Download Physics - New Horizon School

ASSIGNMEN OF PHYSICS Class 12
Chapter-1
ELECTRIC CHARGES and COULOMB’S LAW
Q.1.Two charged particles placed at a distance of 1cm. What can be the minimum force between them?
[2.3 x 10-24N]
Q.2.Two positive point charges 0.1m apart repel each other by a force of 18 N. If the sum of two charges
is 9 C, find the charges.
[5C, 4C]
Q.3.Two free point charges +4q and +q are at a distance of ‘a’. Where should a third point charge Q be
placed between them so that the entire system is in equilibrium? What will be the magnitude and sign
of Q?
[Q= - 4q/9 at 2a/3 from +4q]
-7
Q.4.Two particles, each having a mass of 5g and charge 10 C, stay in limiting equilibrium on a horizontal
table with a separation of 10cm between them. The coefficient of friction between each particle and the
table is same. Find the value of this coefficient.
[=0.18]
Q.5.Two similarly and equally charged identical metal spheres A and B repel each other with a force of 2
x 10-5 N. A third identical, uncharged sphere C is touched with A and then placed at the mid point
between A and B. What is the net electric force on C?
[2 x 10-5 N towards A]
Q.6.Charges q1 = +1.5 mC, q2 = +0.2 mC and q3 = – 0.5mC are placed at points A, B and C respectively of a
triangle right angled at B. If AC = 1.2m and BC = 0.6m, calculate magnitude of resultant force on q2.
[3125 N]
Q.7.Two opposite corners of a square carry Q charge each and the other two opposite corners of the
same square carry q charge each. If the resultant force on q is 0, how are Q and q related?[q = - 2 2 Q]
Q.8.A pith ball A of mass 9 x 10-5 kg carries a charge of 5 C. What must be the magnitude and sign of
the charge on another ball B held 2 cm above ball A, such that A remains suspended stationary above
the ground?
[7.84x10-12C]
-7
Q.9.Two point charges of 6.5 x 10 C each are separated by a distance of 50 cm. What is the force of
repulsion between them if (i) they are placed in air?(ii) they are placed in water?
[1.521 N, 0.019 N]
Q.10.Four point charges 2C, –5 C, 2 C and –5 C are placed at the corners A, B, C and D respectively,
of a square ABCD of side 10 cm. Find the force on a charge of 1 C placed at the centre O of the square.
Q.11.A polythene piece rubbed with wool is found to have a negative charge of 3 x 10-7 C. (i) Find the
number of electron transferred and state whether electrons are transferred from wool to polythene or
otherwise. (ii) Is there a transfer of mass?
[2x1012 from wool to polythene, yes]
Q.12.Calculate the force between 2 alpha particles separated by a distance of 1.6 x 10-15 m.
[360 N repulsive]
-6
Q.13.Three equal charges, 2.0 x 10 C each, are held fixed at the three corners of an equilateral triangle
of side 5 cm. find the coulomb force experienced by one of the charges due to the rest two.
[14.4 N at 30 with a side of ]
[ELECTRIC FIELD]
Q.1.A test charge 2nC, placed at origin, experiences a force of 8 x 10-4 N in the positive y – direction. Find
electric field at origin. What would be the force on charge – 4nC placed at origin?
[4x105 N/C, -16x10-4 N]
Q.2.Find the magnitude of electric field which can balance a deuteron of mass 3.2 x 10-27 kg.
[19.6x10-8N/C]
Q.3.A charged particle of mass 1.0 g is suspended through a silk thread of length 40 cm in a horizontal
electric field of 4.0 x 104 N/C. If the particle stays at a distance of 24 cm from the vertical line passing
through its point of suspension, find the charge on the particle.
[1.8 x 10-7 C]
Q.4.ABC is an equilateral triangle of side 5 cm. Two charges  50/3 x 10-3 C are placed at A & B
respectively. Calculate magnitude and direction of field at C.
[6 x 104 N/C, ║ to AB]
Q.5.Two charges  10 C are held at 5 mm apart. Calculate their dipole moment. What is the electric
field intensity at a distance of 15 cm from the centre of dipole on its axial line?
[5 x 10-8 Cm, 2.7 x 105 N/C]
Q.6.An electric dipole of length 2 cm is placed with its axis making an angle of 30 with a uniform electric
field of 105 N/C. If it experiences a torque of 10 3 Nm, calculate (i) magnitude of charges on dipole (ii)
potential energy of dipole.
[1.732 x 10-2C, - 4.64 J]
Q.7.In a certain region of space, electric field is along the positive z – direction whose magnitude
increases uniformly at the rate of 105 N/Cm along the positive z – direction. What are the forces and
torque experienced by dipole of dipole moment 10-7 Cm in the negative z – direction?
[-10-2 N, 0]
Q.8.An oil drop of 12 excess electron is held stationary under a constant electric field 2.55 x 104 V/m in
Milikan’s oil drop experiment. The density of oil is 1.26 g/cm3. Find the radius of the drop.(Take g = 9.81
m/s2)
[9.81 x 10-4mm]
3
Q.9.A copper ball of density 8.6 g/cm , 1 cm in diameter is immersed in oil of density 0.8 g/cm3. If the
ball remains suspended in oil in an electric field of 36000 N/C acting in upward direction, what is the
charge on the ball?
[1.22C]
Q.10.Calculate the electric field intensity at point P ( 0, 3, -1 ) due to a charge of – 2 C placed at point
[  2 3  10 ( ˆi  ˆj  k̂) N/C]
3
A ( -3, 0, -4 ).
9
Q.11.A charge 4 x 10-9 C is distributed uniformly on a ring of radius 0.3 m. Find field intensity at a point
on the axis of ring at 0.4 m from centre and also at the centre.
[115.2N/C, 0]
-19
-19
Q.12.Two point charges of +3 x 10 C and + 12 x 10 C are separated by a distance of 2.5 m. Find the
point on the line joining them at which the electric field intensity is zero.
[5/6 m from 3 x 10-19 C]
Q.13.Two point charges 3C and – 3 C are located 20 cm apart in vacuum at point A and B respectively.
(i) What is the electric field at the mid point O of the line AB. (ii) If a negative charge of magnitude
1.5 x 10-9 C is placed at this point, what is the force experienced by this charge?
[5.4x106 N/C along OB,8.1x10-3N along OA]
Q.14.Two charges  10C are placed 5 mm apart. Find the electric field at (i) point P on the axis of the
dipole 15 cm away from its center O on the side of positive charge, (ii) point Q, 15 cm away from O on a
line passing through O and normal to axis of the dipole.
[2.7x105N/C along BP,1.33x105N/C along BA]
15. Two dipoles, made from charges ±q and ±Q, respectively, have equal dipolemoments. Give
the (i) ratio between the ‘separations’ of these two pairs ofcharges (ii) angle between the dipole
axis of these two dipoles.
[ELECTRIC FLUX and Gauss’s theorem]
Q.9.(a) A rectangular frame of wire 25 cm x 15 cm is placed in uniform electric field of 2 x 104 N/C such
that the plane of frame is normal to the field. Find electric flux linked with the frame. (b) Find electric
flux if this frame is converted into a square.
[750 Vm; 800Vm]
Q.10.(a) A box encloses an electric dipole of charges  5C and length 10 cm. What is the total electric
flux through the box? (b) If the number of electric field lines from a closed surface are 1000, calculate
the charge enclosed by the surface.
[0; 8.85 x 10-9 C]
Q.11The electric field is ( 5 î  4 ˆj  4 k̂ )  10
over an area of ( 2 î  ˆj )  10 -2 m2.
5
N/C in a region. Calculate electric flux due to this field
[6000 Nm2/C]
1. If S1 and S2 are two hollow spheres enclosing charges Q and 2Q respectively as shown in
the figure
(i) What is the ratio of the electric flux through S1 and S2?
(ii) How will the flux through the sphere S1 change, if a medium of dielectric constant 5
is filled in the space inside S1.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
CHAPTER-2
BASED ON POTENTIAL &POTENTIAL ENERGY
Q.1The electric field and potential at a point due to a point charge are 30 N/C and 15 J/C respectively.
Find the distance of point from the charge and the magnitude of the charge.
[0.5 m, 0.833 x 10-3 C]
Q.2.If 100 J of work is done to move a charge of 4 C from a place of potential – 10 volt to another place
where potential is V volt, find the value of V.
[15 V]
Q.3.An electric field of 20 N/C exists along x – axis. Calculate potential difference VB – VA where
coordinates of pints A and B are ( 4m, 2m ) and ( 0, 0 ) respectively.
[80 V]
Q.4.A point charge 10-8 C is situated at origin. Find the potential difference between points A( 4, 4, 2 )
and B(1, 2, 2 ).
[-15 V]
Q.5.Two positive point charges 10 C and 5 C are 1 m apart. Find the work done in bringing them 0.5 m
apart.
[0.45 J]
Q.6.Two electrons, each with a velocity of 106 m/s are released towards each other. What will be the
closest distance of approach between them?
[2.56 x 10-10 m]
Q.7.Two identical particles, each of mass 10 g and carrying charge 2 x 10-4 C, are kept at a distance of 10
cm and released. What would be the speed of particles, when separation becomes infinitely large?
[600 m/s]
Q.8.An infinite thin plane sheet of charge density 10-8 C/m2 is held in air. How far apart are two
equipotential surfaces, whose potential difference is 5 V? [8.85 x 10-3 m]
9. What is the amount of work done in moving a 200nC charge between two points 5 cm apart on
an equipotential surface?
10. How much work must be done to charge a 24 μF capacitor, when the potential difference
between the plates is 500 V?
11. What is the work done in moving a charge of 100μC through a distance of 1cm along the
equatorial line of dipole?
12. Four charges are placed at the vertices of a square of side d as shown in the figure.(i) Find the
work done to put together this arrangement. (ii) A charge q0is brought to the center E of the
square, the four charges being held fixed at its corners. How much extra work is needed to do
this?
13. A charge of 24μC is given to a hollow sphere of radius 0.2m. Find the potential
(i) at the surface of the sphere, and
(ii) at a distance of 0.1 m from the centre of the sphere.
(iii)at the centre
BASED ON CAPACITANCE
CAPACITANCE
Q.1A spherical conductor has a surface charge density of 0.07 C/m2. When charge is increased by 4.4 C
the density changes by 0.084 C/m2. Find the radius & initial charge.
[2.04 m; 11/3 C]
Q.2If 64 small mercury drops each charged to 220 V coalesce, what is the potential of the bigger drop?
[3520V]
Q.3.At what distance should the plates of area 0.2 m x 0.1 m of air capacitor be placed in order to have a
capacitance as a spherical conductor of radius 0.5 m?
[3.18 mm]
Q.4.A parallel plat air capacitor having plate area 6 x 10-3 m2 and plate separation 3 mm is connected to
100 V supply. Calculate charge on each plate. Explain what would happen when a 3 mm thick mica sheet
( = 6 ) is inserted between plates (a) while voltage supply remains connected (b) after supply is
connected?
[1.77 x 10-9 C; 1.06 x 10-9 C; V=16.7 V]
20F
Q.5.Calculate the value of C for the given figure.if equivalent capacitance between
20F
P and Q is 30 F.
[60F]
P
C
20F
Q.6
What is the capacitance of arrangement of 4 plates each of area A at a distance d in air for the
given figure?
d
d
A
(i) A
B
(ii)
d
d
[20A/d]
B
d
[30A/d]
Q.7.A parallel plate capacitor is filled with two dielectrics as shown in the figures.
Calculate the capacity of each.
(i)
(ii)
[
0A
2d
(  1   2 )]
[
Q.8.Calculate the equivalent capacitance
between A and B for the following figure:
2  0 A  1 2
]
d ( 1   2 )
A
B
5F
10F
15F
30F
[15F]
4 F
Q.9.Take potential of B to be zero in the given figure.
(a) Find potential at C & D.
(b) If a capacitor is placed between C and D,
what charge will appear on this capacitor?
[50/3 V;50/3 V; 0]
8 F
C
A
B
3 F
50 V
D
6 F
Q.10.A 4 F capacitor is charged by 200 V supply. It is disconnected from supply and connected to
another uncharged 2 F capacitor. How much electric energy is lost by first capacitor?
[2.67 x 10-2 J]
Q.11.A capacitor of 20 F and charged to 500 V is connected in parallel with another 10 F capacitor
charged to 200 V. Find the common potential.
[400 V]
Q.12.Two capacitors of capacitances C1 = 3 F and C2 = 6 F arranged in series are connected in parallel
with 3rd capacitor C3 = 4 F. The arrangement is then connected to 6 V battery. Find total energy stored
in the arrangement.
[1.08 x 10-4 J]
5
Q.13.In Van de graf generator, spherical shell of metal has 15 x 10 V potential. The dielectric strength of
surrounding gas is 5 x 107 V/m. Find the minimum radius of the shell.
[0.3 m]
14. What is the equivalent capacity of the network given below?
15. The given graph shows that variation of charge q versus potential difference V for two
capacitors C1 and C2. The two capacitors have same plate separation but the plate area of C2
is double than that of C1. Which of the lines in the graph correspond to C1 and C2 and why?
16. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected and from the supply and is
connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process
17. Keeping the voltage of the charging source constant, what will be the percentage change in the
energy stored in a parallel plate capacitor if the separation between its plates were to be decreased by
10%.
18. A slab of material of dielectric constant has the same area as the plates of a parallel plate capacitor
but has a thickness 3d / 4, where d is the separation of the plates. How is the capacitance changed when
the slab is inserted between the plates?
19. A parallel plate capacitor with air between the plates has a capacitance of 8µF. What will be the
capacitance if the distance between the plates is doubled and the space between them is filled with a
substance of dielectric constant K=6?
20. The capacitors C1, and C2, having plates of area A each, are connected in series, as
shown. Compare the capacitance of this combination with the capacitor C3,again having plates
of area A each, but ‘made up’ as shown in the figure.
21. Two parallel plate capacitor X and Y have same area of plates and same separation between them.
Xhas air between the plates whereas Y has a dielectric of constant k=4
(i) Calculate capacitance of each capacitor if equivalent capacitance is4 μF.
(ii) Calculate potential difference between the plates of X and Y.
(iii) What is the ratio of electrostatic energy stored in X and Y.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
CHAPTER-3
Based on electric current , driftvelocity and current density:
1.(a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional
area 1.0 × 10–7 m2 carrying a current of 1.5 A. Assume that each copper atom contributes
roughly one conduction electron. The density of copper is 9.0 × 103 kg/m3, and its atomic mass
is 63.5 u. (b) Compare the drift speed obtained above with, (i) thermal speeds of copper atoms at
ordinary temperatures, (ii) speed of propagation of electric field along the conductor which
causes the drift motion.
2. (a) The electron drift speed is estimated to be only a few mm s–1 for currents in the range of
a few amperes? How then is current established almost the instant a circuit is closed?
(b) The electron drift arises due to the force experienced by electrons in the electric field inside
the conductor. But force should cause acceleration. Why then do the electrons acquire a steady
average drift speed?
(c) If the electron drift speed is so small, and the electron’s charge is small, how can we still
obtain large amounts of current in a conductor?
(d) 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?
(e) Are the paths of electrons straight lines between successive collisions (with the positive ions
of the metal) in the (i) absence of electric field, (ii) presence of electric field?
3. Plot of current I versus time interval is given below. Find the charge that
flows through the wire during this time period.
4. In a hydrogen atom, an electron moves in an orbit of radius 4.8 x 10-11m
with a speed of 2.5 x 106 m/s. Find the equivalent current.
5. A beam of electrons moving at a speed of 106 m/s along a line produces a current of 1.6 10–6 A. What is
the number of electrons in the 1 metre of the beam [Ans: 107]
6. In the Bohr’s model of hydrogen atom, the electrons moves around the nucleus in a circular orbit of
a radius 5 10–11 metre. It’s time period is 1.5 10–16 sec. What is the current associated [Ans: 1.07 x10 -3
A]
7. An electron is moving in a circular path of radius 5.1 10–11 m at a frequency of 6.8 1015
revolution/sec.What is the equivalent current ?[ Ans: 1.1 10–3 A]
8. A conducting wire of cross-sectional area 1 cm2 has 3 1023 m–3 charge carriers. If wire carries a
current of 24 mA, What is the drift speed of the carrier ? [Ans: 5 x 10-3m/s
9. A current flows in a wire of circular cross-section with the free electrons travelling with a mean drift
velocity v. If an equal current flows in a wire of twice the radius What Is the new mean drift velocity ?
[Ans:v/4 ]
10. Two wires A and B of the same material, having radii in the ratio 1 : 2 and carry currents in the ratio 4
: 1. The ratio of drift speeds of electrons in A and B is[Ans: 1 : 16]
Based on R=(l/A)
1. A wire of length L and resistance R is streched to get the radius of cross-section halfed. What is new
Resistance
[Ans: 16R]
2 The specific resistance of manganin is 50 10–8 m. The resistance of a manganin cube having length
50 cm is
[Ans.106]
3. A rod of certain metal is 1 m long and 0.6 cm in diameter. It’s resistance is 3 10–3. A disc of the
same metal is 1 mm thick and 2 cm in diameter, what is the resistance between it’s circular faces.
A rod of certain metal is 1 m long and 0.6 cm in diameter. It’s resistance is 3 10–3. A disc of the
same metal is 1 mm thick and 2 cm in diameter, what is the resistance between it’s circular faces.
[Ans. 2.7 x10-7]
4.Find the resistivity of the conductor in which a current density of 2.5Am -2 is found to exit , when electric
field is 15V/m .
[ ans.6]
5.Calculate the electrical conductivity of the material of a conductor of length 3m , cross-sectional area
0.02mm2 having a resistance of 2.
[Ans. 75 x106-1 m-1]
5. A wire of 100 ohm resistance is stretched to thrice to its original length. What will be the new resistance
and resistivity ?
[ Ans. 900 resistivity- no change]
6. A cylindrical wire is stretched to increase its length by 10%. Calculate the percentage change change in
resistance.
7.Two wire A and B of equal mass is of same metal are taken. The diameter of A is half of the diameter of B
. If the resistance of A is 24. Calculate the resistance of B.
[Ans. 1.5 ]
8. Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires
is lighter? Hence explain why aluminium wires are preferred for overhead power cables. Al = 2.63 × 10–8 m,Cu = 1.72 ×
10 m, Relative density of Al = 2.7, of Cu = 8.9
[Ans. Aluminum ]
9.Resistivity of the material of conductor of varies along its length as =o(1+x). Express the resistance of the conductor,
if its length and cross-sectional area are L and A .
[Ans. R=o/A[L+ ½ L2]
10,.two wires are of same metals having their length ratio is 1:2 and diameter ratio 2:3 are connected in series and
connected with the battery. Calculate the ratio of the P.d across the wires [Ans.9/8]
11. A wire of length L and resistance R is streched to get the radius of cross-section halfed. What is new
Resistance.
[Ans. 16R]
Bades on the temp. resistance relation
1.An electric toaster uses nichrome for its heating element. When a negligibly small current
passes through it, its resistance at room temperature (27.0 °C) is found to be 75.3 . When the
toaster is connected to a 230 V supply, the current settles, after a few seconds, to a steady
value of 2.68 A. What is the steady temperature of the nichrome element? The temperature
coefficient of resistance of nichrome averaged over the temperature range involved, is 1.70 ×
10–4 °C–1.
[Ans.847oC]
2. The resistance of the platinum wire of a platinum resistance thermometer at the ice point is
5
t is5.23 . When the thermometer is inserted in a hot bath, the
resistance of the platinum wire is 5.795 . Calculate the temperature of the bath. [Ans. 345.65
°C]
3. At room temperature (27.0 °C) the resistance of a heating element is 100 . What is the
temperature of the element if the resistance is found to be 117 , given that the temperature
coefficient of the material of the resistor is 1.70 × 10-4 °C-1.
[Ans.1027oC]
4. A silver wire has a resistance of 2.1 at 27.5 °C, and a resistance of 2.7 at 100 °C.
Determine the temperature coefficient of resistivity of silver. [Ans.0.0039 oC-1]
5.At what temp. resistance becomes doubled its resistance at 0oC.
[Ans. 273oC]
6.An heating element initially gives 3.2A current when it is connected with 230V supply . After
few sec. it reach to steady state 2.8A. What is the steady temp. ?room temperature is 27 oc
Temp. co-efficient is 1.70 x10-4 oC-1
[Ans.8670.30 oC]
7.A metal wire of diameter and length are 2mm and 100m has resistance is 0.5475 at 20oC
and 0.805 at 150oC Find the value of (1) temp. co-efficient of the resistance (ii) Resistance at 0
oC and (iii) resistivity at 00C and 20oC.
8.The resistance of a wire at 20 0C is 20  and at 500oC is 60. At which temperature
resistance will be 25
[Ans.80oC]
The temperature co-efficient of resistance of a wire is 0.0012oC-1. At 300 K. It’s resistance is 1. At what
temp. the resistance of the wire will be 2
[Ans. 1127 k]
Based on resistance and their grouping:
What is the resistance of a carbon resistance which has bands of colours brown, black and
brown.[Ans.100 ]
2.Find the value of the carbon resistance of given color band [9.1 k]
Find the equivalent resistance between A and B of following network
1.
‘
2..(a) Calculate the equivalent resistance between A & B in the figures (i) to (iv).
(b) Calculate resistance between A & B and A & C in figure (v)
(i)
(ii)
(iii)
(iv)
(v)
[9.6Ω, 40/3 Ω, 7.5 Ω, 2 Ω, 27.5 Ω, 30 Ω]
Q.3.Calculate the current
shown by ammeter A. [3.6 A]
Q.4.An infinite ladder net work of resistance is constructed with 1 Ω and
2 Ω resistances, as shown in Figure . The 6 V battery between A and
has negligible internal resistance.
(i) Show that the effective resistance between A and B is 2Ω.
(ii) What is the current that passes through the 2 Ω resistance nearest to the battery?
B
[1.5 A
BASED ON THE EMF AND INTERNAL RESISTANCE OF THE CELL:
1.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 2.2 V. When the terminals of the cell are also connected
to a resistance of 5 Ω as shown in the circuit, the voltmeter reading drops to 1.8 V. Find the internal
resistance of the cell.
[Ans. 1.1]
2. A cell of emf (ε) and internal resistance (r) is connected across a variable external resistance (R) Plot graphs
to show variation of (i) ε with R, and (ii) terminal potential difference of the cell (V) with R.
3. 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? [Ans. 2V ]
4. The following graph shows the variation of terminal potential difference V, across a combination of
three cells in series to a resistor, versus the current I
(i) Calculate the emf of each cell.
(ii) For what current i will the power dissipation of the circuit be maximum?
[emf=2Vand current =1A ]
5. Four cells of identical emf E, internal resistance r, are connected in series to a
variable resistor. The graph shows the variation of terminal voltage of the
combination with the current output. (i) What is the emf of each cell used? (ii)
Calculate the internal resistance of each cell. (iii) For what current from the cells,
does maximum power dissipation occur in the circuit?
[ Ans. Emf=1.4V internal resistance=0.7 current =1A]
6. A 20 V battery of internal resistance 1 Ω is connected to three coils of 12 Ω, 6 Ω and 4 Ω
in parallel, a resistor of 5 Ω and a reversed battery (emf 8 V and internal resistance 2 Ω) as
shown in fig. Calculate (i) the current in the circuit (ii) the current in resistor of 12 Ω coil, and
(iii) potential difference across each battery
[(i) 1.2A (ii)0.2A (iii) 18.8V and 10.4V]
7.The storage battery of a car has an emf of 2V and internal resistance is 0.4 , What is the
maximum current that can be drawn from the battery?
[Ans. 30A]
8. The emfof a battery is 0.6. A wire of resistance 2.4 is connected to the two ends of the
battery. Calculte (i) the current in the circuit and (ii) terminal p.d across the cell.
[Ans.2A and 4.8V]
BASED ON KIRRCHOFF”S RULE
1.Use these rules to write the expressions for the currents I1, I2 and I3 in the circuit diagram shown
[Ans. I1 = 2/13A ,I2= 7/13A , I3=9/13A]
2. State Kirchhoff’s rules. Apply Kirchhoff’s rules to the loops ACBPA and ACBQA Calculate values of I 1, I2 and
I3 in the network. [I1= -84/37A,I2=106/37A ,I3=22/37A]
3. Apply these rules to the loops PRSP and PRQP to write the expressions for the currents I1, I2 and I3 in the given
circuit.
[Ans. I1 = 39/860A,16/860A ,55/860A]
4. For the circuit shown here, calculate the potential difference between the points B and D.
[Ans. V = + 0.154 V.]
5. In the following circuit E1 = 4V, R1 = 2
E2 = 6V, R2 = 2and R3 = 4. What is the value of i1 [Ans. 1.8A]
6. In the circuit shown in figure, find the current through the branch BD
[Ans.5A]
7. The figure shows a network of currents. The magnitude of current is shown here.
8. Consider the circuit shown in the figure. Calculate the value of I3
[Ans.23A]
[ans.-5/6 A]
BASED ON METER BRIDGE:
1. In a metre bridge, the null point is found at a distance of 40 cm from A.
If a resistance of 12 Ω is connected in
parallel with S, the null point occurs at 50.0 cm from A. Determine the
values of R and S. [S=6 R=4]
2. In a metre bridge, the null point is found at a distance of 60.0 cm from
A. If now a resistance of 5 Ω is
connected in series with S, the null point occurs at 50 cm.
Determine the values of R and S.[ans. S = 10 Ω R=15 Ω]
3. In metre bridge, the null point is found at a distance of l2 cm from A. If now a resistance
of X is connected in
parallel with S the null point occurs at l2cm. Obtain a formula for X in terms of l1, l2 and
𝑆(100−𝑙1 )𝑙2
[Ans. [𝑋 =
]
100[𝑙1 −𝑙2 ]
4. The figure shows experimental set up of a metre bridge. When the two unknown
resistances X and Y are inserted, the null point D is obtained 40 cm from
the end A. When a resistance of 10 Ω is connected in series with X, the null point shifts by 10 cm. Find
the position of the null point when the 10 Ω resistance is
instead connected in series with resistance ‘Y’.
Determine the values of the resistances X and Y.
[Ans.X=20 , Y=30 l=33.33cm]
5The given figure shows the experimental set up of a meter bridge. The null point is
found to be 60 cm away from the end A with X and Y in position as shown.
When a resistance of 15 Ω is connected in series with Y, the null point is
found to shift by 10 cm towards the end A of the wire. Find the position
of null point if a resistance of 30 Ω were connected in parallel with Y.[Ans. 75 cm. ]
potentiometer:
1. Two students X and Y perform an experiment on potentiometer separately using
the circuit diagram shown here. Keeping other things unchanged
(i) X increases the value of resistance R
(ii) Y decreases the value of resistance S in the set up.
How would these changes affect the position of the null point in each case and why?
2. For the potentiometer circuit shown in the given figure, points X and Y represent the two terminals of an
unknown emf ε. A student observed that when the jockey is moved from the end A to the end B of the
potentiometer wire, the direction of the deflection in the galvanometer remains in the same direction.
What may be the two possible faults in the circuit that could result in this observations?
If the galvanometer deflection at the end B is (i) more, (ii) less, than that at the
end A which of the two faults, listed above, would be there in the circuit?
Give reasons in support of your answer in each case.
3. 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 light resistance R, used in the secondary circuit affect the balance point? Justify your
Answer
[Ans: 2.0 V.]
4. A 10 m long wire of uniform cross-section and 20 Ω resistance is used in a potentiometer. The wire is
connected in series with a battery of 5 V along with an external resistance of 480 Ω. If an unknown emf E
is balanced at 6.0 m length of the wire calculate.
[1]the potential gradient of the potentiometer wire, (ii) the value of unknown emf
[0.02V/m, 0.12V]
5.Potentiometer wire PQ of 1 m length is connected to a standard cell E 1. Another cell E2 of emf 1.02 V is
connected as shown in the circuit diagram with a resistance ‘r’ and switch S. With switch S open, null
position is obtained at a distance of 51 cm from P. Calculate (i) potential gradient of
the potentiometer wire and (ii) emf of the cell E1. (iii) When switch S is closed,
will null point towards P or towards O? Give reason for your answer.
[Ans: 0.02 V cm-1 , 2 V]
6. AB is one metre long uniform wire of 10 Ω resistance.
The other data are shown in the circuit diagram given: Calculate
(i) Potential gradient along AB, and
(ii) length AO of the wire, when the galvanometer
shows no deflection.
[(i) 0.8 V/m (ii) AO = 37.5 cm
 NCERT QUESTIONS EXAMPLE AND EXERCISE
CHAPTER-4
1.A current of 5 A is flowing from south to north in a straight wire. Find the magnetic field due to a 1cm
piece of wire at a point 1m north east from the piece of wire.
2.The electrons in a hydrogen atom circles around the proton with a speed of 2.8 x 106 ms-1 in an orbit of
radius 5.3 x 10-11m. Calculate (a) the equivalent current (b) magnetic field produced at the proton.
3.A circular coil of 120turns has a radius of 18cm and carries a current of 3.0 A. What is the magnitude of
the magnetic field (i) at the centre of the coil (ii) at a point on the axis of the coil at a distance from the
centre equal to the radius of the coil?
4.Two wires A and B have the same length equal to 44cm. and carry a current of 10A each. Wire A is
bent into a circle and wire B is bent into a square.(a) Which wire produces a greater magnetic field at the
centre. (b) Obtain the magnitudes of the field at the centers of the two wires.
5.The wire shown in fig carries a current of 10A Determine the magnitude of magnetic field induction at
the centre O. Given the radius of the bent coil is 3cm.
6.A toroid has a core of inner radius 20cm and outer radius 22cm around which 4200turns of a wire are
wound. If the current in wire is 10A, What is the magnetic field (a inside the core of toroid (b) outside
the toroid (c) in the empty space surrounded by toroid?
7.A charge Q is spread uniformly over an insulted ring of radius R.What is the magnetic moment of the
ring if it is rotated with an angular velocity with respect to normal axis?
8.Show that the magnetic field along the axis of a current carrying coil of radius r at a distance x from
the centre of the coil is smaller by the fractions 3 x2 /2 r2 than the field at the centre of the coil carrying
current.
9.How will the magnetic field intensity at the centre of the circular coil carrying current change , if the
current through the coil is doubled and the radius of the coil is halved?
10.An element dl=dx (where dx= 1cm) is alced at the origin and carries a large current l=10A.What is the
magnetic field on the y-axis at a distance of 0.5m.
11.Two insulting wires of infinite length are lying mutually at right angles to each other as shown.
Currents of 2A and 1.5 A respectively are flowing in them. Find the magnetic field induction at P.
12.A straight wire of /2metre, is bent into a circular shape. If the wire were to carry a current of
5A,Calculate the magnetic field, due to it, before bending, at a point distance 0.01 times the radius of
the circle formed from it. Also calculate the magnetic field, at the centre of the circular loop for the
same value of current.
13.The electron of hydrogen atom moves along a circular path of radius 0.5 x 10-10 m (i) with the speed
of 4.0x 106 ms-1.(ii) calculate the magnetic filed produced at the centre of the circular path.
14.A circular coil of 5turns has a radius of 2.0m and carries a current of 2A.What is the magnetic field at
a point on the axis of the coil at a distance equal to radius of the coil from the centre.
15.An electric current of I ampere is flowing in a long conductor CG as shown in fig. Find the magnitude
and direction of magnetic induction at the centre O of circular part.
16.A solenoid of length 0.20m, having 120 turns carries a current of 2.5 A.Find the magnetic field:
(i)In the interior of the solenoid ,
(ii)At one end of the solenoid
17.A long wire carries a current of 20A along the directed axis of a long solenoid. The field due to a
solenoid is 4mT.Find the resultant field at a point 3mm from the solenoid axis.
18. In the fig given are shown two parallel current carrying wires I and II .Find the magnitudes and
directions of the magnetic field induction at the points P, Q and R in the plane of paper.
19.Fig shows a rectangular current carrying loop placed 2cm away from the long, straight, current
carrying conductor. What is the direction and magnitude of the net force acting on the loop?
20. A circular coil of 100 turns, radius 10 cm carries a current of 5 A. It is suspended vertically in a
uniform horizontal magnetic field of 0.5 T, the field lines making an angle of 600 with lane of coil.
Calculate the magnitude of the torque that must be applied on it to prevent it from the turning.
21. The current sensitivity of a moving coil galvanometer increases by 20%when its resistance is
increased by factor 2.Calculate by what factor the voltage sensitivity changes.
22. When a galvanometer having 30divisions scale and 100 resistance is connected is series to the
battery of e.m.f. 3 volt through a resistance of 200 ,shows full scale deflection. Find the figure of merit
of the galvanometer in microampere.
23.A galvanometer having 30divisiosns has a current sensitivity of 20µ A division. It has a resistance of
25. How will you convert it into an ammeter upto 1ampere? How will you convert this ammeter into a
voltmeter u to 1volt?
24. A charged particle is moving in a magnetic field of magnitude 10-2 weber/m2 with a velocity of
107ms1 in a circular path of radius 0.6cm.Find out the specific charge of the particle.
25.An infinite long straight conductor XY is carrying a current of 10A.An electron is moving with a speed
of 105 ms-1 parallel to the conductor in air from point A and B, shown in fig.
26.A proton and an -particle enter a uniform magnetic field at right angles to it with same velocity.
Find the ratio of time period of revolution -particle and the proton.
27.A proton with the kinetic energy 8eV is moving in a uniform magnetic field. Find the kinetic energy of
a deuteron moving in the same path in the same magnetic field.
28.A cyclotrons oscillator frequency is 10MHz.What should be the operating magnetic field for
accelerating -particles? If the radius of the dees is 60cm,What is the kinetic energy of -particle beam
produced by the accelerator ? Given a charge of an electron is 1.6 x10-19C,mass of each nucleon is 1.67 x
10-27kg.
29.A conductor of length 20cm is placed (i) parallel (ii)perpendicular (iii)inclined at an angle 300, to a
uniform magnetic field of 2T .If the charge of 10C Passes through it in 5 s,find the force experienced by
the conductor.
30.A long horizontal rigidly supported wire carries a current of 100A.Directly above it and parallel to it is
a fine wire that carries a current of 200A and weighs0.05N/m. How far above the lower wire should the
fine wire be kept two support it by magnetic repulsion.
31.To increase the current sensitivity of a moving coil galvanometer by 50% its resistance is increased so
that the new resistance becomes twice its initial resistance. By what factor does its voltage sensitivity
change.
32. A resistance of 900 is connected in series with a galvanometer of resistance 100.A potential
difference of 1 volt produces 100 division deflection in the galvanometer. Find the figure of merit
galvanometer.
33.An ammeter gives full scale deflection with the current of 1 ampere.Find the ratio of the resistance of
ammeter to shunt resistance used.
34.An ammeter of resistance 0.2 and range 10m A is to be used to read potential difference upto 1V
.What is to be done.
35. A galvanometer has a sensitivity of 60division/ampere. When a shunt is used its sensitivity becomes
10division/ampere. What is the value of shunt used if the resistance of galvanometer is 20.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
CHAPTER-5
1.Two circular coils, one of radius r and the other of radius R are placed coaxially with their centres
coinciding. For R >> r, obtain an expression for the mutual inductance of the arrangement.
2.A circular coil of radius 8 cm and 20 turns rotates about its vertical diameter with an angular speed of
50 s-1 in a uniform horizontal magnetic field of magnitude 3 x 10-2 T. Find the maximum and average
value of the emf induced in the c
3 A 0.5 long metal rod PQ completes the circuit as shown in the figure. The area of the circuit is perpendicular to
the magnetic field of flux density 0.15 T. If the resistance of the total circuit is 3W, calculate the force needed to
move the rod in the direction as indicate with a constant speed of 2 ms-1.
4. How is the mutual inductance of a pair of coils affected when:
(i) separation between the coils is increased?
(ii) the number of turns of each coil is increased ?
(iii) a thin iron sheet is placed between the two coils, other factors remaining the same? Explain your
answer in each case
5. The figure shows two identical rectangular loops (1) and (2), placed on a table along with a straight
long current carrying conductor between them.
(i) What will be the directions of the induced currents in the loops when they are pulled away from the
conductor with same velocity v ?
(ii) Will the e.m.f. induced in the two loops be equal? Justify your answer.
6. A metallic rod of length l is rotated at an angular speed
, normal to a uniform magnetic field B. Derive
expressions for the (i) emf induced in the rod (ii) heat dissipation, if the resistance of the rod is R.
7.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 the two coils. Justify your
answer.
8. Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’ as shown in the
figure. Predict the polarity of capacitor.
9.coil Q is connected to low voltage bulb B and placed near another coil P as shown in the figure. Give reasons to
explain the following observations:
(a) The bulb ‘B’ lights.
(b) The bulb gets dimmer if the coil Q is moved towards left.
10.Predict the direction of induced current in metal rings 1 and 2 when current I in the wire is steadily
decreasing?
11. Define self- inductance of a coil. Show that magnetic energy required to build up the current I in a
coil of self inductance L is given by ½ LI2
12.An air-cored solenoid with length 30cm, area of cross-section 25cm2 and number of turns 500 carries
a current of 2.5A. The current is suddenly switched off in a brief time of 10-3s. How much is the average
back emf induced across the ends of the open switch in the circuit?
13.A train is moving with speed 72km/hr on a rail track separated by distance 120cm and vertical component of
earth’s magnetic field is 3x10-4T. Find – a) the average emf induced across the width of the train
b) if the resistance between the rails is 100ohm.Find the retarding force on the train due to the magnetic field.
14. A 0.2m long copper wire with its length parallel to x-axis moves along Y-axis with a constant velocity of 4m/sec
in a region where a magnetic field of induction 0.05 Wb/m2 is present, which is pointing parallel to Z-axis. If the
two ends of the wire are connected to a resistance of 2ohm,calculate.
a) the emf developed between the two ends of the copper wire.
b) The current in the circuit.
c) The force required to keep the wire moving.
d) The rate at which work is done by the applied force.
e) The rate at which heat is produced.
15.A magnetic field perpendicular to the plane of a rectangular frame of wire is concentrated about O. If the field
decreases, will there be any emf induced in the loop 1?In the loop 2?
16. An inductor coil of inductance 1H stores 32 J of magnetic field energy and dissipates energy as heat at the rate
of 640w. Find the resistance if this is joined across a battery.
17. When the current changes from +2A to –2A in 0.05 second, an emf of 8 volt is induced in a coil. Find the coefficient of self induction of the coil.
18. A train is moving in the North-South direction with a speed of 72 km/hr. Find the amount of emf generated
between two wheels, if the length of axle be 2m. Assume that the vertical component of earth’s field is 8x10 5wbm-2
19.A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 rad/sec. If the
horizontal component of earth’s magnetic field is 0.2 x 10-4 T, then find the emf developed between the two ends
of the conductor.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
CHAPTER-6 ALTERNATING CURRENT
1. Given below are two electric circuits A and B.Calculate the ratio of power factor of the circuit B to the power
factor of circuit A.
[√𝟐]
2.Distinguish between the terms ‘effective value’ and ‘peak value’ of an alternating current. An alternating current
from a source is represented by
I = 10 sin (314 t)
Write the corresponding values of
(i) its ‘effective value’
(ii)frequency of the source [7.07A,50hz]
3.In a series LCR circuit, the voltages across an inductor, a capacitor and a resistor are 30 V, 30 V and 60 V
respectively. What is the phase difference between the applied voltage and the current in the circuit? [zero]
4. Calculate the current drawn by the primary of a transformer which steps down 200V to 20V to operate a device
of resistance 20
. Assume the efficiency of the transformer to be 80%[0.125A]
5. An a.c. voltage of 100V, 50 Hz is connected across a 20ohm resistor and 2 mH inductor in series. Calculate (i)
impedence in the circuit, (ii) rms current in the circuit. [20Ω, 5A]
6. The given circuit diagram shows a series LCR circuit connected to a variable frequency 230 V source:
(a) Determine the source frequency which drives the circuit in resonance.
(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
(c) Determine the rms potential drops across the three elements of the circuit.
(d) How do you explain the observation that the algebraic sum of the voltages across the three elements obtained
in (c) is greater than the supplied voltage?[ 50rad/sec, 8.1A1437.5V230V]
7. The primary coil of an ideal step-up transformer has 100 turns and the transformation ratio is also 100. The
input voltage and the power are 220 V and 1100 W respectively. Calculate:
(i) number of turns in the secondary
(ii) the current in the primary
(iii) voltage across the secondary
(iv) the current in the secondary
(v) power in the secondary [10000, 5A,2200V,0.05A, 1100W]
8.An alternating voltage of frequency f is applied across a series LCR circuit. Let fr be the resonance frequency for
the circuit. Will the current in the circuit lag, lead or remain in phase with the applied voltage when (i) f > fr, (ii) f <
fr? Explain your answer in each case.
9.When an inductor L and a resistor R in series are connected across a 12V, 50 Hz supply, a current of 0.5 A flows in
the circuit. The current differs in phase from applied voltage by
/3 radian. Calculate the value of R.[ans. 12
ohms. ]
10. In a series R - C circuit, R=30 , C=0.25µF and V=100V and w= 10000radian second. Find the current in the
circuit and calculate the voltage across the resistor and the capacitor.
Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.[.249A, 7.5V ,
100V,voltage across R and C are not in phase and they cannot be added in a normal manner. ]
11.What is the power dissipated in an a.c. circuit in which voltage and current are given by,
12. A bulb and a capacitor are connected in series to an a.c. source of variable frequency. How will the brightness
of the bulb change on increasing the frequency of the a.c. source? Give reason.
13.Explain the phenomenon of resonance in a series L-C-R circuit. Hence obtain the resonant frequency and Qfactor with L=3H, C=27 F and R=7.4ohm.[ 111.1rad/sec , 45]
14. Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied
voltage of the a.c. source? Justify your answer.
15. The power factor of an a.c circuit is 0.5. What will be the phase difference between voltage and current in this
circuit?
16. An inductor 200 mH, a capacitor of 500 F and a resistor of 10 are connected in series to a 100 V, variable
frequency a.c. source. Calculate the
(i) frequency at which the power factor of the circuit is unity
(ii) current amplitude at this frequency
(iii) Q-factor.
17.An inductor of unknown value, a capacitor of 100 F and a resistor of 10 are connected in series to a 200 V, 50
Hz a.c. source. It is found that the power factor of the circuit is unity. Calculate the inductance of the inductor and
the current amplitude.An inductor of unknown value, a capacitor of 100 F and a resistor of 10 are connected in
series to a 200 V, 50 Hz a.c. source. It is found that the power factor of the circuit is unity. Calculate the inductance
of the inductor and the current amplitude.[101.4mH , 20A ]
18.An a.c. source generating a voltage V is connected to a capacitor of capacitance to a capacitor C. Find the
expression for the current, I, flowing through it. Plot a graph of v and I versus w to show that the current is /2
ahead of the voltage.
A resistor of 200 and a capacitor of 15.0 µF are connected in series to a 220 V, 50 Hz a.c. source. Calculate the
current in the circuit and the rms voltage across the resistor and the capacitor. Is the algebraic sum of these
voltages more than the source voltage? If yes, resolve the paradox.
19.An electric lamp having coil of negligible
inductance connected in series with a capacitor and an AC source is glowing with certain brightness. How does the
brightness of the lamp change on reducing the (i) capacitance, and (ii) the frequency? Justify your answer.
20.(a) Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase.
(b) A horizontal straight wire of length L extending from east to west is falling with speed v at right angles to the
horizontal component of Earth’s magnetic field B. (i) Write the expression for the instantaneous value of the e.m.f.
induced in the wire. (ii) What is the direction of the e.m.f.? (iii) Which end of the wire is at the higher potential?
21. Derive an expression for the impedance of a series LCR circuit connected to an AC supply of variable frequency.
Plot a graph showing variation of current with the frequency of the applied voltage.
Explain briefly how the phenomenon of resonance in the circuit can be used in the tuning mechanism of a radio or
a TV set
22. An alternating voltage given by V = 280 sin 50t is connected across a pure resistor of 40. Find
(i) the frequency of the source.
(ii) the rms current through the resistor
23.An alternating voltage given by V = 70 sin 100t is connected across a pure resistor of 25. Find
(i) the frequency of the source.
(ii) the rms current through the resistor
24. figure shows a series LCR circuit with L = 10.0 H, C =50µF, R = 5o connected to a variable frequency 240 V
source, calculate
(i) the angular frequency of the source which drives the circuit at resonance,
(ii) the current at the resonating frequency,
(iii) the rms potential drop across the inductor at resonance.
25. a.c. source of frequency 50 Hz is connected to a 50 mH inductor and a bulb. The bulb glows with some
brightness. Calculate the capacitance of the capacitor to be connected in series with the circuit so that the bulb
glows with maximum brightness
26.Obtain the resonant frequency and Q-factor of a series L-C-R circuit with L = 3H, C = 27μF and R = 7.4.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
Electromagnetic Waves
Q.1.A charged particle oscillates about its mean equilibrium position with a frequency of 109 Hz. What is
the frequency of the electromagnetic waves produced by the oscillator?
[109 Hz ]
Q.2.A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the
directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its
wavelength?[ E and B in x-y plane and are mutually perpendicular, 10 m. ]
Q.3.The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510
nT. What is the amplitude of the electric field part of the wave?
[ 153 N/C ]
Q.4.Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8
rad/m) y + (5.4 × 106 rad/s)t]} î .(a) What is the direction of propagation?(b) What is the wavelength λ?
(c) What is the frequency ν?
(d) What is the amplitude of the magnetic field part of the wave? (e) Write an expression for the
magnetic field part ofthe wave.
[  ˆj ],[ 3.5 m ],[ 86 MHz ],[ 100 nT ],[ B = {(100 nT) cos[(1.8 rad/m)y + (5.4 × 106 rad/s)t]}k ]
Q.5.In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 1010
Hz and amplitude 48 V m–1. (a) What is the wavelength of the wave? (b) What is the amplitude of the
oscillating magnetic field? (c) Show that the average energy density of the E field equals the average
energy density of the B field.
[ 1.5 x 10-2 m , 1.6 x 10-7 T
Q.6.Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its
frequency is ν = 50.0 MHz. (a) Determine, B0 , ω,
k , and λ.
(b) Find expressions for E and B.[ Ans. (a)
400 nT, 3.14 × 108 rad/s, 1.05 rad/m, 6.00 m. (b) E = { (120 N/C) sin[(1.05 rad/m)]x – (3.14 × 108 rad/s)t]}
ˆj B = { (400 nT) sin[(1.05 rad/m)]x – (3.14 × 108 rad/s)t ]}k]
Q.7.Relative electric permittivity of a medium is 8 and relative magnetic permeability is close to
unity.What is the speed of em waves in the medium?
Q.8.What do you mean by electromagnetic waves? State its 4 properties. Show its propagation by a
diagram.
Q.9.(i) What oscillates in electromagnetic waves? (ii) Which component E or B of an em wave is
responsible for visible effect?
Q.10.Name the different radiations present in the electromagnetic spectrum in the increasing order of
their frequency.
Q.11.Write two uses of each of the following radiations: (i) radio waves (ii) ultraviolet (iii) gamma rays.
Q.12.Name the electromagnetic radiations used for viewing objects through the haze and fog.
Q.13.How are X – rays produced? Write one use of X – rays.
Q.14.While doing arc welding, a welder wears special glass goggles or face mask. Why?
Q.15.Name the radiations which are known as ‘Heat Waves’. Why are they called so?
Q.16.Name the radiations used in radars. Why are these used in radars? What are their frequency
range?
Q.17.Name the electromagnetic radiation whose wavelength is in the range of (i) 10-2 m. (ii) above 10-12
m.
Q.18.How does an oscillating charge at certain frequency produce electromagnetic waves?
Q.19.State the condition under which a microwave oven heats up a food item containing water
molecules most efficiently.
Q.20Electromagnetic radiations with wavelength (i) 1 are used to kill germs in water purifiers. (ii) 2
are used in TV
communication systems. (iii) 3 play an important role in maintaining the earth’s warmth. Name the
part of electromagnetic spectrum to which these radiations belong. Arrange these wavelengths in
decreasing order of their magnitude.
Q.21Write Maxwell’s Equations for electromagnetic waves. Mention quantities for which the symbols
used in it stands?

NCERT QUESTIONS EXAMPLE AND EXERCISE
RAY OPTICS ASSIGNMENT
1.A convex lens of refractive index 1.5 has a focal length of 18cm in air. Calculate the change in its focal
length when it is immersed in water of refractive index 4/3.
2.Define the term ‘resolving power’ of an astronomical telescope. How does it get affected on
(i) Increasing the aperture of the objective lens?
(ii)Increasing the wavelength of the light used?. Justify your answer in each case.
3.Define resolving power of compound microscope. How does the resolving power of a compound
microscope change when
(i) Refractive index of the medium between the object and objective lens increases?
(ii) Wavelength of the radiation used is increased?
4.A double convex lens of glass of refractive index 1.6 has its both surfaces of equal radii of curvature of
30cm each. An object of height 5 cm is placed at a distance of 12.5 cm from the lens. Calculate the size
of the image formed.
5. A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in:
(i) medium A of refractive index 1.65
(ii) medium B of refractive index 1.33
Explain, giving reasons, whether it will behave as a converging lens or a diverging lens in each of these
two media.
6.A beam of light converges to a point P. A lens is placed in the path of the convergent beam 12cm
from P. At what point does the beam converge if the lens is
(a) a convex lens of focal length 20cm,
(b) a concave lens of focal length 16 cm?
Do the required calculations.
7. A compound microscope with an objective of 2.0 cm focal length and an eye-piece of 4.0 cm focal
length, has a tube length of 40 cm. Calculate the magnifying power of the microscope, if the final image
is formed at the near point of the eye.
8.An astronomical telescope, in normal adjustment position has magnifying power 5. The distance
between the objective and the eye-piece is 120 cm. Calculate the focal lengths of the objective and of
the eye-piece.
9.The magnifying power of an astronomical telescope in the normal adjustment position is 100. The
distance between the objective and the eye-piece is 101 cm. Calculate the focal lengths of the objective
and of the eye-piece.[100cm , 1cm]
10.A compound microscope with an objective of 1.0 cm focal length and an eye-piece of 2.0 cm focal
length has a tube length of 20 cm. Calculate the magnifying power of the microscope, if the final image
is formed at the near point of the eye.[250]
11.A double convex lens made of glass of refractive index 1.5 has its both surfaces of equal radii of
curvature of 20 cm each. An object of 5 cm height is placed at a distance of 10 cm from the lens. Find
the position, nature and size of the image.[20cm , 10cm]
12.Three rays of light - red (R), green (C) and blue (B) - are incident on the face AB of a right-angled
prism ABC. The refractive indices of the material of the prism for red, green and blue wavelengths are
1.39, 1.44 and 1.47 respectively. Trace the path of the rays through the prism.
13. A figure divided into squares, each of size 1 mm2 is being viewed at a distance of 9cm through a
magnifying lens of local length 10cm, held close to the eye.
(i) Draw a ray diagram showing the formation of the image.
(ii) What is the magnification produced by the lens? How much is the area of each square in the virtual
image?
(iii) What is the angular magnification of the lens?
14.A converging lens of refractive index 1.5 is kept in a liquid medium having same refractive index.
What would the focal length of the lens in this medium?
15.Three light rays red (R), green (G) and blue (B) are incident on a right angled prism ‘abc’ at face ‘ab’.
The refractive indices of the material of the prism for red, green and blue wavelengths are 1.39, 1.44
and 1.47 respectively. Out of the three which colour ray will emerge out of face ‘ac’? justify your
answer. Trace the path of these rays after passing through face ‘ab’.
16.Two lenses of powers 10 D and -5 D are placed in concact.
(i) Calculate the power of new lens.
(ii) Where should the object be held from the lens, so as to obtain a virtual image of magnification 2?
17. How the angle of minimum deviation changes if the violet light is replaced by the red light.
18.You are given following three lenses. Which two lenses will you use as an eyepiece and as an
objective to construct an astronomical telescope?
Lens
Power
Aperture
L1
3D
8cm
L2
6D
1cm
L3
10D
1cm
19.The image obtained with a convex lens is erect and its 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.
20. A converging lens is kept coaxially in contact with a diverging lens – both the lenses being of equal
focal lengths. What is the focal length of the combination?
21.Calculate the speed of light in a medium whose critical angle is 30o.
22.Find the radius of curvature of the convex surface of a plano-convex lens whose focal length is 0.3
m and the refractive index of the material of the lens is 1.5.
23.A biconvex lens has a focal length (2/3) times the radius of curvature of either surface. Calculate
the refractive index of lens material.
24.When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in
speed imply a decrease in the energy carried by the light wave? Justify your answer.
25.A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in (i) a medium of
refractive index 1.6, (ii) a medium of refractive index 1.3.
(a) Will it behave as a converging or a diverging lens in the two cases? (b) How will its focal length
change in the two media?
26. A converging lens has a focal length of 20cm in air. It is made of a material of refractive index 1.6. It
is immersed in a liquid of refractive index 1.3. Calculate its new focal length.
27.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 × 106 m and the radius of the lunar orbit is 3.8 × 108
m.
28. For the same value of angle of incidence, the angles of refraction in three media A, B and C are 15°,
25° and 35° respectively. In which medium would the velocity of light be minimum?
29.You are given three lenses L1, L2 and L3 each of focal length 20 cm. An object is kept at 40 cm in
front of L1, as shown. The final real image is formed at the focus ‘I’ of L3. Find the separations between
L1, L2 and L3.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
ASSIGNMENT OF WAVE OPTICS
1. In Young's double slit experiment, if the widths of the slit are in the ratio 4:9,Whatis the ratio of
intensity of maxima to intensity of minima ?
[25:1]
2. Angular width of a central max. is 30o when the slit is illuminated by light of wavelength 6000 Å.
Then what is width of the slit ?.
[ans.12x1o-7m]
3. Light of wavelength 6000 12 × 10–6 m is incident on a single slit. First minimum is obtained at a
distance of 0.4 cm from the centre. If width of the slit is 0.3 mm, what is the distance between slit and
screen [ans. 2m]
4. Monochromatic light of wavelength 589 nm is incident from air on a water surface.
What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index
of water is 1.33.
[ans. 2. 25 x 10 8 m/s, 442.8 nm, 5 .1x 1014 Hz]
5. What is the shape of the wavefront in each of the following cases
(a) Light diverging from a point source.
[b] Light emerging out of a convex lens when a point source is placed at its focus.
(c) The portion of the wavefront of light from a distant star intercepted by the Earth.
6.(a)The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is
3.0 × 108 m s–1)(b) Is the speed of light in glass independent of the colour of light? If not, which of the
two colours red and violet travels slower in a glass prism?
[ans. 2 x108 m/ s
7.In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m
away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2
cm. Determine the wavelength of light used in the experiment.
[ans. 600nm]
9.The refractive index of the denser media is 1.732. Calculate: (i) the polarising angle of medium. (ii) the
angle of refraction at the polarising angle.
[60°, 30°]
10.Determine the angular separation between central maximum and first order maximum of the
diffraction pattern due to a single slit of width 0.25 mm, when light of wavelength 5890 Å is incident on
it normally.
[0.0035 radian]
Q.11In Young’s double slit experiment; the slits are separated by 0.24 mm. The screen is 1.2 m away
from the slit? The fringe width is 0.3 cm. Calculate the wavelength of light used in the experiment.
[6000 Å]
Q.12.Two coherent sources whose intensity ratio is 81 : 1, produce interference fringes. Calculate the
ratio of (i) the amplitudes of light waves (ii) intensity of maxima and minima in the fringe system.
[9:1, 100:64]
Q.13The two slits in Young’s double slit experiment are separated by a distance of 0.03 mm. An
interference pattern is produced on a screen 1.5 m away. The 4th bright fringe is at a distance of 1 cm
from the central maximum. Calculate the wavelength of light used.
[500 Å]
Q.14.In Young’s double slit experiment, while using a source of light of wavelength 5000 Å, the fringe
width obtained is 0.6 cm. If the distance between the slits and the screen is reduced to half, calculate
the new fringe width.
[0.3 cm]
Q.15. Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in
which the bright fringes are separated by 8.1 mm. A second light produces an interference pattern in
which the fringes are separated by 7.2 mm. Calculate the wavelength of the second light. [560 nm]
Q.16.Consider interference between two sources of intensities I and 4I. Obtain intensity at a point
where the phase difference is λ /2.
[5 I]
Q.17.In Young’s double slit experiment a light of 5000 Å is used. The third bright fringe is formed on the
screen at 1 cm from central bright band. If the screen is at a distance of 1.5 m from the center of the two
narrow slits, calculate the separation between the slits.
[0.225 x 10-3m]
Q.18.A double slit is illuminated by light of λ= 6000 Å. The slits are 0.1 cm apart and the screen is placed
1 m away. Calculate: (a) angular position of 10th maxima in radi (b) separation of two adjacent minima.
[0.006 radian, 0.6 ]
Q.19The ratio of intensities of maxima and minima in an interference pattern is found to be 25 : 9.
Calculate the ratio of the intensities of the sources producing this pattern.
[Ans. 16: 1]
Q.20. In Young’s double slit experiment; two slits are separated by 3 mm distance and illuminated by
light of wavelength 480 nm. The screen is at 2 m from the plane of the slits. Calculate the separation
between the 8th bright fringe and the 3rd dark fringe observed with respect to the central bright fringe.
[1.76 x 10-3 m]
Q.21.A ray of light falls on a transparent slab of refractive index 1.732. If reflected and refracted rays are
mutually perpendicular, what is the angle of incidence?
[600]
Q.22.In a Young’s double slit interference experiment, the first minima on the screen is found just in
front of one of the slits when the slits are illuminated with a monochromatic source of wavelength
6000Å. If the distance of the screen from the slits is 60 cm, calculate the separation between the slits.
Q23..In Young’s double-slit experiment using monochromatic light of wavelength λ, the intensity of light
at a point on the screen where path difference is λ, is K units.
What is the intensity of light at a point where path difference is λ/3?
[K/4]
Q.24. In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m
away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire
experimental apparatus is immersed in water? Take refractive index of water to be 4/3.
[0.15°]
Q.25.In double-slit experiment using light of wavelength 600 nm, the angular width of a fringe formed
on a distant screen is 0.1º. What is the spacing between the two slits?
[3.4 × 10-4 m.]
Q.26.Assume that light of wavelength 6000Å is coming from a star. What is the limit of resolution of a
telescope whose objective has a diameter of 100 inch?
 NCERT QUESTIONS EXAMPLE AND EXERCISE
Conceptual Questions
Q1: A partially plane polarized beam of light is passed through a polaroid. Show graphically the variation
of the transmitted light intensity with angle of rotation of the Polaroid.
Q2: Soap bubble shows beautiful colours in sun light. Why?
Q3: Colored spectrum is observed, when we see through a muslin cloth. Why?
Q4: Why value of the Brewster angle for transparent medium is different for light of different colours?
Q5: Why is diffraction effect more predominant through the slit formed by two blades than by slit
formed by two fingers?
Q6: Why is light from two individual sources of equal wavelength is incoherent?
Q7: Which principle is used in L.C.D (liquid crystal display) in T.V & computers?
Q8. How does the focal length of a convex lens change if monochromatic red light is used instead of
monochromatic blue light?
Q9. How many angles of incidence are possible when the angle of deviation is minimum?
Q10. The lens shown in the figure is made of two different transparent materials. A point object is
placed on its axis. How many images of the object will be formed?
Q11. The graph shows the variation of the angle of deviation with the angle of incidence for the two
glass prism A & B. which glass prism has the larger refractive index?
Q12. A simple microscope using single lens often shows colored image of a white source. Why?
Q13. A concave lens is immersed in a liquid and image formed is shown in the figure. Whose refractive
index is greater, glass or the liquid?
Q14. Why focal lengths of the eye piece and objective both should be short in the case of a compound
microscope?
Q15. You are given 3 lenses having powers as P1=6D, P2=3D & P3=12D. Which two of these lenses will
you select to construct a microscope?
Q16. How is the intensity of scattered light related to the wavelength of light?
Q17. The far point of myopic person is 80cm in front of the eye. The power of the lens required to
enable him to see very distant objects clearly is -1.25D. Does the lens magnify the very distant objects?
Q.18. How is an optical fibre a better device than a coaxial cable?
Ans. Characteristic of optical fiber (no loss of energy and no external interference).
Q.19. When a low flying aircraft passes overhead, we sometimes notice a shaking of the picture on our
T.V screen. Suggest a possible explanation?
Ans. When a low flying aircraft passes overhead, the metallic body of the aircraft reflects T.V signal. A
slight shaking of the picture on the T.V screen takes place due to interference of the reflected signal
from the aircraft & the direct signal
received by the antenna.
20. Draw the graph showing the variation of v with u for a convex lens.
21. Two lenses of power -15D and 5D are in contact with each other
a) What is focal length of this combination?
b) An object of size 4cm is placed at 20cm from this combination. Calculate position and size of image.
22. The principle section of Glass prism is an isosceles ΔPQR with PQ=PR. The face PR is silvered. A ray is
incident perpendicularly on face PQ and after two reflections it emerges from base QR normal to it. Find
angle QPR of Prism.
23. An astronomical telescope consist of two thin lens set 36cm apart and has a magnifying power 8.
Calculate the focal length of the lens.
24. A fish at a depth of √7cm below the surface of water sees the outside world through a circular
horizon. What is the radius of the circular horizon? Refractive index of water w.r.t. air is 4/
 NCERT QUESTIONS EXAMPLE AND EXERCISE
Dual Nature and photoelectric effect
Q.1 .Define the terms ‘threshold frequency’ and ‘stopping potential’ in the study of photoelectric emission. Explain
briefly the reasons why wave theory of light is not able to explain the observed features in photoelectric effect?
[2011, 2008 C D,2010 F,2012]
2 .Show the variation of photo current with collector plate potential for different intensities but same frequency of
incident radiation.
[2011 F,2011,2010]
Q.3. The figure shows a plot of three curves a, b, c showing the variation of photo current vs collector plate
potential for three different intensities I1,I2andI3 having frequencies ν1,ν2andν3 respectively incident on a
photosensitive surface. Point out the two curves for which the incident radiations have same frequency but
different intensities.
[2009 D]
4 . The stopping potential in an experiment on photoelectric effect is 1.5 V. What is the maximum kinetic energy of
the photo electrons emitted?
[ans.1.5ev] [ 2011,2009]
5 The maximum kinetic energy of a photo electron is 3 eV. What is its stopping potential? [2009
Q.6 .The given graph shows variation of photoelectric current with collector plate potential for different
frequencies of incident radiations.
(a) Which physical parameter is kept constant for the three curves?
(b) Which frequences (ν1,ν2orν3) is the highest?
Show graphically how the maximum kinetic energy of electrons emitted from a photosensitive surface varies with
the frequency of incident radiations?
[2007]
Q.8 Write Einstein’s photoelectric equation. State clearly the three salient features observed in photoelectric
effect, which can be explained on the basis of above equation.
[2010,2009]
Q.9. Ultraviolet radiations of different frequencies ν1andν2 are incident on two photosensitive materials having
work vbfunctions W1andW2 (W1>W2) respectively. The kinetic energy of the emitted electrons is same in both the
cases. Which one of the two radiations will be higher frequency?
Q.10 .Sketch a graph between frequency of incident radiations and stopping potential for a given photosensitive
material. What information can be obtained from the value of the intercept on the potential axis? A source of light
of frequency greater than the threshold frequency is placed at a distance of 1m from the cathode of a photo-cell.
The stopping potential is found to be V. If the distance of the light source from the cathode is reduced, explain
giving reasons, what change will you observe in the
(a) Photoelectric current (b) Stopping potential.
[ 2006]
Q.11 Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two
different photo sensitizes materials having work functions W1andW2(W1>W2) On what factors does the
(a) Slope and (b) Intercept of the lines depend?
[2010 D,2007 F]
Q.12. Figure shows variation of stopping potential (V0) with the frequency (ν) for two photosensitive
materials M1andM2.
(a) Why is the slope same for both lines?
(b) For which material will the emitted electrons have greater kinetic energy for the incident radiation of the same
frequency? Justify your answer.
[2009 F]
Q.13 Plot a graph showing variation of stopping potential (V0) with the frequency (ν) of the incident radiation for
a given photosensitive material. Hence, state the significance of the threshold frequency in photoelectric emission.
Using the principle of energy conservation, write the equation relating the energy of incident photon, threshold
frequency and the maximum kinetic energy of the emitted photoelectrons.
Q.14. Write two characteristic features observed is photoelectric effect which supports the photon pictures of
electromagnetic radiation. Draw a graph between the frequency of incident radiation (ν) and the maximum kinetic
energy of the electrons emitted from the surface of a photosensitive material state clearly how this graph can be
used to determine. (a) Planck’s constant and (b) Work function of the material?
Q.15 Write two characteristic features observed is photoelectric effect which supports the photon pictures of
electromagnetic radiation. Draw a graph between the frequency of incident radiation (ν) and the maximum kinetic
energy of the electrons emitted from the surface of a photosensitive material state clearly how this graph can be
used to determine. (a) Planck’s constant and (b) Work function of the material?
[ 2012 F]
Q.16 Radiations of frequency 1015 Hz are incident on two photosensitive surfaces A and B. Following observations
are recorded. Surface A No photo-emission takes place. Surface B Photo-emission takes place but photoelectrons
have zero energy. Explain the above observations on the basis of Einstein’s photo- electric equation. How will the
observation with surface B change when the wavelength of incident radiations is decreased?
[ 2007 D]
Q.17 .(a) Ultraviolet light of wavelength 2271 Å from a 100 W mercury source is incident on a photocell made of
molybdenum metal. If the stopping potential is 1.3 V, estimate the work function of the metal. (b) How would the
photocell respond to high intensity? (105W/m2) red light of wavelength 6328 Å produced by a He-Ne
laser?[ans.4.22ev]
[2011 D]
Q.18 The following graph shows the variation of stopping potential V0 with the frequency ν of the incident
radiation for two photosensitive metals X and Y
(a) Which of the metals has larger threshold wavelength ? Give reason.
(b) Explain, giving reason which metal gives out electrons, having larger kinetic energy. For the same wavelength of
the incident radiation.
(c) If the distance between the light source and metal X is halved, how will the kinetic energy of electrons emitted
from it change? Give reason.
[2008]
Q.19. An electromagnetic wave of wavelength λ is incident on a photosensitive surface of negligible work
function. If the photo electrons emitted from this surface have the de-B roglie wavelength λ1,provethat
λ=(2mch)/λ12
[2008 D]
Q.2o. In a plot of photoelectric current versus anode potential, how does
(a) The saturation current vary with anode potential for incident radiations of different frequencies but same
intensity?
(b) The stopping potential vary for incident radiations of different intensities but same frequency?
(c) Photoelectric current vary for different intensities but same frequency of incident radiations?
Justify your answer in each case.
21. An electron and a proton have same kinetic energy. Which of the two has a greater wavelength? Explain
22.Two metals A & B have work functions 2eV & 4 eV respectively. Which metal has lower
threshold wavelength?
23. A 100 W sodium lamp radiates energy. The lamp is located at the centre of a large sphere. The wavelength of
sodium light is 589 nm. What is the energy per photon? At what rate are the photons delivered to the sphere?
24. The work function of caesium is 2.14 eV. Find (i) threshold frequency for caesium. (ii) the wavelength of the
incident light if the photocurrent is brought to zero by a stopping potential of 0.60 eV.
25 Monochromatic light of frequency 6 x 1014 Hz is produced by a laser. The power emitted is 2 x 10-3 W. What is
the energy of a photon in the beam? How many photons per second are emitted by the source?
26. The work function of caesium is 2.14 eV. When light of frequency 6 x 10 14 Hz is incident on its surface,
photoemission occurs. What is the (i) maximum K.E. of emitted electrons, (ii) stopping potential, (iii) maximum
speed of emitted electrons?
27 The work function of elements A, B and C are 5 eV, 3.8 eV and 2.8 eV respectively. A radiation of wavelength
4125 Ǻ is made to be incident on each of these elements. By appropriate calculations find in which case
photoelectrons will not be emitted.
26 The work functions for the following metals is given: Na: - 2.75 eV, K: - 2.30 eV, Mo: - 4.17 eV, Ni: - 5.15 eV.
Which of the following metals will not give photoelectric emission for a radiation of wavelength 3300 Ǻ from a He
– Cd laser placed 1m away from the photocell? What happens if the laser is brought nearer and placed 50 cm
away?
27. An alpha particle and a proton are accelerated through the same potential difference. Calculate the ratio of
velocities acquired by the two particles.
28. Light of frequency 7.21 x 1014 Hz is incident on a metal surface. Electrons with a maximum speed of 6 x 10 5 m/s
are ejected from the surface. What is the threshold frequency for photoemission of electrons?
29. What is the de Broglie wavelength associated with an electron, accelerated through a potential difference of
100 V?
30. On using light of wavelength 5000 Ǻ, the stopping potential for a photocell is 2.4 V. If the light of wavelength
4000 Ǻ is used, then find the value of stopping potential.
 NCERT QUESTIONS EXAMPLE AND EXERCISE
ATOMIC NUCLEUS
Q.1.In a head on collision between an  particle and gold nucleus (Z = 79), the closest distance of
approach is 41.3 fermi. Calculate the energy of  particle.
(5.51 MeV)
Q.2.Find the energy of hydrogen atom in its ground state and in the energy levels whose quantum
number are 2 and 3.
(-13.6 eV, -3.4 eV, -1.51 eV)
Q.3.Find the energy radiated in the Lyman series of hydrogen atom spectrum when its electron jumps
from 3rd energy level to ground state.
Q.4.Determine the longest wavelength in Lyman series of hydrogen spectrum.
(1210 Å)
Q.5.The total energy of electron in the first excited state of hydrogen atom is about -3.4 eV. (a) What is
the kinetic energy of electron this state?(b) What is the potential energy of electron this state? (c) Which
of the K.E., P.E. or total energy will change if the choice of zero reference of potential energy is
changed?
(3.4 eV, -6.8 eV, P.E. & T.E.)
Q.6.What is the ground state energy of electron in case 3Li7?
(-30.4 eV)
Q.7.Find the ratio of radii of two nuclei with mass numbers 1 and 27 respectively.
(1:3)
Q.8.Two nuclei have radii in the ratio 1:8, what is ratio of their nuclear densities and mass numbers?
Q.9.The half life of a radioactive substance is 30 days. What is the time taken for 3/4th of its original
mass to disintegrate?
Q.10.The half life of a radioactive substance is 1.192 x 107 s. Find the decay rate when 3.18 x 1015 atoms
are present.
Q.11.In a particular fission reaction, a 92U235 nucleus captures a slow neutron. The fission products are 3
neutrons, a 57La142 and a fission product ZXY. What is the value of Y and Z?





B 
C 
D

E
Q.12.The sequence of stepwise decay of a radioactive nucleus is A 
. If nucleon number and atomic number for C are respectively 176 and 71, what are corresponding
values for other nuclei?
Q.13.Find the half life of a radioactive material if its activity drops to 1/16th of its initial value in 30 years.
Also find its mean value & disintegration constant.
Q.14.The half life of a radioactive substance is 30 s. calculate the decay constant and the time taken to
decay to 3/4th of its initial value.
(0.23 /s,60s)
6
Q.15.A neutron is absorbed by a 3Li nucleus with subsequent emission of an alpha particle. Write the
nuclear reaction. Calculate the energy released in this reaction. (Given: m(3Li6) = 6.015126 u ; m(2He4) =
4.0026044 u ; m(0n1) = 1.0086654 u ; m(1H3) = 3.016049 u )
Q.16. 92U238 decays successively to form 90Th234 , 91Pa234 , 92U234 , 90Th230 , 88Ra226 and 86Rn222. What are
the radioactive radiations emitted in each decay?
Q.17. Two radioactive nuclei X and Y initially contain equal number of atoms. Their half life is 1 hour and
2 hours respectively. Calculate the ratio of their rates of disintegration after two hours.
(1:1)
Q.18.A helium nucleus of energy 10 MeV collides head on with a 29Cu64 nucleus and retraces its path.
Find the radius of Cu nucleus.
Q.19.The half life of 92U238 against alpha decay is 4.5 x 109 years. What is activity of 1g of 92U238 ?
(1.23x104 Bq)
Q.20.Titanium has a half life of 12.5 years. What fraction of a sample of pure titanium will remain
undecayed after 25 years?
Q.21.A radioactive isotope has a half life of T years. After how much time is its activity reduced to 6.25%
of its original activity?
Q.22.Obtain the binding energy of nuclei 26Fe56 and 83Bi209 in units of MeV from the given data: mH =
1.007825 u ; mn = 1.008665 u ; m(26Fe56) = 55.934939 u ; m(83Bi209) = 208.980388 u . Which nucleus has
greater B.E. per nucleon?
(8.79 MeV, 7.85 MeV)
Q.23.The nucleus 10Ne23 decays by beta emission. Write the beta decay equation and find the maximum
K.E. of the electron emitted. (Given that: m(10Ne23) = 22.994466 u ; m(11Na23) = 22.089770 u)
(4.374 MeV)
 NCERT QUESTIONS EXAMPLE AND EXERCISE
SEMICONDUCTOR
Q.1.A p-n photodiode is fabricated from a semiconductor with band gap of 2.8 eV. Can it detect a
wavelength of 6000 nm?
[No]
Q.2.In half-wave rectification, what is the output frequency if the input frequency is 50 Hz? What is the
output frequency of a full-wave rectifier for the same input frequency?
[50 Hz, 100 Hz]
Q.3.For a CE-transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2 V.
Suppose the current amplification factor of the transistor is 100, find the input signal voltage and base
current, if the base resistance is 1 kΩ.
[0.01 V, 10A]
Q.4.Two amplifiers are connected one after the other in series (cascaded). The first amplifier has a
voltage gain of 10 and the second has a voltage gain of 20. If the input signal is 0.01 volt, calculate the
output ac signal.
[2 V]
Q.5.For a CE transistor amplifier, the audio signal voltage across the collector resistance of 2.0 kΩ is
2.0 V. Suppose the current amplification factor of the transistor is 100, What should be the value of RB in
series with VBB supply of 2.0 V if the dc base current has to be 10 times the signal current. Also calculate
the dc drop across the collector resistance. (Take VBE = 0.6 V)
[14 kΩ, 10 mA]
Q.6.The VBB supply can be varied from 0 V to 5.0 V. The Si transistor has βdc = 250 and RB = 100 kΩ, RC =
1 kΩ, VCC = 5.0V. Assume that when the transistor is saturated, VCE = 0 V and VBE = 0.8 V. For Base –
Emitter junction, knee voltage is 0.6 V. Calculate (a) the minimum base current, for which the transistor
will reach saturation. Hence, (b) find the ranges of Vi for which the transistor is ‘switched off’ and
‘switched on’. [20 A, Vi = 0.0V to 0.6V then ‘switched off’, If Vi = 2.8V to 5.0V then ‘switched on’]
Q.7.Suppose a pure Si crystal has 5 × 1028 atoms m–3. It is doped by 1 ppm concentration of pentavalent
As. Calculate the number of electrons and holes. Given that ni =1.5 × 1016 m–3.
[5 ×1022 m–3, 4.5 x 109 m–3]
Q.8.A p-n junction diode when forward biased has a drop of 0.5 V which is assumed to be independent
of current. If we want to use a l.5 V battery to forward bias diode, what should be the value of resistor
used in series with the diode so that the maximum current does not exceed 5 mA?
[ 200 Ω
]
Q.9.The width of depletion region in a P-N junction diode is 500 nm and an intense electric field of 5 x
105 V/m is also found to exist in it. Determine the height of the potential barrier. Also calculate the
kinetic energy which a conduction electron must have in order to diffuse from the N-side to P-side.
[ 0.25 V, 0.25 eV ]
Q.10.A p-n diode used in a circuit has a constant voltage drop at 0.5 V at all currents and a maximum
power rating of 100 milliwatt. What should be the value of the resistance R, connected in series and
with diode for obtaining maximum current to forward bias it by a battery of 1.5 V?
[ 5Ω ]
Q.11.In a silicon transistor, base current is changed by 20 A. This results in a change of 0.02 V in baseemitter voltage and a change of 2 mA in the collector current. (a) Find the input resistance, ac and
transconductance of the transistor. (b) The transistor is used as an amplifier with the load resistance 5 k
Ω. What is the voltage gain of the amplifier?
[ (a) 1 kΩ, 100, 0.1 Ω-1 (b) 500]
Q.12.A load resistance of 2 kΩ is connected in the collector branch of an amplifier circuit using a
transistor in common emitter mode. The current gain  = 40. The input resistance of transistor is 0.40
kΩ. If the input current is changed by 40 A (a) by what amount does the output voltage change (b) by
what amount input voltage change (c) what is the power gain ?
[(a) 3.2 V (b) 0.016 V (c) 8000]
 NCERT QUESTIONS EXAMPLE AND EXERCISE
COMMUNICATION SYSTEM
Q.1.What are the essential parts of a communication system? Draw a block diagram to show these
elements in a communication system.
Q.2.What is a transducer? Give an example of transducer.
Q.3.What is transmitter in a communication system? Draw a block diagram of a transmitter.
Q.4.What is receiver in a communication system? Draw a block diagram of a receiver.
Q.5.What do you mean by (i) point-to-point communication and (ii) broadcast communication? Write
one example of each.
Q.6.What is a message signal? What are the two types of message signals? Explain them by drawing
their curves.
Q.7.Which type of communication system is more advantageous, analog or digital? Why?
Q.8.How is an analog signal converted into a digital signal? Which one is exact representation of original
information?
Q.9.What do you mean by the following terms related to a signal: (i) attenuation (ii) bandwidth?
Q.10.Write the bandwidths of the following signals: (i) speech (ii) music (iii) video (iv) television.
Q.11.How much should be the bandwidth of a digital signal and why?
Q.12.Write the bandwidths of the following transmission medium: (i) coaxial cables (ii) optical fibers (iii)
free space. Also write the frequencies over which they operate.
Q.13.What do you mean by modulation? What is the need of modulation? Explain three reasons.
Q.14.What are the different types of modulation for a (i) sinusoidal carrier wave (ii) digital carrier wave?
Q.15.What do you mean by amplitude modulation? Explain by drawing curves for analog message signal,
analog carrier wave and AM wave. Derive an expression for amplitude modulated wave
Q.16.Define modulation index for an amplitude modulated wave. In amplitude modulation, modulation
index μ ≤ 1 is used. What will happen if μ > 1?
Q.17.What do mean by side bands of an amplitude modulated wave?
Q.18.What do you mean by frequency modulation? Explain by drawing curves for analog message signal,
analog carrier wave and FM wave.
Q.19.What are the advantages of FM wave over AM wave?
Q.20.What do you mean by demodulation?
Q.21.What do you mean by ground wave? What is the frequency range for ground wave propagation?
On what factors the attenuation of ground waves depend and how?
Q.22.What is ionosphere? Name the various layers of ionosphere. Which layer of the ionosphere
efficiently reflects High Frequency radio waves? The reflection of HF by ionosphere is similar to a
phenomenon in optics. Name that phenomenon.
Q.23.How does ionosphere behave for radio waves of (i) Medium Frequency ( 0.3 – 3 MHz ) (ii) High
Frequency ( 3 – 30 MHz ) (iii) Very High Frequency ( 30 – 300 MHz ) (iv) Ultra High Frequency ( > 300
MHz ). Draw a diagram to show these behaviour.
Q.24.What do you mean by sky wave? What is the frequency range for sky wave propagation? What do
you mean by skip zone?
Q.25.What do you mean by space wave? What is the frequency range for space wave propagation?
Which two communication methods make use of this mode of propagation?
Q.26.What does the term LOS communication mean? Name the types of waves that are used for this
communication. Which of the two-height of transmitting antenna and height of receiving antenna - can
affect the range over which this mode of communication remains effective?
Q.27.Derive an expression for the maximum distance upto which signals can be received via LOS
communication in terms of heights of transmitter and receiver.
Q.28.What are repeaters? For what purpose are they used?
Q.29Which of the following frequencies will be suitable for beyond the horizon communication using sky
waves? (a) 10 kHz
(b) 10 MHz
(c) 1 GHz
(d) 1000 GHz Give
reasons for your answer.
Q.30.What are the frequency ranges reserved for (i) standard AM broadcast (ii) FM broadcast?
Q.31.(i) Why ground wave propagation is not suitable for higher frequencies?(ii) Why do long distance
radio broadcast use short wave band? (iii) Why is it necessary to use satellite for long distance TV
transmission?(iv) Optical and radio telescopes are built on the ground but X – ray astronomy is possible
only from the satellites. Why?(v) At the receiving end the AM sigfnals are noisy but FM are not. Why?
Q.32.What do you mean by the following terms: (i) LAN,
(ii) WAN
(iii) Internet
Q.33.Arrange the following networks in increasing order of the number of computers that may be
present in the network: Internet ; LAN ; WAN
Q.34.What are protocols? Name the set of protocols used these days.
Q.35(i) What is a webpage? (ii) What is hyperlinking?
Q.36What do you mean by (i) World Wide Web and (ii) website?
Q.37.Explain the terms: (i) Internet surfing, (ii) e – mail, (iii) E-Banking, (iv) E-shopping, (v) E-commerce,
(vi) E-booking, (vii) social networking.
Q.38.What do you mean by (i) cell (ii) MTSO?
Q.39.What should be the shape of cells to completely cover a given area?
Q.40Describe the working principle of mobile telephone.
Q.41.Draw a block diagram to show the process of mobile phone call from dialer to caller.
Q.42.What do you mean by a SIM card?
Q.43.Name the organization which regulate the mobile phone system in India.
Q.44.What do you mean by 1G, 2G, 3G and 4G mobile network?
Q.45.What is GPS? What are the information you get from a GPS device?
Q.46.(a) How many satellites are monitoring earth’s surface in GPS system? How many times each of it
revolves around the earth in a day and at what distance?
(b) What is the minimum number of satellites that enables a Global Positioning System (GPS) receiver to
determine (i) one’s longitude/latitude position, i.e., to make a 2D position fix. (ii) longitude/latitude
position as well as altitude position i.e., 3D position?
Q.47.List four applications of GPS.
Q.48.A TV transmitting antenna is 81m tall. How much service area can it cover if the receiving antenna
is at the ground level?
[ 3258
2
km ]
Q.49A carrier wave of peak voltage 12V 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%?
[9V]
Q.50.For an amplitude modulated wave, the maximum amplitude is found to be 10V while the minimum
amplitude is found to be 2V. Determine the modulation index, . What would be the value of  if the
minimum amplitude is zero volt?
[ 2/3, 1
]
Q.51.A message signal of frequency 10 kHz and peak voltage of 10 volts is used to modulate a carrier of
frequency 1 MHz and peak voltage of 20 volts. Determine (a) modulation index, (b) the side bands
produced.[ 0.5, 990 kHz, 1010 kHz ]
Q.52.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 LOS
mode? Given, radius of earth = 6.4 × 106 m.
[ 45.5 km ]
Q.53.By what percentage will the transmission range of a TV tower be affected when the height of the
tower is increased by 21%?
[ 10 %
increase ]
Q.54.A modulating signal is a square wave, as shown in Figure.
The carrier wave is given by c(t) = 2 sin(8 t) volts.
(i) Sketch the amplitude modulated waveform
(ii) What is the modulation index?
[ 0.5 ]
Q.55.A microwave telephone link operating at the central frequency of 10 GHz has been established. If 2
% of this is available for communication channel, then how many telephones can be granted if each
telephone is allotted a bandwidth of 8 kHz.
[ 2.5 x
4
10 ]
Q.56.A ground receiver station is receiving a signal at (a) 5 MHz and (b) 100 MHz, transmitted from
transmitter at a height of 300 m located at a distance of 100 km. Identify wheth
 NCERT QUESTIONS EXAMPLE AND EXERCISE