Emf

ISG/Dept. of Physics/Class XII/WS/Electrostatics/Force and Field /2009-10

1 MARK QUESTIONS

1. Is the force acting between two point electric charges q1 and q2 kept at some distance apart in

air, attractive or repulsive when (i) q1q2 > 0 (ii) q1q2 < 0 ? (2007)

2. Which physical quantity has its SI unit as (i) C-m (ii) Vm. (2007)

3. How does the force between two point charges change if dielectric constant of medium in which

they are kept increases.

4. Which orientation of an electric dipole in a uniform electric field would correspond to stable

equilibrium? (2008)

5. Define electric dipole moment of a dipole. State its SI unit. (2008)

6. Why is it necessary that the field lines from a point charge placed in the vicinity of a conductor must

be normal to the surface of the conductor at every point? (2009)

7.A 500 µC charge is at the centre of a square of side 10cm. Find the work done in moving a charge of

10 µC between two diagonally opposite points on the square. (2008)

8. Vehicles carrying inflammable materials usually have metallic ropes touching the ground during

motion. Why?

9. Ordinary rubber is an insulator. But the special rubber tyres of aircraft are made conducting. Why is

this necessary?

2 MARK QUESTIONS

1. The electric field E due to a point charge at any point near it is defined as E= 0

lim→q q

F where q is the

test charge and F is the force acting on it. What is the physical significance of0

lim→q

in this expression?

Draw the electric field lines of a point charge Q when (i) Q>0 and (ii) Q<0. (2007)

2. Figure shows two large metal plates P1 and P2 tightly held against each other and placed between

two equal and unlike point charges perpendicular to the line joining them.

P1 P2

+Q _Q

(i) What will happen to the plates when they are released?

(ii) Draw the pattern of electric field lines for the system. (2009)

INDIAN SCHOOL AL GHUBRA

CLASS XII

WORKSHEET-1

ELECTROSTATICS- FORCE AND FIELD, POTENTIAL AND POTENTIAL

DIFFERENCE


3. The sum of two point charges is 7µC. They repel each other with a force of 1N when kept 30cm

apart in free space. Calculate the value of each charge. (2009)

4. Define electric field →

E at a point in space due to a distribution of charges. Draw electric field lines

due to (i) two similar charges (ii) two opposite charges separated by a distance. (2007Compt)

5. Derive an expression for the torque acting on an electric dipole, which is held in a uniform electric

field when the axis of the dipole makes an angle θ with the electric field. (2008)

6. Two point charges 4µC and -2µC are separated by a distance of 1 m in air. Calculate at what point

on the line joining the two charges is the electric potential zero. (2007)

7. Two point charges q1= 10 x 10-8

C and q2 = -2 x 10 -8

C are separated by a distance of 60cm in air.

(i) Find at what distance from the first charge q1 would the electric potential be zero?

(ii) Also calculate the electrostatic potential energy of the system. (2008)

8. Two point charges 4Q, Q are separated by 1 m in air. At what point on the lie joining the charges is

the electric field intensity zero? Also calculate the electrostatic potential energy of the system.

(2008)

9. Three point charges A, B, C lie in a uniform electric field (E) of 5 x 103 NC

-1 as shown in the figure.

Find the potential difference between A and C. (2009)

10. Derive an expression for the potential energy of an electric dipole of dipole moment →

p in an

electric field→

E .

11. Two identical plane metallic surfaces A and B are kept parallel to each other in air separated by

a distance of 1.0cm as shown in the figure.

Surface A is given a positive potential of 10V and the outer surface of B is earthed. (i) What is

the magnitude and direction of the uniform electric field between points Y and Z? (ii) What is the

work done in moving a charge of 20 µC from point X and point Y?

12. The two graphs drawn below, show the variation of electrostatic potential (V) with (r being

distance of the field point from the point charge) for two point charges q1 and q2.

A B

3cm

5cm

C


(i) What are the signs of the two charges?

(ii) Which of the two charges has a larger magnitude and why? 2

3 MARKQUESTIONS

1. Three charges - 2 µC, 2 2 µC and - 2 µC are arranged along a straight line as shown in the

figure. Calculate the total electric field intensity due to all these three charges at point P.

2. A point charge of +2µC is kept fixed at the origin. Another point charge of +4µC is brought from a

far off point to a point distance 50 cm from the origin. Calculate the electrostatic potential energy

of this two charge system.

Another charge of +1µC is brought to a point distance 100 cm from each of these two charges

(assumed to be kept fixed). What is the work done?

3. An electric dipole of moment →

p is placed in a uniform electric field of intensity →

E .Write the

expression for the torque →

τ experienced by the dipole. Identify two pairs of perpendicular vectors

from the expression.

Show diagrammatically the orientation of dipole in the field for which the torque is (i) maximum

(ii) half the maximum value (iii) zero.

4. A charge Q located at a point →

r is in equilibrium under the combined electric field of three charges

q1,q2, q3. If the charges q1, q2 are →

p located at points→

1r and→

2r respectively, find the direction of the

force on Q, due to q3 in terms of q1,q2, →

1r ,→

2r and→

r .

5. Define the term electric dipole moment of a dipole and state its SI unit. Write expressions for the

(i) electric field due to a dipole, at a far off point on its axis

(ii) torque on a dipole in a uniform electric field. (2007 Compt)

6. Deduce an expression for the electric potential due to an electric dipole at any point on its axis.

Mention one contrasting feature of electric potential of a dipole at a point as compared to that due

to a single charge. (2007)

7. Define the term electric dipole moment. Is it scalar or vector?


Deduce an expression for the electric field at a point on the equatorial plane of an electric dipole

of length 2a. (2009)

8. The following data was obtained for the dependence of the magnitude of electric field, with

distance, from a reference point O, within the charge distribution in the shaded region.

(i) Identify the charge distribution and justify your answer.

(ii) If the potential due to this charge distribution has a value V at the point A, what is its value at

the point A/?

5 MARK QUESTIONS

1. Define the term dipole moment→

p of an electric dipole indicating its direction. Write its SI unit.

An electric dipole is placed in a uniform electric field→

E . Deduce the expression for the torque

acting on it. In a particular situation, it has its dipole moment aligned with the electric field. Is the

equilibrium stable or unstable?

2. Derive an expression for the magnitude of electric field intensity at any point along the equatorial

line of the short electric dipole. Give the direction of electric field intensity at that point. For a

short dipole what is the ratio of electric field intensities at two equidistant points from the centre of

the dipole, one along the axial line and another along the equatorial line?

3. An electric dipole is held in a uniform electric field.

(i) Show that no translatory force acts on it.

(ii) Derive an expression for the torque acting on it.

(iii) The dipole is aligned parallel to the field. Calculate the work done in rotating it through 180°.

4. An electric dipole of dipole moment →

p is held in a uniform electric field→

E .

(i) Prove that no translatory force acts on the dipole.

(ii) Hence prove that the torque acting on the dipole is given by pE Sin θ, indicating the direction

along which it acts.

(iii) How much work is required in turning the electric dipole, from the position of the most stable

equilibrium to the position of the most unstable equilibrium?

5. (i) Derive an expression for the torque experienced by an electric dipole kept in a uniform electric

field.

(ii) Calculate the work done to dissociate the system of three charges placed on the vertices of a

triangle as shown. Here q = 1.6 x 10-10

C. (2008)


1 MARK QUESTIONS

1. Draw an equipotential surface for a system consisting of two charges Q,-Q separated by a distance r

in air. (2008)

2. In the figure given below, X, Y represent parallel plate capacitors having the same area of the plates

and the same distance of separation between them. What is the relation between the energies stored

in the two capacitors?

3. 3. A metal plate is introduced between the plates of a charged parallel plate capacitor. What is the

effect on the capacitance of a capacitor? (2009)

4. How is the leakage of charge minimized from the Van- de Graff generator?

5. The following graph shows the variation of charge Q, with voltage V, for two capacitors K and L.

In which capacitor is more electrostatic energy stored?

q

10cm 10 cm

-4q 10cm +2q

L


CLASS XII

WORKSHEET-2

ELECTROSTATICS- ELECTRIC FLUX, GAUSS’S THEOREM AND

CAPACITORS

Q

K

V

+ V -

εr = 6


6. A metal plate is introduced between the plates of a charged parallel plate capacitor. What is the

effect of the capacitance of the capacitor? (2009)

7. State Gauss’s law in electrostatics. (2008 C)

8. Define the term ‘dielectric constant’ of a medium in terms of capacitance of a capacitor. (2006)

2 MARK QUESTIONS

1. State Gauss's theorem in electrostatics. Apply this theorem to derive an expression for electric field

intensity at a point near an infinitely long straight charged wire. (2007)

2. An 800pF capacitor is charged by a 100 V battery. After some time the battery is disconnected.

The capacitor is then connected to another 800pF capacitor. What is the electrostatic energy

stored? (2009)

3. Two capacitors of capacitance 3µF and 6µF are charged to potentials 2V and 6V respectively. These

two charged capacitors are connected in parallel. Find the charge across each of the capacitors

now.

4. A point charge causes an electric flux of -3 x 104Nm

2/C to pass through a spherical Gaussian

surface.

(i)Calculate the value of the point charge.

(ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the

surface?

5. Figure shows a sheet of aluminium foil of negligible thickness placed between the plates of a

capacitor. How will its capacitance be affected if

(i) the foil is electrically insulated ?

(ii) The foil is connected to the upper plate with a conducting wire? (2009)

6. Define electric flux. Write its S.I. units. A spherical rubber balloon carries a charge

that is uniformly distributed over its surface. As the balloon is blown up and increases in size, how

does the total electric flux coming out of the surface change ? Give reason. (2007)

7. A spherical Gaussian surface encloses a charge of 8.85 x 10-10

C.

(i) Calculate the electric flux passing through the surface.

(ii) How would the flux change if the radius of the Gaussian surface is doubled and why?(2007)

8. Two large parallel thin metallic plates are placed close to each other. The plates have surface

charge densities of opposite signs and of magnitude 20 x 10 -12

c/m2. Calculate the electric field

intensity (i) in the outer region of the plates and (ii) in the interior region between the plates.

9. Use Gauss’s theorem to calculate the electrostatic field due to a uniformly charged infinite plane

sheet of charge. (2007)

10. Use Gauss’s theorem to prove that, for external points, the field due to a uniformly charged

spherical shell as its entire charge were concentrated at its centre. (2007 C)


11. The adjoining figure shows the variation of potential V with distance X for a given charge

distribution. From the points marked A,B and C, identify the point at which the electric field is (i)

zero (ii) maximum. ( Sam.paper 2002)

3 MARKQUESTIONS

1. Explain the underlying principle of working of a parallel plate capacitor.

If two similar plates, each of area A, having surface charge densities +σ and -σ are separated by a

distance d in air, write expressions for

(i) the electric field at points between the two plates.

(ii) the potential difference between the plates.

(iii) the capacitance of the capacitor so formed. (2007)

2. A parallel plate capacitor, each with plate area A and separation d, is charged to a potential

difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d

and dielectric constant K is now placed between the plates. What change, if any, will take place in

(i) charge on the plates

(ii) electric field intensity between the plates

(iii) capacitance of the capacitor. Justify your answer in each case. (2007)

3. A parallel plate capacitor has its two plates kept 0.02m apart. A dielectric slab, of thickness 0.01m,

is introduced between the plates with its faces parallel to them. The distance between the plates is

readjusted to make the capacity of the capacitor 2/3rd

of its original value. Given the dielectric

constant of the slab =5, find the new distance between the plates. (2007)

4. Two capacitors with capacity C1 and C2 are charged to potential V1 and V2 respectively and then

connected in parallel. Calculate the common potential across the combination, the charge on each

capacitor, the electrostatic energy stored in the system and the change in the electrostatic energy

from its initial value.

5. State Gauss’s theorem. Show by using suitable example, that this theorem is based on Coulomb’s

inverse square law.

6. The two plates of a parallel plate capacitor are 5mm apart. A slab of thickness 4mm is introduced

between the plates with its face parallel to them. The distance between the plates is adjusted so that

C

V

X

A B


the capacitance of the capacitor becomes equal to its original value. If the new distance between

the plates equals 8mm, what is the dielectric constant of the dielectric used? (2008C)

7. Derive the expression for the energy stored in a parallel plate capacitor with air between the plates.

How does the stored energy change if air is replaced by a medium of dielectric constant K?

(2006C)

8. Explain the underlying principle of working of a parallel plate capacitor. If two similar plates, each

of area A having surface charge densities +σ and -σ are separated by a distance d in air, write

expressions for

1. the electric field at points between the two plates.

2. the potential difference between the plates.

3. the capacitance of the capacitor so formed. (2007)

9. Two point charges q1 = +5.4 x 10-6

C

and q2 =-5.4 x 10-6

C are located at the points A (0,-5) and b

(0, +5) respectively in the x-y plane, the distances being measured in meter. Draw a schematic

diagram and calculate the electric dipole moment of this charge system. Mark one point each in the

diagram where the electric field of this charge system is

a) parallel to its dipole moment

b) anti parallel to its dipole moment. ( Sam.paper 2002)

10. Three hollow concentric spheres A, B and C having radii a, b, and c (a <b< c ) have uniform

surface charge densities +σ , - σ and +σ respectively. Compute the electric potential at the surface

of each sphere.

( Sam.paper 2002)

5 MARK QUESTIONS

1. (i) Derive an expression for the energy stored in a parallel plate capacitor C, charged to a potential

difference V. (ii) Obtain the equivalent capacitance of the network given below. For a supply of

300V, determine the charge and voltage across C4. (2008)

2. Explain the principle on which Van-de Graff generator operates. Draw a labelled schematic sketch

and write briefly its working.

A Van -de Graff type generator is capable of building up potential difference of 15 x 106 V, The

dielectric strength of the gas surrounding the electrode is 5x 107

Vm-1

. What is the minimum radius

of the spherical shell required? (2008)


3. Derive the expression for the energy stored in a parallel plate capacitor of capacitance C with air as

medium between its plates having charges Q and — Q. Show that this energy can be expressed in

terms of electric field as 2

1ε0E

2Ad where A is the area of each plate and d is the separation

between the plates.

How will the energy stored in a fully charged capacitor change when the separation between the

plates is doubled and a dielectric medium of dielectric constant 4 is introduced between the plates?

(2007)

4. (i) What is an equipotential surface? Draw schematically equipotential surface corresponding to a

field that uniformly increases in magnitude but remains constant, say in the z-direction.

(ii) Using Gauss’s law deduce an expression for the electric field at a point near an infinitely long

straight uniformly charged wire. (2008)

6. Use Gauss’s law to obtain an expression for the electric field due to an infinitely long straight

uniformly charged wire.

Electric field in the above figure is directed along + X direction and given by Ex = 5Ax + 2B,

where E is in NC-1 and x is in metre, A and B are constants with dimensions.

Talking A = 10 NC-1

m-1

and B = 5NC-1

calculate.

(i) the electric flux through the cube.

(ii) net charge enclosed within the cube. (2008)

7. Obtain an expression for the capacitance of a parallel plate (air) capacitor.

The given figure shows a network of five capacitors connected to a 100V supply. Calculate the

total charge and energy stored in the network.

8. Using Gauss’s law, derive an expression for the electric field intensity at any point outside a

uniformly charged thin spherical shell of radius R and charge density σ C/m2. Draw the field

lines when the charge density of the sphere is (i) positive (ii) negative.

(ii) A uniformly charged conducting sphere, 2.5m in diameter, has a surface charge density of

100µC/m2. Calculate (i) charge on the sphere. (ii) total electric flux passing through the sphere(08)

9. Define the terms (i) Capacitance of a capacitor (ii) dielectric strength of a dielectric. When a

dielectric is inserted between the plates of a charged parallel plate capacitor, fully occupying the

intervening region, how does the polarization of the of the dielectric medium affect the net electric

field? For linear dielectrics, show that the introduction of a dielectric increases its capacitance by a

factor K, (2008 C)


10. (a) Define electric flux. Write its SI unit. (b) A uniform electric field →

E = Ex i N/C for x >0 and →

E = - Ex i N/C for x< 0 are given. A right circular cylinder of length l cm and radius r cm has its

centre at the origin and its axis along the x-axis. Find out the net outward flux. Using Gauss’s law,

write the expression for the net charge within the cylinder. (2008 C)

1 MARK QUESTIONS

1. A steady current flows in a metallic conductor of non-uniform cross-section. Which of these

quantities is constant along the conductor:

Current, current density, drift speed, electric field? (2009)

2. Write an expression for the resistivity of a metallic conductor showing its variation over a limited

range of temperatures. (2008 Compt)

3. A physical quantity associated with electrical conductivity, has the SI unit Ohm meter. Identify this

physical quantity. (2008 Compt)

4. A (i) series (ii) parallel combination of two given resistors is connected, one by one, across a cell. In

which case will the terminal potential difference, across the cell have a higher value?

(2008 Compt)

2 MARK QUESTIONS 1. The following graph shows the variation of terminal potential difference V, across a combination

of 3 cells in series to a resistor, versus current i:

(i) Calculate the emf of each cell.

(ii) For what current i, will the power dissipation of the circuit be maximum? (2008)

2. Two wires X,Y have the same resistivity, but their cross-sectional areas are in the ratio 2:3 and

lengths in the ratio 1:2. They are first connected in series and then parallel to a d.c source. Find out

the ratio of the drift speeds of the electrons in the two wires for the two cases. (2008)


CLASS XII

WORKSHEET-3

CURRENT ELECTRICITY


3. A voltage of 30 V is applied across a carbon resistor with first, second and third rings of blue, black

and yellow colours respectively. Calculate the value of current, in mA, through the resistor.

(2007)

4. A cylindrical metallic wire is stretched to increase its length by 5%. Calculate the percentage

change in its resistance. (2007)

5. A series combination of a 2KΩ resistance and a 1KΩ resistor is connected across a battery of emf

6Vand negligible internal resistance. The potential drop across the 2KΩresistor is measured by (i)

a 30 KΩ voltmeter (ii) a 1KΩ voltmeter and (iii) both these voltmeters connected across it. If the

voltmeter readings in the three cases are V1,V2 and V3 respectively, arrange these readings in the

descending order.

How will these readings compare with one another if the potential drops were measured across the

series combination of the 2KΩ and the 1KΩ resistor? i.e. across the points A and B.

(Sample paper 2007)

6. Under what condition is the heat produced in an electric circuit

(i) directly proportional

(ii) Inversely proportional to the resistance of the circuit? (Sample paper 2007)

7. The I-V characteristics of a resistor are observed to deviate from a straight line for higher values of

current as shown below. Why?

8. Explain how electron mobility changes for a good conductor when (i) the temperature of the

conductor is decreased at constant potential difference and (ii) applied potential difference is

doubled at constant temperature. (2006 C)

9. Write the mathematical relation between mobility and drift velocity of charge carriers in a

conductor. Name the mobile charge carriers responsible for conduction of electric current in (i) an

electrolyte (ii) an ionized gas. (2006)


9. You are given ‘a’ resistors, each of resistance ‘r’. These are first connected to get minimum possible

resistance. In the second case, these are again connected differently to get maximum possible

resistance. Compute the ratio between the minimum and maximum values of resistance so

obtained. (2006)

10. Draw a circuit diagram using a metre bridge and write the necessary mathematical relation used to

determine the value of an unknown resistance. Why cannot such an arrangement be used for

measuring very low resistances? (2006)

11. Two identical cells, of emf 1.5 V each are joined in parallel providing supply to an external circuit

consisting of two resistors of 13 Ω each joined in parallel. A very high resistance voltmeter

reads the terminal voltage of the cells to be 1.4 V. Find the internal

resistance of each cell. (2005)

3 MARKQUESTIONS 1. (i) State the principle of working of a potentiometer.

(ii) Figure shows the circuit diagram of a potentiometer for determining the emf ε of a cell of

negligible internal resistance.

(a) What is the purpose of using high resistance R2?

(b) How does the position of balance point J change when the resistance R1 is decreased

(c) Why cannot the balance point be obtained (i) when the emf E is greater than 2V, and

(ii) when the key K is closed? (2009)

2. State Kirchhoff’s rules. Use Kirchoff’s rules to show that no current flows in the given circuit.

(2009)

E 1=2V r1 E2=2V r2

3. A resistance R=5Ω is connected to one of the gaps in a meter bridge which uses a wire of length

1m.An unknown resistance X >5Ω is connected in the other gap as shown in the figure.The

balance point is noticed at l cm from the positive end of the battery.On interchanging R and X

it was found that the balance point further shifts by 20 cm away from end A. Neglecting the

end correction, calculate the value of unknown resistance X used.

(2008)

2V R1

J

A E B

R2

Key


4. Draw the circuit diagram of a potentiometer which can be used to determine the internal resistance

(r) of a given cell of emf E. Explain briefly how the internal resistance of the cell is determined.

(2008 Compt)

5. Draw a circuit showing a Wheatstone bridge. Use Kirchoff’s rule to obtain the balance condition in

terms of the values of the four resistors for the galvanometer to give null deflection.

(2008 Compt)

6. For the potentiometer circuit shown in the given figure, points X and Y represent the two terminals

of an unknown emf E'. A student observed that when the jockey in moved from the end A to the

end B of the potentiometer wire, 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 observation? 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. (2007)

7. The given figure shows a network of resistances R1, R2, R3 and R4.n Using Kirchhoff's laws,

establish the balance condition for the network.

8. State Kirchhoff's rules of current distribution in an electrical network. Using these rules determine

the value of the current I1 in the electric circuit given below. (2007)


9. Write the mathematical relation for the resistivity of a material in terms of relaxation time, number

density and mass and charge of charge carriers in it. Explain, using this relation, why the resistivity

of a metal increases and that of a semi-conductor decreases with rise in temperature. (2007)

10. On what principle does a meter bridge work? Draw a circuit diagram and explain how this device

can be used for determination of an unknown resistance. (2007)

11. Define the term current density of a metallic conductor. Deduce the relation connecting current

density (J) and the coductivity of the conductor, when an electric field E, is applied to it.

12. 4 cells of identical emf E, internal resistance r, are connected in series to a variable resistor. The

following graph shows the variation of terminal voltage of the combination with the current

output:

(i) What is the emf of each cell used?

(ii) For what current from the cells, does maximum power dissipation occur in the circuit?

(iii) Calculate the internal resistance of each cell. (2006C)

13. Two cells E1 and E2 in the given circuit diagram have an emf of 5 V and 9 V and internal

resistance of 0.3Ω and 1.2Ω respectively.


Calculate the value of current flowing through the resistance of 3Ω.

14. Define the term 'resistivity' and write its S.I. unit. Derive the expression for the

resistivity of a conductor in terms of number density of free electrons and relaxation time.

15. State the principle of potentiometer. Draw a circuit diagram used to compare the e.m.f.

of two primary cells. Write the formula used. How can the sensitivity of a potentiometer be

increased ?

16. A heating element using nichrome connected to a 230 V supply draws an intial current

of 3.2 A which settles after a few seconds at a steady value of 2.8 A. What is the

steady temperature of the heating element if the room temperature is 27° C ?

Temperature coefficient of resistance of nichrome averaged over the temperature range involved is

1.7×10-4

°C-1

.

5 MARK QUESTIONS

1. A cell of unkonown emf E and internal resistance r, two unknown resistances R1 and R2 (R2>R1) and

a perfect ammeter are given. The current in the circuit is measured in five different situations: (i)

Without any external resistance in the curcuit, (ii) With resistance R1 only, (iii) With resistance R2

only, (iv) With both R1 and R2 used in series combination and (v) With R1 and R2 used in parallel

combination. The current obtained in the five cases are 0.42A, 0.6A, 1.05A, 1.4A, and 4.2A, but

not necessarily in that order. Identify the currents in the five cases listed above and calculate E, r,

R1 and R2.

2. Describe the formula for the equivalent EMF and internal resistance for the parallel combination of

two cells with EMF E1 and E2 and internal resistances r1 and r2 respectively. What is the

corresponding formula for the series combination? Two cells of EMF 1V, 2V and internal

resistances 2 and 1 respectively are connected in (i) series, (ii) parallel. What should be the

external resistance in the circuit so that the current through the resistance be

the same in the two cases? In which case more heat is generated in the cells ? (2007 Sample

paper)

3. State Kirchoff’s laws of an electrical network. Using Kirchoff’s laws, calculate the potential

difference across the 8 ohm resistor.

4. State the working principle of a potentiometer. Explain, with the help of a circuit diagram, how

the emf of two primary cells are compared by using a potentiometer.

In a potentiometer arrangement, a cell of emf 1.20 volt gives a balance point at 30 cm length of


the wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emfs of

the two

5. cells is 1.5, calculate the difference in the balancing length of the potentiometer wire in the two

cases.

1 MARK QUESTIONS

1. Magnetic field line can be entirely confined within the core of of a toroid, but not

within a straight solenoid. Why? (2009)

2. An electron does not suffer any deflection while passing through a region of uniform

magnetic field. What is the direction of the magnetic field? (2009)

3. The coils in certain galvanometers have a fixed core made of a non-magnetic material.

Why does the oscillating coil come to rest quickly in such a core? (2008 Compt)

4. How does the value of the maximum safe current, through a galvanometer change, when its

coil is shunted by a low resistance? (2008 Compt)

5. What is the direction of the force acting on a charged particle q, moving with a velocity v in a

uniform magnetic field B ? (2008)

6. An electron is moving a along +ve x-axis in the presence of uniform magnetic field along

+ ve y-axis. What is the direction of the force acting on it? (2007)

7. An α particle and a proton are moving in the plane of the paper in a region where there is a uniform

magnetic field (B) directed normal to the plane of the paper. If the two particles have equal linear

momenta, what will be the ratio of the radii of their trajectories in the field?

(2008 Sam.paper)

8. Write two properties of a material used as a suspension wire in a moving coil galvanometer.

(2006 Compt)

9. Why a cyclotron is not suitable to accelerate electrons?

2 MARK QUESTIONS

1. A point charge is moving with a constant velocity perpendicular to a uniform magnetic

field as shown in the figure. What should be the magnitude and direction of

the electric field so that the particle moves undeviated along the same path?

(2009)

2. A wire of length L is bent round in the form of a coil having N turns of same radius.

If a steady current I flows through it in a clockwise direction, find the magnitude and

direction of the magnetic field produced at its centre. (2009)


CLASS XII

WORKSHEET-4

MAGNETIC EFFECTS OF ELECTRIC CURRENT


3. A charge q moving along the x- axis with a velocity v is subjected to a uniform

magnetic field B acting along the z-axis as it crosses the origin O.

(i) Trace its trajectory.

(ii) Does the charge gain KE as it enters the magnetic field? Justify your answer. (2009)

4. State Biot –Savart law. A current I flows in a conductor placed perpendicular to the

plane of the paper. Indicate the direction of the magnetic field due to a small current

element →

dl at a point P situated at a distance →

r from the element as shown in

the figure.

(2009)

5. Define current sensitivity and voltage sensitivity of a galvanometer. Increasing

the current sensitivity may not necessarily increase the voltage sensitivity of a

galvanometer. Justify. (2009)

6. Write the expression for the force on a charge moving in a magnetic field. Use this

expression to define the SI unit of magnetic field. (2008 Compt)

7. Find out the expression for the magnetic field at a point on the central axis of a long

solenoid carrying current I and having n number of turns per unit length. (2008 Compt)

8. Write the relation for the forece F acting on a charge carrier q moving with a velocity v through a

magnetic field B in vector notation. Using this relation, deduce the conditions under which this

force will be (i) maximum (ii) minimum. (2007)

9. A galvanometer has a resistance of 30 Ω. It gives full scale deflection with a current

of 2 mA. Calculate the value of the resistance needed to convert it into an ammeter of range

0-0.3 A. (2007)

10. A charged particle moving with a uniform velocity →

v enters a region where uniform electric and

magnetic fields →

E and →

B are present. It passes through the region without any change in its

velocity. What can we conclude about the

(i) Relative directions of→

v , →

E , and →

B ?

(ii) Magnitudes of→

E , and →

B ?


11. A student records the following data for the magnitudes (B) of the magnetic field at axial points at

different distances x from the centre of a circular coil of radius a carrying a current I. Verify (for

any two) that these observations are in good agreement with the expected theoretical variation of B

with x.

(2008 Sam.paper)

12. In the figure, the straight wire AB is fixed while the loop is free to move under the influence of the

electric currents flowing in them. In which direction does the loop begin to move? Give reason for

your answer.

3 MARK QUESTIONS

1. Deduce an expression for the torque experienced by a rectangular loop carrying a steady

current I and placed in uniform magnetic field Br

. Indicate the direction of torque acting

on the loop. (2009)

2. Deduce an expression for the magnetic dipole moment of an electron revolving

around the nucleus in a circular orbit of radius r. Indicate the direction of magnetic

dipole moment. (2009)

3. Derive an expression for the force per unit length between two long straight parallel

current carrying conductors. Hence define one Ampere. (2009)

4. Explain the principle and working of a cyclotron with the help of a schematic diagram.

Write the expression for cyclotron frequency. (2009)

5. Depict the field line pattern due to a current carrying solenoid of finite length.

(i) in what way do these lines differ from those due to an electric dipole.?

(ii) Why can’t two magnetic field lines intersect each other? (2009)

6.A solenoid, of length 1m has a radius of 1cm, and has a total of 1000turnswound on it.

It carries a current of 5A.Calculate the magnitude of the axial magnetic field inside

the solenoid .If an electron were to move with a speed of 104ms

-1along the axis

of this current carrying solenoid, what would be the force experienced by this

electron? (2008 Compt)


7.A long straight wire of circular cross section, of radius a carries a steady current I. The current is

uniformly distributed across the cross-section of the wire. Use Ampere’s circuital law to show that

the magnetic field , due to this wire in the region inside the wire increases in direct proportion to

the distance of the field point from the axis of the wire.

Write the value of this magnetic field on the surface of the wire. (2008 Compt)

8. Write the expression for the force acting on a charged particle of charge q moving with velocity in

the presence of magnetic field. Show that in the presence of this force

(i) the kinetic energy of the particle does not change.

(ii) its instantaneous power is zero. (2007)

5 MARK QUESTIONS

1. Draw a schematic sketch of a cyclotron. Explain briefly how it works and how it is used to

accelerate the charged particles.

(i) Show that the time period of ions in a cyclotron is independent of both the speeds and radius

of circular path.

(ii) What is resonance condition? How is it used to accelerate charged particles? (2009)

2. (i) Derive an expression for the force per unit length between two long straight parallel current

carrying conductors carrying currents.I1 and I2 in the same direction.

Depict the pattern of magnetic field lines around them.

(ii) A rectangular current carrying loop EFGH is kept in a uniform magnetic field as shown in the

figure.

(a) What is the direction of the magnetic moment of the current loop?

(b) When is the torque actin on the loop (A) maximum (B) zero? (2009)

3. (a) Using Biot-Savart’s law, derive an expression for the magnetic field at the centre of a

circular coil of radius R, number of turns N, carrying current i.

(b) Two small identical circular coils marked 1, 2 carry equal currents and are placed with their

geometric axes perpendicular to each other as shown in the figure. Derive an expression for

the resultant magnetic field at O.

E F

I II

G H

N S


(2008)

4. Draw a schematic diagram of a cyclotron. Explain its underlying principle and working,

stating clearly the function of the electric and magnetic fields applied on a charged particle.

Deduce an expression for the period of revolution and show that it does not depend on the

speed of the charged particle. (2008)

5. Draw a labelled diagram of a moving coil galvanometer. State the principle on which it works.

Deduce an expression for the torque acting on a rectangular current carrying loop kept in a

uniform magnetic field. Write two factors on which the current sensitivity of a moving coil

galvanometer depend. (2007)

6. Explain, with the help of a labelled diagram, the principle and construction of a cyclotron.

Deduce an expression for the cyclotron frequency and show that it does not depend on

the speed of the charged particle. (2007)

7. State Biot-Savart law. Use it to derive an expression for the magnetic field at the centre of a

circular loop of radius R carrying a steady current I. Sketch the magnetic field lines for such a

current carrying loop. (2007

8. (i) Describe an expression for the magnetic field at a point on the axis of a current carrying circular

loop.

(ii) Two coaxial circular loops L1 and L2 of radii 3cm and 4cm are placed as shown. What should be

the magnitude and direction of the current in the loop L2 so that the net magnetic field at the

point O be zero?

(2008 Sam. Paper)

9. (i) What is the relationship between the current and the magnetic moment of a current carrying

circular loop? Use the expression to derive the relation between the magnetic moment of an

electron moving in a circle and its related angular momentum?

(ii) A muon is a particle that has the same charge as an electron but is 200 times heavier than it. If

we had an atom in which the muon revolves around a proton instead of an electron, what would

be the magnetic moment of the muon in the ground state of such an atom?

(2008 Sam. Paper)

10. Derive an expression for the magnetic field along the axis of an air-cored solenoid, using

Ampere’s circuital law.

Sketch the magnetic field lines for a finite solenoid. Explain why the field at the exterior mid-point

is weak while at the interior it is uniform and strong.


************************

1 MARK QUESTIONS

1. Why should the material used for making permanent magnets have high coercivity?

(2007)

2. A (hypothetical) bar magnet (AB) is cut into two equal parts. One part is now kept over the other, so

that pole C2 is above C1. If M is the magnetic moment of the original magnet, what would be the

magnetic moment of the combination so formed? (2008

Sam.Paper)

3. What type of magnetic material is used in making permanent magnets?

4. Horizontal component of Earth's magnetic field at a place is 3 times the vertical component. What

is the value of angle of dip at this place?

5. Horizontal component and vertical component of Earth's magnetic field at a place are equal. what is

the value of angle of dip at this place?

6. What is the value of the horizontal component of the earth's magnetic field at magnetic poles?

7. Write the SI unit of (i) magnetic pole strength (ii) magnetic dipole moment of a bar magnet.

8. Why do magnetic lines of force prefer to pass through ferromagnetic substance thaan through air?

2 MARK QUESTIONS

1. Define magnetic susceptibility of a material. Name two elements, one having positive

susceptibility and the other having negative susceptibility. What does negative susceptibility

signify?

(2008)

2. Define the terms magnetic inclination and horizontal component of Earth's magnetic field at a place.

Establish the relationship between the two with the help of the diagram.

3. An electron in an atoms revolves around the nucleus in an orbit of radius 0.53 A. Calculate the

equivalent magnetic moment if the frequency of revolution of electron is 6.8 x 109 MHz.

4. Explain with the help of diagram the terms (i) magnetic declination and (ii) angle of dip at a given

place.

5. Define neutral point. Draw magnetic lines of force when two identical magnets are placed at a finite

distance apart with their N-poles facing each other. Locate the neutral point.


CLASS XII

WORKSHEET-5

MAGNETISM


6. Derive an expression for the potential energy of a magnetic dipole of dipole moment →

M in a

uniform magnetic field →

B .

7. State and illustrate Curie’s law in magnetism.

8. A magnetized needle is placed 30° with the direction of uniform magnetic field of intensity 3x 10-2

T. The torque acting on the needle is 7.2 x10-4

J.Calculate the magnetic moment of the needle.

3 MARK QUESTIONS

1. (i) What happens when a diamagnetic substance is placed in a varying magnetic field?

(ii) Name the properties of a magnetic material that make it suitable for making a (a) permanent

magnet and (b) core of an electromagnet.

(2009)

2. (i) How does the angle of dip change as one goes from magnetic pole to magnetic equator of the

earth?

(ii) A uniform magnetic field gets modified as shown below when two specimens X and Y are

placed in it. Identify whether specimens X and Y are diamagnetic , paramagnetic, or

ferromagnetic.(2009)

3. If χ stands for the magnetic susceptibility of a given material , identify the class of materials for

which (i) -1 ≤ χ < 0

(ii) 0 < χ < ε (ε stands for a small positive number)

(a) Write the range of relative magnetc permeability of these materials.

(b) Draw the pattern of the magnetic field lines when these materials are placed in an

external magnetic field. (2008

Compt)

4. Name three elements required to specify the earth’s magnetic field at a place. Draw a labeled

diagram to define these elements. Explain briefly how these elements are determined to find

out the magnetic field at a given place on the surface of the earth. (2008

Compt)

5. Name and define the two elements of the earth’s magnetic field otherthan the horizontal component

Earth’s magnetic field.

Why do say that at places like Delhiand Mumbai, a magnetic needle shows the true north direction

quiet accurately as compared to other places in India. (2008

Compt)

6.Draw the field lines of (a) a bar magnet (b) a current carrying finite solenoid and (c) an electric

dipole.

What basic difference do you notice between the magnetic and electric field lines? How do

you explain this difference? (2008

Compt)

X


7. Three identical specimens of magnetic materials Nickel, Antimony, Aluminium are kept in a non-

uniform magnetic field. Draw the modification in the field lines in each case. Justify your answer

8. Why does a paramagnetic substance display greater magnetization for the same magnetizing field

when cooled? How does a diamagnetic substance respond to similar temperature changes?

9. Two similar bars made from two different materials P and Q, are placed, one-by-one, in a non-

uniform magnetic field. It is observed that

(i) bar P tends to move from the weak to the strong field region.

(ii) bar Q tends to move from the strong to the weak field region.

What is the nature of the magnetic materials used for making these two bars? Show, with the help of

a diagram, the behaviour of the field lines, due to an external magnetic field, near each of these two

bars.

10. A short bar magnet placed with its axis inclined at 300 to the external magnetic field of 800 G

acting horizontally experiences a torque of 0.016 Nm. Calculate

(i) the magnetic moment of the magnet,

(ii) the work done by an external force in moving it from most stable to most unstable position.

(iii) What is the work done by the force due to the external magnetic field in the process mentioned

in (ii)?

5 MARK QUESTIONS

1. Distinguish the magnetic properties of dia, para- and ferro-magnetic substances in terms of

(i) susceptibility, (ii) magnetic permeability and (iii) coercivity. Give one example of each of

these materials. Draw the field lines due to an external magnetic field near a (i) diamagnetic,

(ii) paramagnetic substance.

(2007)

1 MARK QUESTIONS

1. Define self-inductance. Give its SI units.

(2009)

2. State the Faraday’s law of electromagnetic induction.

(2009)

3. Define mutual inductance. Give its SI unit.

(2009)

4. A rectangular wire frame, shown below, is placed in a uniform magnetic field directed upward and

normal to the plane of the paper. The part AB is connected to a spring. The spring is stretched and

released when the wire AB has come to the position A’B’ (t=0). How would the induced emf vary

with time? Neglect damping. (2008 Sam.paper)


CLASS XII

WORKSHEET-6

ELECTROMAGNETIC INDUCTION AND AC


5. The electric current in a wire in the direction from B to A is decreasing. What is the direction of

induced current in the metallic loop kept above the wire as shown in the figure?

2 MARK QUESTIONS

1. The flux linked with a large circular coil, of radius R is 0.5 x10-3Wb when a current of 0.5A

flows through small neighbouring coil of radius r. Calculate the co-efficient of mutual inductance

for the given pair of coil. If the current through the small coil suddenly falls to zero, what

would be its effect in the larger coil ? (2008

Compt)

2. Define the co-efficient of mutual inductance and write its SI units.

Obtain the mutual inductance of a pair of circular coils of radii r1 and r2 such that r1<< r2.

The coils have been placed co-axially with their centers coinciding. (2008

Compt)

3. Calculate the current drawn by the primary of a transformer which steps down 200 V to 20 V to

operate a device of resistance20 Ω . Assume the efficiency of the transformer to be 80%.

(2007)

4. Figure shows two long coaxial solenoids, each of length ‘L’. The outer solenoid has an area of

cross- section A and number of turns/ length n1 . The corresponding values for the inner solenoid

are A2 and n2. Write the expression for self inductance L1, L2 of the two coils and their mutual

inductance M. Hence show that M< 21 LL . (2008 Sam.paper)

5. A conducting rod of length l is moved in a magnetic field of magnitude B with velocity v such

that the arrangement is mutually perpendicular. Prove that the emf induced in the rod

is E = B / v. (2006

Compt)

6. A rectangular coil of area A, having number of turns N is at f revolutions per second in a uniform

magnetic field B, the field being perpendicular to the coil Prove that the maximum emf induced in

the coil is . (2006

Compt)

7. Prove that an ideal capacitor, in an a.c. circuit does not dissipate power.

(2008)

8. Derive an expression for the impedance of a.c. circuit consisting of an inductor and a resistor.(2008)

9. Distinguish between the terms 'average value' and 'rms value' of an alternating current. The

instantaneous current from an a.c. source is I = 5 sin (314 t) ampere. What are the average and

rms values of the current?

(2007)


10. An electric bulb B and a parallel plate capacitor C are connected in series to the a.c. mains as

shown in the given figure. The bulb glows with some brightness. How will the glow of the bulb be

affected on introducing a dielectric slab between the plates of the capacitor ? Give reasons in support

of your answer.

(2007)

11. Calculate the current drawn by the primary of a transformer which steps down 200 V to

20 V to operate a device of resistance. Assume the efficiency of the transformer to be 80%.

(2007)

12. An a.c. voltage of 100 V, 50 Hz is connected across a 20 ohm resistor and mH inductor in series.

Calculate (i) impedance of the circuit, (ii) rms current in the circuit

(2007)

13. An air-core solenoid is connected to an a.c source and a bulb. If an iron-core is inserted in the

solenoid, how does the brightness of a bulb change? Give reasons.

14. Derive expression for the mutual inductance of a pair of co-axial solenoids having number of

turns N1 and N2.

15. Define the term ‘self-inductance’ Give its unit. Write an expression for the energy stored in an

inductor when a steady current ‘I’ is passed through it. Is this energy electrical or magnetic”

16. A bar magnet M is dropped so that it falls vertically through the coil C. The graph obtained for

voltage produced across the coil vs. time is shown in figure (b).

(i) Explain the shape of the graph.

(ii) Why is the negative peak longer than the positive peak?

17. In the circuit shown below, R represents an electric bulb. If the frequency of the supply is doubled,

how should

the values of C and L be changed so that the glow in the bulb remains unchanged?


18. An air cored coil L and a bulb B are connected in series to the ac mains as shows in the given

figure

The bulb glows with some brightness. How would the glow of the bulb change if an iron rod

were inserted in the coil? Give reasons in support of your answer.

19. Fig. shows a light bulb (B) and iron cored inductor connected to a DC battery through a switch

(S).

(i) What will one observe when switch (S) is closed?

(ii) How will the glow of the bulb change when the battery is replaced by an ac source of rms

voltage equal to the voltage of DC battery? Justify your answer in each case.

Electromagnetic radiations with wavelength

3 MARK QUESTIONS

1. (i) Define self inductance. Write its SI unit.

(ii) Derive an expression for the self –inductance of a long solenoid of length l, cross-sectional area

A having N number of turns.

(2009)

2. (i) State Faraday’s law of electromagnetic induction.

(ii) A jet plane traveling towards west, at a speed of 1800Km/h. What is the voltage difference

developed between the ends of the wings having a span of 25m, if the Earth’s magnetic field at the

location has a magnitude of 5 x 10-4

T and the dip angle is 30°.

(2009)

3. A metallic rod of length l is rotated at a constant angular speedω, normal to a uniform magnetic

field B. Derive an expression for the current induced in the rod, if the resistance of the rod is

R.(2008)

4. A circular copper disc 10 cm in radius rotates at a speed of 20π rad/s about an axis through its

centre and perpendicular to the disc. A uniform magnetic field of 0.2 T acts perpendicular to the

disc.

(i) Calculate the potential difference developed between the axis of the disc and the rim.

(ii) What is the induced current if the resistance of the disc is 2 Ω ? (2007)

5. Deduce an expression for the self-inductance of a long solenoid of N turns, having a core of

relative permeability (2006 Compt)


6. What are eddy currents? How are these minimized? Mention two applications of eddy currents.

(2006

Compt)

7. A metallic square loop ABCD of size 15 cm and resistance 1Ωis moved at a uniform velocity of v

m/s, in a uniform magnetic field of 2 Tesla, the field lines being normal to the plane of the

paper. The loop is connected to an electrical network of resistors, each of resistance 2Ω.

Calculate the speed of the loop, for which 2 m A current flows in the loop.

8. An inductor 200mH, capacitor 500 µ F, resistor 10Ω are connected in series with 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

(2008)

9. 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.

10. In a series LCR circuit, define the quality factor (Q) at resonance. Illustrate its significance by

giving one example. Show that power dissipated at resonance in LCR circuit is maximum.

(2007)

11. A resistor of 200Ω and a capacitor of 40 µF are connected in series to 220 V a.c. source with

angular frequency ω= 300Hz. Calculate the voltages (rms) across the resistor and the capacitor.

Why is the algebraic sum of these voltages more than the source voltage? How do you resolve this

paradox?

(2007

)

12. When an alternating voltage of 220 V is applied across a device X, a current of 0.5A flows through

it and is in phase with the applied voltage. When the same voltage is applied across another device

Y, the same current flows again through Y but it leads the applied voltage by π/2 radians.

a) Name the devices X and Y

b) Calculate the current flowing in the circuit when same voltage is applied across the series

combination of X and Y.

13. Give any three energy losses in a transformer. Give one method in each to reduce the same.


14. Show diagrammatically two different arrangements used for winding the primary and secondary

coils in a transformer.

Assuming the transformer to be an Ideal one, write expressions for the ratio of its

(i) output voltage to input voltage

(ii) output current to Input current in terms of the number of turns in the primary and secondary

coils. Mention two reasons for energy losses in an actual transformer.

5 MARK QUESTIONS

1. (i) State Lenz’s law. Give one example to illustrate this law. ‘The Lenz’s law is a consequence of

principle of conservation of energy. Justify this statement.

(ii) Deduce an expression for the the mutual inductance of two long co-axial solenoids but having

different radii and different number of turns.

(2009)

2. State the working principle of AC generator with the help of a labeled diagram.

Derive an expression for the instantaneous value of the emf induced in the coil.

Why is the emf maximum when the plane of the armature is parallel to the magnetic field.

(2009)

3. Draw a labeled diagram of a step-up transformer and explain briefly its working.

Deduce the expressions for the secondary voltage and secondary current in terms of the number of

turns of primary and secondary windings.

How is the power transmission and distribution over long distances done with the use of

transformers? (2009)

4. Explain the term 'inductive reactance'. Show graphically the variation of inductive reactance with

frequency of the applied alternating voltage.

An a.c. voltage E =E0 Sin ωt is applied across a pure inductor of inductance L. Show

mathematically that the current flowing through it lags behind the applied voltage by a phase angle

of 2

π. (2007)

5. Explain the term 'capacitive reactance'. Show graphically the variation of capacitive

reactance with frequency of the applied alternating voltage.

An a.c. voltage E =E0 Sin ωt is applied across a pure capacitor of capacitance C. Show

mathematically that the current flowing through it leads the applied voltage by a phase angle2

π

(2007)\

1 MARK QUESTIONS

1. Name the electromagnetic radiations which are produced when high energy electrons are

bombarded on a metal target? (2008Compt,2009)


CLASS XII

WORKSHEET-7

ELECTROMAGNETIC WAVES


2. Name the EM waves used for studying crystal structure of solids. What is its frequency range?

(2009)

3. Write the following radiations in ascending order in respect of their frequencies:

X-rays, microwaves, UV rays and radio waves. (2009)

4. Name the part of the electromagnetic spectrum of wavelength 10-2

m and mention its one

application. (2008)

5. Which physical quantity is the same for X-rays of wavelength 10-10

m and red light of wavelength

6800 Ǻ and radio waves of wave length 500 m?

6. Name the electromagnetic radiation to which the following wavelengths belong:

(a)10-3

m (b) 1 A

7. Which part of the electromagnetic spectrum is used in operating a RADAR ?

8. Which of the following has the shortest wavelength : microwaves, ultra-violet rays, X-rays?

9. A TV tower has a height of 71 m. What is the maximum distance upto which TV transmission can

be received ? Given that the radius of the earth = 6.4 × 106 m. 1

10. What should be the length of dipole antenna for a carrier wave of frequency 6 x 108

Hz ?

11. Name the electromagnetic radiations used for viewing objects through haze and fog.

12. Name the characteristics of electromagnetic waves that

(i) increases

(ii) remains constant

in the electromagnetic spectrum as one moves from radiowave region towards ultravoilet region.

13. From the following, identify the electromagnetic waves having the (i) Maximum (ii) Minimum

frequency.

(i) Radio waves (ii) Gamma-rays (iii) Visible light

(iv) Microwaves (v) Ultraviolet rays, and (vi) Infrared rays.

14. State the condition under which a microwave oven heats up a food item containing water

molecules most efficiently.

15. Special devices like klystron valve or the magnetron valve are used for the production of

electromagnetic waves. Name these waves and also write one of their applications. (2008Compt)

16. What is the ratio of the speeds of γ rays to radiowaves.

17. Give a reason to show that microwaves are better carriers of signals for long range transmission

than radio waves

18. Name the electromagnetic waves that have frequencies greater than these of ultraviolet light but

less than those of gamma rays.


19. What is the name given to that part of electromagnetic spectrum which is used in ‘Radar’?

2 MARK QUESTIONS

1. Name the electromagnetic radiations having the wavelength range from 1mm to 700 nm. Give its

two important applications. (2009)

2. Name the electromagnetic radiations having the wavelength range from 10-1

m to 10-3

m. Give its

two important applications. (2009)

3. Answer the following questions:

(i) Optical and radio telescopes are built on the ground while X-ray astronomy is

possible only from satellites orbiting the Earth. Why?

(ii) The small ozone layer on top of the stratosphere is crucial for human survival.

Why? (2009)

4. The following table gives the wavelength range of some constituents of the electromagnetic

spectrum:

S. No Wavelength range

1

2

3

4

1mm to 700nm

400nm to1nm

1nm to 10-3

nm

<10-3

nm

Select the wavelength range and name the electromagnetic waves that are

(i) Widely used in remote switches of household electronic devices.

(ii) Produced in nuclear reactions. ? (2008Compt,2009)

5. The oscillating magnetic field in a plane electromagnetic wave is given by

By = (8 x 10-6

) sin [2 x10π t + 300π x] j T

(i) Calculate the wavelength of the electromagnetic wave.

(ii) Write down the expression for the oscillating electric field. (2008)

6. A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a

particular point in space and time the electric vector is Calculate at this

point.

7. Draw a labelled diagram of Hertz's experiment for producing electromagnetic waves.

8. Derive the expression for the maximum range up to which T.V. signals can be received on earth's

surface.

9. Why are infrared radiations referred to as heat waves also? Name the radiations which are next to

these radiations in electromagnetic specturm having

(i) Shorter wavelength.

(ii) Longer wavelength.


10. Experimental observations have shown that X-rays

(i) travel in vaccum with a speed of 3 x 108 ms

-1,

(ii) exhibit the phenomenon of diffraction and can the polarized.

What conclusion can be drawn about the nature of X-rays from each of these observations?

11. The following table gives the wavelength range of some constituents of the electromagnetic

spectrum:

S. No Wavelength range

1

2

3

4

> 0.1/m

700 nm to 400nm

400 nm to 1nm

1nm to 10-3

nm

Select the wavelength range and name the electromagnetic waves that are

(i) Used to kill germs in water purifiers.

(ii) Produced by rapid acceleration and deceleration of electrons in aerials.(2008 Compt)

12. An em wave is traveling in a medium with a velocity ivv ˆ=r

The electric field oscillations , of this em

wave are along the y-axis.

(i) Identify the direction in which magnetic field oscillations are taking place.

(ii) How are the magnitudes of electric fields and magnetic fields are related to each other?(2008

Compt)

13. A plane electromagnetic wave travels, in vacuum, along the y-direction. Write the (i) ratio of the

magnitudes, and (ii) the directions of its electric and magnetic field vectors

14. Identify the part of the electromagnetic spectrum which is

(i) suitable for radar systems used in aircraft navigation.

(ii) adjacent to the low frequency end of the electro-magnetic spectrum.

(iii) produced in nuclear reactions.

(iv) produced by bombarding a metal target by high speed electrons.

15. Find the wavelength of electromagnetic waves of frequency 5 x 1019

Hz in free space. Give its two

applications.

16. Find the wavelength of electromagnetic waves of frequency 4 x 109 Hz in free space. Give its two applications.

3 MARK QUESTIONS

1. Draw a labelled diagram o the experimental set-up used by Hertz to produce electromagnetic waves.

Explain how the electromagnetic waves are detected.

2. Define the term ‘critical frequency’ in relation to sky wave propagation of electromagnetic waves.

On a particular day, the maximum frequency reflected from the ionosphere is 10 MHz. On another


day, it was found to decrease to 8 MHz. Calculate the ratio of the maximum electron densities of

the ionosphere on the two days.

3. Draw a labelled diagram of Hertz’s experimental set-up to produce electromagnetic waves.

Explain the generation of- electromagnetic waves using this set-up.

4. The height of a T.V. tower at a place is 400 m. Calculate

(i) the maximum range upto which signals can be received from time tower and

(ii) area covered by the transmission.(Radius of the Earth 6400 km)

5. Explain surface wave and sky wave propagations of radio waves. Why is short wave

communication over long distances not possible by surface wave propagation.

6. Name the following constituent radiations of electromagnetic spectrum which

1. produce intense heating effect.

2. is absorbed by the ozone layer in the atmosphere.

3. is used for studying crystal structure. Write one more application for each of these radiations.

7. Identify the following em waves and give (i) order of frequency (ii) Origin of such waves

(iii)Devices used to detect them.

(a) Used in warfare to see through fog

(b) Absorbed by ozone layer

(c) Used as a tracer probe

(d) Used in telecommunication

(e) Reflected by ionosphere

(f) Stopped by ionosphere.

8. When can a charge act as a source of electromagnetic waves? How are the directions, of the electric

and magnetic field vectors, in an electromagnetic wave, related to each other and to the

direction of propagation of the wave?

Which physical quantity, if any, has the same value for waves belonging to the different parts of the

electromagnetic spectrum?

***************


1 MARK QUESTIONS

1. Draw the wave front coming out of a convex lens when a point source of light is placed at its focus.

(2009)

2. Unpolarised light of intensity I is passed through a Polaroid. What is the intensity of light

transmitted by the Polaroid? (2009)

3. Why are coherent sources required to create interference of light? (2009)

4. Sketch the shape of wavefront emerging from a (i) point source of light (ii) a distant light source

and also mark the rays. (2009)

5. How would the angular separation of interference fringes in Young’s double slit experiment change

when the distance between the slits and the screen is (i) doubled (ii) halved? (2009)

6. If the angle between the axis of the polarizer and the analyzer is 45°, write the ratio of intensities of

original light and the transmitted light after passing through the analyzer. (2009)

7. A partially plane polarised beam of light is passed through a polaroid. Show graphically the

variation of the transmitted light intensity with angle of rotation of the polaroid.

8. Draw the diagram to show the behaviour of plane wavefronts as they pass through (i) a thin prism

(ii) a thin convex lens. (2008Compt)

9. The polarising angle of a medium is 60o. What is the refractive index of the medium?

10. Two identical coherent waves, each of intensity I, are producing an interference pattern. Write the

value of the resultant intensity at a point of (i) constructive interference and (ii) destructive

interference

2 MARK QUESTIONS

1. Define the term linearly polarized light.

When does the intensity of transmitted light become maximum, when a Polaroid sheet is rotated

between two crossed polaroids? (2009)

2. How is a wavefront defined? Using Huygen’s construction draw a figure showing the

propagation of plane wave refraction at a plane surface separating two media. Hence verify Snell’s

law of refraction. (2008)


CLASS XII

WORKSHEET-8

WAVE OPTICS


3. Give two differences between fringes formed in single slit diffraction and Young's double slit

experiment.

4. Light of wavelength 600nm is incident on an aperture of size 2mm. Calculate the distance up to

which the ray of light can travel such that its spread is less than the size of the aperture.

5. What does the statement, “natural light emitted from the sun is unpolarized” mean in terms of the

direction of electric vector ? Explain briefly how plane polarized light can be produced by

reflection at the interface separating the two media

6. Light of wavelength 550 nm. is incident as parallel beam on a slit of width 0.1mm. Find the

angular width and the linear width of the principal maxima in the resulting diffraction pattern on a

screen kept at a distance of 1.1m from the slit. Which of these widths would not change if the

screen were moved to a distance of 2.2m from the slit?

7. What is meant by coherent sources of light? Can two identical and independent sodium lamps act

as coherent sources? Give reason for your answer.

8. Draw a diffraction pattern due to a single slit illuminated by a monochromatic source of light.

Light, of wavelength 500 nm, falls, from a distant source on slit 0.50 mm wide. Find the distance

between the two dark bands, on either side of the central bright band, of the diffraction pattern

observed, on a screen placed 2 m from the slit.

3 MARK QUESTIONS

1. (a) Why do we not encounter diffraction effects of light in everyday observations?

(b) In the observed diffraction pattern due to a single slit, how will the width of the central

maximum be affected if

(i) the width of the slit is doubled?

(ii) the wavelength of light used is increased?

Justify your answer in each case. (2009)

9. In Young’s double slit experiment, monochromatic light of wavelength 630nm illuminates the pair

of slits and produces an interference pattern in which two consecutive bright fringes are separated

by 8.1mm.Another source of monochromatic light produces the interference pattern in which two

consecutive bright fringes are separated by 7.2 mm. Find the wavelength of the light from the

second source.

What is the effect on the interference fringes if the monochromatic source is replaced by a source

of white light? (2009)

3.(a) In a single slit diffraction experiment, a slit of width d is illuminated by red light of wavelength

650nm.For what value of d will

(i) the first minimum fall at an angle of diffraction of 30° and

(ii) the first maximum fall at an angle of diffractin 30°?


(b) Why does the intensity of the secondary maximum become less as compared to the central

maximum? (2009)

4. In a single slit diffraction experiment, when a tiny circular obstacle is placed in the path of light from

a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?

State two points of difference between the interference pattern obtained in Young’s double slit

experiment and the diffraction pattern due to a single slit?? (2009)

5. Explain, using Huygen’ principle, how diffraction is produced by a narrow slit which is illuminated

by a monochromatic light.

Show that central maximum is twice as wide as the other maxima and the pattern becomes narrower

as the width of the slit is increased.

6. Two wavelengths of sodium light 590 nm, 596 nm are used, in turn, to study the diffraction taking

place at a single slit of aperture 2 x 10-6

m. The distance between the slit and the screen is 1.5 m.

Calculate the separation between the positions of first maximum of the diffraction pattern obtained

in the two cases.

7. In Young’s slit experiment, interference fringes are observed on a screen, kept at D from the slits. If

the screen is moved towards the slits by 5 x 10-2

m, the change in fringe width is found to be 3 x 10-

5 m. If the separation between the slits is 10

-3 m, calculate the wavelength of the light used.

8. Why is diffraction of sound waves easier to observe than diffraction of light waves? What two main

changes in diffraction pattern of a single slit will you observe when the monochromatic source of

light is replaced by a source of white light?

9. What are coherent sources of light ? Why are coherent sources required to obtain sustained

interference pattern ? State three characteristic features which distinguish the interference pattern

due to two coherently illuminated sources as compared to that observed in a diffraction pattern due

to a single slit.

10. In a double slit interference experiment, the two coherent beams have slightly different intensities

I and δI(δI << I) . Show that the resultant intensity at the maxima is nearly 4I while that

at the minima is nearly at the minima is nearlyI

I

4

2δ

11. (a) light from a monochromatic source , is made to fall on a single slit of variable width.An

experimentalist records the following data for the linear width of of the principal maxima on a screen

kept at a distance if 1m from the plane of the slit.

S.NO 1 2 3 4 5

Width of the slit

0.1mm

0.2mm

0.3mm

0.4mm

0.5mm


Liner width of the

principal maxima

6mm 3mm 1.98mm 1.52mm 1.2mm

Use any two observations from this data to estimate the value of wavelength of light used.

(b) Show that the Brewster angle ib for a given pair of transparent media is related to their

critical angle ic through the relation ic =Sin -1

(cotib)

12. Verify Snell's law of refraction using Huygens' wave theory.

13. Describe an experiment to show that light waves are transverse in nature

14. State two conditions to obtain sustained interference of light

In Young’s double slit experiment, using light of wavelength 400 nm, in terference fringes of width

‘X’ are obtained. The wavelength of light is increased to 600 nm and the separation between the slits

is halved. If one wants the observed fringe width on the screen to be the same in the two cases, find

the ratio of the distance between the screen and the plane of the interfering sources in the two

arrangements.

15. Two narrow slits are illuminated by a single monochromatic source. Name the pattern obtained on

the screen. One of the slits is now completely covered. What is the name of the pattern now obtained

on the screen? Draw Intensity pattern obtained in the two cases. Also write two differences between

the patterns obtained in the above two cases.

5 MARK QUESTIONS

1. What is interference of light? Write two essential conditions for sustained interference pattern to e

produced on the screen. Draw a graph showing the variation of intensity versus the position on the

screen in Young’s experiment when (a) both the slits are opened and (b) one of the slits is closed.

What is the effect on the interference pattern in Young’s double slit experiment when:

(i) screen is moved closer to the plane of slits?

(ii) separation between two slits is increased. Explain your answer in each case.

2. What is diffraction of light? Draw a graph showing the variation of intensity with angle in a single

slit diffraction experiment. Write one feature which distinguishes the observed pattern from the

double slit interference pattern.How would the diffraction pattern of a single slit be affected when:

(i)the width of the slit is decreased?

(ii) the monochromatic source of light is replaced by a source of white light?

3. State the principle which helps us to determine the shape of the wavefront at a later time from its

given shape at any time. Apply this principle to (i) Show that a spherical/ plane wavefront contiunes


to propagate forward as a spherical/plane wave front. (ii) Derive Snell’s law of refraction by drawing

the refracted wavefront corresponding to a plane wavefront incident on the boundary separating a

rarer medium from a denser medium.

4. What do we understand by ‘polarization’ of a wave? How does this phenomenon help us to decide

whether a given wave is transverse or longitudinal in nature?

Light from an ordinary source (say a sodium lamp) is passed through a polaroid sheet P1 .The

transmitted light is then made to pass through a second polaroid sheet P2 which can be rotated so

that the angle (θ ) between the two polaroid sheets varies from0° to90° .

Show graphically the variation of the intensity of light, transmitted by P1 and P2, as a fuction of the

angle . Take the incident beam intensity as I0. Why does the light from a clear blue portion of the

sky, show a rise and fall of intensity when viewed through a polaroid which is rotated?

5. (a) What are polaroids? How are they used to demonstrate that (i) light waves are transverse in

nature (ii) If an unpolarized light wave is incident, then light wave will get linearly polarized?

(b) What is Brewster’s angle? When an unpolarized light is incident on a plane glass surface, what

should be the angle of incidence so that the reflected and refracted rays are perpendicular to each

other? (2008Compt)

6. What is meant by a linearly polarised light? Which type of waves can be polarised? Briefly explain a

method for producing polarised light.

Two polaroids are placed at 900 to each other and the intensity of transmitted light is zero. What will

be the intensity of transmitted light when one more polaroid is placed between these two bisecting the

angle between them? Take intensity of unpolarised light as I.

1. A sunshine recorder globe of 30cm diameter is made of glass of µ=1.5. A ray enters the globe

parallel to the axis. Find the position from the centre of the sphere where the ray crosses the

axis.

2. Where an object should be placed from a converging lens of focal length 20cmsoto obtain a

real image of magnification 2?

3. A needle placed 35cm from a lens forms an image on a screen placed 90cm on the other side of

the lens. Identify the type of lens and determine its focal length. What is the size of the image

if the size of the needle is 5.0cm?

4. The radius of curvature of each face of bi-concave lens, made of glass of refractive index 1.5 is

30cm. Calculate the focal length of the lens in air.


CLASS XII

WORKSHEET-9

RAY OPTICS


5. An equiconvex lens of focal length 15cm is cut into two equal halves in thickness. What is the

focal length of each half?

6. A convex lens of focal length 0.2m and made of glass (µ=1.5) is immersed in water (µ=1.33).

Find the change in the focal length of the lens.

7. An object is placed at the focus of a concave lens. Where will its image be formed

8. What happens to the frequency when light passes from one medium to another

9. What is the ratio of velocities of two light waves traveling in vacuum and having wavelengths

4000A0 and 8000A

0

10. For the same angle to incidence, the angles of refraction in media P, Q and R are 350,25

0, 15

0

respectively. in which medium will the velocity of light be minimum

11. A convex lens is held in water. What would be the change in the focal length

12. What is the twinkling effect of starlight due to?

13. Watching the sunset on a beach, one can see the sun for several minutes after it has ‘actually

set’. Explain

14. A concave lens made of a material of refractive index gµ is immersed in a medium whose

refractive index lµ is (i) greater than (ii) equal to (iii) less than gµ . When a parallel beam of

light is incident on the lens, trace the path of the emergent rays in each of the above cases.

15. What is total internal reflection? How is critical angle related to refractive index

16. A ray of light while traveling from a denser to a rater medium undergoes total internal

reflection. Derive the expression for the critical angle in terms of the speed of light in the

respective media

17. Show by drawing ray diagrams how a totally internal reflecting glass prism can be used to

deviate a ray of light through (i) 900 (ii) 180

0 and invert it

18. How do optical fibers transmit light without significant absorption? Mention one practical

application of optical fibres

19. What are optical fibres? How are light waves propagated in them?

20. What is critical angle? Give an application of total internal reflection

21. Show through a labeled ray diagram the formation of mirage in deserts

22. write the conditions for total internal reflection to take place

23. Draw a ray diagram showing the formation of image by a concave lens for µ∠f. describe the

nature of image

24. Prove that µ=sinC

1, where C is the critical angle

25. Derive the lens formula for a convex lens


26. In a Young’s experiment, the width of the fringes obtained with light of wavelength 6000A0 is

2.0mm. what will be the fringe width, if the entire apparatus is immersed in a liquid of

refractive index 1.33

27. Show that a convex lens produces an N times magnified image when the object distances, from

the lens, have magnitudes Here f is the magnitude of the focal length of the lens.

Hence find the two values of object distance, for which a convex lens, of power 2.5 D, will

produce an image that is four times as large as the object? (3mks-2004compt)

28. A converging and \diverging lens of equal focal lengths are placed coaxially in contact. Find

the power and focal length of the combination.(2mks 2004)

29. Draw a ray diagram to show the formation of the image of a point object

placed in medium of refractive index ‘n1' on the principal axis of a convex spherical surface of

radius of curvature ‘R’ and refractive index ‘n2'. Using the diagram, derive the relation

where ‘u’ and ‘v’ have their usual meanings.

A converging lens of focal length 50 cm is placed coaxially in contact with another lens of

unknown focal length. If the combination behaves like a diverging lens of focal length 50 cm,

find the power and nature of the second lens. (5mks 2004)

30. Draw a ray diagram to show the formation of the image of a distant object by an astronomical

telescope in the normal adjustment position. Obtain an expression for the magnifying power of

the telescope in this adjustment

Define resolving power of a telescope. How would it change with the increase of (i) aperture of

the objective and (ii) wavelength of light? (5mks 2004)

31. With the help of a ray diagram, show the formation of image of a point object by refraction of light

at a spherical surface separating two media of refractive indices n1 and n (n2 > n1) respectively.

Using this diagram, derive the relation.

Write the sign conventions used. What happens to the focal length of convex lens when it is

immersed in water? 5

32. 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. 2

33. A compound microscope with an objective of 2.0 cm focal length and an eye-piece of 4.0 cm focal

length, his 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. 2


34. A spherical surface of radius of curvature R, separates a rarer and a denser medium as shown In

the figure.

35. Complete the path of the incident ray of light, showing the formation of a real image. Hence derive the relation connecting object distance ‘u’, image distance ‘v’, radius of curvature R and the refractive indices a and ; of the two media Briefly explain, how the focal length of a convex lens changes, with increase in wavelength of incident light.

36. Using the data given below, state as to which of the given lenses will you prefer to use as (i) an

eyepiece, and (ii) an objective, to construct an astronomical telescope. Give reason for your

answer. 2

Lens Power Aperture

L1

L2

L3

L4

1D

10D

10D

20D

0.01 m

0.05 m

0.02 m

0.02 m

37. Using the data given below, state as to which of the given lenses will you prefer to use as (i) an

eye-piece, and (ii) an objective, to design a compound microscope. Give reason for your

answer. 2

lens Power Aperture

A 20 D 0.02 m

B 10 D 0.02 m

C 10 D 0.05 m

D 1.0 D 0.1 m


1. 1. Light of wavelength 3500A0 is incident on two metals A and B. Which metal will yield

photoelectrons if their work functions are 4.2eV and 1.9eV respectively? Given h=6.62×10-

34Js.

2. Find the photon energy in eVfor electromagnetic wave of wavelength 1m. Given h=6.63×10-

34Js.

3. Calculate the threshold frequency of photon for photoelectric emission from a metal of work

function 0.1eV.

4. Calculate the kinetic energy of photoelectrons in eV emitted on shining light of wavelength

6.2×10-8

m on a metal surface. The work function of metal is 0.1eV. Given h=6.6×10-34

Js.

5. If the intensity of incident radiation on a metal surface is doubled, what happens to the kinetic

energy of the electrons emitted?

6. Assuming that electrons are free inside a solid, sketch graphically the distribution n (ν) of

electrons with speedν.

7. The maximum kinetic energy of electrons emitted by a photocell is 3eV. What is the stopping

potential

8. What is the effect on the velocity of the emitted photoelectrons if the wavelength of the

incident light is decreased?

9. Is photoelectric emission possible at all frequencies? Give reasons fro your answer

10. All the photoelectrons are not emitted with the same energy. The energies of photoelectrons

are distributed over a certain range. Why?

11. radiation of frequency 1015

Hz is incident on two photosensitive surfaces P and Q. following

observations are made

(i) Surface P: photoemissions occurs but the photoelectrons have zero kinetic energy

(ii) Surface Q: photoemission occurs and photoelectrons have some kinetic energy

Which of these has a higher work function? If the incident frequency is slightly reduced,

what will happen to photoelectron emission in the two cases?

12. If the frequency of incident radiation on a photocell is doubled for the same intensity, what

changes will you observe in (i) kinetic energy of photoelectrons emitted (ii) photoelectric

current

13. A radio transmitter operates at a frequency of 880Hz and a power of 10kW. Find the number

of photons emitted per second. Given h=6.6×10-34

Js.

14. Two metals A and B have work functions 2eV, 4eVrespectively. Which metal has lower

threshold wavelength for photoelectric effect

15. Draw a graph showing the variation of stopping potential with frequency of incident radiation

in relation to photoelectric effect. Deduce an expression for the slope of this graph using

Einstein’s photo electric equation?


CLASS 12

WORKSHEET-10

DUAL NATURE OF MATTER AND RADIATION


16. Draw a graph to how the variation of stopping potential with frequency of radiation incident on

a metal plate. How can the value of Plank’s constant be determined from this graph

17. An electron and a photon have the same de Brogile wavelength of 10-10

m. which of the two

has greater kinetic energy

18. An electron and photon have got the same de Brogile wavelength, which of the two has

greater total energy

19. What is the rest mass of a photon?

What is the momentum of a photon of wavelengthλ?

20. Which photon is more energetic-violet or red?

21. Calculate the de Brogile wavelength of electron of energy400Ev. Given h=6.6×10-34

Js.

22. What is photoelectric effect ? Give any two practical applications of this effect. Write

Einstein’s photoelectric equation and use it to explain the (i) independence of maximum

energy of the emitted photoelectrons from intensity of incident light. (ii) Existence of a threshold

frequency for a given photosensitive surface.

23. A photon of wavelength 3310 A° falls on a photocathode and an electron of energy 3 × 10-19J is

ejected. If the wavelength of the incident photon is changed to 5000 A°, the energy of the ejected

electron is 7.91 × 10-20 J. Calculate the Planck’s constant and the threshold wavelength of the

photon for this photo cathode.

24. Define work function for a given metallic surface.

25. Name the experiment for which the following graph, showing the variation of intensity of

scattered electrons with the angle of scattering, was obtained. Also name the important

hypothesis that was confirmed by this experiment.

26. Obtain Einstein’s photoelectric equation. Explain how it enables us to understand the

(i) linear dependence, of the maximum kinetic energy of the emitted electrons, on the

frequency of the incident radiation.

(ii) existence of a threshold frequency for a given photo emitter.

27. Define the term ‘work function’ of a metal. The threshold frequency of a metal is f0. When the

light of frequency 2f0 is incident on the metal plate, the maximum velocity of electrons emitted

is v1. When the frequency of the incident radiation is increased to 5f0, the maximum velocity of

electrons emitted is v2. Find the ratio of v1 to v2.

28. Red light, however bright it is, cannot produce the emission of electrons from a clean zinc

surface. But even weak ultraviolet radiation can do so. Why?


X-rays of wavelength fall on photosensitive surface, emitting electrons. As sinning X-rays

of wavelength fall on a photosensitive Surface, emitting electrons. Assuming that the work

function of the surface can be neglected, prove that the de Broglie wavelength of electrons

emitted will be

29. Two metals A and B have work functions 4 eV and 10eV respectively. Which metal has higher

threshold wavelength?

30. Given below is the graph between frequency (v) of the incident light and maximum kinetic

energy (Ek) of emitted photoelectrons. Find the values of (1) thresh old frequency, and (ii)

work function from the graph.

31. In a photoelectric effect experiment, the graph between the stopping potential 'V' and

frequency 'v' of the incident radiations on two different metal plates P and Q are shown in the

figure.

(a) Which of the two metal plates, P and Q has greater value of work function?

(b) What does the slope of the lines depict?

32. Electrons are emitted from a photosensitive surface when it is illuminated by green light but

electron emission does not take place by yellow light. Will the electrons be emitted when the

surface is illuminated by (i) red light, and (ii) blue light?

33. Ultraviolet light of wavelength 2271 from a 100 W mercury source radiates a photo cell

made of molybdenum metal. If the stopping potential is 1.3 V, estimate the work function of

the metal. How would the photo cell respond to high intensity (10 5 Wm -2 ) red light of

wavelength 6328 produced by a He - Ne laser? Plot a graph showing the variation of


photoelectric current with anode potential for two light beams of same wavelength but different

intensity.

34.Ultraviolet light is incident on two photosensitive materials having work functions W1 and W2

( W1 > W2), In which case will the kinetic energy of the emitted electrons be greater? Why?

35. Mention the significance of Davisson-Germer experiment. An particle and a proton are

accelerated from rest through the same potential difference V. Find the ratio of de-Broglie

wavelengths associated with them.

36. With that purpose was famous Davisson-Germer experiment with electrons performed?

37. Define the terms threshold frequency and stopping potential in relation to the phenomenon of

photoelectric effect. How is the photoelectric current affected on increasing the (i) frequency

(ii) intensity of the incident radiations and why?

38. 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 1

m 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

(i) photoelectric current,

(ii) stopping potential.

39. Calculate the de-Broglie wavelength of (i) an electron (in the hydrogen atom) moving with a

speed of the speed of light in vacuum and (ii) a ball of radius 5mm and mass 3 x 10-2 kg.

moving with a speed of 100ms-1.Hence show that the wave nature of matter is important at the

atomic level but is not really relevant at the macroscopic level.

40. Show that the de- Broglie wavelength of electron of energy E is given by the relation

λ =mE

h

2


01. 1. A nucleus makes a transition from one permitted energy level to another level of lower

energy. Name the region of electromagnetic spectrum to which the emitted photon belongs.

What is the order of its energy in electron volts?

02. Write four characteristics of nuclear forces.

03. Neutrons, in thermal equilibrium with matter at a temperature T Kelvin, are known to have an

average kinetic energy of 2

3 kT. Compute the de-Broglie wavelength associated with a

neutron at 300K.

04. A star converts all its hydrogen to helium achieving 100 % helium composition. It then

converts helium to carbon via the reaction

MeV. 7.27 C He He He 12

6

4

2

4

2

4

2 +→++

The mass of the star is 5.0 × 1032

kg and it generates energy at the rate of 5 × 1030

watt. How long will it take to convert all its helium to carbon.

05. A nucleus of mass M, initially at rest, splits into two fragments of masses M/3 and 2M/3. Find

the ratio of de-Broglie wavelengths of the two fragments.

06. Define the terms (i) disintegration constant and (ii) half-life for a radioactive nucleus. Obtain

the relation between these two.

07. Define mass number (A) of an atomic nucleus. Assuming the nucleus to be spherical, give the

relation between the mass number (A) and the radius of nucleus. Calculate the density of

nuclear matter. Radius of nucleus of H1

1 = 1.1 × 10-5

A°. What is the ratio of the order of

magnitude of density of nuclear matter and density of ordinary matter?

08. Obtain the relationship between stopping potential and frequency of incident radiations for the

photo emission.

09. X – rays of wavelength 0.82 A° fall on a metallic surface. Calculate the de-Broglie wavelength

of the emitted photo electrons. Neglect the work function of the surface.

10. A radioactive nucleus decays by emitting β particle. How will the proton-neutron ratio of the

daughter nucleus change as compared to the parent nucleus?

11. Calculate the de Broglie wavelength associated with an electron of energy 200 eV. What will

be the change in this wavelength if the accelerating potential is increases to four times its

earlier value.

12. Prove mathematically that the fractionN

N o , of a radioactive element left over after a time t

equals 2 x wherex

1 Tt

= and T denotes half life of the element.


CLASS 12

WORKSHEET-11

ATOMS AND NUCLEI


13. A graph is plotted between the maximum kinetic energy of emitted photoelectrons and the

frequency of incident radiations. Which physical constant can be determined from the slope of

this graph ?

14. Define the term binding energy of a nucleus. Which of the two, Baor U 144

56

235

92 has a higher

value of B.E/nucleon ? Give the formula for B.E/nucleon for a nucleus of mass number A and

atomic number Z.

15. Name the nucleus of low atomic number that is much more stable than its immediate

neighbours.

16. On the basis of photon theory, obtain Einstein’s photo electric equation. Use this equation to

show that there must exist a threshold frequency for each photo sensitive surface.

17. Radiations of frequencies ν1 and ν2 are made to fall in turn, on a photo sensitive surface. The

stopping potentials required for stopping the most energetic emitted photo electrons in the two

cases are V1 and V2 respectively. Obtain a formula for calculating Planck’s constant and the

threshold frequency in terms of these parameters.

18. What are thermal neutrons? Why are neutrons considered as ideal particles for nuclear fission?

19. A photon of wavelength 3310 A° falls on a photo cathode and an electron of energy 3 × 10-19

J

is ejected. If the wavelength of the incident photon is changed to 5000 A°, the energy of the

ejected electron is 7.91 × 10-20

J. Calculate the value of Planck’s constant and the threshold

wavelength of the photon for this photo cathode.

20. A radioactive isotope decays in the following sequence :

C B A 01 →→+ αβ

If the mass number and the atomic number of C are

176 and 71 respectively, find the mass number and the atomic number of A and

B. Which of these are isobars?

21. A nucleus, of mass number at has a mass defect . Give the formula, for the binding energy

per nucleon, of this nucleus.

22. Explain how radioactive nuclei can emit even though atomic nuclei do not

contain these particles. Hence explain why the mass number of a radioactive nuclide does not

change during

Use the basic law of radioactive decay, to show that radioactive nuclei follow an exponential

decay law. Hence obtain a formula, for the half-life of a radioactive nuclide, in terms of its

disintegration constant.

23. Draw the general shape of the plot of the binding energy per nucleon versus the mass number

for different nuclei. Hence explain why we must expect a release of nuclear energy during (i)

nuclear fission, (ii) nuclear fusion.

24. Group the following six nuclides into three pairs of 8sotones and (iii) isobars:

How does the size of a nucleus depend on its mass number’ Hence explain why the density of

nuclear matter should be independent of the Size of the nucleus.

25. The decay constant, for a given radionuclide, has a value of 1.386 day-1

. After how much time

will a given sample of this radionuclide get reduced to only 6.25% of its present number?


26. Write the nuclear decay process for of

27. ‘Heavy water is often used as a moderator in thermal nuclear reactors.’ Give reason.

28. Draw the graph showing the variation of binding energy per nucleon with mass number.

Explain, using this graph, why heavy nuclei can undergo fission.

29. Define the terms: ‘half-life period’ and ‘decay constant’ of a radioactive sample. Derive the

relation between these terms.

30. When a deuteron of mass 20141 u and negligible kinetic energy is absorbed by a lithium

nucleus of mass 6.0155 u, the compound nucleus disintegrates spontaneously into two

a1pha pari!cles, each of mass 4.0026 u. Calculate the energy in joules carried by each alpha p

(lu — 1.66 x 1027

kg)

31. Calculate the binding energy per nucleon of nucleus

[Given:

mn (mass of a neutron) =1.008665 u

mp (mass of a proton) =1.007825 u]

32. Write the nuclear reactions for the following:

(i)

(ii)

(iii)

33. Draw a labelled diagram of experimental setup of Rutherford’s alpha particle scattering

experiment. Write two important inferences drawn from this experiment.

34. The sequence of stepwise decays of a radioactive nucleus is

If the nucleon number and atomic number for D2 are 176 and 71 respectively, what are the

corresponding values of D and D3 ? Justify your answer in each case.

35. (a) Draw a graph showing the variation of potential energy of a p of nucleons as a function of

their separation. Indicate the regions in which nuclear force is (i) attractive, and (ii) repulsive.

(b) Write two characteristic features of nuclear force which distinguish it from the Coulomb

force.


36. (a) Draw a graph showing the variation of potential energy of a p of nucleons as a function of

their separation. Indicate the regions in which nuclear force is (i) attractive, and (ii) repulsive.

(b) Write two characteristic features of nuclear force which distinguish it from the coulomb

force.

37. (a) Show that the decay rate 'R' of a sample of a radionuclide is related to the number of

radioactive nuclei 'N' at the same instant by the expression

(b) The half-life of U against a - decay is 1.5 x 1017

s. What is the activity of a sample of

U having 25 x 1020

atoms?

38. (a) Draw the energy level diagram showing the emission of -particles followed by

by a Co nucleus.

(b) Plot the distribution of kinetic energy of J articles and state why the energy spectrum is

continuous.

39. A radioactive sample contains 2.2 ing of pure C which has half-life period of 1224 seconds.

Calculate

(i) the number of atoms present initially.

.(ii) the activity when 5 of the sample will be left.

40. The half-life of U against -decay is 4.5 X 109 years. Calculate the activity of 1 g sample

of U.

41. State two characteristics of nuclear force. Why does the binding energy per nucleon decrease

with increase in mass number for heavy nuclei like 235

U?

42. Define the term decay constant of a radioactive nucleus.

Two nuclei P, Q have equal number of atoms at t = 0. Their half lives are 3 hours and 9 hours

respectively. Compare their rates of disintegration, after 18 hours from the start.

43. Explain, with the help of a nuclear reaction in each of the following cases, how the neutron to

proton ratio changes during (i) alpha-decay (ii) beta-decay?

44. Why is the mass of a nucleus always less than the sum of the masses of its constituents,

neutrons and protons.

45. If the total number of neutrons and protons in a nuclear reaction is conserved, how then is the

energy absorbed or evolved in the reaction? Explain.


+ 5V +7V +2V

1. Give the ratio of the number of holes and the number of electrons in an a] intrinsic semiconductor

b] extrinsic i) n-type ii) p-type semiconductor.

2. In a transistor, the base current is changed by 10 µ A. This results in a change of 0.01V in base to

emitter voltage and change of 1 mA in the collector current. Find (i) the current gain β ac and (ii)

transconductance gm. If this transistor is used as an amplifier with a load resistance of 5k Ω ,

calculate the voltage gain of the amplifier.

3. With the help of energy band diagrams distinguish between conductors, semiconductors and

insulators.

4. If the output of a 2-input NAND gate is fed as the input to a Not gate [i] name the new logic gate

[ii] write down the truth table.

5. If the base region of transistor is made large, as compared to a usual transistor, how does it affect i]

the collector current ii] current gain of the transistor?

6. Draw a circuit diagram with diodes for the following: a] Full wave rectifier b] half wave rectifier

c] demodulator d] OR – gate e] AND – gate .f] Voltage regulator.

7. Draw a circuit diagram with transistors for the following: a] Amplifier b] Oscillator c] NOT – gate

d ] A.M Modulator.

8. Why C.E amplifier is preferred over C.B amplifier?

9. How does the depletion layer width vary when a diode is i] forward biased ii] reverse biased?

10. How does the resistance vary when a diode is i] forward biased ii] reverse biased?

11. In the following diagrams which of the diodes are forward biases and which are reverse biased.

12. Write down the truth table for the following digital circuits

-12 V


CLASS 12

WORKSHEET-12

ELECTRONIC DEVICES


13. If the emitter and base region of a transistor have the same doping concentration, state how i]

collector current and ii] d.c current gain of the transistor will change.

14. Explain why there is a phase difference of π in C.E transistor amplifier.

15. State two reasons for preferring C.E amplifier.

16. Does the following transistor work?

17. The following signal is applied across i] OR gate ii] AND gate iii] NOT gate iv] NAND gate v]

NOR gate vii] XOR gate. Identify the output wave forms.

18. A p-n photodiode is fabricated from a semiconductor with band gap of 2.8eV. Can it detect

wavelength of 6000nm?

19. Explain how a Zener diode can regulate voltage.

20. Why magnetic couplings are used while designing an oscillator. Can you redraw the circuit

replacing the magnetic coupling with any other component?

21. (a) Draw a circuit diagram to study the input and output characteristics of an n-p-n transistor in its

common emitter configuration. Draw the typical input and output characteristics.

(b) Explain with the help of a circuit diagram the working of n-p-n transistor as a common emitter

amplifier.

22. How is a zener diode fabricated so as to make it a special purpose diode. Draw I-V characteristics

of zener diode and explain the significance of breakdown voltage. Explain briefly with the help of

a circuit diagram, how a p-n junction diode work as a half wave rectifier.

0V

+1V

5V

a

0V

5V

b

0V

-2V


CLASS XII

WORKSHEET

COMMUNICATION SYSTEMS


1 MARK QUESTIONS:

1. Suggest a possible communication channel for the transmission of a message signal which

has a band width of 5MHz. (2007)

2. Distinguish between analog and digital communication.

3. Name the types of communication systems according to the made of the transmission.

4. Name an appropriate communication channel needed to send a signal of band-width

100 kHz over a distance of 8 km. (2005)

5. What should be the length of a dipole antenna for a carrier wave of frequency 6×108

Hz ?

6. A TV tower has a height of 71 m. What is the maximum distance upto which TV

transmission can be received ? Given that the radius of the earth = 6.4 × 106

m. (2007)

2 MARK QUESTIONS

1. A T. V transmitting antenna is 125m tall. How much service area can this transmitting

antenna cover, if the receiving antenna is at the ground level? (R=6400Km.) (2008)

2. Draw the block diagram of a simple amplitude modulation. Explain briefly how amplitude

modulation is achieved. (2008)

3. A transmitting antenna at the top of a tower has a height of 36m and the height of receiving

antenna is 49m. What is the maximum distance between them, for satisfactory

communication in the LOS mode? (2008)

4. 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?

5. Distinguish between ‘point to point’ and ‘broadcast’ communication modes. Give one

example of each.

6. We do not choose to transmit an audio signal by just directly converting it to an e.m. wave

of the same frequency. Give two reasons for the same.

7. What is LOS communication? Why is it not possible to use sky wave propagation for

transmission of TV signals? (2009)

8. What is modulation ? Explain the need of modulating a low frequency information

signal.(2007)

3 MARK QUESTIONS

1. What is the role of band pass filter in Amplitude modulation?

Draw a block diagram of a detector of AM signal and briefly explain how the original signal

is obtained from the modulated wave? (2008)

2. Explain why high frequency carrier waves are needed for effective transmission of signals.

A message signal of 12 kHz and peak voltage 20V is used to modulate a carrier wave of

frequency 12MHz and peak voltage 30V. Calculate the (i) modulation index (ii) side band

frequencies. (2008)

3. Draw a plot of the variation of amplitude versus ω for an amplitude modulated wave. Define

modulation index. State its importance for effective amplitude modulation. (2008)


4. In a diode AM demodulator, the output circuit consists of R =1kΩ and C =10pF. A carrier

signal, of 100kHz, is to be demodulated. Is the given set up good for this purpose? If not,

suggest a value of C that would make the diode circuit good for de modulating this carrier

signal. (2007 Compt)

5. Define the term modulation index for an AM wave. What would be the modulation index

for an AM wave for which the maximum amplitude is a while the minimum amplitude is

b?

6. What is space wave propagation? Which two communication methods make use of this

mode of propagation? If the sum of the heights of transmitting and receiving antennae in

line of sight of communication is fixed at h, show that the range is maximum when the two

antennae have a height 2

h each.

7. (i) Draw the block diagram of a communication system.

(ii) What is meant by ‘detection’ of a modulated carrier wave? Describe briefly the essential

steps for detection.

8. What is meant by detection of a communication system? With the help of a block diagram

explain the detection of AM signal? (2009)

9. Explain the following terms :

(i) Ground waves

(ii) Space waves

(iii) Sky waves

10. A ground receiver station is receiving a signal at (a) 5 MHz and (b) 100 MHz, transmitted

from a ground transmitter at a height of 300 m located at a distance of 100 km. Identify

whether it is coming via space wave or sky wave propagation or satellite transponder.

(Given the value of radius of the earth is 6400 km and maximum electron density, Nmax

=1012

m-3

)


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