walking alone on the
road. He asked the boy to come inside the car till the thunderstorm stopped. Dr. Pathak dropped the boy at his
residence. The boy insisted that Dr. Pathak should meet his parents. The parents expressed their gratitude to Dr.
Pathak for his concern for safety of the child.
Answer the following questions based on the above information:
(a) Why is it safer to sit inside a car during a thunderstorm?
(b) Which two values are displayed by Dr. Pathak in his actions?
(c) Which values are reflected in parents’ response to Dr. Pathak?(d) Give an example of a similar action on your
part in the past from everyday life. (4)
ANS: (a) Because the car acts like electric shield. We know that the electric field inside theclosed conductor is
zero.
(b) Awareness and humanity or concern.
(c) Gratitude and obligation.
I was struck in severe thunder storm once in an isolated place. I insisted to go out of the car and enjoy the rain.
My parents advised not to go out of the car otherwise I may get thunderstruck.
2014
Q. Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's
circuital law to include the term due to displacement current. (2)
Ans: 9. Consider the charging of a capacitor. The electric field between the plates of the capacitor is as follows:If the
plates of the capacitor have an area A and a total charge Q, the magnitude of the electric field between the plates is
E=Q/AƐ0
The field is perpendicular to the surface S as shown in the figure.Thus, using Gauss’s law the electric flux through the
surface is
ɸE= E A=QA/AƐ0=Q/Ɛ0
Now, if the charge Q on the capacitor is changing with time, there is a current associated with it, so we have,
dɸE/dt = ( 1/Ɛ0) dQ/dt =( 1/Ɛ0)i
or, I = Ɛ0( d ɸE/dt)
This term is the current due to changing electric field and is called displacement current. Thus, the Ampere’s Circuital
law is modified to give
∫B.dl= &micro;0 𝒊𝒄 + &micro;0Ɛ𝟎 ( d ɸE/dt)
Q. A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged
capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored
initially in the single capacitor.
(2)
ANS: The capacitance of two capacitors is same, i.e. C.
The voltage across charged capacitor is V1 = V and that across uncharged capacitor is V2= 0.
Thus, the initial energy stored in the capacitor is
U1=1/2C1V12=1/2CV2
When the charged capacitor is connected across the uncharged capacitor, the two capacitors form a parallel
combination.Thus, the resultant capacitance is C’ = C + C = 2C.
The initial charge on the capacitor is q = CV.The final potential across the combination will be
V’=q1+q2/C’=q/2C=CV/2C=V/2.
Hence, the final energy in the combination of capacitors is
U2=1/2C’V’2= 1/2(2C)(V/2)2 =CV2/4
Thus, the ratio of energy stored in the combined system to that in the initial single capacitor is given as
U2/U1=1/2.
Q: Draw a labelled diagram of Van de Graff generator. State its working principle to show ,how by introducing a small
charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of
this machine and also point out its limitations. (5)
OR
(a) Deduce the expression for the torque acting on a dipole of dipole moment P in the presence of a uniform
electric field (b) Consider two hollow concentric spheres S1 and S2, enclosing charges 2Q and 4Q respectively
as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux
through the sphere s1 change if a medium of dielectric constant 'Ԑr' is introduced in the space inside s1 in
place of air? Deduce the necessary expression. (5)
4Q
S2
2Q
S1
ANS: Principle:
1) The charge always resides on the outer surface of hollow conductor.
2) The electric discharge in air or gas takes place readily at the pointed ends of the conductors.
Construction:
It consists of a large hollow metallic sphere S mounted on two insulating columns and an endless belt made up of
rubber which is running over two pulleys P1 and P2 with the help of an electric motor.B1 and B2 are two sharp
metallic brushes. The lower brush B1 is given a positive potential by high tension battery and is called a spray brush,
while the upper brush B2 is connected to the inner part of the sphereS.
Working:
When brush B1 is given a high positive potential then it produces ions due to the action of sharp points. Thus, the
positive ions so produced get sprayed on the belt due to repulsion between positive ions and the positive charge on
brush B1. Then it is carried upward by the moving belt.The pointed end of B2 just touches the belt, collects the
positive charge and makes it move to the outer surface of the sphere S. This process continues and the potential of the
shell rises to several million volts.
Uses:
(1) It can be used to separate different charges.
(2) It can be used to accelerate particles like protons, α particles, etc. to high speeds and energies.
Limitations:
(1) It cannot be used to generate potential more than 7 million volts.
(2) There is only one sided movement available for the charges due to series connection.
OR
(a) Consider an electric dipole placed in uniform electric field. The axis of dipole makes an angle Ѳ with the
direction electric field E . Diagram, NCERT Book.
The force acting on charge +q at B is +qEin the direction of E and the force acting oncharge –q at A is –qE in
the direction opposite to E.
These two equal, opposite and parallel non-collinear forces separated by perpendicular distance BP acting on
the electric dipole forms a couple.The torque on the dipole is given as
Ţ = Magnitude of force perpendicular distance between two parallel forces
=qE* BP
=qE* 2lsinѲ
=pEsinѲ( Since, p= q* 2l )
Thus, in vector form, we have, Ţ= p * E.
(b) (i) Let Ф1 and Ф1 be the electric flux through the spheres S1 and S2 respectively.
Then, ɸ1 = 2Q/ Ɛ0......(1)
ɸ2=(2Q + 4Q)/Ɛ0= 6Q/ Ɛ0......(2)
From (1) and (2), we get the ratio of the electric flux passing through the spheres S1 and S2 as
ɸ1/ɸ2=1/3.
(ii) Let E be the electric field intensity on the surface of the sphere S1 due to the charge 2Q present inside the sphere.
Then, according to Gauss’ theorem, we have
ɸ1= ∫E.dS =2Q/ Ɛ0
On introducing a medium of dielectric constantƐr inside the sphere S1, suppose that electric field becomes E'. Then,
we haveE' =E/Ɛr.
The electric flux through the sphere is now Φ1’, then we have
ɸ1’= ∫ E’.dS = 1/Ɛ0 ∫ E’.dS = 2Q/ Ɛ0Ɛr.
Thus if a medium of dielectric constant Ɛr is introduced in the space S1 instead of air the electric flux through the
sphere S1 becomes 2Q/ Ɛ0Ɛr.
2015
Q.Write a relation for polarisationP of a dielectric material in the presence of an external electricfield E.
(1)
Ans: The relation for polarisation P of the dielectric medium in the presence of an external electric field Eis P = ӼE,
where Ӽ susceptibilityis a constant characteristic of the dielectric and is known as the electric of a dielectric material.
Q.Explain briefly the process of charging a parallel plate capacitor when it is connected across a d.c. battery.A
capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time thebattery is disconnected and the
distance between the plates is doubled. Now a slab ofdielectric constant,1&lt;k&lt;2,
is introduced to fill the space between the plates. How will the following be affected?
(a) The electric field between the plates of the capacitor
(b) The energy stored in the capacitor
ANS: Consider a parallel plate capacitor connected across a d.c. battery as shown in the figure. The electric current will
flow through the circuit. As the charges reach the plate, the insulating gap does not allow the charges to move further;
hence, positive charges get deposited on one side of the plate and negative charges get deposited on the other side of
the plate. As the voltage begins to develop, theelectric charge begins to resist the deposition of further charge. Thus,
the current flowing through the circuit gradually becomes less and then zero till the voltage of the capacitor is exactly
equal but opposite
to the voltage of the battery. This is how the capacitor gets charged when it is connected across a d.c. battery.
(a) The electric field between the plates is
E = V/D
The distance between plates is doubled, d' = 2d
E’=V’/D’=(V/K)*1/2d =1/2(E/K)
Therefore, if the distance between the plates is double, the electric field will reduce to one half.
As the capacitance of the capacitor,
(b) As the capacitance of the capacitor,
C’=E0KA/d’=E0KA/2d=1/2C ……(1)
Energy stored in the capacitor is U=Q2/2C
U’=Q2/2C’ = Q2/2(1/2) C = 2(Q2/2C)2U(from 1)
Therefore, when the distance between the plates is doubled, the capacitance reduces to half. Therefore, energy
stored in the capacitor becomes double.
Q.(a) Deduce the expression for the potential energy of a system of two charges q1 and q2 located r1 and
r2,respectively, in an external electric field.
(b) Three point charges, + Q + 2Q and – 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these
charges are displaced to the mid-point A1, B1 and C1,respectively, find the amount of the work done in shifting the
charges to the new locations.
A1
B(+2Q)
B1
C1
C(-3Q)
OR
ANS.(a) Let q1 and q2 be the two charges located at r1 and r2, respectively, in an external electric field. The work done
in bringing the chare q1 from infinity to r1 is W1 = q1V (r1), where V(r1) is the potential. Similarly, the work done in
bringing the chare q1 from infinity to r2 can be calculated. Here, the work is done not only against the external field E
but also against the field due to q1.
Hence, work done on q2 against the external field is W2 = q2V (r2).
Work done on q2against the field due to q1, W12 = q1q2/4 E0r12
where r12 is the distance between q1 and q2.
By the principle of superposition for fields, work done on q2 against two fields will add with work done in bringing q2
to r2, which is given as W2+W12=q2V (r2)+q1q2/4∏E0r12.
Thus, the potential energy of the system U = total work done in assembling the configuration
U=W1+W2+W12.
=q1V (r1)+q2V (r2)+q1q2/4∏E0r12.
(b)q1=+Q, q2=+2Q, q3=-3Q
r = l (for each side)
Intial potential energy of system
U1=1/4∏E0l[q1*q2+q2*q3+q3*q1 ]
=-7Q2/4∏E0l ( putting the value of q1,q2,q3 and after simplification)
U2=1/4∏E0l/2 [q1*q2+q2*q3+q3*q1 ]
=-7Q2/2∏E0l ( putting the value of q1,q2,q3 and after simplification)
Work done=U2-U1
=-7/4(Q2/2∏E0l)
------------------------------------------------------------------------------------------------------------------------------------------
SECTION-B
MINIMUM LEVEL OF LEARNING
Unit-I, Electrostatics (CHAPTER 1- Charge and Electric field.CHAPTER 2- Potential and capacitance.)
Formulas
 Electrostatics is the study of charges at rest.
 Charging a body can be done by friction, induction and conduction.
 Properties of charges: 1 Charge on a body is quantized Q=+ ne
2. charge of an isolated system is conserved
3. Charge on a body is speed independent
 To measure charge electroscopes are used.
𝑘𝑞 𝑞
1
 Coulomb’s law: 𝐹⃗ = 𝑟12 2 𝑟̂ k=4𝜋𝜀 = 9X109 Nm2c-2


0
Principle of superposition: 𝐹𝑡𝑜𝑡𝑎𝑙 = ∑𝑛𝑖=1 ⃗⃗⃗
𝐹𝑖 [vector sum of individual forces]
Coulomb’s law for multiple charges
Ftotal = F12 + F 13 + …. 
qq 
qq 
1 3 r  ....
1 2r  1
2 12 4 r 2 13
4 r12
 13
1

Electric field: Force experienced by a unit positive (or test) charge. It is a vector. SI unitNC-1.

E  Lt
qo  0
F
qo
E
𝑘𝑄
𝑟̂
𝑟2

Field due to a point charge: 𝐸⃗⃗ =

Variation of E with r for point charge is as shown in the graph

Electric field intensity due to multiple point charges : E total 


Dipole: Two equal and opposite charges separated by a small distance.
Dipole moment: Product of magnitude of charge and distance of separation between them. It is a vector. SI
unit: Cm, 𝑝⃗=Q.2𝑎⃗ ; direction of 𝑝⃗ is along line joining the negative to positive charge.
Electric field due to a dipole (for l &lt;r)

r

n
i 1
Er
[vector sum of individual fields]
2𝑘𝑝⃗
(a)at any point on the axial line: 𝑟3 along the direction of dipole moment
(b)at any point on the equatorial line:
𝑘𝑝⃗
𝑟3
opposite to the direction of dipole moment.

Dipole in a uniform electric field experiences no net force and instead experiences a torque. 𝜏⃗=𝑝⃗ &times; 𝐸⃗⃗ ⇒
𝜏⃗=|𝑝⃗||𝐸⃗⃗ | sin 𝜃 𝑛̂


If𝜃= 0&deg; ⇒ stable equilibrium; If𝜃= 180&deg; ⇒ unstable equilibrium.
⃗⃗⃗⃗⃗. 𝐸⃗⃗ =|𝐸⃗⃗ ||∆𝑆
⃗⃗⃗⃗⃗|𝑐𝑜𝑠𝜃 ; It is a scalar; SI unit: NC-1m2 or Vm.
Electric flux: ∅=∆𝑆

Gauss’ theorem in electrostatics:∅𝑡𝑜𝑡𝑎𝑙 =

𝑞𝑡𝑜𝑡𝑎𝑙
𝜀0
Expressions for charge densities for different types of Uniform Charge distributions:
∆𝑞
[Unit Cm-1] for linear charge distribution
∆𝑙
∆𝑞
Surface charge density: 𝜎 = ∆𝑆 [Unit Cm-2] for surface charge distribution
∆𝑞
Volume charge density: 𝜌 = ∆𝑉 [Unit Cm-3]forVolume charge distribution
Linear charge density: 𝜆 =

Electric Field Intensity on extreme left, In between and on extreme right of uniformly and oppositely charged
thin conducting plates
+𝜎−𝜎
𝝈
EI =0
Charge
distribution
Infinitely
long
straight
uniformly
charged
conductor
Linear
charge
density
EIII =0
Cylindrical
Surface area for
which 𝑬. 𝒅𝒔 ≠
𝑜
Lateral surface
area 2𝜋𝑟𝑙
𝑬. 𝒅𝒔
𝐸. 2𝜋𝑟ℎ
Gauss’s
theorem
𝐸. 2𝜋𝑟𝑙
𝑞
=
Electric
field
Intensity
𝐸=
0

20
𝑞
𝑙
Surface
charge
density
=
uniformly
Charged
spherical
shell
𝟎
APPLICATION OF GAUSS’S THEOREM
Charge
Types of Gauss’s surfaces
density
=
Infinitely
extended
plane sheet
of
Charge
EII =𝜺
Plane
Plane surface
2𝐴
𝐸2𝐴
𝐸2𝐴=
𝐸=
𝑞
0

0
𝑞
𝐴
Surface
charge
density
𝑞
=
𝐴
Spherical
surface 4𝑟 2
𝐸. 4𝑟 2
𝐸. 4𝑟 2
𝑞
=
0
𝐸
=
1
𝑞
40 𝑟 2
Properties of electric field lines:.
1.The imaginary path along which a unit positive charge placed in the electric field tends to follow is the magnetic line
of force
2. The electric lines of force emanate from a positive charge and terminate on a negative charge.
The tangent to an electric field line at any point gives the direction of the electric field at that point.
3. No two electric lines of force cross each other. If they do, then at the point of intersection, there will be two
tangents. It means there are two values of the electric field at that point, which is not possible. 6. Electric lines of
force are closer (crowded) where the electric field is stronger and the lines spread out where the electric field is
weaker.
4. Electric lines of force contract lengthwise to represent attraction between two unlike charges and Electric lines of
force exert lateral (sideways) pressure to represent repulsion between two like charges.
Electrostatic Potential: Work done per unit positive Test charge to move it from infinity to that point in an electric field
against the field direction . It is a scalar. SI unit: J/C or V
V = W / qo
Electric potential at any point at a distance r from a point charge q: 𝑉 =
𝑘𝑞
𝑟
Graphs:Variation of E &amp; V due to a point charge at any point in the field with r (Graph-1) and Variation of V with 1/r
(Graph-2)


Electric field is conservative. This means that the work done is independent of the path followed and the
total work done in a closed path is zero.
Potential due to a system of charges: v
  in1 kqi
ri
total

Potential due to a dipole at any arbitrary point

on its axial line: 𝑉𝑎𝑥𝑖𝑎𝑙 =

on its equatorial line:𝑉𝑒𝑞 = 0 (Since 𝜃=90&deg;)
𝑘|𝑝⃗|
𝑟2
𝑘|𝑝⃗|
𝑐𝑜𝑠𝜃
𝑟2
(since 𝜃=0&deg;)
1
1
𝐴
𝐵

Potential difference

Potential energy of charge q1 in the field of q2 or vice versa :


Potential energy of a dipole in a uniform electric field:
U = 𝑝⃗. 𝐸⃗⃗ = p E [𝑐𝑜𝑠𝜃0 -𝑐𝑜𝑠𝜃1 ]
Electrostatics of conductors
(i) Inside a conductor Electrostatic field is zero
(ii) On the surface E is always Normal
(iii) No charge inside the conductor but gets distributed on the surface
(iv) Charge distribution on the surface is uniform if the surface is smooth
(v) Charge distribution is inversely proportional to ‘r’ if the surface is uneven
(vi) Potential is constant inside and on the surface
Equipotential surfaces: The surfaces on which the potential is same at all the points of the surface.

𝑑𝑉
As E= - 𝑑𝑟
𝑉𝐴 − 𝑉𝐵 = 𝑘𝑞 [𝑟 − 𝑟 ]
U=
𝑘𝑞1 𝑞2
𝑟
1
If Vis constant, E∝ 𝑑𝑟and if E is constant, V∝ 𝑟

Capacitor: A device to store charges and electrostatic potential energy.

Capacitance: C 

Q
, Ratio of charge and potential difference. Scalar,
V
Capacitance of a parallel plate capacitor: 𝐶 =
𝜀0 𝐴
𝑑
Capacitance of a parallel plate capacitor with a dielectric medium in between:
 Cm =

𝜖𝑜 𝐴
𝑡
𝑘
(𝑑−𝑡+ )
Combination of capacitors:
1 n 1
Capacitors in series:  
c i 1 ci
Capacitors in parallel : c 
n
c
i 1
i

1
1
1 Q2
Energy stored in capacitors: U  CV 2  QV 
2
2
2 C
V
Q
1

Area shaded in the Q-V graph = U = 2 𝑄𝑉

Energy density :𝑈𝑑 = 2 𝜀0 𝐸 2 =2𝜀

Values of Different quantities after Introducing dielectric slab between the plates of the charged capacitor:
Description ⇣ When Battery connected
When Battery disconnected
Charge
K Q0
Q0
Potential
V0
V0/K
difference
Electric
E0
E0/K
field
Capacitance KC0
KC0
1
1
2
Energy
K times 𝜀0 𝐸 [Energy is supplied
1/K times 𝜀0 𝐸 2 [Energy used for
𝜎2
1
0
2

By battery]
On connecting two charged capacitors:
Common Potential:
Loss of energy: ∆𝑈 =
𝐶1 𝑉1 +𝐶2 𝑉2
𝑉1 +𝑉2
1 𝐶1 &times;𝐶2
(𝑉 − 𝑉2 )2
2 𝐶1 +𝐶2 1
2
Polarization]
𝑉=
Heat generated in the capacitors on connecting them is equal to
this loss of energy.
CONCEPT MAP
FORCE/FIELD/POTENTIAL/P.E
CONCEPT MAP
CHARGE ITS IMPACT
QUESTION FOR MLL
Very Short Questions(1 mark)
1. Is the force acting between two point electric charges 𝑞1 and 𝑞2 kept at some distance apart in air, attractive or
repulsive when (i) 𝑞1 𝑞2 &gt; 0 (ii)𝑞1 𝑞2&lt;0 ?
(i. Repulsive ii. Attractive)
2. Which physical quantity has its SI unit as (𝑖) 𝐶 − 𝑚 (𝑖𝑖) 𝑉/𝑚.
𝑖)𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝐷𝑖𝑝𝑜𝑙𝑒𝑚𝑜𝑚𝑒𝑛𝑡(𝑖𝑖)𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑓𝑖𝑒𝑙𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦.
3. How does the force between two point charges change if dielectric constant of medium in which they are kept
increases.
(decreases)
4. Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium?
5. Define electric dipole moment of a dipole. State its SI unit.
6. Why is it necessary that the field lines from a point charge placed in the vicinity of a conductor must be normal to
the surface of the conductor at every point?
7.A 500 &micro;C charge is at the Centre of a square of side 10cm.Find the work done in moving a charge of 10 &micro;C between
two diagonally opposite points on the square.
(Solution:- The 500 μC charge is placed at the centre of a square. This charge is, therefore, at the same distance from
all the corners of the square. The opposite corners, say A and C, will have the same potential i.e., . Work done in
moving a charge q between points A and C is given as: W = q(VC − VA) = q &times; 0 = 0 Hence, no work is done in moving the
charge between two diagonally opposite points on the square.)
8. Vehicles carrying inflammable materials usually have metallic ropes touching the ground during motion.
Why? (To leak the charge developed on the body of the vehicle due to air friction to the earth to avoid any hazardous
incident)
9. Ordinary rubber is an insulator. But the special rubber tires of aircraft are made conducting. Why is this
necessary?(During landing , the tires of space craft get charged due to friction between the tyres and the ground. In
case the tyres are slightly conducting , the charge developed on the tyres will not stay on them and leak to the earth)
10. In the followingfig.calculatethepotentialdifferenceacrosscapacitorC 2.
GivenpotentialatAis90V.C 1=20&micro;F,C2=30&micro;F,andC3=15&micro;F.
C1
C2
C3
A
Resultant capacitance Cs =(20/3)&micro;F Charge on Cs = (20/3)&micro;F*90V =600&micro;C Charge on C2 is also 600&micro;C Potential
across C2=600&micro;C/30&micro;F=20V
Shorts Questions (2 marks)
1.Deriveanexpressionfortheworkdoneinobtaininganelectricdipolefromitsequilibriumpositiontoananglewiththeuniform
electrostaticfield.
2.Showthatthereisalwaysalossofenergywhentwocapacitorscharged
todifferentpotentialssharecharge(connectedwitheachother).
3.Four point charges +5 mC, +2 mC, +10mC and +2 mC are kept at the corners of a square of side 10 cm. A charge
q=+1mC is placed at its centre. Find the net force on q.
4. Calculate the distance between two protons such that the electrostatic force between them is equal to the weight
of either.
5. Two point charges are 0.1 m apart and their combined charge is 9 mC. If they repel each other with a force 18N,
then calculate the magnitude of each charge.
6. Calculate the Coulomb force between two alpha particles separated by a distance of 3.2 x 10-15 m
7. A proton moves through a uniform electric field of 5.01 x 10 3 N/C. Calculate (a) the acceleration with which the
proton is moving and (b) the time taken by the proton to cover a distance of 4.8 cm.
8.How many electrons would have to be removed from or added to apenny to leave it charged with 1.0 x 10-6
C [Ans: 6.25 x 10 12]
9. What is the Coulomb’s force between two small charged spheres having charges of 2.0 x 10-7 C and 3.0 x 10-7C
placed 30 cm in air?
[Ans: 6.0 x 10-3N]
10.Twopointcharges–qand+qareplaced2𝑙metreapart,asshowninfig. GivethedirectionofelectricfieldatpointsA,B,CandD.
D
(along AB at A,
along BA at B,
B–qA + qC
along AC at C
along AB at D)
11. Calculate the work required to separate two charges4&micro;c and –2&micro;c placed a (3cm,0,0)and(+3cm,0,0)infinitelyawayfromeachother.
12. What is meantby dielectric polarization? Why does the electric field inside
13.Calculatetheworkdoneintakingachargeof1&micro;Cinauniformelectric
fieldof10N/CfromBtoCgivenAB=5cmalongthefieldandAC=10 cmperpendiculartoelectricfield.
A
B
𝑬
C
14. The plates of a parallel plate air capacitor are separated by a distance of 1 mm. What mustbe the plate area if the
capacitance of the capacitor is to be 1F?
1.
Find the equivalence capacitance between X and Y.
X
3 μf
3 μf
3 μf
Y
As the combination is parallel, Cp=(3+3+3)&micro;F = 9&micro;F
2.Assuming earth to be an isolated conducting sphere of radius 6400 km, what is the capacitance of earth?
3.An isolated sphere has a capacitance of 50pF.Calculate its radius. How muchcharge should be placed on it to raise its
potential to 104V?
4.Twenty seven spherical drops, each of radius 3mm and carrying 10–12C of charge arecombined to form a single drop. Find
the capacitance and potential of the bigger drop.
5. Defineelectrostaticpotential and write itsunit.Obtainexpressionforelectrostatic
PotentialatapointPinthefieldduetoapointcharge.
6.Calculatetheelectrostaticpotentialenergyforasystemofthreepoint
chargesplacedatthecornersofanequilateraltriangleofside‘a’.
thattheirsurfacedensityofcharges are equal.Find Potential atthe commonc entre.
8. Defineelectricflux.WriteitsSIunit. How many units of electricfluxpasses
chargeplacedatthecentre?
(1)WhatisthechargeenclosedbyGaussiansurface?
9.Whatisanequipotentialsurface?Writethreeproperties.Sketch
equipotentialsurfacesof
(i)Isolatedpointcharge(ii) Uniformelectricfield(iii) Dipole
10. What are dielectrics?Give some examples of polar and non polarmolecules. Distinguish polar
and nonpolar dielectrics.
11.Derive an expression for the electric field due to an electric dipole at a point on (a) the axial line (b)
the equatorial line.
12.Derive an expression for the torque acting on an electric dipole placed in a uniform electric field.
13.Show that the work done in rotating an electric dipole of dipole moment p in a uniform electric field
E by an angle 𝜃&cedil; from the equilibrium position 𝑊 = 𝑃𝐸(1 − 𝑐𝑜𝑠𝜃)
14.State and verify Gauss theorem .Use Gauss theorem to derive an expression for the electric field at a
point due to an infinite plane sheet of charge of uniform charge density σ
15. Derive an expression for the electric field at a point due to a thin infinitely long straight conductor of charge of
uniform charge density 𝜆
16.Derive an expression for the electric field at a point due to uniformly charged spherical shell using Gauss’ law.
17.Derive an expression for the capacitance of a parallel plate capacitor.
18.A dielectric slab of thickness t introduced between the plates of a parallel plate capacitor separated
by a distance d. (t &lt; d). Derive an expression for the capacitance of the capacitor.
Formula based Nemerical Questions
1. Force between two points electric charges kept at a distance d apart in air is F.If these charges
are kept at the same distance in water, how does the force between them get effected ?
2. Two point charges 10&micro;C and 20&micro;C are separated by a distance r in air. If an additional charge of 8&micro;C is given to each, by what factor does the force between the charges change?
3. Calculate the Coulomb force between a proton and an electron separated by a
distanceof0.8x10-15m.
4. Two point charges Q are kept at a distance r from each other. A third charge q is place on the
line joining the above two charges such that all the three charges are in equilibrium, what is the
magnitude, sign and the position of the charge q?
5. A charge q is placed at the centre of the line joining two equal charges Q and Q. Calculate the
value of charge q such that all the three charges are in equilibrium. Also mention the nature of
this charge.
6. Two point charges of charge values Q and q are placed at a distance of x and x/2 respectively
from a third charge of charge value 4q, all charges being in the same straight line. Calculate the
magnitude and nature of charge Q such that the net force experienced by the q charge is zero.
7. Two point electric charges of values q and 2q are kept at a distance d apart from each other in
air. A third charge Q is to be kept along the same line in such a way that the net force on q and
2q is zero. Calculate the position of the charge Q in terms of q and d.
8. Force of attraction between two point charges placed at a distance‘d’ apart in a medium is ‘F’.
What should be the distance in the same medium so that the force between them becomes 9F?
9. Two similarly and equally charged identical metal spheres A and B repel each other with a force
of 2x10-5 N. A third identical uncharged sphere C is touched with A and then placed at the
midpoint between A and B. Calculate the net electric force on C.
VALUEBASEDQUESTIONS
1.AnelderlywomanwentalonetotheRegistrar’sofficetodisburseherproperty.Whens
helpofthepasser–byandgothere for getting the Xeroxdone.
a)Whatvaluesdidthepasser-byhave?
b)Howdoesaneutralbodygetchargedbyelectrostaticinduction?
of
acrowdedcorner.
WhereBalloons
weresold.Achildwasseentroublinghisparentandcryingforsomething.Onseeingthis,R
amwenttothechildandsaidthathewouldperformatrickwithballoons.Ramtooktwob
alloonsandShyamhelpedhimtoinflateandtie.Whentheballoonswererubbedwiththe
sweaterhewaswearing,theywereattracted.Whentakennearertowall,theballoonsgot
stuck.Thechildenjoyedandstoppedcrying.
a)GivetwovaluesofRamandShyam.
b)Howdidtheballoonsgetattracted?Willtheyrepelalso?
toldthemtodospraypaintingofmountaindewcolour.Thecompanyalsorepliedthattheyusually
performspraypainting onlyaswastageisminimizedandevenpaintingachieved.
a)Whatvaluesdidthecarservicecompanyhave?
b)Ifspraypaintingisdonebyelectrostaticinduction,howisevenpaintingachieved?
.4)InAkash’sclassroomthefanabovetheteacherwasrunningveryslowly.Duetowhichhiste
acherwassweatingandwasrestlessandtired.Allhisclassmateswantedtorectifythis.Theyca
lledforanelectricianwhocameandchangedthecapacitoronlyafterwhichthefanstartedrun
ningfast.
a)WhatvaluesdidAkashandhisclassmateshave?
b)Whatenergyisstoredinthecapacitorandwhere?
Important Information
1.Van de Graaff is omitted from syllabus.
2. Direct formula based Numericalare asked only
3. To revise solved examples &amp;numericals givenin NCERT Text Book
QUESTION BANK OF PROBABLE QUESTIONS FOR AISSCE 2016
Questions that have been repeated at least three or more times
UNIT – 1: ELECTROSTATICS
(Chapter – 1: Electric charges and fields, chapter-2: Electrostatic
potential and capacitance)
1. Using Gauss’s law obtain the expression for the electric field due
to a uniformly charged thin spherical shell of radius R at a point
outside, inside and on the surface of the shell. Draw a graph
showing the variation of electric field with r, for r&gt;R and r&lt;R.
2. State Gauss theorem in electrostatics. Apply this theorem to
obtain the expression for the electric field at a point due to an
infinitely long, thin, uniformly charged straight wire of linear
charge density λ C/m.
3. Derive an expression for the energy stored in a parallel plate
capacitor Charged to a potential difference V. Hence derive an
expression for the energy density of a capacitor.
QUESTION BANK OF PROBABLE QUESTIONS FOR AISSCE 2016
Questions that have been repeated one or two times
UNIT – 1: ELECTROSTATICS
(Chapter – 1: Electric charges and fields, chapter-2: Electrostatic
potential and capacitance)
1. Find an expression for the electric field strength at a distant point
situated (i) on the axis and (ii) along the equatorial line of an
electric dipole.
2. Find expression for the torque on an electric dipole kept in a
uniform electric field. Identify two pairs of perpendicular vectors
in the expression.
3. Briefly explain the principle of a capacitor. Derive an expression
for the capacitance of a parallel plate capacitor, whose plates are
separated by a dielectric medium.
4. Derive the expression for the electric potential at a point due to
an electric dipole. Mention the contrasting features of electric
potential of a dipole at a point as compared to that due to a single
charge.
5. Define electric flux. Write its S.I. unit. Using Gauss’s law, prove
that the electric field at a point due to a uniformly charged infinite
plane sheet is independent of the distance from it.How is the field
directed if (i) the sheet is positively charged,(ii) negatively
charged?
CHAPTER:3 CURRENT ELECTRICITY
ONE MARK QUESTIONS
1
Define the term ‘mobility’ of charge carriers. Write its S.I. unit.
2008
2
V – I graph for a metallic wire at two different temperatures T1 and T2 is as shown in
the figure. Which of the two temperatures is higher and why?
2015
3
Two metallic resistors are connected first in series and then in parallel across a d.c.
supply. Plot of I – V graph is shown for the two cases. Which one represents a
parallel combination of the resistors and why?
2015
4
I – V graph for two identical conductors of different materials A and B is shown in
the figure. Which one of the two has higher resistivity?
2015
5
Distinguish between emf and terminal voltage of a cell.
2008
6
Show variation of resistivity of copper as afunction of temperature in a graph
2007
7
When electrons drift in a metal from lower to higher potential, does it mean that all
the free electrons of the metal are moving in the same direction?
2012
8
Show on a graph the variation of resistivity with temperature for a typical
semiconductor?
2012
9
A 10 V battery of negligible internal resistance is connected across a 200 V battery
and a resistance as shown in the figure find the value of current in the circuit.
2013
10
Two wires, one of copper and the other of manganin, have same resistance and
Two wires, one of copper and the other of manganin, have same resistance and
Two conducting wires X and Y of same diameter but different materials are joined in
series acrossa battery. If the number density of electrons in X is twice that in Y, find
the ratio of drift velocityof electrons in the two wires.
A steady current flows in a metallic conductor of non-uniform cross-section.
Which of thesequantities is constant along the conductor:
Current, current density, drift speed, electric field?
A wire of resistance 8 R is bent in the form of a circle. What is theEffective resistance
between the ends of a diameter AB ?
Show on a graph the variation of resistivity of carbon with temperature for a typical
semiconductor?
The variation of potential difference V with length l in case of two potentiometers P
and Q is as shown, which of these two you will prefer for comparing emfs of two
primary cells?
2009
2012
2012
11
12
13
14
15
16
TWO MARKS QUESTIONS
2010
2011
2009
2010
2006
2006
1
2009,
2015
Calculate the current drawn from the battery by the network of resistors shown in figure
2
Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary
formula to describe how it is used to compare the emfs of the two cells.
2008
3
With the help of the circuit diagram, explain the working Principle of meter bridge. How it is
used to determine the unknown resistance of a given wire? Write the necessary precautions
to minimize the error in the result.
Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship
between current density and resistivity of the conductor.
A steady current flows in a metallic conductor of non-uniform cross-section.Which of these
quantities is constant along the conductor :
current, currentdensity, electric field, drift speed ?
2007
2009
Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone
bridge.
A variable resistor R is connected across a cell of emf E and internal resistance r as shown
in the figure. Draw a plot showing the variation of (i) terminal voltage V and (ii) the
current I, as a function of R.
2009
2013
2011
In the potentiometer circuit shown, the null point is at X. State with reason, where the
balance point will be shifted when
(a) Resistance R is increased, keeping all other parameters unchanged;
(b) Resistance S is increased, keeping R constant.
2012
4
5
6
7
8
2009
2012
9
State the two Kirchhoff’s rules used in electric networks. How are these rules justified?
2008
10 Define the term ‘power loss’ in a conductor of resistance R carrying a current I. In what
form does this power loss appear? Show that to minimize the power loss in the
transmission cables connecting the power stations to homes, it is necessary to have the
connecting wires carrying current at enormous high values of voltage.
11 In the circuit diagram shown, AB is a uniform wire of resistance 15 Ω and length 1 m. It is
connected to a cell E1of emf 2 V and negligible internal resistance and a resistance R. The
balance point with another cell E2of emf 75 mV is found at 30 cm from end A. Calculate
the value of the resistance R.
2011
12 Use Kirchhoff ’s rules to determine the potential difference between the points A and D
when no current flows in the arm BE of the electric network shown in the figure.
2007
13 A potentiometer wire of length 1m has a resistance of 10 Ω . it is connected to a 6V battery in
series with a resistance of 5Ω . Determine the emf of the primary cell which gives the balance
point at 40 cm
14
(a) State the working principle of a potentiometer. With the help of a circuit diagram,
explain how a potentiometer is used to compare the emfs of two primary cells. Obtain
the required equation used for the comparing of emfs.
(b) Write two possible causes for one sided deflection in a potentiometer experiment.
2005
15 A cell of emf E and internal resistance r is connected to two external resistances R1 and R2 and a
perfect ammeter. The current in the circuit is measured in four different situations:
2012
2009
2013
(i) without any external resistance in the circuit.
(ii) with resistance R1 only
(iii) with R1 and R2 in series combination
(iv) with R1 and R2 in parallel combination.
The currents measured in the four cases are 0.42 A, 1.05 A, 1.4 A and 4.2 A, but not
necessarily in that order. Identify the currents corresponding to the four cases mentioned above.
16 In the meter bridge experiment, balance point was observed at J with AJ = l.
2011
17 In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine
2011
18 Show that the electric field at the surface of a charged conductor is given by
2007
(i) The values of R and X were doubled and then interchanged. What would be the new position of
balance point?
(ii) If the galvanometer and battery are interchanged at the balance position, how will the balance point
get affected?
the potential at point B.

E =0) n,
19
where is the surface charge density and \$ n is a unit vector normal to the surface in the outward
direction.
The plot of the variation of potential difference across a combination of three identical cells in
series, versus current is as shown below. What is the emf of each cell ?
2008
20 A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a
2009
21
2009
graph showing the variation of terminal potential ‘V’ with resistance R. Predict from the graph
the condition under which ‘V’ becomes equal to ‘E‘.
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation
time.
22 A wire of 15 resistances is gradually stretched to double its original length. It is then cut into
two equal parts. These parts are then connected in parallel across a 3 00 volt battery. Find the
current drawn from the battery.
23 (a) You are required to select a carbon resistor of resistance 47 k10% from a large
collection.
What should be the sequence of colour bands used to code it?
(b) Write the characteristics of manganin which make it suitable for making standard
resistance.
2009
2012
THREE MARKS QUESTIONS
1
In the two electric circuits shown in the figure, determine the readings of ideal
Ammeter (A) and the ideal voltmeter (V).
2015
2
In the circuit shown in the figure, find the current through each resistor.
2015
3
(a) Deduce the relation between current I flowing through a conductor and
drift velocity dof the electrons.
(b) Figure shows a plot of current ‘I’ flowing through the cross-section of a
wire versus the time‘t’. Use the plot to find the charge flowing in 10s through
2014
the wire..
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 , the current is 1 A and when R is increased to 9
, the current reduces to 0.5 A. Find the values of the emf E and internal
resistance r.
A potential difference V is applied across a conductor of length L and diameter D. How
is the drift velocity, vd, of charge carriers in the conductor affected when (i) V is halved,
(ii) L is doubled and (iii) D is halved ? Justify your answer in each case.
2013
6
Two wires X, Y have the same resistivity, but their cross-sectional areas are in the ratio 2 : 3 and
lengths in the ratio 1 : 2. They are first connected in series and then in parallel to a d.c. source.
Find out the ratio of the drift speeds of the electrons in the two wires for the two cases.
2011
7
Define the electric resistivity of a conductor.
Plot a graph showing the variation of resistivity with temperature in the case of a (a)
conductor, (b) semiconductor.
Briefly explain, how the difference in the behaviour of the two can be explained in
terms of number density of charge carriers and relaxation time.
Plot a graph showing the variation of current density (j) versus the electric field (E) for
two conductors of different materials. What information from this plot regarding the
properties of the conducting material, can be obtained which can be used to select
suitable materials for use in making (i) standard resistance and (ii) connecting wires in
electric circuits ?
Electron drift speed is estimated to be of the order of mm s–1. Yet large current of the
order of few amperes can be set up in the wire. Explain briefly.
2010
4
5
8
9
2015
2009
A 16 Ω resistance wire is bent to form a square. A source of emf 9 V is connected across 2014
one of its sides as shown. Calculate the current drawn from the source. Find the
potential difference between the ends C and D.
If now the wire is stretched uniformly to double the length and once again the same cell
is connected in the same way, across one side of the square formed, what will now be
the potential difference across one of its diagonals?
10
When a metallic conductor is subjected to a certain potential V across its
2009
ends, discuss briefly how the phenomenon of drift occurs. Hence define
the term ‘drift velocity’ of charge carriers and show that the current density j is related to the
applied electric field E by the relation
j= E
where defines the conductivity of the material.
11
12
State the underlying principle of a potentiometer. Write two factors by which current
sensitivity of a potentiometer can be increased. Why is a potentiometer preferred over
a voltmeter for measuring the emf of a cell ?
Find the relation between drift velocity and relaxation time of charge carriers in a
conductor.
A conductor of length L is connected to a d.c. source of emf ‘E’. If the length of the
conductor is tripled by stretching it, keeping ‘E’ constant, explain how its drift velocity
would be affected.
2007
2006
2010
13
14
Write any two factors on which internal resistance of a cell depends. The reading on a high
resistance voltmeter, when a cell is connected across it, is 20 V. When the terminals of the
cell are also connected to a resistance of 3as shown in the circuit, the voltmeter reading
drops to 15 V. Find the internal resistance of the cell.
State Kirchhoff’s rules. Use these rules to write the expressions for the currents I1, I 2 and I 3
inthe circuit diagram shown.
2010
17
2005
Prove that the current density of a metallic conductor is directly proportional to the
drift speed ofElectrons.
A number of identical cells, n, each of emf E, internal resistance r connected in series 2007
are chargedby a d.c. source of emf E, using a resistor R.
(i) Draw the circuit arrangement.
(ii) Deduce the expressions for
(a) the charging current and
(b) the potential difference across the combination of the cells.
A potentiometer wire of length 1 m is connected to a driver cell of emf 3 V as shown
in the figure.When a cell of 15 V emf is used in the secondary circuit, the balance
point is found to be 60 cm.On replacing this cell and using a cell of unknown emf,
the balance point shifts to 80 cm.
(i) Calculate unknown emf of the cell.
(ii) Explain with reason, whether the circuit works, if the driver cell is replaced with
a cell of emf 1 V.
(iii) Does the high resistance R, used in the secondary circuit affect the balance
18
A network of resistors is connected to a 16 V battery of internal resistance of 1 as shown
in theFigure.
15
16
(a) Compute the equivalent resistance of the network.
(b) Obtain the voltage drops VAB and VCD .
19
Calculate the value of the resistance R in the circuit shown in the figure so that the current in the
circuit is 0.2 A. What would be the potential difference between points B and E?
2012
20
In the figure a long uniform potentiometer wire AB is having a constant potential gradient
along itslength. The null points for the two primary cells of emfs 1and 2 connected in the
manner shownare obtained at a distance of 120 cm and 300 cm from the end A. Find
(i)
1 / 2 and
(ii)
position ofnull point for the cell 1.
How is the sensitivity of a potentiometer increased?
2012
FOUR MARKS (VALUE BASED)/FIVE MARKS QUESTIONS
1
Ameen had been getting huge electricity bill for the past few months. He was upset
2015
2
3
4
5
Ameen was using traditional incandescent lamps and using old fashioned air
conditioner. In addition there was no proper earthing in the house. Rohit advised him
to use CFL bulbs of 28 W instead of 1000 W – 220 V and also advised him to get
proper earthing in the house. He made some useful suggestion and asked him to
spread this message to his friends also.
(i) What qualities/values, in your opinion did Rohit possess ?
(ii) Why CFLs and LEDs are better than traditional incandescent lamps ?
(iii) In what way earthing reduces electricity bill
2015
Ajit had a high tension tower erected on his farm land. He kept complaining to the
authorities to remove it as it was occupying a large portion of his land. His uncle, who
was a teacher, explained to him the need for erecting these towers for efficient
transmission of power. As Ajit realized its significance, he stopped complaining.
(a) Why is it necessary to transport power at high voltage ?
(b) A low power factor implies large power loss. Explain.
(c) Write two values each displayed by Ajit and his uncle.
During a thunderstorm the ‘live’ wire of the transmission line fell down on the ground 2014
from the poles in the street. A group of boys, who passed through, noticed it and some
of them wanted to place the wire by the side. As they were approaching the wire and
trying to lift the cable, Anuj noticed it and immediately pushed them away, thus
preventing them from touching the live wire. During pushing some of them got hurt.
Anuj took them to a doctor to get them medical aid.
Based on the above paragraph, answer the following questions :
(a) Write the two values which Anuj displayed during the incident.
(b) Why is it that a bird can sit on a suspended ‘live’ wire without any harm whereas
touching it on the ground can give a fatal shock ?
(c) The electric power from a power plant is set up to a very high voltage before
transmitting it to distant consumers. Explain, why.
(a) State Kirchhoff ’s rules and explain on what basis they are justified.
(b) Two cells of emfs E1 and E2 and internal resistances r1 and r2 are connected in
parallel. Derive the expression for the (i) emf and (ii) internal resistance of a single
equivalent cell which can replace this combination.
Two heating elements of resistances R1 and R2 when operated at a constant supply of
voltage V, consumes powers P1 and P2 respectively. Deduce the expressions for the power
of their combinations when they are, in turn, connected in (i) Series and (ii) parallel across
the same voltage supply.
2010
2011
EXPECTED QUESTIONS FOR REVISION/MLL
CHAPTER:3 CURRENT ELECTRICITY
1
Define the terms
I.
‘Mobility’ of charge carriers.
II.
Average relaxation time.
III.
Quantization of charge
IV. Drift velocity of electrons
V. Temperature co efficient of resistivity.
VI. Current density
2
V – I graph for a metallic wire at two different temperatures T1 and T2 is as shown in the figure.
Which of the two temperatures is higher and why?
3
Two metallic resistors are connected first in series and then in parallel across a d.c. supply. Plot of
I – V graph is shown for the two cases. Which one represents a parallel combination of the
resistors and why?
4
I – V graph for two identical conductors of different materials A and B is shown in the figure.
Which one of the two has higher resistivity?
5
Distinguish between emf and terminal voltage of a cell.
6
Show variation of resistivity as afunction of temperature in a graph for
I. Metals
II.
III.
Semiconductors
Alloys
+
7
Find the colour code for a resistance 23 KΩ−20%.
8
9
Write any two limitations of Ohm’s law.
10
Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary formula to
describe how it is used to find internal resistance of a primary cell
11
With the help of the circuit diagram, explain the working Principle of meter bridge. How it is used to
determine the unknown resistance of a given wire?
12
13
Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone bridge.
In the potentiometer circuit shown, the null point is at X. State with reason, where the balance point
will be shifted when
(a) Resistance R is increased, keeping all other parameters unchanged;
(b) Resistance S is increased, keeping R constant
(c) the potential of the driving cell is less than the experimental cell
Also write any two possible causes of one-sided deflection.
A potential difference V is applied across a conductor of length L and diameter D. How is the drift
velocity, vd, of charge carriers in the conductor affected when (i) V is halved, (ii) L is doubled and (iii) D
14
Draw a circuit diagram of a potentiometer .State its working principle. Derive the necessary formula to
describe how it is used to compare the emfs of the two cells.
15
In the meter bridge experiment, balance point was observed at J with AJ = l.
(i) The values of R and X were doubled and then interchanged. What would be the new position of
balance point?
(ii) If the galvanometer and battery are interchanged at the balance position, how will the balance point
get affected?
16
State the underlying principle of a potentiometer. Write two factors by which current sensitivity of a
potentiometer can be increased. Why is a potentiometer preferred over a voltmeter for measuring
the emf of a cell ?
17
Deduce the relation between current I flowing through a conductor and drift velocity dof
the electrons.
18
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these
quantities is constant along the conductor :
current, current density, electric field, drift speed ?
19
State Kirchhoff’s rules. Use these rules to write the expressions for the currents I1, I 2 and I 3 inthe circuit
diagram shown.
20
21
22
23
Two cells of emfs E1 and E2 and internal resistances r1 and r2 are connected in parallel. Derive the
expression for the (i) emf and (ii) internal resistance of a single equivalent cell which can replace this
combination.
Write the characteristics of Manganin which make it suitable for making standard resistance. Why
Manganin is used in the Metre Bridge?
A battery has an emf E and internal resistance r. A variable resistance R is connected across the
terminals of the battery. Find the value of R such that
I. The current is maximum
II.
The potential difference across the terminals is maximum
III.
Plt a graph between V and R.
Explain how a meter bridge is used to determine the resistivity of the material of a wire in the
laboratory. Why it is preferred to get a null point almost at the middle of the wire?
CHAPTER:4 MAGNETIC EFFECT OF CURRENT
ONE MARK QUESTIONS
1
2
3
4
Write the expression in a vector form for the Lorentz magnetic force F due to a charge
moving with a velocity V in a magnetic field B .What is the direction fo the magnetic force
What is the direction of the force acting on a charge particle q, moving with a velocity vin a
uniform magnetic field B?
An electron does not suffer any deflection while passing through a region of
uniform magnetic field. What is the direction of the magnetic field?
A beam of particles projected along +x-axis, experiences a force due to a magnetic field
along
the +y-axis. What is the direction of the magnetic field?
2013
2008
2009
2012
2007
5
6
7
8
9
10
Write two factors by which voltage sensitivity of a galvanometer can be increased.
Write two properties of a material used as a suspension wire in a moving coil
galvanometer.
An electron moving through a magnetic field does not experience a force; under what
condition is it possible?
Name the physical quantity whose S I unit is Wb-m2, is it ascalar or vector quantity?
Two wires of equal length are bent in the form of two loops , One of the loops is square
shaped and another is circular. These loops are suspended in a uniform magnetic field and
same current is passed through them. Which loop will experience greater torque?
How does the magnetic moment of an electron in a circular orbit of radius ‘r’ and moving
with a speed ‘v’ change ,when the frequency of revolution doubled?
2008
2006
2005
2005
2005
2005c
TWO MARKS QUESTIONS
1
2
2015
A square loop of side 20 cm carrying current 1 A is kept near an infinitely long straight wire
carrying current 2 A ,calculate the magnitude and direction of net force on the loop due to
the current carrying con doctor.
A square shaped plane coil of area 100 cm2 of 200 turns caries a steady current of 5 A . it is
placed in a uniform magnetic field of 0.2 T acting perpendicular to the plane of the coil.
2014
3
4
Calculate the torque on the coil when its plane makes an angle of 60o with the direction of
the field. In which orientation will the coil be in stable equilibrium?
An ammeter of resistance 0.80 can measure current upto 1.0 A.
(i) What must be the value of shunt resistance to enable the ammeter to measure current
upto 5.0 A?
(ii) What is the combined resistance of the ammeter and the shunt?
Two identical circular wires P and Q each of radius R and carrying current ‘I’ are kept in
perpendicular planes such that they have a common centre as shown in the figure. Find the
magnitude and direction of the net magnetic field at the common centre of the two coils.
6
2012
2012
2014
5
5
2013
2007
Two identical circular loops, P and Q, each of radius r and carrying currents I and 2I
respectively are lying in parallel planes such that they have a common axis. The direction of
current in both the loops is clockwise as seen from O which is equidistant from the both
loops. Find the magnitude of the net magnetic field at point O.
A wire of length L is bent round in the form of a coil having N turns of same radius. If a
steady current I flows through it in a clockwise direction, find the magnitude and direction
of the magnetic field produced at its centre
A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 20 cm as
2009
2010
shown. What is the magnetic field B

7
8
9
at O due to (i) straight segments (ii) the semi-circular arc?
A jet plane is travelling west at 450 ms 1. If the horizontal component of earth’s magnetic
2008
field atthat place is 4 104tesla and the angle of dip is 30&deg;, find the emf induced between the
ends ofwings having a span of 30 m.
Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with
2012
velocity v in a magnetic field B . Show that no work is done by this force on the charged
particle.
A steady current (I1) flows through a long straight wire. Another wire carrying steady
2012
current (I2) in the same direction is kept close and parallel to the first wire. Show with the
help of a diagram, how the magnetic field due to the current I1 exerts a magnetic force on
the second wire. Write the expression for this force.
10
A rectangular loop of wire of size 4 cm &times; 10 cm carries a steady current of 2A. A straight
long wire carrying 5A current is kept near the loop as shown. If the loop and the wire are
coplanar, find
(i) the torque acting on the loop and
(ii) The magnitude and direction of the force on the loop due to the current carrying wire.
11
A particle of charge ‘q’ and mass ‘m’ is moving with velocity V. It is subjected to a uniform
magnetic field B directed perpendicular to its velocity. Show that it describes a circular
path. Write the expression for its radius
2012
THREE MARKS QUESTIONS
1
A closely wound solenoid of 2000 turns and cross sectional area 1.6 x10–4m2 carrying a current
of 4.0 A is suspended through its centre allowing it to turn in a horizontal plane. Find
the magnetic moment associated with the solenoid,
(ii) Magnitude and direction of the torque on the solenoid if a horizontal magnetic field of
7.5x10–2T is set up at an angle of 30with the axis of the solenoid.
2014
2
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 R1 in series with the coil. If a
resistance R2 is connected in series with it, then it can measure upto V/2 volts. Find the
resistance, in terms of R1 and R2, required to be connected to convert it into a voltmeter that
2 V. Also find the resistance G of the galvanometer in terms of R1 and R2.
2015
3
(a) Why is the magnetic field radial in a moving coil galvanometer? Explain how it is achieved.
(b) A galvanometer of resistance ‘G’ can be converted into a voltmeter of range (0-V) volts by
connecting a resistance ‘R’ in series with it. How much resistance will be required to change its
range from 0 to V/2?
2013
4
Deduce the expression for the torque acting on a planar loop of area A and carrying current I
placed in a uniform magnetic field B,
If the loop is free to rotate, what would be its orientation in stable equilibrium?
2010
5
A cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field
for accelerating protons? If the radius of its ‘dees’ is 60 cm, calculate the kinetic energy (in
MeV) of the proton beam produced by the accelerator.
2006
6
State Biot – Savart law. Deduce the expression for the magnetic field at a point on the axis
of a current carrying circular loop of radius ‘R’, distant ‘x’ from the centre. Hence write the
magnetic field at the centre of a loop.
A uniform magnetic field of 6&middot;5 10– 4 T is maintained in a chamber. An electron enters into
the field with a speed of 4&middot;8 106 m/s normal to the field. Explain why the path of the
electron is a circle. Determine its frequency of revolution in the circular orbit. Does the
frequency depend on the speed of the electron ? Explain.
A uniform magnetic field is set up along the positive x-axis. A particle of charge ‘q’ and mass ‘m’
moving with a velocity v enters the field at the origin in X-Y plane such that it has velocity
components both along and perpendicular to the magnetic field B
Trace, giving reason, the trajectory followed by the particle. Find out the expression for the
distance moved by the particle along the magnetic field in one rotation.
2007
A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD carrying 5A
is held directly above AB at a height of 1 mm. Find the mass per unit length of the wire CD so that it
remains suspended at its position when left free. Give the direction of the current flowing in CD with
respect to that in AB. [Take the value of g = 10 ms–2]
Depict the field-line pattern due to a current carrying solenoid of finite length.
(i) In what way do these lines differ from those due to an electric dipole?
(ii) Why can’t two magnetic field lines intersect each other?
2010
7
8
9
10
2008
2011
2013
2009
11 A long straight wire AB carries a current I. A proton P travels with a speed v, parallel to the wire, at a
2010
12
2010
distance d from it in a direction opposite to the current as shown in the figure. What is the force
experienced by the proton and what is its direction?
An -particle and a proton moving with the same speed enter the same magnetic field region at
right angles to the direction of the field. Show the trajectories followed by the two particles in
the region of the magnetic field. Find the ratio of the radii of the circular paths which the two
particles may describe.
FOUR MARKS (VALUE BASED QUESTIONS)
1 Asha’s uncle was advised by his doctor to have an MRI (magnetic resonance imaging) scan of his
brain. Her uncle felt that it was too expensive and wanted to postpone it. When Asha learnt about
this, she took the help of her family and when she approached the doctor, he also offered a
substantial discount. She thus convinced her uncle to undergo the test to enable the doctor to
know the condition of his brain. The resulting information greatly helped his doctor to treat him
properly.
Based on the above paragraph, answer the following questions :
(a) What according to you are the values displayed by Asha, her family and the doctor ?
(b) What in your view could be the reason for MRI test to be so expensive?
(c) Assuming that MRI test was performed using a magnetic field of 0&middot;1 T, find the maximum and
minimum values of the force that the magnetic field could exert on a proton (charge = 1&middot;6 x 10–
19C) that was moving with a speed of 104 m/s.
2 Deepika and Ruchika were asked by their teacher to perform an experiment using a
galvanometer. Before doing the experiment they were very keen to know the different parts of
the galvanometer which was given to them in the form of a small box. They approached the
teacher and asked for the permission. The teacher thought it would be a good idea if the
galvanometer be opened before the whole class and explained its construction and working to all
of them.
Based on the above paragraph, answer the following questions :
(a) What, in your opinion, were the qualities displayed by Deepika, Ruchika and the teacher?
(b) State briefly the working principle of the galvanometer.
(c) What is the shape of the magnets used and why is it so designed?
2015
2014
FIVE MARKS QUESTIONS
1
(a) Use Biot-Savart law to derive the expression for the magnetic field due to a circular coil
of radius R having N turns at a point on the axis at a distance ‘x’ from its centre. Draw the
magnetic field lines due to this coil.
(b) A current ‘I’ enters a uniform circular loop of radius ‘R’ at point M and flows out at N as
shown in the figure. Obtain the net magnetic field at the centre of the loop.
2010
2015
2
(a) Show how Biot-Savart law can be alternatively expressed in the form of Ampere’s
2003
circuital law. Use this law to obtain the expression for the magnetic field inside a solenoid of
length ‘l’, cross-sectional area ‘A’ having ‘N’ closely wound turns and carrying a steady
current ‘I’. Draw the magnetic field lines of a finite solenoid carrying current I.
(b) A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two
vertical wires at its ends. A current of 5.0 A is set up in therod through the wires. Find the
magnitude and direction of the magnetic field which should be set up in order that the
tension in the wire is zero.
3
(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
(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) Draw the magnetic field lines due to a circular loop of area A carrying current I. Show
that it acts as a bar magnet of magnetic Moment m =AI .
(b) Derive the expression for the magnetic field due to a solenoid of
length ‘2 l’, radius ‘a’ having ‘n’ number of turns per unit length and carrying a steady
current ‘I’ at a point on the axial line, distant ‘r’ from the centre of the solenoid. How does
this expression compare with the axial magnetic field due to a bar magnet of magnetic
moment ‘m’?
(a) Draw a labelled diagram of a moving coil galvanometer. State its working principle. What
is the function of a cylindrical soft iron core used in it ?
(b) Define the terms (i) current sensitivity and (ii) voltage sensitivity.
(c) Explain the underlying principle used in converting a galvanometer into a (i) voltmeter
and (ii) ammeter.
Draw a schematic sketch of a cyclotron. Explain its working principle. Obtain the necessary
mathematical expression to show how this machine is used to accelerate charged particles
(a) State Ampere’s circuital law. Show that the magnetic field B at a distance r outside the
straight infinite wire carrying current I is tangential and is given by
B = &micro;o I / (2πr).
(b) Consider a long straight cylindrical wire of circular cross-section of radius a, as shown in
the figure. The current I is uniformly distributed across this cross-section. Calculate the
magnetic field B in the region r &lt; a and r &gt; a. Plot a graph of B versus r from the centre of
the wire.
4
5
6
7
2008
2005
2013
2014
2011
2014
8
Two infinitely long straight parallel wires, ‘1’ and ‘2’, carrying steady currents I1 and I2 in
the same direction are separated by a distance d. Obtain the expression for the
magnetic field due to the wire ‘1’ acting on wire ‘2’. Hence find out, with the help of a
suitable diagram, the magnitude and direction of this force per unit length on wire ‘2’
due to wire ‘1’. How does the nature of this force change if the currents are in opposite
direction? Use this expression to define the S.I. unit of current
2011
9
Explain, using a labelled diagram, the principle and working of a moving coil galvanometer.
What is the function of (i) uniform radial magnetic field, (ii) soft iron core?
2004
2012
Define the terms (i) current sensitivity and (ii) voltage sensitivity of a galvanometer.
Why does increasing the current sensitivity not necessarily increase voltage
sensitivity?
10
a) Derive the expression for the torque on a rectangular current carrying loop
suspended in a uniform magnetic field.
b) A proton and a deuteron having equal momentum enter in a region of uniform
magnetic field at right angle to the direction of the field. Depict their trajectories in
the field.
11
(a) Using Biot-Savart’s law, derive an expression for the magnetic field at the centre of a
circular coil of radius R,number of turns N, carrying current I.
(b) Two small identical circular coils marked 1 and 2 carry equal currents and are placed
with their geometric axes perpendicular to each other as shown in the figure. Derive an
expression for the resultant magnetic field at O.
12
If a particle of charge q is moving with velocity v along the y-axis and the magnetic field B is
2008
2009
acting along the z-axis, use the expression Fq ( v B) to find the direction of the force F
acting on it. A beam of proton passes undeflected with a horizontal velocity v, through a
region of electric and magnetic fields, mutually perpendicular to each other and
perpendicular to the direction of the beam. If the magnitudes of the electric and magnetic
fields are 100 kV/m, 50 mT respectively,
Calculate (i) velocity of the beam
(ii) Force exerted by the beam on a target on the screen, if the proton beam
carries a current of 080 mA.
2009
13
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write
the expression for cyclotron frequency.
2007
2010
14
If a particle of charge q is moving with velocity v along the y-axis and the magnetic
field B isacting along the z-axis, use the expression
2008

F q ( v x B) to find the direction of the force F acting on it.
A beam of proton passes undeflected with a horizontal velocity v, through a region of
electric andmagnetic fields, mutually perpendicular to each other and perpendicular
to the direction of thebeam. If the magnitudes of the electric and magnetic fields are
100 kV/m, 50 mT respectively,calculate
(i) Velocity of the beam v.
(ii) force exerted by the beam on a target on the screen, if the proton beam carries a
current of 080 mA
15
(a) State the principle of the working of a moving coil galvanometer, giving its labelled
diagram.
(b) “Increasing the current sensitivity of a galvanometer may not necessarily increase its
voltage sensitivity.” Justify this statement.
(c) Outline the necessary steps to convert a galvanometer of resistance RG into an ammeter
of a given range.
2011
16
a) Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long
Solenoid at a point inside the solenoid on its axis.
(b) In what respect is a toroid different from a solenoid? Draw and compare the pattern of
the magnetic field lines in the two cases.
(c) How is the magnetic field inside a given solenoid made strong?
2011
EXPECTED QUESTIONS FOR REVISION/MLL
CHAPTER:5 MAGNETISM
1
Write the magnetic properties of materials used preparing
I.
permanent magnets
II.
electromagnets
III.
Core of the transformer
Give one example each.
2
The horizontal component of the earth’s magnetic field is equal to the vertical component at a place.
Find the angle of dip?
3
Define the three elements to describe Earth’s magnetism at a place,show them in a diagram.
4
A uniform magnetic field gets modified as shown below when two specimens X and Y are
placed in it. Identify whether specimens X and Y are diamagnetic, paramagnetic or ferromagnetic.
5
Which of the following substances are diamagnetic?
Bi, Al, Na, Cu, Ca and Ni
6
How does angle of dip change as one goes from magnetic pole to magnetic equator of the
Earth?
7
8
9
The permeability of a magnetic material is 0.9983. Name the type of magnetic materials it represents.
The susceptibility of a magnetic material is 1.9 &times; 10 –5. Name the type of magnetic materials it represents.
The susceptibility of a magnetic materials is –4.2 &times; 10 6 . Name the type of magnetic materials it represents.
10 In what way is Gauss’s law in magnetism different from that used in electrostatics? Explain briefly.
The Earth’s magnetic field at the Equator is approximately 0.4 G; Estimate the Earth’s magnetic
dipole moment. Given: Radius of the Earth = 6400 km.
11 How the following magnetic materials behave with the rise of temperature
Para,Ferro,Dia-magnetic substances
12 Distinguish between Para, Ferro Dia-magnetic substances, give one example each
13 Deduce the expression for magnetic dipole moment of an electron revolving around the
Nucleus in a circular orbit of radius ‘r’. Indicate the direction of the magnetic dipole moment.
14 Deduce the expression for magnetic field due to a magnetic dipole at any point on the
I.
Axial line
II.
Equatorial line
Describe the expression for torque experienced by a dipole in a uniform magnetic field.
15 How magnetic field lines are different from electric field lines? Write any two properties of magnetic
field lines.
16 Define the terms
I.
Magnetic permeability
II.
Retentively
III.
IV.
Coercively
Susceptibility
What do the area of the Hysteresis loop and slope of the graph between I and H signify?
QUESTION BANK OF PROBABLE QUESTIONS FOR AISSCE 2016
CHAPTER – 6 (ELECTROMAGNETIC INDUCTION)
Questions that have been asked one time
VERY SHORT ANSWER QUESTIONS (1 MARK)
1. How does the mutual inductance of a pair of coils change when
(i) distance between the coils is increasedand
(ii) number of turns in the coils is increased? [CBSE (AI) 2013]
Ans. (i) Decreases (ii) Increases
2. The motion of copper plate is damped when it is allowed to
oscillate between the two poles of a magnet. What is the cause of
this damping?
[CBSE (AI) 2013]
Ans. As the plate oscillates, the changing magnetic flux through
the plate produces a strong eddy current in the direction which
opposes the cause. Also, copper being diamagnetic substance, it
gets magnetized in the opposite direction, so the plate motion
gets damped.
3. The closed loop PQRS is moving into a uniform magnetic field
acting at right angles to the plane of the paper as shown. State
the direction of the induced current in the loop. [CBSE (AI) 2012]
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
P
Q
X
X
X
X
X
X
X
X
X
X
R
S
Ans. along PSRQP
4. When current in a coil changes with time, how is the back emf
induced in the coil related to it?
[CBSE (AI) 2008]
Ans. The back emf induced in the coil opposes the change in
current.
5. Write Faraday’s laws of electromagnetic induction[CBSE (AI) 2009]
Ans.(i) whenever the amount of magnetic flux linked with a closed
circuit changes, an emf is induced in the circuit which lasts as long
as the change in flux lasts.(ii) The magnitude of the induced emf in
a circuit is equal to the time rate of change of magnetic flux
through circuit.
SHORT ANSWER QUESTIONS (2, 3 MARKS)
1. Two identical loops, one of copper and the other of aluminium,
are rotated with the same angular speed in the same magnetic
field. Compare (i) the induced emf and (ii) the current produced in
[CBSE (AI) 2010]
Ans.
(i) Induced emf is same in both loops (B,A and ω are same for
both loops)
(ii) As area A, length l and emf E are same for both loops but
the resistivity of copper is less than aluminium therefore
current induced is larger in copper loop.
2. Define self-inductance of a coil. Obtain an expression for the
energy stored in a solenoid of self-inductance L when the current
through it grows from zero to I.
[CBSE (AI) 2015]
Ans. Self-inductance of a coil is numerically equal to the magnetic
flux linked with the coil when a unit current flows through it.
Energy stored in an inductor = &frac12; LI2
3. Define the term mutual inductance between the two coils. Obtain
the expression for mutual inductance of a pair of long co-axial
solenoids each of length l and radii r1and r2.Total number of turns
in the two solenoids are N1 and N2 respectively.
[CBSE (AI) 2014, 2009]
Ans. When current flowing in one of two nearby coil, the coil, in
which current is changed is called primary coil and the coil in
which emf is induced is called the secondary coil.
The si unit of mutual inductance is henry.
Mutual Inductance: Suppose there are two coils C1 and C2. The
current I1 flowing in primary coil c1 ; due to which an effective
magnetic flux Φ2 is linkedwith secondary coil C2 .
Φ2=M21I1 , M21 is the mutual inductance of coil 2 w.r.t. coil 1
Mutual inductance between two coils (M21) is numerically equal
to the flux linkage with secondary coil, when current flowing in
primary coil is 1 ampere.
Mutual inductance of two co-axial solenoids: Consider two long
coaxial solenoids each of length l with number of turns N1 and N2
wound one over the other. I1 is the current flowing in outer
solenoid and B1 is the magnetic field produced within this
solenoid.
B1= &micro;0n1I1 n1 is the number of turns per unit length of outer
solenoid
Φ2= n2lB1A2= &micro;0n1I1 n2lA2 , n2 is the number of turns per unit
length of inner solenoid, A2 is the cross-sectional area of inner
solenoid, Φ2 is the flux linkage with inner solenoid.
M21 = &micro;0n1 n2lA2 , Similarly M12 = &micro;0n1 n2lA2
1. State Faraday’s law of electromagnetic induction. Figure shows a
rectangular conductor PQRS in which the conductor PQ is free to
move in a uniform magnetic field B perpendicular to the plane of
the paper. The field extends from x=0 to x=b and is zero for x&gt;b.
Assume that only the arm PQ possesses resistance r. When the
arm PQ is pulled outward from x=0 to x=2b and is then moved
backward to x=0 with constant speed v, obtain the expression for
the flux and the induced emf. Sketch the variations of these
quantities with distance 0≤x≤2b.
[CBSE (AI) 2010]
. . . . . . . .
.S . . . . . . .
. . . . . . P.
. . . .
. . .
. . .
. . Q.
.
R. . .
. x=0.
.
.
. . . .
. x=b.
x=2b
ANS. When the magnetic flux linked with a coil or circuit changes, an
emf is induced in the coil. The emf and current last so long as the
change in magnetic flux lasts
The magnitude of induced emf is proportional to the rate of change of
magnetic flux linked with the circuit.
NCERT TEXT BOOK PART 1 page no. 217, Example 6.8
Questions that have been repeated two times
1. What are eddy currents? How are they produced? In what sense
eddy currents are considered undesirable in a transformer? How
can they be minimized? Give two applications of eddy currents.
[CBSE (AI) 2006, 2011]
ANS. Eddy currents are the currents induced in conductors when
they are placed in changing magnetic flux region.
When a metallic plate is placed in a time varying magnetic field, the
magnetic flux linked with the plate changes, the induced currents are
set up in the plate, and these currents are called eddy currents
Production: For diagram Refer NCERT TEXT BOOK PART 1 page No. 218
In transformer, there is a huge loss of energy due to production of eddy
currents, so these currents are undesirable in transformer.
Eddy currents may be minimized by using laminated core of soft iron.
APPLICATIONS: Induction furnace, Electromagnetic braking in trains,
Electric power meters, Electromagnetic damping
2. State the working of a.c. generator with the help of a labelled
diagram. The coil of an ac. Generator having N turns, each of area
A, is rotated with a constant angular velocity. Deduce the
expression for the alternating emf generated in the coil. What is
the source of energy generation in this device?
[CBSE (AI) 2008C, 2011]
ANS. AC generator: A dynamo or generator is a device which
converts mechanical energy into electrical energy.
Principle: It works on the principle of electromagnetic induction.
When a coil rotates continuously in a magnetic field with its axis
perpendicular to the magnetic field, the magnetic flux linked with
the coil changes and an induced emf and hence a current is set up in
it.
Construction:
(i) Field Magnet: It produces the magnetic field. In the case of a low
power dynamo. The magnetic field is generated by a permanent
magnet, while in the case of large power dynamo, the magnetic field
is produced by an electromagnet.
(ii) Armature: It consists of a large number of tums of insulated wire
in the soft iron drum or ring. It can revolve round an axle between the
two poles of the field magnet. The drum or ring serves the two
purposes: (i) It serves as a support to coils and (ii) It increases the
magnetic field due to air core being replaced by an iron core.
(iii) Slip rings: The slip rings are the two metal rings to which the
ends of armature coil are connected. These rings are fixed
to the shaft which rotates the armature coil so that the
rings also rotate along with the armature.
(iv) Brushes: These are two flexible metal plates or carbon rods
which are fixed and constantly touch the revolving rings.
The output current in external load is taken through these
brushes.
Diagram: Refer NCERT TEXT BOOK PART-1 page NO. 225
Working: when the armature coil is rotated in the strong magnetic
field, the magnetic flux linked with the coil changes and the current
is induced in the coil, its direction being given by Fleming’s right
hand rule,
Expression for Induced. emf: If N is the number of
Turns in coil, f the frequency of rotation, A area of coil
And B the magnetic induction, then induced emf
e = - 𝑑𝛷/𝑑t
= d/dt (NBA (cos 2πft))
= 2𝜋𝑁𝐵𝐴𝑓 sin 2πft
The source of energy generation is the mechanical energy of rotation
of armature coil.
Expected Questions for MLL
1. State Lenz’s law
(1)
ANS. The polarity of the induced emf is such that it tends to
produce a current which opposes the change in magnetic flux that
produced it.
2. Write S.I unit of magnetic flux. Is it a scalar or vector quantity? (1)
ANS. Weber (wb). Scalar.
3. Write an expression for the energy stored in an inductor of
inductance L, when a steady current is passed through it. Is the
energy electric or magnetic?
(1)
ANS. &frac12; LI2 , Magnetic energy.
4. Show that Lenz’s law is in accordance with the law of conservation
of energy.
(2)
ANS. When the north pole of a coil is brought near a close to coil,
the direction of current induced in the coil is such as to oppose
the approach the North Pole. For this the nearer face of coil
behaves as North Pole. This necessitates an anticlockwise current
in the coil when seen from the magnet side. (Fig a)
Similarly where North Pole of the magnet is moved away from coil
the direction of current in the coil will be such as to attract the
magnet. For this the nearer face of coil behaves as South Pole.
The necessitates a clock wise current in the coil when seen from
the magnet. (Fig b)
N
S
N
FIG. (a)
Anticlockwise
S
N
FIG. (b)
S
Clockwise
5. Derive expression for self-inductance of a long air-cored solenoid
of length l, cross-sectional area A and having number of turns N.
(3)
ANS. Consider a long air solenoid having ‘n’ number of turns per
unit length. If current in solenoid is I, the magnetic field inside the
solenoid, B = &micro;0nI
If A is cross-sectional area of solenoid, then effective flux linked
with the solenoid of length ’l’;Φ = (NBA), where N=nl is the number of
turns in length ‘l’ of solenoid.
Φ = (nlBA)
Substituting the value of B from (i)
Φ = nl (&micro;0nI ) A = &micro;0n2AlI
Self-inductance of air solenoid
L = Φ/I = &micro;0n2Al
If N is total number of turns in length l, then
n= N/l
Self-inductance
L =&micro;0(N/l)2Al
=&micro;0N2A/l
Q. 1. What do you mean by mutual inductance of two nearby coils?
Find an expression for mutual inductance of two co-axial solenoid. (5)
[CBSE (F) 2013, 2010]
Ans. When current flowing in one of two nearby coils is changed, the
magnetic flux linked with the other coil changes; due to which an emf is
induced in it (other coil). This phenomenon of electromagnetic
induction is called the mutual induction. The coil, in which current is
changed is called primary coil and the coil in which emf is induced is
called the secondary coil.
The si unit of mutual inductance is henry.
Mutual Inductance: Suppose there are two coils C1 and C2. The current
I1 flowing in primary coil c1 ; due to which an effective magnetic flux Φ2
is linkedwith secondary coil C2 .
Φ2=M21I1 , M21 is the mutual inductance of coil 2 w.r.t. coil 1
Mutual inductance between two coils (M21) is numerically equal to the
flux linkage with secondary coil, when current flowing in primary coil is
1 ampere.
Mutual inductance of two co-axial solenoids: Consider two long coaxial
solenoids each of length l with number of turns N1 and N2 wound one
over the other. I1 is the current flowing in outer solenoid and B1 is the
magnetic field produced within this solenoid.
B1= &micro;0n1I1 n1 is the number of turns per unit length of outer solenoid
Φ2= n2lB1A2= &micro;0n1I1 n2lA2 , n2 is the number of turns per unit length of
inner solenoid,A2 is the cross-sectional area of inner solenoid, Φ2 is the
M21 = &micro;0n1 n2lA2 , Similarly M12 = &micro;0n1 n2lA2
QUESTION BANK OF PROBABLE QUESTIONS FOR AISSCE 2016
CHAPTER – 6 (ALTERNATING CURRENT)
Questions that have been asked one time
VERY SHORT ANSWER QUESTIONS (1 MARK)
1. Mention the two characteristic properties of the material
suitable for making core of a transformer.
[ CBSE (AI) 2012]
ANS. (i) Low hysteresis loss (ii) Low coercivity.
2. In a series LCR circuit, the voltage across an inductor, a capacitor
and a resistor are 30 volt, 30 volt and 60 volt respectively. What
is the phase difference between the applied voltage and current
in the circuit?
[ CBSE (AI) 2007]
Ans. tanΦ = ( VL - VC ) / VR
Φ = 00
3. The instantaneous current and voltage of an a.c circuit are given
by i= 10 sin 314t ampere, v= 50 sin 314t volt. What is the power
dissipation in the circuit?
[ CBSE (AI) 2008]
Ans. Power = p = &frac12; V0 I0 cosΦ = 250 watt. Here Φ=00
SHORT ANSWER QUESTIONS (2, 3 MARKS)
1. (a) For a given a.c, i= i0sinωt, Show that the average power
dissipated in a resistor R over a complete cycle is &frac12;( i0 )2 R.
(b) A light bulb is rated at 100 watt for a 220 volt a.c supply.
Calculate the resistance of the bulb.
[CBSE (AI) 2013]
Ans. (a) Derivation of average power
Average power = &frac12;( i0 )2 R
(b) Average power = ( irms)2R = (Vrms )2 /R Vrms =220 volt
R = 484 ohm.
2. State the principle of working of a transformer. Can a
transformer be used to step up or step down a d.c voltage?
[CBSE (AI) 2011]
Ans. Mutual induction, No, because there is no change in
magnetic flux.
When d.c voltage is applied across a primary coil of a
transformer, the current in primary coil remain same, so there is
no change in magnetic flux and hence no voltage is induced
across the secondary coil.
3. How is the large scale transmission of electric energy over long
distances done with the use of transformers? [CBSE (AI) 2012]
Ans. At the power generating station. The step up transformers
step up the output voltage which reduces the current through
the cables and hence reduce resistive power loss. Then at the
consumer end, a step down transformer step down the voltage.
Hence in this way the large scale transmission of electric energy
over long distances can be done by transformer.
4. An a.c voltage V= V0sin wt is applied across a
(a)Series RC circuit in which capacitive reactance is a times the
resistance of the circuit.
(b) Series RL circuit in which inductive impedance is ‘b’ times
the resistance in the circuit.
Find the value of power factor of the circuit in each case.
ANS. Power factor cosΦ = (R/Z), when Z=√ (R2+X2)
(i) X=XC=aR,
Z= √(R2+(aR2)) = R√(1+a2)
CosΦ = R/ (R√1+a2)) = 1/√ (1+a2)
(ii) X=XL=bR
(iii) Z=√(R2+(bR2)) = R√(1+b2)
CosΦ = R/ (R√1+b2)) =1/√ (1+b2)
5. An AC source of voltage V= Vmsin wt is applied across a series LCR
circuit. Draw the phasor diagrams for the circuit, when
(i) Capacitive reactance exceeds the inductive reactance.
(ii) Inductive reactance exceeds capacitive reactance.
[CBSE (AI) 2008C]
ANS. When XC&gt;XL: the phasor diagram is shown in fig. (a).
V - axis
VL
VR
I0
I - axis
Φ
VC - VL
VC
Fig (a)
(iii) When XL&gt;Xc, the phasor diagram is shown in fig. (b).
V - axis
VL
VL - VC
Φ
VR
I0
I - axis
VC
FIG (b)
6. A voltage V= Vosin wt is applied to a series LCR circuit. Derive the
expression for the average power dissipated over a cycle. Under
what condition is (i) no power dissipated even though the
current flows through the circuit. (ii) Maximum power dissipated
in the circuit.
[CBSE (AI) 2014]
Ans. Average power = p = &frac12; V0 I0 cosΦ
(i) When Φ = 900 or -900 , purely inductive or purely
capacitive circuit
(ii) When Φ = o0 , at resonance(behaves like purely resistive
circuit)
7. You are given three circuit elements X,Y and Z. When the
element X is connected across an a.c. source of a given voltage,
the current and the voltage are in the same phase. When the
element Y is connected in series with X across the source,
voltage is ahead of the current in phase by π/4. But the current
is ahead of the voltage in phase by π/4 when Z is connected in
series with X across the source. Identify the circuit elements X, Y
and Z. When all the three elements are connected in series
across the same source, determine the impedance of the circuit.
Draw a plot of the current versus the frequency of the applied
source and mention the significance of this plot.[CBSE (AI) 2015]
Ans. X= resistor, Y= inductor, Z= capacitor
Impedance = {R2 + (XL - XC) 2}1/2
For plotting of current versus frequency refer NCERT text book
part 1 page no. 248
1. Define the term capacitive reactance. Show graphically the
variation of capacitive reactance with frequency of applied
alternating voltage.
An ac voltage V= Vosinwt is applied across a pure capacitor of
capacitance C. Find an expression for current flowing through it. Show
mathematically the current flowing through it leads the applied
voltage by angle (π/2). [CBSE (AI) 2008C]
ANS. Capacitive Reactance: The resistance offered by capacitor
alone to the flow of alternating current is called the capacitive
reactance.
It is denoted by XC. Its value isXC = (1/ωC) = (1/2πfC)
XC is inversely proportional to capacitance.
Phase Difference between current and applied voltage in purely
Capacitive Circuit:
Circuit Containing Pure Capacitance: Consider a capacitor of
capacitance C; its plates are connected to the terminals of a source of
alternating voltage.
C
V= V0sinωt
V= Vo sinωt , q= cVo sinωt
I= dq/dt = cωV0 coswt
I ={ V0/(1/ωC) } cos ωt = I0 sin(ωt + π/2)
Where I0= V0/XC Here
XC= 1/ωC
Current leads the applied emf by an angle of π/2.
2. State the condition for resonance to occur in series LCR a.c
circuit and derive an expression for resonant frequency. Draw
a plot showing the variation of the peak current with the
frequency of the a.c source used. Define quality factor Q of
the circuit.[CBSE (AI) 2008]
Ans. For resonance the current produced in the circuit and emf
applied must always be in the same phase.
For resonance Φ = 00, XC = XL
1/ω0C = ω0L
ω0 = resonant angular frequency
ω0 = 1/√LC f0 = resonant frequency
Quality factor is defined as the ratio of resonant frequency
to the band width of the circuit.
Q= ω0L/R
For graph refer NCERT TEXT BOOK PART 1 page NO. 248
3. Draw a schematic diagram of a step-up transformer. Explain
its working principle. Deduce the expression for the
secondary to primary voltage in terms of the number of turns
in the two coils. In an ideal transformer, how is the ratio
related to the currents in the two coils? How is the
transformer used in large scale transmission and distribution
of electrical energy over long distances?
Ans. Transformer is a device by which an alternating voltage
may be decreased or increased. It is based on the principle of
mutual induction.
Construction: It consists of laminated core of soft iron on
which two coils of insulated copper wire are separately
wound. These coils are kept insulated from each other and
from the iron core, but are coupled through mutual induction.
The number of turns in these coils are different. Out of these
coils one coil is called primary coil and the other is called the
secondary coil. The terminals of primary coils are connected
to A.C mains and the terminals of the secondary coil are
connected to external circuit in which alternating current of
desired voltage is required. Transformers are of two types:
1. Step up transformer: It transforms the alternating low
voltage to alternating high voltage and in this the number
of turns in secondary coil is more than that in primary coil
2. Step down transformer: It transforms the alternating high
voltage to alternating low voltage and in this the number
of turns in secondary coil is less than that in primary coil
Diagram: Refer NCERT TEXT BOOK PART 1 PAGE NO- 260
Working: When alternating current source is connected to
the ends of primary coil, the current changes continuously
in the primary coil, due to which the magnetic flux linked
with the secondary coil changes continuously, therefore
the alternating emf of same frequency is developed across
the secondary.
NS/NP = VS/VP
NS is the number of turns in secondary coil
NP is the number of turns in primary coil
VP is the alternating voltage applied to primary coil
VS is the alternating voltage across the secondary coil
IS/IP = NP/NS
In an ideal transformer input power = output power
VPIP=VSIS
NS/NP = VS/VP= IP/IS
At the power generating station. The step up transformers step
up the output voltage which reduces the current through the cables
and hence reduce resistive power loss. Then at the consumer end, a
step down transformer step down the voltage. Hence in this way the
large scale transmission of electric energy over long distances can be
done by transformer.
Expected questions for MLL
1. What is the phase difference between the voltages across the
inductor and a capacitor in an AC circuit?
(1)
ANS. 1800 .
2. What is phase difference between voltage and current in a LCR
series circuit at resonance?
(1)
ANS. 00.
3. The peak value of e.m.f. in ac is E0. Write its (i) rms (ii)average
value over a complete cycle.
[CBSE (F) 2011] (1)
ANS. E0= peak value of emf
(i) rms value [Erms] =( E0/√2)
(ii) (ii) average value [Eav]= zero.
4. An electrical element X when connected to an alternating voltage
Identify X and write an expression for its reactance . (1)
ANS. Capacitor, XC= 1/wc .
5. What will be the effect on inductive reactance and capacitive
reactance if frequency of AC source increased?
(1)
ANS. Inductive reactance will increase with the increase of
frequency and capacitive reactance will decrease with the
increase of frequency.
6. What is wattless current?
[CBSE (DELHI) 2011] (1)
ANS. when pure inductor or pure capacitor is connected to AC
source the current flows in the circuit but with no power loss.
Such a current is called wattless current.
7. Define power factor? State the conditions under which it is
maximum and minimum.
[CBSE (DELHI) 2010] (2)
ANS. Power factor is the ratio of resistance and impedance of an
AC circuit.
When Z=R, power factor in maximum (purely resistive).
Power factor is minimum (zero) when circuit is purely inductive or
purely capacitive.
8. An air cored coil L and a bulb B are connected in series to the AC
mains. The bulb closed with brightness. How would the glow of
the bulb change if an iron rod were inserted in the coil? give
(2)
ANS. When iron rod is inserted in the coil, the inductance of coil
increases; so impedance of circuit increases and hence, current in
circuit I = ( V/√(R2+(wL)2 ) decreases.
Consequently, the glow of bulb decreases.
9. Explain why the reactance provided by a capacitor to an
alternating current decreases with increasing frequency. (2)
ANS. A capacitor does not allow flow of direct current through it
as the resistance across the gap is infinite. When an alternating
voltage is applied across the capacitor plates, the place are
alternately charged and discharged. The current through the
capacitor is a result of this charging voltage(or charge). Thus, a
capacitor will pass more current through it if the voltage is
changing at a faster rate, i.e., if the frequency of supply is higher.
This implies that the reactance offered by a capacitor is less with
increasing frequency; it is given by 1/wC .
QUESTION BANK OF PROBABLE QUESTIONS FOR AISSCE 2016
CHAPTER – 6 (ELECTROMAGNETIC WAVES)
Questions that have been asked one time
VERY SHORT ANSWER QUESTIONS (1 MARK)
1. What are the directions of electric and magnetic field vectors
relative to each other and relative to the direction of
propagation of electromagnetic waves?
[CBSE(AI)2012]
ANS.They are perpendicular to each other and also perpendicular
to the direction of propagation.
2. Identify the part of the electromagnetic spectrum to which the
following wavelengths belong:
(i) 10-1m
(ii) 10-12 m[CBSE (AI) 2008]
ANS. (i) short radio waves (ii) gamma rays
3. Identify the part of the electromagnetic spectrum to which the
following wavelengths belong:
(i) 1 mm
(ii) 10-11 m
[CBSE (AI) 2008]
ANS. (i) microwaves
(ii) gamma rays.
4. Welders wear special goggles or face masks with glass windows
to protect their eyes from electromagnetic radiations. Name the
radiations and write the range of their frequency.[CBSE(AI)2013]
ANS. Ultraviolet radiations, frequency range: 1015-1o17 Hz
5. Name the electromagnetic radiations used for studying the
crystal structure of solids and write its frequency range
[CBSE (AI) 2007, 2009]
ANS. X- rays, frequency range 1017 to 1020 HZ
6. The speed of an electromagnetic wave in a material medium is
given by v = 1/√&micro;ε, &micro; being the permeability of the medium and
€ its permittivity. How does its frequency change?
[CBSE (AI) 2012]
ANS. No change
7. How are X-rays produced?[CBSE(AI)2011]
ANS. X-rays are produced when high energetic electron beam is
made incident on a metallic target of high melting point and high
atomic weight.
8. The frequency of oscillation of the electric vector of a certain
electromagnetic wave is 5x1014 Hz. What is the frequency of
oscillation of the corresponding magnetic field vector and to
which part of the electromagnetic spectrum does it belong?
[CBSE (AI) 2008C]
ANS. 5x1014 Hz, visible region.
9. Which of the following has the shortest wavelength?
Microwaves, Ultraviolet rays, X-rays[CBSE (AI) 2010]
ANS. X-rays
10.
To which part of the electromagnetic spectrum does a
wave of frequency 5x1019 Hz belong?[CBSE (AI) 2014]
Ans. Gamma rays.
SHORT ANSWER QUESTIONS (2, 3 MARKS)
1. What is meant by the transverse nature of electromagnetic
waves? Draw a diagram showing the propagation of an
electromagnetic wave along X-direction, indicating clearly the
directions of oscillating electric and magnetic fields associated
with it.
[CBSE (AI) 2008]
ANS. In an electromagnetic wave, the electric and magnetic field
vectors oscillate, perpendicular to the direction of propagation of
wave. This is called transverse nature of electromagnetic wave
Diagram: Refer NCERT TEXT BOOK page NO. 275
Accordingly if a wave is propagating along z-axis, the electric vector
oscillates along x- axis and magnetic field vector oscillates along y-axis.
2. Identify the following electromagnetic radiations as per the
wavelengths given below.
(a) 10-3 nm
(b) 10-3m
(c) 1 nm
Write one application of each.[CBSE (AI) 2008]
Radio therapy or to initiate nuclear reactions.
(b) Microwaves
(c) X-ray
In medical science for detection of fractures, stones in kidneys,
3. Identify the following electromagnetic radiations as per the
frequencies given below:
(a)1020 HZ (b) 109 HZ (c) 1011 HZ
Write one application of each. [CBSE (AI) 2008]
ANS. (a) gamma radiation, for treatment of cancer
distances.
(c) Micro waves, for cooking in microwave oven.
4. Write the order of frequency range and one use of each of the
(a)Microwaves (b) Ultraviolet rays (c) Gamma rays
[CBSE (AI) 2006]
ANS. (a) Microwaves: 3X 1011- 1X 108Hz. These are suitable for the
Ultraviolet rays: 1X106 - 8X1014Hz. They are used to detect
invisible writing, forged documents and finger prints.
Gamma rays: 5X 1023- 3X1019Hz. For the treatment of cancer cells.
5. A capacitor of capacitance of ‘C’ is being charged by connecting
it across a dc source along with an ammeter. Will the ammeter
show a momentary deflection during the process of charging? If
so, how would you explain this momentary deflection and the
resulting continuity of current in the circuit? Write the
expression for the current inside the capacitor.[CBSE (AI) 2012]
ANS. Yes, because of the production of displacement current
between the plates of capacitor on account of changing electric
field.
Current inside the capacitor
Id= ε0 (dφE/dt)
6. A capacitor, made of two parallel plates each of plate area A and
separation d, is being charged by an external ac source. Show
that the displacement current inside the capacitor is the same as
the current charging the capacitor. [CBSE (AI) 2013]
ANS.
+q
-q
E
Ic = dq/dt Ic is the conduction current.
Id= ε0 (dφE/dt) φE is the electric flux
φE = q/ε0, so Id = dq/dt Id is the displacement current.
Both conduction current and displacement current are equal.
7. Considering the case of a parallel plate capacitor being charged,
show how one is required to generalize Ampere’s circuital law to
include the term due to displacement current.[CBSE (AI) 2014]
ANS. ∮ 𝐵. 𝑑𝑙 = &micro;0IC + &micro;0ε0 dɸE/dt
Here Id= ε0 (dφE/dt) = displacement current
IC = conduction current.
8. Arrange the following electromagnetic eaves in the order of
their increasing wavelength:
Gamma rays, microwaves, x rays, radio waves.
How are infra-red waves produced? What role does infra-red
radiation play in (i) maintaining the Earth’s warmth and (ii)
physical therapy?
[CBSE (AI) 2015]
ANS. Gamma rays, x rays, microwaves, radio waves.
Infra-red waves are produced by the vibration of atoms and
molecules
(i) The earth radiates infrared waves which are reflected by the
gases in the lower atmosphere. This phenomenon, called
greenhouse effect, keeps the earth warm.
(ii) Infrared lamps in the treatment of muscular complaints.
Expected questions for MLL
1. Name the electromagnetic waves, which (i) maintain Earth’s
warmth and (ii) are used in aircraft navigation.[CBSE (F) 2012]
(1)
ANS. (i) Infrared rays.
(ii)Microwaves.
2. Why are infra-red radiations referred to as heat waves? Name
electromagnetic spectrum having (i) shorter wavelength (ii)
longer wavelength.
[CBSE (F) 2013]
(2)
ANS. Infrared waves are produced by hot bodies and
molecules, so are referred to as heat waves.
(i)Em wave having short wavelength than infrared waves are
visible, UV, X-rays and ϒ-rays.
(ii) Em wave having longer wavelength than infrared waves are
3. What do electromagnetic waves consist of? Explain as what
factors does its velocity in vacuum depend?
(2)
ANS. Electromagnetic waves consist of mutually perpendicular
electric and magnetic field vectors. Its velocity in vacuum is
given by
C= (1/√&micro;0ε0) = same for electromagnetic waves.
In other words its velocity in vacuum does not depend on any
factor.
4. Give two characteristics of electromagnetic waves. Write the
expression for velocity of electromagnetic waves in terms of
permittivity and permeability of the medium.
(2)
ANS. Characteristics of electromagnetic waves:
(i)Electromagnetic waves travel in free space with speed of
light c= 3X 108m/s.
(ii) Electromagnetic waves are transverse in nature.
Expression for velocity of em waves in vacuum, c= (1/√&micro;0ε0)
5. (a)How are electromagnetic waves produced by oscillating
charges?
(b)State clearly how a microwave oven works to heat up a food
item containing water molecules.
6. (c)Why microwaves are found useful for the radar systems in
[CBSE (F) 2013]
(3)
ANS. (a) if a charge particle oscillates with some frequency,
produces an oscillating electric field in space, which produces
an oscillating magnetic field, which in turn is a source of
electric field, and so on. Thus oscillating electric fields and
magnetic fields regenerate each other, and an electromagnetic
wave propagates in the space.
(b) In microwave oven, the frequency of the microwaves is
selected to match the resonant frequency water molecules so
that energy from the waves get transferred efficiently to the
kinetic energy of the molecules. This kinetic energy raises the
temperature of any food containing water.
(c)Microwaves are short wave length radio waves with
frequency of order GHz. Due to short wave length, they have
high penetrating power with respect to atmosphere and less
diffraction in the atmospheric layers. So these waves are
RAY OPTICS AND OPTICAL INSTRUMENTS
QUESTIONS HAVE BEEN ASKED ONE TIME
SL.
QUESTIONS
M.M. YEAR
NO.
1
An object is held at the principal focus of a concave lens 1
2008
of focal length f. Where is the image formed?
2
A converging lens is kept co-axially in contact with a 1
2010
diverging lens – both the lenses being of equal focal
lengths. What is the focal length of the combination?
3
4
5
6
7
8
An astronomical telescope uses two lenses of power 10
D and 1 D. what is its magnifying power in normal
The image of a candle is formed by a convex lens on a
screen. The lower half of the lens is painted black to
make it completely opaque. Draw the ray diagram to
show the image formation. How will this will be different
from the one obtained when the lens is not painted
black?
A convex lens of refractive index 1.5 has a focal length of
18 cm in air. Calculate the change in its focal length
when it is immersed in water of refractive index 4/3.
The focal length of the objective and eye-lens of a
compound microscope are 2 cm,6.25cm respectively.
The distance between the lenses is 15 cm.(i)How far
from the objective lenses, will the object be kept, so as
to obtain the final image at the near point of the
eye?(ii)also calculate its magnifying power.
Define refractive index of a transparent medium.
A ray of light passes through a triangular prism. Plot a
graph showing the variation of the angle of deviation
with the angle of incidence.
An object AB is kept in front of a concave mirror as
shown in the figure.
A
B
C
F
1
2010
2
2006
2
2007
2
2008
2
2009
2
2012
(i)
Complete the ray diagram showing the
formation of the image.
How will the position and intensity of the
image be affected if the lower half of the
mirror`s reflecting surface is painted black?
(ii)
9
10
(a) Write the necessary conditions for the phenomenon
of total internal reflection to occur.
(b)Write the relation between the refractive index and
critical angle for a given pair of optical media.
When monochromatic light travels from rarer to denser
medium, explain the following, giving reasons :
2
2013
2
2013
(i)
11
12
Is the frequency of reflected and refracted
light same as the frequency of incident
light?
(ii)
Does the decrease in speed imply a
reduction in energy carried by light wave
A convex lens of focal length 25 cm is placed coaxially in 2
contact with a concave lens of focal length 20 cm.
Determine the power of the combination. Will the
system be converging or diverging in nature?
2
Two monochromatic rays of light are incident normally
on the face AB of an isosceles right-angled prism ABC.
The refractive indices of the glass prism for the two rays
‘1’ and ‘2’ are respectively 1.35 and 1.45. Trace the path
of these rays after entering through the prism.
A
1
2
B
C
2013
2014
13
14
15
16
17
18
19
2
2015
2
2015
2
2015
2
2015
2
2015
3
2006
Define the term ‘resolving power’ of an astronomical 3
2007
A biconvex lens of glass of refractive index 1.5 having
focal length of 20 cm is placed in a medium of refractive
index 1.65. Find its focal length. What should be the
value of refractive index of the medium in which the
lens should be placed so that it acts as a plane sheet of
glass?
A ray of light incident on an equilateral glass prism
propagates parallel to the base line of the prism inside
it. Find the angle of incidence of this ray. Given
refractive index of material of glass prism is √3.
You are given two converging lenses of focal lengths
1.25 cm and 5 cm to design a compound microscope. If
it is desired to have a magnification of 30, find out the
separation between the objective and the eyepiece.
A small telescope has an objective lens of focal length
150 cm and eyepiece of focal length 5 cm. What is the
magnifying power of the telescope for viewing distant
If this telescope is used to view a 100 m tall tower 3 km
away, what is the height of the image of the tower
formed by the objective lens?
Use mirror equation to show that an object placed
between f and 2f of a concave mirror produces a real
image beyond 2f.
A figure divided into squares, each of size 1 mm2 , is
being viewed at a distance of 9 cm through a magnifying
lens of focal length 10 cm, held close to the eye.
(a) Draw a ray diagram shoeing the formation of
the image.
(b) What is the magnification produced by the
lens? How much is the area of each square in
the virtual image?
(c) What is the angular magnification of the lens?
20
telescope. How does it get affected on
(i)
Increasing the aperture of the objective
lens?
(ii)
Increasing the wavelength of the light
used?
In the figure given below, light rays of blue, green, red 3
wavelength are incident on an isosceles right-angle
prism. Explain with reason. Which rays of light will be
transmitted through the face AC. The refractive index of
the prism for red, green, blue light are 1.39, 1.424, 1.476
respectively
2008
A
B
C
21
Write three distinct advantages of a reflecting type 3
telescope over a refracting type telescope.
A convex lens of focal length 10 cm is placed coaxially 5
cm away from a concave lens of focal length 10 cm. If an
object is placed 30 cm in front the convex lens, find the
position of the final image formed by the combined
system.
2009
22
With the help of a suitable diagram, derive the mirror 3
formula for a concave mirror.
Why must both the objectives and the eye-piece of a 3
compound microscope have short focal lengths?
The image obtained with a convex lens is erect and its
2009
23
2010
24
25
26
27
28
29
length is four times the length of the object. If the focal
length of the lens is 20 cm, calculate the object and
image distances.
A convex lens is used to obtain a magnified image of an 3
object on a screen 10m from the lens. If the
magnification is 19, find the focal length of the lens.
A convex lens lens made up of glass of refractive index
1.5 is dipped, in turn, in (i) a medium of refractive index
1.65, (ii) a medium of refractive index 1.33.
 Will it behave as a converging or a diverging
lens in the two cases?
 How will its focal length change in the two
media?
Use the mirror equation to show that
(a) An object placed between 𝘧 and 2𝘧 of a
concave mirror produces a real image beyond
2𝘧.
(b) A convex mirror always produces a virtual
image independent of the location of the
object.
(c) An object placed between the pole and focus
of a concave mirror produces a virtual and
enlarged image.
A compound microscope uses an objective lens of focal
length 4 cm an eyepiece lens of focal length 10 cm. an
object is placed at 6 cm from the objective lens.
Calculate the magnifying power of the compound
microscope. Also calculate the length of the microscope.
A giant refracting telescope at an observatory has an
objective lens of focal length 15 m. If an eyepiece lens of
focal length 1.0 cm is used, find the angular
magnification of the telescope.
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 3.42 x 106 m
and the radius of the lunar orbit is 3.8 x 108 m.
A converging lens has a focal length of 20 cm in air. It is
made of a material of refractive index 1.6. it is immersed
2010
3
2011
3
2011
3
2011
3
2011
3
2011
30
in a liquid of refractive index 1.3. Calculate its new focal
length.
You are given three lenses L1, L2 and L3 each of focal 3
length 15 cm. An object is kept at 20 cm in front of L1 , as
shown. The final image is formed at the focus ‘I’ of L3.
Find the separations between L1, L2 and L3.
L1
L2
2012
L3
I
20 cm
31
32
33
34
15 cm
Draw a ray diagram showing the image formation by a
compound microscope. Hence obtain expression for
total magnification when the image is formed at infinity.
A convex lens of focal length 20 cm is placed coaxially
with a convex mirror of radius of curvature 20 cm. The
two are kept at 15 cm from each other. A point object
lies 60 cm in front of the convex lens. Draw a ray
diagram to show the formation of the image by the
combination. Determine the nature and position of the
image formed.
A convex lens of focal length 20 cm is placed coaxially
with a concave mirror of focal length 10 cm at a distance
of 50 cm apart from each other. A beam of light coming
parallel to the principal axis is incident on the convex
lens. Find the position of the final image formed by this
combination. Draw the ray diagram showing the
formation of the image.
a) A ray of light is incident normally on the face AB
of a right angled glass prism of refractive index
aμg= 1.5 . The prism is partly immersed in a liquid
of unknown refractive index. Find the value of
refractive index of the liquid so that the ray grazes
along the face BC after refraction through the
3
2013
3
2014
3
2014
3
2015
prism.
b) Trace the path of the ray if it were incident
normally on the face AC.
A
60o
B
C
35
(i) A concave mirror produces real and magnified 5
image of an object kept in front of it. Draw a ray
diagram to show the image formation and use it derive
mirror equation.
(ii) A beam of light converges at a point P. Now a lens
is placed in the path of the convergent beam 12 cm
from P. At what point does the beam converge if the
lens is
(a) a convex lens of focal length 20 cm,
(b) a concave lens of focal length 16 cm?
2015
36
(a) A ray PQ of light is incident on the face AB of a glass 5
prism ABC and emerges out of the face AC.Trace the
path of ray. Show that
/i +/e =/A + /δ
Where δ and e denote the angle of deviation and angle
of emergence respectively.
2015
A
i
Q
P
B
C
Plot a graph showing the variation of angle of deviation
as a function of angle of incidence. State the condition
under which /δ is minimum.
(b) Find out the relation between the refractive index(μ)
of the glass and /A for the case when the angle of prism
(A) is equal to the angle of minimum deviation. Hence
obtain the value of the refractive index for angle of
prism A = 60o.
37
A point object O is kept in a medium of refractive index 5
n1 in front of a convex spherical surface of radius of
curvature R which separates the second medium of
refractive index n2 from the first one. Draw the ray
diagram showing the formation of image and deduce
the relationship between the object distance and the
image distance in terms of n1, n2 and R.
When the image formed above acts as virtual object for
a concave spherical surface separating the medium n2
from n1 (n2&gt; n1), draw this ray diagram and write the
similar relation. Hence obtain the expression for lens
maker’s formula.
2015
SL.
QUESTIONS
M.M. YEAR
NO.
1
For the same value of angle incidence, the angles of 1
[2012,
o
o
o
refractive in three media A, B and C are 15 , 25 and 35
2015]
respectively. In which medium would the velocity of
light be minimum?
2
Draw a labeled ray diagram of a compound microscope 2
and write an expression for its magnifying power.
[2008,
2010]
3
Draw a labeled ray diagram to show the formation of 2
image in an astronomical telescope for a distant object.
[2008,
2009]
4
Draw a neat labeled ray diagram of an astronomical
2
telescope in normal adjustment. Explain briefly its
working.
Draw a labeled ray diagram of an astronomical 5
telescope, in normal adjustment position and write the
expression for its magnifying power.
An astronomical telescope uses an objective lens of
focal length 15 m and eye lens of focal length 1cm. What
is the angular magnification of the telescope?
If this telescope is used to view moon, what is diameter
of the image of moon formed by objective lens?
(Diameter of moon =3.5X106 m, radius of lunar
orbit=3.8X108 m).
5
RAY OPTICS AND OPTICAL INSTRUMENTS
[2009,
[2008,
2011]
EXPECTED QUESTIONS FOR MLL
SL.
QUESTIONS
M.M.
NO.
1
An object AB is kept in front of a concave mirror as shown in 2
the figure.
A
B
(iii)
(iv)
2
C
Complete the ray diagram showing the formation of
the image.
How will the position and intensity of the image be
affected if the lower half of the mirror`s reflecting
surface is painted black?
When monochromatic light travels from rarer to denser
medium, explain the following, giving reasons :
(iii)
3
F
2
Is the frequency of reflected and refracted light
same as the frequency of incident light?
(iv) Does the decrease in speed imply a reduction in
energy carried by light wave
In the figure given below, light rays of blue, green, red 3
wavelength are incident on an isosceles right-angle prism.
Explain with reason. Which rays of light will be transmitted
through the face AC. The refractive index of the prism for red,
green, blue light are 1.39, 1.424, 1.476 respectively
A
4
5
6
7
8
A small telescope has an objective lens of focal length 150 cm
and eyepiece of focal length 5 cm. What is the magnifying
power of the telescope for viewing distant objects in normal
If this telescope is used to view a 100 m tall tower 3 km away,
what is the height of the image of the tower formed by the
objective lens?
Use the mirror equation to show that
(d) An object placed between 𝘧 and 2𝘧 of a concave
mirror produces a real image beyond 2𝘧.
(e) A convex mirror always produces a virtual image
independent of the location of the object.
(f) An object placed between the pole and focus of a
concave mirror produces a virtual and enlarged
image.
A convex lens of focal length 20 cm is placed coaxially with a
convex mirror of radius of curvature 20 cm. The two are kept
at 15 cm from each other. A point object lies 60 cm in front of
the convex lens. Draw a ray diagram to show the formation of
the image by the combination. Determine the nature and
position of the image formed.
A giant refracting telescope at an observatory has an objective
lens of focal length 15 m. If an eyepiece lens of focal length 1.0
cm is used, find the angular magnification of the telescope.
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 3.42 x 106 m and the radius
of the lunar orbit is 3.8 x 108 m.
Draw a neat labeled ray diagram of an astronomical telescope
in normal adjustment. Explain briefly its working.
Derive the expression for its magnifying power
Draw a labeled ray diagram of a compound microscope and
derive the expression for its magnifying power.
3
3
3
5
3
9
10
11
12
13
Define the term ‘resolving power’ of an astronomical
telescope. How does it get affected on
(iii) Increasing the aperture of the objective lens?
(iv) Increasing the wavelength of the light used?
Define the term ‘resolving power’ of a compound microscope.
telescope. Write its expression. How does it get affected on
(i)
Increasing the aperture of the objective lens?
(ii)
Increasing the focal length of the objective?
Derive lens maker’s formula
For refraction at a spherical surface derive the relation
𝑛2 𝑛1
𝑛2 − 𝑛1
−
=
𝑣
𝑢
𝑅
(a) A ray PQ of light is incident on the face AB of a glass prism
ABC and emerges out of the face AC.Trace the path of ray.
Show that
/i +/e =/A + /δ
Where δ and e denote the angle of deviation and angle of
emergence respectively.
A
i
Q
P
B
C
Plot a graph showing the variation of angle of deviation as a
function of angle of incidence. State the condition under which
/δ is minimum.
(b) Find out the relation between the refractive index(μ) of the
glass and /A for the case when the angle of prism (A) is equal
to the angle of minimum deviation. Hence obtain the value of
the refractive index for angle of prism A = 60o.
3
3
3
3
5
WAVE OPTICS
QUESTIONS HAVE BEEN ASKED ONE TIME
SL. QUESTION
NO.
1
What is the geometrical shape of the wavefront when a
plane wave passes through a convex lens?
2
How wouldthe angular separation of interference
fringes in Young’s double slit experiment change when
the distance between the slits and screen is doubled?
3
How does the fringe width, in Young’s double-slit
experiment, change when the distance of separation
between the slits and screen is doubled?
4
Compare and contrast the pattern which is seen with
two coherently, illuminated narrow slits in Young’s
experiment with that seen from coherently illuminated
single slit producing diffraction.
5
Define the term ‘linearly polarised light’.
When does the intensity of transmitted light become
maximum, when a Polaroid sheet is rotated between
two crossed Polaroids?
6
A beam of light consisting of two wavelengths, 800 nm
M.M. YEAR
1
2008
1
2009
1
2012
2
2006
2
2009
2
2012
7
8
9
10
11
and 600 nm is used to obtain the interference fringes in
a Young’s double slit experiment on a screen placed 1.4
m away. If the two slits are separated by 0.28 mm,
calculate the least distance from the central bright
maximum where the bright fringes of the two
wavelengths coincide.
Two wavelengths of sodium light 590 nm and 596 nm
are used, in turn, to study the diffraction taking place at
a single slit of aperture 2 x 10-4 m. The distance between
the slit and the screen is 1.5 m. Calculate the separation
between the positions of the first maxima of the
diffraction pattern obtained in the two cases.
State clearly how an unpolarised light gets linearly
polarised when passed through a Polaroid.
a) Unpolarised light of intensity Io is incident on
Polaroid P1 which is kept near another Polaroid P2
whose pass axis is parallel to that of P1. How will the
intensities I1 and I2, transmitted by the Polaroids P1 and
P2 respectively change on rotating P1 without disturbing
P2?
b) Write the relation between the intensities I1 and I2.
Use Huygens` principle to show how a plane wave front
propagates from a denser to rarer medium. Hence verify
snell`s law of refraction.
(a) When a tiny circular obstacle is placed in the
path of light from a distance source, a bright
spot is seen at the centre of the shadow of the
obstacle. Explain, why?
(b) How does the resolving power of a microscope
depend on (i) the wave length of the light used
and (ii) the medium between the object and
the objective lens?
In Young’s doubled slit experiment , monochromatic
light of wavelength 630 nm illuminates the pair of slits
and produces an interference pattern in which two
consecutive bright fringes are separated by 8.1 nm.
another source of monochromatic light produces the
interference pattern in which the two consecutive
2
2013
3
2015
3
2015
2
2015
3
2009
12
bright fringes are separated by 7.2 nm . Find the wave
length of light from the second source.
What is the effect on the interference fringes if the
monochromatic source is replaced by a source of white
light?
How does an unpolarised light get polarized when 3
passed through polaroid?
2010
Two polaroids are set in crossed positions. A third
polaroid is placed between the two making an angle 𝞱
with the pass axis of the first polaroid. Write the
expression of the intensity of light transmitted from the
second polaroid. In what orientations will the
transmitted intensity be (i) minimum and (ii) maximum?
13
14
(a) State Huygens` principle. Using this principle 3
explain how a diffraction pattern is obtained on a
screen due to a narrow slit on which a narrow beam
coming from a monochromatic source of light is
incident normally.
(b) Show that the angular width of the first diffraction
fringe is half of that of the central fringe.
(c) If a monochromatic source of light is replaced by
white light, what change would you observe in the
diffraction pattern?
3
(a) Using the phenomenon of polarisation, show how
transverse nature of light can be demonstrated.
2011
2014
(b)Two polaroids P1 and P2are placed with their pass
axes perpendicular to each other. Unpolarised light of
intensity I0is incident on P1 . A third polaroid P3is kept in
between P1and P2 such that its pass axis makes an angle
of 300 with that of P1. Determine the intensity of light
transmitted through P1,P2 and P3.
15
(a) The light from a clear blue portion of the sky shows a
rise and fall of intensity when viewed through a Polaroid
which is rotated. Describe, with the help of a suitable
diagram, the basic phenomenon/process which occurs
3
2015
to explain this observation.
(b) Show how light reflected from a transparent
medium gets polarized. Hence deduce Brewster’s law
16
(a) Define a wave front.
3
2015
(b) Using Huygens` principle, draw diagrams to show the
nature of the wave fronts when an incident plane wave
front gets
(i) reflected from a concave mirror,
(ii) refracted from a convex lens.
17 What are coherent sources? Why are coherent sources 5
required to produce interference of light? Give an
example of the interference of light in everyday life.
In Young’s double slit experiment, the two slits are 0.03
cm apart and the screen is placed at a distance of 1.5 m
away from the slits. The distance between the central
bright fringe and fourth bright fringe is 1 cm. Calculate
the wavelength of light used.
18 State the condition under which the phenomenon of 5
diffraction of light takes place. Derive the expression for
the width of the central maximum due to diffraction of
light at a single slit.
A slit if width ‘a’ is illuminated by a monochromatic light
of wavelength 700 nm at normal incidence. Calculate
the value of ‘a’ for position of
(i)
First minimum at an angle of diffraction of
30o.
(ii)
First maximum at an angle of diffraction of
30o.
19 (a) In a single slit diffraction experiment, a slit of which 5
‘d’ is illuminated
by red light of wavelength 650 nm.
For what value of ‘d’ will:
(i) The first minimum fall at an angle diffraction of
30o, and
(ii)The first maximum fall at an angle of diffraction 30o?
(b)Why does the intensity of the secondary maximum
2007
2007
2009
become less as compared to the central maximum?
20
In Young’s double slit experiment, the two slits 0.15 mm 5
apart are illuminated by monochromatic light of
wavelength 450 nm. The screen is 0.1 m away from the
slits.
(a) Find the distance of the second (i) bright
fringe, (ii) dark fringe from the central
maximum.
(b) How will the fringe pattern change if the
screen is moved away from the slits?
2010
21
State the importance of coherent sources in the 5
phenomenon of interference.
In Young’s double slit experiment to produce
interference pattern, obtain the conditions for
constructive and destructive interference. Hence
deduced the expression for the fringe width. How does
the fringe width get affected, if the entire experimental
apparatus of Young is immersed in water?
5
1. How does an unpolarised light incident on a
polaroid get polarised?
Describe briefly, with the help of the necessary
diagram, the polarisation of light by refection from a
transparent medium.
2. Two polaroids ‘A’ and ‘B’ are kept in crossed
position. How should a third Polaroid ‘C’ be placed
between them so that the intensity of polarised light
transmitted by Polaroid ‘B’ reduces to 1/8th of the
intensity of unpolarised light incident on A?
(a) In Young’s double slit experiment, describe briefly 5
how bright and dark fringes are obtained on the screen
kept in front of a double slit. Hence obtain the
expression for the fringe width.
(b) The ratio of the intensities at minima to the maxima
in the Young’s double slit experiment is 9:25. Find the
ratio of the widths of the two slits.
(a) Describe briefly how a diffraction pattern is 5
2011
22
23
24
2012
2014
2014
25
26
obtained on a screen due to a single narrow slit
illuminated by a mono-chromatic source of light. Hence
obtain the conditions for the angular width of
secondary minima.
(b) Two wave lengths of sodium light of 590 nm and
596 nm are used in turn to study the diffraction taking
place at a single slit of aperture 2x 10-6 m. The distance
between the slit and the screen is 1.5 m. Calculate the
separation between positions of first maxima of the
diffraction pattern obtained in the two cases.
Consider two coherent sources S1 and S2 producing 5
monochromatic waves to produce interference
pattern. Let the displacement of the wave produced by
S1 be given by Y1 = a cosωtand the displacement by S2
be Y2 = a cos (ωt+ϕ).
Find out the expression for the amplitude of the
resultant displacement at a point and show that
intensity at that point will be
I =4a2cos2ϕ/2.
Hence establish the condition for constructive and
destructive interference.
What is the effect on the interference fringes in
Young’s double slit experiment when (i) the width of
the slit is increased ; (ii) the monochromatic source of
light is replaced by a source of white light?
(a) Using Huygens` construction of secondary 5
wavelets explain how a diffraction pattern is obtained
on a screen due to a narrow slit on which a narrow
beam coming from a monochromatic source of light is
incident normally.
(b) Show that the angular width of the first diffraction
fringe is half of that of the central fringe.
1 𝜆
(c) Explain why the maxima at 𝜃 = [𝑛 + ]
2 𝑎
becomes weaker and weaker with increasing n.
2015
2015
SL.
NO
.
QUESTIONS HAVE BEEN ASKED THREE TIMES OR MORE
SL.
NO.
1
QUESTIONS HAVE BEEN ASKED TWO TIMES
2
In what way is diffraction from each slit related to the
interference pattern in a double slit experiment?
M.M. YEAR
M.M. YEAR
1
In Young’s double slit experiment, derive the condition 3
for
(i) Constructive interference and (ii) Destructive
interference at a point on the screen.
[2013,
2015]
[2011,
2012]
1
State Huygens’ principle. With the help of a suitable 3
diagram, prove Snell’s law of refraction using Huygens’
principle.
2
In Young’s double slit experiment, deduce the conditions 3
for
(i) constructive, and(ii) destructive interference at a
point on the screen. Draw a graph showing variation of
the resultant intensity in the interference pattern
against position ‘x’ on the screen.
[2006
,
2013,
2015]
[2006
,
2011,
2012]
[
2
0
0
6
,
2
0
1
1
,
2
0
1
2
]
WAVE OPTICS
EXPECTED QUESTIONS FOR MLL
SL.
QUESTIONS
M.M.
NO.
1
State Huygens’ principle. With the help of a suitable diagram, 3
prove Snell’s law of refraction using Huygens’ principle.
2
State Huygens’ principle. With the help of a suitable diagram, 3
prove the laws of reflection using Huygens’ principle.
3
In Young’s double slit experiment, deduce the conditions for
(ii) constructive, and(ii) destructive interference at a point on
the screen. Draw a graph showing variation of the resultant
intensity in the interference pattern against position ‘x’ on
the screen.
4
State the importance of coherent sources in the phenomenon
of interference.
In Young’s double slit experiment to produce interference
pattern, obtain the conditions for constructive and destructive
interference. Hence deduced the expression for the fringe
width. How does the fringe width get affected, if
(i)
the entire experimental apparatus of Young is immersed
in water?
(ii)
The wavelength of light is increased?
(iii) Separation between the two slits decreased?
(iv) Monochromatic light is replaced by white light?
(v)
Distance of the screen is increased?
(d) Using Huygens` construction of secondary wavelets 5
explain how a diffraction pattern is obtained on a screen due
to a narrow slit on which a narrow beam coming from a
monochromatic source of light is incident normally.
(e) Show that the angular width of the first diffraction fringe
is half of that of the central fringe.
5
(f) Explain why the maxima at 𝜃 = [𝑛 +
weaker and weaker with increasing n.
1 𝜆
]
2 𝑎
becomes
6
7
3. How does an unpolarised light incident on a polaroid get
polarised?
Describe briefly, with the help of the necessary diagram, the
polarisation of light by refection from a transparent medium.
4. Two polaroids ‘A’ and ‘B’ are kept in crossed position.
How should a third Polaroid ‘C’ be placed between them so
that the intensity of polarised light transmitted by Polaroid ‘B’
reduces to 1/8th of the intensity of unpolarised light incident
on A?
5
(a) The light from a clear blue portion of the sky shows a rise
and fall of intensity when viewed through a Polaroid which is
rotated. Describe, with the help of a suitable diagram, the basic
phenomenon/process which occurs to explain this observation.
(b) Show how light reflected from a transparent medium gets
polarized. Hence deduce Brewster’s law
8
(a) Define a wave front.
(b) Using Huygens` principle, draw diagrams to show the nature
of the wave fronts when an incident plane wave front gets
(i) reflected from a concave mirror,
(ii) refracted from a convex lens.
QUESTIONS THAT HAVE BEEN ASKED ONE TIME FROM CHAPTER -11 DUAL NATURE OF RADIATION AND
MATTER
1.An electron, an alpha-particle and a proton have the same kinetic energy. Which one of these particles
has the largest de-Broglie wave length? (1)(2007)
2.In an experiment on photoelectric effect, the following graphs were obtained between the
photoelectric current (I) and the anode potential (V). Name the characteristic of the incident
radiation that was kept constant in this experiment. (1) (2005)
3.Write the expression for the de Broglie wavelength associated with a charged particle having charge
‘q’ and mass ‘m’, when it is accelerated by a potential V.(1)(2013)
4. (a) Draw the energy level diagram showing the emission of β-particles followed
by γ-rays by a Co6027 nucleus.(b) Plot the distribution of kinetic energy of βparticles and state why the energy spectrum is continuous. (3) (2005)
5.Write Einstein’s photoelectric equation and point out any two characteristic properties of photons on
which this equation is based. Briefly explain the three observed features which can be explained by this
equation.(3)(2013)
6.Define the terms threshold frequency and stopping potential in relation to thephenomenon
of photoelectric effect. How is the photoelectric current affected on increasing the (i) frequency
(ii) intensity of the incident radiations and why? (3) (2006)
QUESTIONS THAT HAVE BEEN ASKED TWO TIMES FROM DUAL NATURE OF RADIATION AND MATTER.
1.A proton and an electron have same velocity. Which one has greater de-Broglie wavelength and
why?(1) (2007,2012)
2.The graph shows variation of stopping potential V0 versus frequency of incident radiation v for two
photosensitive metals A and B. Which of the two metals has higher threshold frequency and why?(1)
(2005,2014)
3.The graph shows the variation of stopping potential with frequency of incident radiation for two
photosensitive metals A and B. Which one of the two has higher value of work-function? Justify your
4.A proton and an electron have same kinetic energy. Which one has greater de-Broglie wavelength and
why?(1)(2007,2012)
5.Define the term ‘stopping potential’ in relation to photoelectric effect.(1) (2006,2011)
6.The stopping potential in an experiment on photoelectric effect is 1 .5 V. What is the maximum kinetic
energy of the photoelectrons emitted? (1) (2008, 2009)
7.The maximum kinetic energy of a photoelectron is 3eV.What is its stopping potential?(1)(2008,2009)
8.With what purpose was famous Davisson-Germer experiment with electrons performed.(1)
(2005,2006)
9.An α-particle and a proton are accelerated from rest by the same potential. Find the ratio of their deBroglie wavelengths.(2) (2005,2010)
10.Set up Einstein’s photoelectric equation using the photon picture of electromagnetic radiation.
Explain briefly how this equation accounts for all the observations in the photoelectric
effect.(3)(2013,2015)
11.Define the term ‘intensity of radiation’ in photon picture of light. Ultraviolet light of wavelength 2270
&Aring; from 100 W mercury source irradiates a photo cell made of a given metal. If the stopping potential is –
1&middot;3 V, estimate the work function of the metal. How would the photo cell respond to a high intensity (~
105 Wm–2 ) red light of wavelength 6300 &Aring; produced by a laser ? (3) (2013, 2014)
12.An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie
wavelength associated with the electrons. Taking other factors, such as numerical aperture etc. to be
same, how does the resolving power of an electron microscope compare with that of an optical
microscope which uses yellow light? (3) (2013, 2014)
13.In a plot of photoelectric current versus anode potential, how does (i) the saturation current vary
with anode potential for incident radiations of different frequencies but same intensity? (ii) the stopping
potential vary for incident radiations of different intensities but same frequency ? (iii) photo electric
each case.(3) (2005,2007)
QUESTIONS THAT HAVE BEEN ASKED THREE TIMES FROM DUAL NATURE OF RADIATION AND MATTER
1.Draw a plot showing the variation of photoelectric current with collector plate potential for
two different frequencies, v 1&gt;v 2 , of incident radiation having the same intensity. In which case
ADDITIONAL IMPORTANT QUESTIONS FRCM TEXT BOOK.
1. What is the de Broglie wavelength associated with (a) anelectron moving with a speed of
5.4&times;106 m/s, and (b) a ball of mass 150 g travelling at 30.0 m/s?
2.An electron, an α-particle, and a proton have the samekinetic energy. Which of these
particles has the shortest de Broglie wavelength?
3.What is the de Broglie wavelength associated with anelectron, accelerated through a
potential difference of 100 volts?
4.The work function of caesium metal is 2.14 eV. When light offrequency 6 &times;1014Hz is incident
on the metal surface, photoemission of electrons occurs. What is the(a) maximum kinetic
energy of the emitted electrons?
(b) Stopping potential, and
(c) Maximum speed of the emitted photoelectrons?
5.In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of
incident light is found to be 4.12 &times; 10–15 V s. Calculate the value of Planck’s constant.
6.The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for
incident radiation of wavelength 330 nm?
7.An electron and a photon each have a wavelength of 1.00 nm. Find (a) their momenta,
(b) the energy of the photon, and(c) the kinetic energy of electron.
8.Calculate the(a) momentum, and
(b) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
TOPICS TO BE COVERED IN M.L.L FROM;-
I. Dual nature of matter and radiation
(1) Definition of de-Broglie wave/ matter wave
(2) de-Broglie wavelength
ℎ
or
𝑚𝑣
a) General formula, λ=
, λ=
ℎ
𝑝
ℎ
√2𝑚𝐸
b)In terms of kinetic energy( E) , λ=
c) In term of potential difference (V),λ=
ℎ
√2𝑚𝑞𝑉
ℎ
=,
√2𝑚𝑒𝑉
d) For electron accelerating in potential difference (V), λ=
e) For a molecule of gas at absolute temperature (T), λ=
12.27
√𝑉
A0
λ=
ℎ
√3𝑚𝑘𝑇
3) Most of the questions are asked to compare wavelength
a) When velocity is same but mass is different (Hint :λ=
ℎ
𝑚𝑣
1
)
𝑚
or λα
ℎ
1
𝑣
b) When mass is same velocity is different (Hint: λ=𝑚𝑣 or λα
c) Kinetic energy is same but masses are different (Hint: λ=
ℎ
√2𝑚𝐸
d) Kinetic energy is different but masses are same (Hint: λ=
)
ℎ
√2𝑚𝐸
or λα
ℎ
E ) Same charge accelerating in different potential (Hint :λ=
√2𝑚𝑞𝑉
ℎ
f) Different charge accelerating in same potential (Hint: λ=
1
).
√𝑚
or λα
1
).
√𝐸
or λα
or λα
1
).
𝑚𝑞
√
12.27 0
A
√𝑉
or λα
√2𝑚𝑞𝑉
g) For an electron accelerating in potential difference V (Hint: λ=
ℎ
h) Molecule of same gas at different temperatures (Hint: λ=
1 0
A
√𝑉
1
√3𝑚𝑘𝑇
i) Molecule of different gases at same temperatures (Hint: λ=
1
).
√𝑉
or λα 𝑇).
ℎ
√3𝑚𝑘𝑇
√
or λα
1
).
√𝑚
3) Conclusion of Davission- Germer’s experiment (Hint: It proves dual nature of matter and
II. Photo -electric Effect
1) Definition of work function (∅), Threshold frequency (𝜐0 ) and Threshold wavelength (𝜆0 ).
2) Dependence of work function on Threshold frequency (𝜐0 ) and Threshold wavelength (𝜆0 ).(Hint : ∅ =
ℎ𝑐
ℎ𝜈0 = 𝜆
0
3) Graph between photo current and anode potential at constant intensity of
light.From that part
a) Relation between frequencies for different curves
b) Which one has high stopping potential and why (Hint : 𝑒𝑉0 = ℎ𝜈 − ℎ𝜈0 𝑖. 𝑒. , 𝑉0 𝛼 𝜈)
4) Graph between photocurrent and Anode potential at constant frequency.From
that part
a) Comparison between intensities i.e., which one is less or more or ratio.
b) Why is stopping potential same for two different intensities? (Hint: 𝑒𝑉0 = ℎ𝜈 − ℎ𝜈0 𝑖. 𝑒. , 𝑉0 𝛼 𝜈but
𝑉0 does not depend upon intensity).
c) Why saturation current are different at different intensities? (Hint: photocurrent α photoelectrons
and photoelectrons α intensity, it means photocurrent 𝛼 intensity).
5) Graph between kinetic energy and frequency and its three applications as
a) Calculation of threshold frequency.
b) Calculation of work function from intercept
c) Calculation of Plank’s constant by slope of graph.
QUESTIONS THAT HAVE BEEN ASKED ONE TIME FROM CHAPTER -12(ATOM)
1. Define ionisation energy. What is its value for a hydrogen
atom?(1)(2010)
2. Find the ratio of energies of photons produced due to transition of
an electron of hydrogen atom from its: (i) second permitted energy
level to the first level, and (ii) the highest permitted energy level to
the first permitted level.(1)(2010)
3. The ground state energy of hydrogen atom is – 13.6 eV. What are
the kinetic and potential energies of electron in this state?(2) (2010)
2. Using Bohr’s postulates of the atomic model, derive the expression
for radius of n th electron orbit. Hence obtain the expression for
1. Using Rutherford model of the atom, derive the expression for the
total energy of the electron in hydrogen atom. What is the
significance of total negative energy possessed by the electron?
(2)(2014)
1. Determine the value of the de Broglie wavelength associated with
the electron orbiting in the ground state of hydrogen atom(Given En
=–13&middot;6/n2) eV and Bohr radius ro = 0&middot;53 &Aring;). How will the de Broglie
wavelength change when it is in the first excited state ? (2)(2015)
1. Show that Bohr’s second postulate, ‘the electron revolves around
the nucleus only in certain fixed orbits without radiating energy' can
be explained on the basis of de-Broglie hypothesis of wave nature of
electron.(3)(2008)
1. Draw a schematic arrangement of the Geiger-Marsden experiment.
How did the scattering of a-particles of a thin foil of gold provide an
important way to determine an upper limit on the size of the nucleus?
Explain briefly.(3) (2009)
1. Using Bohr’s postulates, derive the expression for the frequency of
radiation emitted when electron in hydrogen atom undergoes
transition from higher energy state (quantum number ni ) to the lower
state, (nf ). When electron in hydrogen atom jumps from energy state
ni =4 to nf =3, 2,1, identify the spectral series to which the emission
lines belong.(5)(2013)
QUESTIONS THAT HAVE BEEN ASKED TWO TIMES FROM CHAPTER -12
ATOM
1. (a) Using de Broglie’s hypothesis, explain with the help of a suitable
diagram, Bohr’s second postulate of quantization of energy levels in a
hydrogen atom. (b) The ground state energy of hydrogen atom is –
13.6 eV. What are the kinetic and potential energies of the electron in
this state?(3) ( 2010,2011)
1. In a Geiger– Marsden experiment, calculate the distance of closest
approach to the nucleus of Z =75, when an a-particle of 5 MeV energy
impinges on it before it comes momentarily to rest and reverses its
direction. How will the distance of closest approach be affected when
the kinetic energy of the a-particle is doubled?(5) (2009,2012)
QUESTIONS THAT HAVE BEEN ASKED THREE TIMES FROM CHAPTER 12
2. The ground state energy of hydrogen atom is –13.6 eV. If an
electron makes a transition from an energy level – 0.85 eV to – 1.51
eV, calculate the wavelength of the spectral line emitted. To which
series of hydrogen spectrum does this wavelength belong?(5)
(2010,2011,2012)
2. Given the value of the ground state energy of hydrogen atom as –
13&middot;6 eV, find out its kinetic and potential energy in the ground and
second excited states.(3) (2010,2011,2012,2015).
TOPICS TO BE COVERED IN M.L.L
I. Atoms and Nuclei







Rutherford experiment and its limitation.
Bohr’s postulates derivation for radius of orbits and total energy.
Energy level diagram and region of spectral series.
Binding energy per nucleon versus Mass Number (A) graph.
Inference of graph(Fission and Fusion)
Graph showing the variation of Nuclear force versus separation between
Nucleons; specify the region in the graph showing attraction and repulsion
nature of Nuclear forces.
 Numericals based on Binding Energy and Binding Energy per Nucleon.
 Characteristics of Nuclear force, Graph showing the variation of potential
energy versus separation between Nucleons.
 Properties of 𝛼, 𝛽 𝑎𝑛𝑑 𝛾 rays.
 Derivation of 𝑁 = 𝑁0 𝑒 −𝜆𝑡 and graph showing the variation of N and t.
 Derivation𝑇1⁄ =
2




0.693
𝜆
.
Define Activity and it’s S.I. unit.
Numericals based on group displacement law and half life.
Conversion from Nickel to Cobalt emission of 𝛾 ray.
Components of Nuclear reactor(Moderator,Coolant,Control rod, Nuclear
fuel)
 Concept of Slow neutron.
QUESTIONS THAT HAVE BEEN ASKED ONE TIME FROM CHAPTER -13, NUCLEI
1. The radioactive isotope D decays according to the sequence
β-particle
α-particle
D------------------D1-------------------D2
If the mass number and atomic number of D2 are 176 and 71
respectively,
what is (i) the mass number (ii)atomic number of D? (1) (2007)
2.What is the nuclear radius of 125 Fe, if that of 27Al is 3.6 fermi? (1)
(2008)
3. Why is it found experimentally difficult to detect neutrinos in nuclear
β-decay? (1) (2014)
4. Draw a plot of potential energy of a pair of nucleons as a function of
their separation. What is the significance of negative potential energy
in the graph drawn ? (2) (2007)
5. A radioactive sample contains 2.2 mg of pure C which has half-life
period of 1224 seconds. Calculate
(i) the number of atoms present initially.
.(ii) the activity when 5 μg of the sample will be left. (3) (2005)
6. The half-life of
U against α-decay is 4.5 X 109 years. Calculate the
activity of 1 g sample of
U. (3)(2005)
7. Explain, with the help of a nuclear reaction in each of the following
cases, how theneutron to proton ratio changes during (i) alpha- decay
(ii) beta-decay? (3) (2006)
8. Why is the mass of a nucleus always less than the sum of the masses
of its constituents,neutrons and protons? If the total number of
neutrons and protons in a nuclear reaction is conserved, how then is
the energy absorbed or evolved in a reaction? Explain.(3) (2006)
9. Draw a graph showing the variation of binding energy per nucleon
with mass numberfor different nuclei. Explain, with the help of this
graph, the release of energy by the process of nuclear fusion.(3) (2006)
10. State the law of radioactive decay. If N0 is the number of radioactive
nuclei in the sample at some initial time, t 0 , find out the relation to
determine the number N present at a subsequent time. Draw a plot of
N as a function of time. (3) (2008)
11. Distinguish between isotopes and isobars. Give one example for
each of the species. A radioactive isotope has a half-life of 5 years. How
long will it take the activity to reduce to 3.125%? (3) (2008)
12. (a) Write symbolically the β - decay process of 15P32.
(b) Derive an expression for the average life of a radionuclide. Give its
relationship with the half- life.(3) (2010)
QUESTIONS THAT HAVE BEEN ASKED TWO TIMES FROM CHAPTER -13, NUCLEI
1. Two nuclei have mass numbers in the ratio 1 : 8. What is the ratio of
2. Two nuclei have mass numbers in the ratio 8 : 125. What is the ratio
of their nuclear radii? (1) (2008,2009)
3. Two nuclei have mass numbers in the ratio 27 : 125. What is the ratio
4. Define the activity of a given radioactive substance. Write its S.I.
unit.(1)(2009,2013)
5. (a) The mass of a nucleus in its ground state is always less than the
total mass of its constituents – neutrons and protons. Explain.(2)
(2006,2009)
6. Draw a plot of the binding energy per nucleon as a function of mass
number for a large number of nuclei. Explain the energy release in the
process of nuclear fission from the above plot. Write a typical nuclear
reaction in which a large amount of energy is released in the process of
nuclear fission.(3) (2006,2008)
7. Define the activity of a radionuclide. Write its S.I. units. Give a plot of
the activity of a radioactive species versus time. How long will a
radioactive isotope, whose half life is T years, take for its activity to
reduce to 1/8th of its initial value?(3) (2008,2009)
8. Draw a plot of potential energy of a pair of nucleons as a function of
their separations. Mark the regions where the nuclear force is (i)
attractive and (ii) repulsive. Write any two characteristic features of
nuclear forces.(3) (2007,2012)
QUESTIONS THAT HAVE BEEN ASKED THREE TIMES FROM CHAPTER -13, NUCLEI
1. Write any two characteristic properties of nuclear
force.(1)(2008,2009,2011)
2. Draw a plot showing the variation of binding energy per nucleon
versus the mass number A. Explain with the help of this plot the release
of energy in the processes of nuclear fission and
fusion.(3)(2006,2008,2009)
3. Draw a plot showing the variation of binding energy per nucleon
versus the mass number A. Explain with the help of this plot the release
of energy in the processes of nuclear fission and
fusion.(3)(2006,2008,2009)
4.Draw a plot of potential energy of a pair of nucleons as a function of
their separation. Write two important conclusions which you can draw
regarding the nature of nuclear forces.(3)(2007,2009,2010)
5.Draw a plot of the binding energy per nucleon as a function of mass
number for a large number of nuclei, 2≤ A ≤ 240. How do you explain
the constancy of binding energy per nucleon in the range 30 &lt; A&lt; 170
using the property that nuclear force is short-ranged? Nuclear forces
are short ranged, so every nucleon interacts with their neighbours only;
so binding energy per nucleon remains
constant.](3)(2006,2008,2009,2010)
6.1. Using the curve for the binding energy per nucleon as a function of
mass number A, state clearly how the release in energy in the processes
of nuclear fission and nuclear fusion can be explained.(3)
(2006,2008,2009,2010,2011)
2. (a) Draw the plot of binding energy per nucleon (BE/A) as a function
of mass number A. Write two important conclusions that can be drawn
regarding the nature of nuclear force. (b) Use this graph to explain the
release of energy in both the processes of nuclear fusion and fission. (c)
Write the basic nuclear process of neutron undergoing b–decay. Why is
the detection of neutrinos found very difficult?(5)
(2006,2008,2009,2010,2011,2013)
Text Book : PHYSICS PART II ( NCERT)
Chapter 14: Semiconductor Electronics: Materials, devices and Simple circuits
Frequency :
Sl.No.
1
( Asked three times or more )
Question
,where
is the current gain, RL is the load resistance and riis the input
resistance of the transistor. What is the significance of the negative sign in
the expression for the voltage gain?
2
Marks Year
2012(D)
Questions of
similar
in
2008,
2009
Draw a simple circuit of a CE transistor amplifier. Explain its working.
Show that the voltage gainAV, of the amplifier is given by
5
2006,
2013
Explain the function of base region of a transistor. Why is this region made
thin and lightly doped?
Draw a circuit diagram to study the input and output characteristics of n-pn transistor in a common emitter (CE) configuration. Show these
characteristics graphically. Explain how current amplification factor of the
transistor is calculated using output characteristics.
5
3
4
5
6
OR
(i) Draw a circuit diagram to study the input and output characteristics of
an n-p-n transistor in its common emitter configuration. Draw the typical
input and output characteristics.
(ii) Explain, with the help of a circuit diagram, the working of n-p-n
transistor as a common emitter amplifier.
(i) With the help of circuit diagrams distinguish between forward biasing
and reverse biasing of a p-n junction diode.
(ii) Draw V-I characteristics of a p-n junction diode in (a) forward bias, (b)
reverse bias.
(a) Why is zener diode fabricated by heavily doping both p-and n-sides of
the junction?
(b) Draw the circuit diagram of zener diode as a voltage regulator and
briefly explain its working.
OR
How is a zener diode fabricated so as to make it a special purpose diode?
Draw I-Vcharacteristics of zener diode and explain the significance of
breakdown voltage.
OR
Name the semiconductor device that can be used to regulate an unregulated
dc power supply.With the help of I-V characteristics of this device, explain
its working principle.
Draw a circuit diagram of a full-wave rectifier. Explain its working
principle.
Draw the input/output wave-forms indicating clearly the functions of the
two diodes used.
Explain, with the help of suitable diagram, the two important processes that
2009(D)
2009,
2010,
2014(D)
3
2008,
2009,2010(F)
2012,
2014(F)
3
2009(D)
2
2011(D)
3
3
2007,
2008,2012
2009,
2
2010,
2012,
2015
2010
2
2013(D)
3
2014(F)
2
2010(AI)
2
2008(D)
2
2010(AI)
Write the truth table for the logic circuit shown below and identify the logic
operation performed by this circuit.
2
2011(D)
In the circuit shown in the figure, identify the equivalent gate of the circuit
2
2013(AI)
occur during the formation of p-n junction. Hence define the terms :
depletion region and barrier potential.
7
8
Draw the circuit diagram of an illuminated photodiode in reverse bias.
How is photodiode used to measure light intensity?
OR
Explain, with the help of a circuit diagram, the working of a photo-diode.
Write briefly how it is used to detect the optical signals.
OR
(a) How is photodiode fabricated?
(b) Briefly explain its working. Draw its V–I characteristics for two
different intensities of illumination.
(i)
Identify the logic gates marked P and Q in the given logic
circuit.
(ii)
Write down the output at X for the inputs A = 0, B = 0 and A
=1, B =1.
OR
The given inputs A, B are fed to a 2-input NAND gate. Draw the output
wave form of the gate.
OR
(iii)
Identify the logic gates marked P and Q in the given logic
circuit.
(ii)
Write down the output at X for the inputs A = 0, B = 0
and A =1, B =1.
OR
and make its truth table.
OR
Write the truth table for the combination of the gates shown. Name the gates used.
2
2014(D)
2
2014(D)
OR
Identify the logic gates marked ‘P’ and ‘Q’ in the given circuit. Write the truth
table for the combination.
Frequency :
Sl.No.
1
2
3
4
5
6
Question
Marks Year
5
2010,
2013
Explain, with the help of a circuit diagram, the working of a p-n junction
diode as a half-wave rectifier.
The current in the forward bias is known to be more (~mA) than the current
in the reverse bias (~&micro;A). What is the reason, then, to operate the photodiode
in reverse bias?
Mention the important considerations required while fabricating a p-n
junction diode to be used as a Light Emitting Diode (LED). What should be
the order of band gap of an LED if it is required to emit light in the visible
range?
OR
How is a light emitting diode fabricated ? Briefly state its working. Write
any two important advantages of LEDs over the conventional incandescent
low power lamps.OR
Explain, with the help of a schematic diagram, the principle and working of a
Light Emitting Diode. What criterion is kept in mind while choosing the
semiconductor material for such a device ? Write any two advantages of
Light Emitting Diode over conventional incandescent lamps.
What are energy bands? How are these formed? Distinguish between a
conductor, an insulator and a semiconductor on the basis of energy band
diagram. OR
Draw energy band diagrams of an n-type and p-type semiconductor at
temperature T &gt; 0 K. Mark the donor and acceptor energy levels with their
energies.OR
Distinguish between a metal and an insulator on the basis of energy band
diagrams.
3
2006,
2014
2008 ,2012
What happens to the width of depletion layer of a p-n junction when it is (i) forward
biased, (ii) reverse biased?
2
(a) Draw the circuit diagram of a base-biased n-p-n transistor in C-E
configuration. Explain how this circuit is used to obtain the transfer
characteristic (Vo –Vi characteristics).
(b) The typical output characteristics (IC–VCE) of an n-p-n transistor in
C-E configuration is shown in the figure. Calculate (i) the output
resistance r0 and (ii) the current amplification factor 𝛽ac .
2
2
2013,
2015
3
2015(Bhubaneswar)
3
2007(D)
5
2006(AI)
2
2014(F)
2
2011(AI),2008(AI)
Frequency :
Sl.No.
Question
Marks Year
2006(D)
Draw a circuit diagram for use of NPN transistor as an amplifier in common 3
01
emitter configuration. The input resistance of a transistor is 1000Ω. On
changing its base current by 10&micro;A, the collector current increases by 2 mA.
If a load resistance of 5kΩ is used in the circuit, calculate:
(i) The
Current
gain
(ii) voltage gain of the
amplifier
(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 CEconfiguration amplifies a small sinusoidal input voltage.
Write the expression for the ac current gain.
5
2014(D)
Chapter : Communication Systems
Frequency:
Sl.
No.
Question
Marks
Year
01
What is meant by term ‘modulation’? Draw a block diagram of a simple modulator
for obtaining an AM signal.
2
2009,
2010(F)
2014(F)
02
Write briefly any two factors which demonstrate the need for modulating a signal.
Draw a suitable diagram to show amplitude modulation using a sinusoidal signal
as the modulating signal.
OR
Why are high frequency carrier waves used for transmission?
OR
Write two factors justifying the need of modulation for transmission of a signal.
3
2011(AI),
2012(D),
2013(D),
2
2009(D)
2
2009(AI)
03
04
05
Name the type of waves which are used for line of sight (LOS) communication.
What is the range of their frequencies?
A transmitting antenna at the top of a tower has a height of 20 m and the height of
the receiving antenna is 45 m. Calculate the maximum distance between them for
satisfactory communication in LOS mode.
(Radius of the Earth = 6.4 &times; 106 m)
OR
A transmitting antenna at the top of a tower has a height of 36 m and the height of
the receiving antenna is 49 m. What is the maximum distance between them, for
satisfactory communication in the LOS mode ? (Radius of earth = 6400 km).
OR
What does the term ‘LOS communication’ mean ? Name the types of waves that
are used for this communication. Give typical examples, with the help of a suitable
figure, of communication systems that use space wave mode propagation.
OR
(i) Why is communication using line of sight mode limited to a frequencies above
40 MHz?
(ii) A transmitting antenna at the top of a tower has a height 32 m and the height of
the receiving antenna is 50 m. What is the maximum distance between them for
satisfactory communication in line of sight mode?
Name the three different modes of propagation of electromagnetic waves. Explain,
using a proper diagram the mode of propagation used in the frequency range above
40 MHz.
OR
Name the three different modes of propagation of electromagnetic waves. Explain,
using a proper diagram the mode of propagation used in the frequency range from
a few MHz to 40 MHz.
Mention three ‘different modes of propagation used in communication system.
Explain with thehelp of a diagram how long distance communication can be
achieved by ionospheric reflection of
Explain briefly the following terms used in communication system:
(i) Transducer
(ii) Repeater
(iii) Amplification
OR
Mention the function of any two of the following used in communication system:
(i) Transducer (ii) Repeater
(iii) Transmitter (iv) Bandpass Filter
Frequency:
Sl.
No.
01
3
2013(AI)
2
2008(D)
3
2008(AI)
3
2010(D)
3
2012(D)
3
2012(D)
3
2012(AI)
3
2012(AI)
2014(AI)
2
2012(D)
Question
Distinguish between ‘sky wave’ and ‘space wave’ modes of propagation. Why is
the sky wave mode of propagation restricted to frequencies upto 40 MHz ?
OR
Describe briefly, by drawing suitable diagrams, the (i) sky wave and (ii) space
Marks
2
3
Year
2015(Bhu
ban
eswar)
2014(F)
02
03
04
wave modes of propagation. Mention the frequency range of the waves in these
modes of propagation.
Draw a block diagram of a simple modulator for obtaining amplitude modulated
signal.
A carrier wave of peak voltage 12 V is used to transmit a message signal. What
should be the peak voltage of the modulating signal in order to have a modulation
index of 75% ?
Which mode of propagation is used by short wave broadcast services having
frequencies range from a few MHz upto 30 MHz? Explain diagrammatically how
long distance communication can be achieved by this mode. Why is there an upper
limit to frequency of waves used in this mode?
In standard AM broadcast, what mode of propagation is used for transmitting a
signal? Why is
this mode of propagation limited to frequencies upto a few MHz?
In the given block diagram of a receiver, identify the boxes labelled as X and Y
and write their functions.
Frequency:
Sl.
No.
01
02
03
04
05
06
3
2015(Bhu
ban
eswar)
2010(AI)
3
2010(AI)
2011(AI)
2
2010(F)
2
2012(AI)
2013(D)
Question
(a) Define the terms (i) ‘amplitude modulation’ and (ii) ‘modulation index’.
(b) If a low frequency signal in the audio frequency range is to be transmitted over
long distances, explain briefly the need of translating this signal to high
frequencies before transmission.
What is meant by detection of a signal in a communication system? With the help
of a block diagram explain the detection of AM signal.
(i) Define modulation index.
(ii) Why is the amplitude of modulating signal kept less than the amplitude of
carrier wave?
Draw a schematic diagram showing the (i) ground wave (ii) sky wave and (iii)
space wave propagation modes for em waves.
Write the frequency range for each of the following:
(ii) Television
(iii) Satellite communication
Distinguish between ‘Analog and Digital signals’.
In the block diagram of a simple modulator for obtaining an AM signal, shown in the
figure, identify the boxes A and B. Write their functions.
Marks
Year
3
2009(F)
3
2009(F)
2
2011(D)
3
2011(D)
2
2
2012(D)
2013(AI)
07
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.
1
2014(D)
08
Why is frequency modulation perferred over amplitude modulation for
transmission
1
2007(D)
of music ?
```