HOTS QUESTIONS

SUB.: PHYSICS , CLASS-XII

UNIT-1

ELECTROSTATICS

1. Find the charge on the capacitor as shown in the circuit. 2. In a parallel plate capacitor with air between the plates, each plate has an area of 5 × 10–3 m2 and the separation between the plates is 2.5 mm. (i) Calculate the capacitance of the capacitor. (ii) If this capacitor is connected to 100 V supply, what would be the charge on each plate? (iii) How would charge on the plates be affected, if a 2.5 mm thick mica sheet of K = 8 is inserted between the plates while the voltage supply remains connected? 3. A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another

uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

4.A fully charged capacitor C with initial charge qo is connected to a coil of self inductance L at t=0.

What is the time at which the energy is stored equally between the electric and magnetic field?

5.A thin semicircular ring of radius r has a positive charge q distributed uniformly over it. Find net

field E at the centre O

6.A battery is used to charge a parallel plate capacitor till the potential difference between the plates

becomes equal to the electromotive force of the battery. What is the ratio of the energy stored in the

capacitor and the work done by the battery.

7.A charged particle q is shot towards another charged particle Q which is fixed, with a speed of v. It

approaches Q up to a closest distance r and then returns. If q was given a speed 2v, what would be the

closest distance of approach.

8.Five identical cells, each of emf E and E and internal resistance r, are connected in series to form a)

an open b) closed circuit. If an ideal voltmeter is connected across three cells, what will be its reading

9.An electron in a hydrogen atom is considered to be revolving around a proton with a velocity e2/n

in a circular orbit of radius n2 /me2. If I is the equivalent current express it in terms of m, e, n.

10.In the given circuit with a steady current, calculate the potential

drop across the capacitor in terms of V

11.The length of a wire of a potentiometer is 100 cm and the emf of its stand and cell is E volt. It is

employed to measure the emf of a battery whose internal resistance is 0.5 ohm. If the balance point is

obtained at l= 30 cm from the positive end, What is the emf of battery?

12.A wire when connected to 220 V mains supply has power dissipation P1. Now the wire is cut into

two equal pieces which are connected in parallel to the same supply . Power dissipation in this case is

P2. Then Find P2:P1?

13.(a) A point charge (+Q) is kept in the vicinity of uncharged conducting plate. Sketch electric field lines between the charge and the plate. (b) Two infinitely large plane thin parallel sheets having surface charge densities ϭ1 and ϭ2 as shown in the figure. Write the magnitudes and directions of the net fields in the regions marked II and III.

14. Two equal balls having equal positive charge ‘q’ coulombs are suspended by two insulating strings of equal length. What would be the effect on the force when a plastic sheet is inserted between the two? 15. Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10–7 m2 carrying a current of 1.5 A. Assume the density of conduction electrons to be 9 1028 m–3. 16. Figure shows the field lines due to a negative point charge. Give the sign of the potential energy difference of a small negative charge between the points A and B. 17. Two charges of magnitudes -2Q and + Q are located at point (a, 0) and (4a, 0) respectively. What is

the electric flux due to these charges through a sphere of radius ‘3a’ with its centre at the origin?

18. Let two conducting spheres of radii r1 and r2 be joined by thin wire and total charge q be given to them. Prove that the charges on the spheres will be in the ratio of their radii.

19.. Two charges -q and + q are located at points A(0, 0, - a) and B(0, 0, + a) respectively. How much

work is done in moving a test charge from point P (7, 0, 0) to Q (-3, 0, 0)?

20. A parallel plate capacitor is charged to a potential difference V by a dc source. The capacitor is

then disconnected from the source. If the distance between the plates is doubled ,state with

reason how the following will change

i) electric field between the plates ii) capacitance iii) energy stored in the capacitor

21. A test charge ‘q’ is moved without acceleration from A to C along

the path from A to B, then from B to C in electric field E as shown in

the figure.

(i) Calculate the potential difference between A and C.

(ii) At which point (of the two) is the electric potential more and why?

22.S1 and S2 are two hollow concentric spheres enclosing charges Q and 2Q as shown in the figure. 2Q (i) What is the ratio of the electric flux through S1 and S2? Q (ii) How will the electric flux through sphere S1 change, if S1 S2

a medium of dielectric constant 5 is introduced in the

space inside S1 in place of air?

23. A point charge q is placed at O as shown in the figure.

Is Vp-Vq +ve or –ve when (i) q>0, (ii) q<0? Justify your answer.

24.The graph shows the variation of voltage V across the plates of two capacitors A and B versus increase of charge Q stored on them. Which of the two capacitor shave higher capacitance? Give reason for your answer?

25.Two dielectric slabs of dielectric constant K1 and K2 are filled in between the two plates, each of area A, of the parallel plate

capacitor as shown in the figure. Find the net capacitance of

the capacitor? Area of each plate = A/2

26.Two point electric charges of value q and 2q are kept at a distance d apart from each other in air. A third charge Q is to be kept along the same line in such a way that the net force acting on q and 2q is zero. Calculate the position of charge Q in terms of q and d.

27. Why should electrostatic field be zero inside a conductor?

28. Net capacitance of three identical capacitors in series is 1μ F. What will be their net capacitance if

connected in parallel? Find the ratio of energy stored in the two configurations if they are both

connected to the same source.

29.Consider a uniform electric field E = 3 X 103 i N/C. what is the net flux passing through a cube of side 20 cm oriented so that its faces are parallel to the coordinate plane ?

30. Obtain the equivalent capacitance of the network in

adjoining figure. For a 300V supply, determine the charge

and voltage across each capacitor.

31. A hollow cylindrical box of length 1 m and area of cross-

section 25 cm2 is placed in a three dimensional coordinate

system as shown in the figure. The electric field in the region

is given by E = 50 x ,

where E is in NC–1 and x is in meters. Find

(i) Net flux through the cylinder.

(ii) Charge enclosed by the cylinder.

32. A proton is placed in a uniform electric field directed along the positive x- axis. In which direction will it tend to move? 33. Why the electric field inside a dielectric decreases when it is placed in an external electric field? 34. A hallow metal sphere of radius 5 cm is charged such that the potential on it surface is 10V. What is the potential at the center of the sphere ? 35. Show graphically the variation of charge q with time t when a condenser is charged. 36. If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux

through the Gaussian surface change?

37. In which orientation ,a dipole placed in a uniform electric field is in (i) stable , (ii) unstable equilibrium ? 38.Net capacitance of three identical capacitors in series is 1μ F. What will be their net capacitance if

connected in parallel? Find the ratio of energy stored in the two configurations if they are both

connected to the same source.

39 .Consider a uniform electric field E = 3 X 103 i N/C. what is the net flux passing through a cube of side 20 cm oriented so that its faces are parallel to the coordinate plane ? 40. A capacitor of 200 pF is charged by a 300V battery. The battery is then disconnected and the

charged capacitor is connected to another uncharged capacitor of 100 pF. Calculate the difference

between the final energy stored in the combined system and the the initial kinetic energy stored in

single capacitor,

41. A hollow cylindrical box of length 1 m and area of cross-

section 25 cm2 is placed in a three dimensional coordinate

system as shown in the figure. The electric field in the region

is given by E = 50 x , where E is in NC–1 and x is in meters. Find

(i) Net flux through the cylinder.

(ii) Charge enclosed by the cylinder.

42. A 4μF capacitor is charged by a 100V supply. The supply is then disconnected and the charged

capacitor is connected to another uncharged 2μF capacitor. What is common potential .How much

electrostatic energy of the first capacitor is lost in the process of attaining the steady situation?

43. A proton is placed in a uniform electric field directed along the positive x- axis. In which direction

will tend to move?

44. What is the work done in moving a test charge q through a distance 1cm along the equatorial axis

of an electric dipole?

45.Three point charges +2q, -q and + 3q are enclosed within a surface .Within a surface S .What is the

electric flux due to this configuration?

46. A hallow metal sphere of radius 5cm is charged such that the potential on it surface is 10V. What is

the potential at the center of the sphere ?

47. A metal plate is introduced between the plates of a charged parallel plate capacitor. What its effect

on the capacitance of the capacitor?

48. A spherical Gaussian surface encloses a charge of 8.85 x10 -10 C (i) Calculate the electric flux

passing through thr surface (ii) How would the flux change if the radius of the Gaussian surface is

doubled and why?

49.State Gauss’s law in electrostatics. Use this law to derive the expression for the electric field due to

a uniformly charged infinite thin plate sheet.

50. A capacitor of 200 pF is charged by a 300V battery. The battery is then disconnected and the

charged capacitor is connected to another uncharged capacitor of 100 pF. Calculate the difference

between the final energy stored in the final energy stored in the combined system and the initial

energy stored in the initial kinetic energy stored in single capacitor,

51. Two point charge 3 micro coulomb and -3 micro coulomb are located 20cm a part in vacuum (i)

Calculate the electric field at the midpoint O of the line AB joining two charges (ii) What is the force

experienced by negative test charge of magnitude 1.5 x 10-9 C placed at this point.

52. An infinitely long cylinder of radius R carries a uniform volume charge density q C/m3 . Obtain

an expression for electric field at a point (a) inside (b) out side the cylinder

53. Let two conducting sphere spheres of radii r1 and r2 be joined by a thin wire and a total charge q

be given to them , prove that the charges on the spheres will be in the ratio of their radii.

54.A slab material of dielectric constant K has the same area as the plates of a parallel plate capacitor

but has a thickness ½ d , Where d is the separation between the plate . Find the expression for the

capacitance when the slab is inserted between the plates.

55. A dielectric slab of thickness t is introduced between the plates of parallel plate capacitor

,separated by distance d (t<d) .Derive an expression for the capacitance of the capacitor .What will be

its capacitance when t=d

56. Show by graph how q given to a capacitor varies with a potential difference .Using the graph or

otherwise , Prove that energy is ½ CV2 .Calculate the energy density of electrostatic field in a parallel

plate capacitor.

57. A test charge ‘q’ is moved without acceleration from A to C along

the path from A to B, then from B to C in electric field E as shown in

the figure.

(i) Calculate the potential difference between A and C.

(ii) At which point (of the two) is the electric potential more and why?

58.Two point electric charges of value q and 2q are kept at a distance d apart from each other in air. A third charge Q is to be kept along the same line in such a way that the net force acting on q and 2q is zero. Calculate the position of charge Q in terms of q and d.

59. Net capacitance of three identical capacitors in series is 1μ F. What will be their net capacitance if

connected in parallel?

Find the ratio of energy stored in the two

configurations if they are both connected to the same

source.

60. Obtain the equivalent capacitance of the network in

adjoining figure. For a 300V supply, determine the charge

and voltage across each capacitor.

61. A hollow cylindrical box of length 1 m and area of cross-

section 25 cm2 is placed in a three dimensional coordinate

system as shown in the figure. The electric field in the region

is given by E = 50 x , where E is in NC–1 and x is in meters. Find

(i) Net flux through the cylinder.

(ii) Charge enclosed by the cylinder.

62.Two sides of a square plate having length L are charged with linear charge density λ1 andλ2

respectively. Then find out the electric field intensity at the Centre of the square?

63.Two large thin conducting plates are placed parallel to each other . One of the plates is given a

charge Q. Find the charges on each surfaces of the plates. If the second plate is earthed then find out

the charges on the surfaces of the plates?

64.If two dipoles of dipole moment P1 and P2 are placed parallel to each other at a distance x apart.

Find out their potential energy?

65.A point charge Q is placed at a distance r from an infinite plane metallic earthed conductor. Find

out the force between them?

66. A metallic sphere of radius R is charged with surface charged density ς.Find out the electrostatic pressure on its surface? 6.A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10-12 F). What will be the capacitance if the distance between the

plates is reduced by half and the space between them is filled with a substance of dielectric constant 6?

67.Derive an expression for the total work done in rotating an electric dipole through an angle in a uniform electric field? 68.Prove that energy stored per unit volume in a capacitor is given by1/2 o E2, where E is the electric field of the capacitor? 69. (a) An air capacitor is given a charge of 2 C raising its potential to 200 V. If on inserting a dielectric medium, its potential falls to 50 V, what is the dielectric constant of the medium? (b) A conducting stab of thickness‘t’ is introduced without touching between the two plates?

70.If two concentric spheres have radii R1 and R2 respectively and the inner sphere is given a charge Q

then find out its capacitance?

71-A capacitor of capacitance C is charged to V volt and disconnected from the source. Find out the

work required to insert a dielectric in to the capacitor completely?

72-A capacitor is connected to a battery. If the energy stored in capacitor is Uc and energy supplied by

battery is Ub then find the relation between them?

73-If a point charge is placed at a distance d from the centre of an earthed metallic sphere having

radius r such that r˂d then find the charge that will appear on the sphere?

74-If 8 equal mercury droplets each at potential V volt collasce together to form a single drop then

find out its potential?

75.The electric field components in Fig. are Ex = a(x)1/2, Ey = Ez = 0, in which a = 800 N/C m1/2. Calculate (a) the flux through the cube, and (b) the charge within the cube. Assume that a = 0.1 m. 76. An electric field is uniform, and in the positive x direction for positive x, and uniform with the same magnitude but in the negative x direction for negative x. It is given that E = 200 ˆi N/C for x > 0 and E = –200 ˆi N/C for x < 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one face is at x = +10 cm and the other is at x = –10 cm . (a) What is the net outward flux through each flat face? (b) What is the flux through the side of the cylinder? (c) What is the net outward flux through the cylinder? (d) What is the net charge inside the cylinder? 77.An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge up to a radius R. The atom as a whole is neutral. For this model, what is the electric field at a distance r from the nucleus? 1.4 A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the

hole is 02

ˆn , where ˆn is the unit vector in the outward normal direction, and s is the surface charge

density near the hole. 78.(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. (b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart. 79.Two charges q and –3q are placed fixed on x-axis separated by distance‘d’. Where a third charge 2q should be placed such that it will not experience any force?

80. S1 and S2 are two hollow concentric spheres enclosing charges Q and 2Q as shown in the figure. (i) What is the ratio of the electric flux through S1 and S2?

(ii) How will the electric flux through sphere S1 change, if

a medium of diel- ectric constant 5 is introduced in the 2Q

Q

S1 S2

space inside S1 in place of air?

81A point charge q is placed at O as shown in the figure. Is VP-VQ +ve or –ve when (i) q>0, (ii) q<0? Justify your answer.

82.The graph shows the variation of voltage V across the plates of two capacitors A and B versus increase of charge Q stored on them. Which of the two capacitorshave higher capacitance? Give reason for your answer?

83.Two dielectric slabs of dielectric constant K1 and K2 are filled in between the two plates, each of area A,of the parallel plate capacitor asshown in the figure.

Find the net capacitance of the capacitor? Area of each plate = A/2

84.Two point electric charges of value q and 2q are kept at a distance d apart from eachother in air. A third charge Q is to be kept along the same line in such a way that the net force acting on q and 2q is zero. Calculate the position of charge Q in terms of q and d.

85.Draw 3 equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant along Z-direction. How are these surfaces different from that of a constant electric field along Z-direction?

86.Can two equipotential surfaces intersect each other? Give reasons. (ii) Two charges -q and + q are located at points A (0, 0, - a) and B (0, 0, + a) respectively. How

much work is done in moving a test charge from point P (7, 0, 0) to Q (-3, 0, 0)?

87. Two charges q and –3q are placed fixed on x-axis separated by distance ‘d’. Where should a third charge 2q be placed such that it will not experience any force?. 88. A paisa coin is made up of Al-Mg alloy and weighs 0.75g. It has a square shape and its diagonal measures 17 mm. It is electrically neutral and contains equal amounts of positive and negative charges.Treating the paisa coins made up of only Al, find the magnitude of equal number of positive and negative charges. What conclusion do you draw from this magnitude?. 89. If the total charge enclosed by a surface is zero, does it imply that the elecric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero. 90. Total charge –Q is uniformly spread along length of a ring of radius R. A small test charge +q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring (a) Show that the particle executes a simple harmonic oscillation. (b) Obtain its time period. 91. Consider a sphere of radius R with charge density distributed as ρ (r ) = kr for r ≤ R = 0 for r > R . (a) Find the electric field at all points r. (b) Suppose the total charge on the sphere is 2e where e is the electron charge. Where can two protons be embedded such that the force on each of them is zero. Assume that the introduction of the proton does not alter the negative charge. 92. Find the equation of the equipotentials for an infinite cylinder of radius r0, carrying charge of linear density λ. 93. A capacitor is made of two circular plates of radius R each, separated by a distance d<<R. The capacitor is connected to a constant voltage. A thin conducting disc of radius r<<R and thickness t<<r is placed at a centre of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is m. 94. Two metal spheres, one of radius R and the other of radius 2R,both have same surface charge density ς . They are brought in contact and separated. What will be new surface charge densities on them? 95. Two charges –q each are separated by distance 2d. A third charge + q is kept at mid point O. Find potential energy of + q as a function of small distance x from O due to – q charges. Sketch P.E. v/s x and convince yourself that the charge at O is in an unstable equilibrium. 96.A positive charge Q is uniformly distributed in a ring of radius R. A small test charge q is placed at

the centre. The charge is displaced a little (x<<R). What will be the nature of the q such that it will

execute SHM. Find the period of oscillation.

97.There is a plane of uniform +ve charge density ς parallel to YZ plane and located at a distance x=2d.

A point charge +q is placed at the origin. Where should be a +ve test charge be placed along +ve x axix

so that net force on the test charge is 0.

98.A –ve charge q and mass m is revolving around a line charge of charge density λ. If its orbital

radius is R , find kinetic energy of the charge.

99.A solid sphere of radius R has a charge Q distributed over its volume with a charge density ρ =kra,

where k and a are constants and r is the distance from centre. If the electric field at r=R/2 is 1/8 times

that at r=R, find the value of a.

100.Using the concept of solid angle and no density of line of force prove that Eα1/r2.

101.An electric dipole of dipole moment 20 X 10-6 C.m is enclosed by a closed surface.What is the net flux coming out of the surface?

102. Why does the electric field inside a dielectric decrease when it is placed in an external electric field?

103. Write the magnitude and direction of electric field intensity due to an electric dipole of length 2a at the mid point of the line joining the two charges.

104. Can electric potential at any point in space be zero while intensity of electric field at that point is notzero? 105. Devise an arrangement of three point charges separated by finite distances that has

zero electric potential energy. 106. Each of the uncharged capacitor in the fig. Has a capacitance of 25μF. What charge

shall flow through the meter M when the switch S is Closed? 107. Charge of 2C is placed at the centre of a cube of volume 8 cm3. What is the electric flux passing

through one face? 108. A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It

approaches Q up to a closest distance r and then returns. If q were given a speed 2v,then find the closest distance of approach.

109. An uncharged capacitor is connected to a battery. Show that half of the energy supplied by the battery is lost as heat while charging the capacitor. UNIT-2

CURRENT ELECTRICITY 1. (a) State the principle of a potentiometer. Define potential gradient. Obtain an expression for potential gradient in terms of resistivity of the potentiometer wire. (b) Figure shows a long potentiometer wire AB having a constant potential gradient. The null points for the two primary cells of emfs 1V and 2V connected in the manner shown are obtained at a distance of l1 =120 cm and l2 =300 cm from the end A. Determine (i) 1/ 2 and (ii) position of null point for the cell 1 only.

2.(a) Define the term ‘drift velocity’ of charge carriers in a conductor. Obtain the expression for the current density in terms of relaxation time. (b) A 100 V battery is connected to the electric network as shown. If the power consumed in the 2 resistor is 200 W, determine the power dissipated in the 5 resistor

3. In the circuit shown in the figure, find the total resistance of the circuit and the current in the arm CD. 4. A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing variation of terminal voltage ‘V’ of the cell versus the current ‘I’. Using the plot, show how the emf of the cell and its internal resistance can be determined. 5. Answer the following: (a) Why are the connections between the resistors in a meter bridge made of thick copper strips? (b) Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire? (c) Which material is used for the meter bridge wire and why? 6. A storage battery of emf 12V and internal resistance of .5 ohm is to be charged by a 120 v d.c supply

of negligible resistance. What resistance is required in the circuit for the charging current to

be 3A? What is the terminal voltage of the battery during charging?

7. The plot of the variation of potential difference across a combination of

three identical cells in series, versus current is as shown below. What is the emf

of each Cell?

8 . In a meter bridge, the null point is found at a distance of 60.0 cm from A.

If now a resistance of 5 ohm is connected in series with S,

null point occurs at 50 cm. Determine the values of R and S.

9. A 10 m long wire of uniform cross-section and 20Ώ resistance is used in

a potentiometer. The wire is connected in series with a battery of 5 V

along with an external resistance of 480Ώ. If an unknown EMF E is

balanced at 6.0 m length of the wire, calculate (i) potential gradient of the

potentiometer (ii) Unknown emf E

10.In a meter bridge, the null point is found at a distance of 40 cm from A.

If a resistance of 12Ω is connected in parallel with S, the null point occurs at 50 cm from A.

Determine the values of R and S.

11.By using Kirchhoff’s laws in electricity find the values of I1 ,I2and I3 in the circuit diagram given

here.

12.By using Kirchhoff’s laws in electricity find the values

of I1,I2and I3 in the circuit diagram given here

13.Two bulbs whose resistance are in the ratio of 1:2 are connected in parallel to a source of constant voltage. What will be the ratio of power dissipation in these?

14.Plot of current I versus time interval is given below. Find the charge that flows through the wire during this time period

15. Two conductors are made of the same material and have the same length. Conductor A is solid wire of diameter 1mm .Conductor B is a hallow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of résistance R1 and R2. 16 .Under what conditions the terminal potential difference of a cell be greater than its e.m.f. 17. Two wires of equal length, one of copper and the other of manganic have the same resistance. Which wire is thicker? 18. A cell, of emf 4V and internal resistance of. 5 ohm is connected across of a load of resistances i) 7.7 ohm ii) 11.5ohm. Calculate the ratio of the difference in the emf of the cell and the potential drop across the load, and the ratio of the current in the two cases. 19. State and explain Kirchhoff’s laws. Using Kirchhoff’s rules determine the value of unknown resistance R in the circuit so that no current flows through 4ῼ resistance. Also find the potential difference between A and D. 20 .Under what conditions the terminal potential difference of a cell be greater than its e.m.f. 21. Why Wheatstone bridge method is considered unsuitable for the measurement of a very high resistance? 22. The graph shown in the figure represents a plot of current versus voltage for a given semiconductor. Identify the region, if any, over which the semiconductor has a negative resistance. 23.Under what condition maximum current can be drawn from a cell?

. 24. A storage battery of emf 12V and internal resistance of .5 ohm is to be charged by a 120 v d.c supply of negligible resistance. What resistance is required in the circuit for the charging current to be 3A? What is the terminal voltage of the battery during charging? 25. Two students ‘X’ and ‘Y’ perform an experiment on potentiometer separately using the circuit given. Keeping other parameters unchanged, how will the position of the null point be affected it (i) ‘X’ increases the value of resistance R in the set-up by keeping the key K1 closed and the K2 open? (ii) ‘Y’ decreases the value of resistance S in the set-up, while the key K2 remain open and the key K1

closed? Justify. 26. Wheatstone bridge method is considered unsuitable for the Measurement of very small resistances. Why? 27. First a set a n equal resistors of R each are connected in Series to a battery of emf E and internal resistance R. A Current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current is increased 10 times. What is ‘n’ ? 28 .Two wires one of managing and other is copper have equal length and equal resistance .Which one of these wires will be thicker? 29. A number of identical cells ,n, each of emf E and internal resistance r connected in series are charged by a d.c. source of emf Eʹ using a resistor R i) Draw the circuit arrangement. ii)Deduce the expressions for (a) the charging current and (b)the potential difference across the combinations of the cells. 30. A 10 m long wire of uniform cross-section and 20Ώ resistance is used in a potentiometer. The wire is connected in series with a battery of 5 V along with an external resistance of 480Ώ. If an unknown EMF E is balanced at 6.0 m length of the wire, calculate (i) potential gradient of the potentiometer (ii) Unknown emf E 31 .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.

32. 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?,

Sketch the graph showing variation of resistivity of carbon with temperature.

33. Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.

34.Define ionic mobility. Write its relationship with relaxation time. How does one understand the

temperature dependence of resistivity of a semiconductor?

35 .State underlying principle of potentiometer. Describe briefly, giving the necessary circuit diagram,

how a potentiometer is used to measure the internal resistance of a given cell.

36. Prove the current density of a metallic conductor is directly proportional to the drift speed .

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

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

38. Two conductors are made of the same material and have the same length. Conductor A is solid

wire of diameter 1mm .Conductor B is a hallow tube of outer diameter 2mm and inner diameter 1mm.

Find the ratio of résistance R1 and R2.

39. Deduce the condition for balance in a Wheatstone bridge. Using the principle of Wheatstone

bridge, describe the method to determine the specific résistance of the wire in in the laboratory. Draw

the circuit diagram and write the formula used .Write any two precautions you would observe while

performing the experiment.

40. State working principle of a potentiometer. Draw a circuit diagram to compare emf of two primary

cells. Derive the formula used (a) which material is used for potentiometer wire and why? (b) How

can the sensitivity of a potentiometer be increased?

41.Aheating element using nichrome connected to 230V supply draws an initial current of 3.2 A

which settles after a few seconds to steady value of 2.8A .What is the steady temperature of the

heating element if the room temperature is 27 deg.cent ? Temperature coefficient of resistance of the

nichrome averaged over the temperature range involved is 1.70x 10-4 /c

42. Six lead –acid type secondary cells each of emf 2V and internal resitance 0.015 ohm are joined in

series to provide a supply to a resistance of 8.5 ohm of 8.5 ohm .What are the current drawn from the

supply and its internal voltage?

43. For two nichrome wire connected in series with a battery , how does the ratio of drift velocity of

electrons in them depend on the their (a) length (b) diameters.

44. A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing variation of terminal voltage ‘V’ of the cell versus the current ‘I’. Using the plot, show how the emf of the cell and its internal resistance can be determined. 45 . In a meter bridge, the null point is found at a distance of 60.0 cm from A.

If now a resistance of 5 ohm is connected in series with S,

null point occurs at 50 cm. Determine the values of R and S.

46.In a meter bridge, the null point is found at a distance of 40 cm from A.

If a resistance of 12Ω is connected in parallel with S, the null point

occurs at 50 cm from A. Determine the values of R and S.

47.Plot of current I versus time interval is given below. Find the

charge that flows through the wire during this time period.

48. State and explain Kirchhoff’s laws. Using Kirchhoff’s rules determine the value of unknown resistance R in the circuit so that no current flows through 4ῼ resistance. Also find the potential difference between A and D.

49-Find out the resistance between the center and the periphery of a disc of resistivity ς and radius R

and thickness T.

50-There is an infinite wire grid with square cells. The resistance of each side is R. Find the equivalent

resistance of the whole grid between any two neighboring points?

51-An electric kettle has two heating element which can boil the water in it in time T1 and T 2 seconds

respectively. Find the time taken to boil the same amount of water when the filaments are connected

in series , and when they are connected in parallel?

52- A cell of emf E and internal resistance r produces the same amount of heat in same time when

connected to the external resistances R1 and R2 respectively. Then express the internal resistance of

the cell in terms of R1 and R2.

53-Two resistance 60 ohm and 40 ohm are connected in series with a cell of EMF 20 volt . If a

voltmeter of resistance of 60 ohm is connected in parallel with the 60 ohm resistance find the

percentage of error in measuring the potential difference?

54- A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be how many times? 55-What is the Time taken by a 836 W heater to heat one litre of water from 10° C to 40° C ? 56- A 220 volt, 1000 watt bulb is connected across 110 volt mains supply. The power consumed will be how many watt? 57- An electric motor operates at 20 rev / sec. What will be the approximate power delivered by the motor, if it supplies a torque of 75 N-m ? 58- 2 litre water kept in a kettle is heated by 1 KW power source. Kettle is open and it loses heat at the rate of 160 J/s. Find the time taken for the temperature of kettle to change from 27° C to 77° C . 59(a) What is the advantage of using thick metallic strips to join wires in a potentiometer? (b) For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in this? ( c) Why are alloys used for making standard resistance coils? 60. Power P is to be delivered to a device via transmission cables having resistance RC. If V is the voltage across R and I the current through it, find the power wasted and how can it be reduced. 61.While doing an experiment with potentiometer (Fig ) it was found that the deflection is one sided and (i) the deflection decreased while moving from one end A of the wire to the end B; (ii) the deflection increased. while the jockey was moved towards the end B. (i) Which terminal +or –ve of the cell E1, is connected at X in case (i) and how is E1 related to E ? (ii) Which terminal of the cell E1 is connected at X in case (ii)? 62.Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm. Find the ratio of resistance RA to RB. 63. A resistance of R Ω draws current from a potentiometer. The potentiometer has a total resistance R0 Ω(Fig. ). A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

64.In a meter bridge, the null point is found at a distance of 40 cm from A. If a resistance of 12Ω is

connected in parallel with S, the null point occurs at 50 cm from A. Determine the values of R and S

65.By using Kirchhoff’s laws in electricity find the values of I1,I2and I3 in the circuit diagram given here.

66.By using Kirchhoff’s laws in electricity find the values of I1,I2and I3 in the circuit diagram given

here

67.Two bulbs whose resistance are in the ratio of 1:2 are connected in parallel to a source of constant voltage. What will be the ratio of power dissipation in these?

68.Plot of current I versus time interval is given below. Find the charge that flows through the wire during this time period

69. Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1mm. Conductor B is a hollow tube of outer diameter 2mm and inner diameter 1mm.Find the ratio of resistance RA to RB. 70. First a set of n equal resistors of R each are connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current is increased 10 times. What is ‘n’? 71.A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side a; (ii) a square of sides a and, (iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case. 72. If the length of the wire conductor is doubled by stretching it , keeping potential

Difference constant by what factor the drift speed of the electron changed. 73. If the temperature of the conductor increases, how does the relaxation time of

electron changes. 74. A heater joined in series with the 60W bulb .With change of bulb with 100 W in the

circuit, the rate heat produce by the heater will more or less or remain same.

75. What will be the change in the resistance of the circular wire , when its radius is halved and length is reduced by . th of original length.

76. Two 120V light bulbs , one of 25W and another of 200W are connected in series . One bulb burnt out almost instantaneously ?.Which one was burnt and why?.

77. A given copper wire is stretched to reduce its diameter is half of its original value.What will the new resistance?.

UNIT-3

MAGNETIC EFFET OF CURRENT AND MAGNETISM 1.Define one tesla using the expression for the magnetic force acting on a particle of charge ‘q’ moving with velocity v in a magnetic field B. 2. Two very small identical circular loops, (1) and (2), carrying equal currents I are placed vertically (with respect to the plane of the paper) with their geometrical axes perpendicular to each other as shown in the figure. Find the magnitude and direction of the net magnetic field produced at the point O. 3. (a) Two long straight parallel conductors ‘a’ and ‘b’, carrying steady currents Ia and Ib are separated by a distanced. Write the magnitude and direction of the magnetic field produced by the conductor ‘a’ at the points along the conductor ‘b’. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors? (b) Show with the help of a diagram how the force between the two conductors would change when the currents in them flow in the opposite directions. 4.Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current. 5. The electric current flowing in a wire in the direction from B to A is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown. 6. In a certain region of space, electric field E and magnetic field B are perpendicular to each other. An

electron enters in the region perpendicular to the directions of both B and E and moves un

deflected. Find the velocity of the electron.

7. A narrow beam of proton and deuterons has same momentum, enter s the uniform magnetic field

perpendicularly . Find the ratio of radius of circular path described by them.

8. A charge ‘q’ moving along the x-axis with a velocity v is subjected to a uniform magnetic field B

along the z-axis as it crosses the origin O.

(i) Trace its trajectory.

(ii) (ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your

answer.

9. A charged particle having a charge q , moving with a speed v , parallel to wire , at a distance d from

it in a direction opposite to the current. What is the force experienced by the charge and what is its

direction?

10. A wire AB is carrying a steady current of 10 A and is lying on the table. Another wire CD carrying 6 A is held directly above AB at a height of 2 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms−2] 11.A long wire carries a steady current. It is bent into a circle of one turn and magnetic field at the

centre of the coil is B. It is then bent into a circular loop of N turn. Find magnetic field at the centre of

the coil ?

12.A magnetic needle lying parallel to a magnetic field requires W unit of work to turn it through 60 0

. What will be The torque needed to maintain the needle in this position?

13.A wire of uniform cross section is bent into a circular loop of radius R. Consider the two points A

and B on the loop, such that angle is β . If now a battery is connected between A and B , show that

magnetic field at the centre of the loop will be zero irrespective of β.

14.A long straight carries a current of 2 A. An electron travels with a speed of 4 X 10 4 m/s parallel to

the wire at a distance of 0.1 m from it in a direction opposite to the electric current. What force does

the magnetic field of the current exert on the moving electron?

15.Does a bar magnet exert a torque on itself due to its own field? Does one element of current –

carrying wire exert a force on another element of the same wire?

16. Give two points to distinguish between a paramagnetic and a diamagnetic substance.

17. Write the expression for the magnetic moment of a circular coil of area A carrying a current I, in a vector form. 18. Show diagrammatically the behaviour of magnetic field lines in the presence of (i) paramagnetic and (ii) Diamagnetic substances. How does one explain this distinguishing feature? 19.An electron moving through a magnetic field does not experience any force. Under what condition is this possible? 20. Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current. (b) Show with the help of a diagram how the force between the two conductors would change when the currents in them flow in the opposite directions. 21.Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current. 22.The electric current flowing in a wire in the direction from B to A is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown.

23. Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry currents of 10A and 5A respectively in opposite direction. Calculate the magnitude and direction of the force on a 20 cm length of the wire Y. 24. Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why? 25. What is the angle of dip at a place where the horizontal and vertical components of earth magnetic field are equal? 26. In hydrogen atom, if the electron is replaced by a particle which is 200 times heavier but has the same charge, how would its radius change. 27. If the current sensitivity of a moving coil galvanometer is increased by 20% , its resistance also increased by 1.5 time How will the voltage sensitivity of galvanometer be affected. 24. Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?

25. What is the angle of dip at a place where the horizontal and vertical components of earth magnetic field are equal? 26 .A narrow beam of proton and deuterons has same momentum, enter s the uniform magnetic field perpendicularly . Find the ratio of radius of circular path described by them. 27. If the current sensitivity of a moving coil galvanometer is increased by 20% , its resistance also increased by 1.5 times,. How will the voltage sensitivity of galvanometer be affected. 28. Two identical circular wires P and Q each of radius R and carrying current ‘I’ are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils. 29. In a cyclotron, a magnetic field induction of 0.4 T is used to accelerate protons. How rapidly should the electric field between the dee be reversed? The mass and charge of proton are 1.67 X 10 -28 kg and 1.6 X 10-19 C respectively. 30. Two small identical circular coils marked 1 and 2 carry equal currents and are placed with their geometric axes perpendicular to each other as shown in the figure.Derive an expression for the resultant magnetic field at O. 31. A proton is moving 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?

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

field whatis the direction of the magnetic field?

33.Under what condition will the force exerted by the magnetic field on a charged particle be (i)

maximum (ii) minimum

34.How do you convert a Galvanometer into an ammeter? Why is an ammeter always connected in

series .

35. Using Ampere’s circuital law , obtain expression expression for magnetic field along the axis of a

current carrying solenoid of length l and having N umber turns.

36. Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry currents of

10A and 5A repectively in opposite direction. Calculate the magnitude and direction of the force on a

20 cm length of the wire Y .

37. If the current sensitivity of a moving coil galvanometer is increased by 20% , its resistance also

increased by 1.5 times,. How will the voltage sensitivity of galvanometer be affected.

38. Draw a schematic sketch of the cyclotron. State its working p0rinciple. Show the cyclotron

frequency is independent of the velocity of the charged particles.

39. Derive an expression for the torque experienced by a rectangular loop carrying a steady current I

and placed in a uniform magnetic field B .Indicate the direction of the torque acting on the loop.

40. Draw a schematic sketch diagram of cyclotron. State its working principle .Describe briefly how it

is used to accelerate the charge particle. Show that the period of revolution of an ion is independent of

its speed or radius of the orbit. Write two important use of cyclotron.

41. An ammeter and milliammeter are converted are converted from the same galvanometer ,out of

the two , which current measuring instrument has higher resistance.

42. What is the advantages of using radial magnetic field in a moving coil galvanometer.

43. An electron of kinetic energy 25 KV moves perpendicular to the direction of uniform magnetic

field of .2 militesla .Calculate the time period of rotation of the electron in the magnetic field.

44.In a galvanometer, there is a deflection of 10 divisions per mA . the internal resistance of the

Galvanometer is 78 ohm .If a shunt of 2 ohm is connected to the galvanometer and there are 75

divisions in all on the scale of the galvanometer, Calculate the maximum current which the

galvanometer can read

45. An electron revolves around a proton in H-atom at a speed of 2.18 x10 6m/s in an orbit of radius

0.53 angstrong .What magnetic field does it produce at the centre of its circular orbit

46. (a) Two long straight parallel conductors ‘a’ and ‘b’, carrying steady currents Ia and Ib are separated by adistanced. Write the magnitude and direction of the magnetic field produced by the conductor ‘a’ at the points along the conductor ‘b’. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors? (b) Show with the help of a diagram how the force between the two conductors would change when the currents in them flow in the opposite directions. 47. In a certain region of space, electric field E and magnetic field B are perpendicular to each other.

An electron enters in the region perpendicular to the directions of both B and E and moves un

deflected. Find the velocity of the electron.

48. A charge ‘q’ moving along the x-axis with a velocity v is subjected to a uniform magnetic field B

along the z-axis as it crosses the origin O.

(i) Trace its trajectory.

(ii) (ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your

answer.

49. Write the expression for the magnetic moment of a circular coil of area A carrying a current I, in a vector Form. 50. Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry currents of 10A and 5A respectively in opposite direction. Calculate the magnitude and direction of the force on a 20 cm length of the wire Y. 51. A long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. Calculate the magnetic field in the region r < a , r > a. 52.The horizontal component of the earth’s magnetic field at a certain place is 3.0 ×10–5 T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is (a) east to west; (b) south to north? 53. Show that a force that does no work must be a velocity dependent force. 54. Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled. 55. A long straight wire carrying current of 25A rests on a table as shown in Fig.. Another wire PQ of length 1m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will PQ rise?

56. Draw magnetic field lines when a (i) diamagnetic, (ii) paramagnetic substance is placed in an

external magnetic field. Which magnetic property distinguishes this behavior of the field lines due to

the two substances?

57. (i) Write two characteristics of a material used for making permanent magnets.

(ii) Why is core of an electromagnet made of ferromagnetic materials?

58.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. 59.Define the term: magnetic dipole moment of a current loop. Write the expression for the magnetic moment when an electron revolves at a speed ‘v’, around an orbit of radius ‘r’ in hydrogen atom. 60. Do magnetic forces obey Newton’s third law. Verify for two current elements dl1 = dlˆi located at the origin and dl2 = dl ˆj located at (0, R, 0). Both carry current I. 61. A current carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin. 62. Consider the plane S formed by the dipole axis and the axis of earth.Let P be point on the magnetic equator and in S. Let Q be the point of intersection of the geographical and magnetic equators. Obtain the declination and dip angles at P and Q. 63. There are two current carrying planar coils made each from identical wires of length L. C1 is circular (radius R ) and C2 is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R. 64. Verify the Ampere’s law for magnetic field of a point dipole of dipole moment m = mkˆ . Take C as the closed curve running clockwise along (i) the z-axis from z = a > 0 to z = R; (ii) along the quarter circle of radius R and centre at the origin, in the first quadrant of x-z plane; (iii) along the x-axis from x = R to x = a, and (iv) along the quarter circle of radius a and centre at the origin in the first quadrant of x-z plane. 65.A magnetic field B is confined to a region r ≤ a and points out of the paper (the z-axis), r = 0 being the centre of the circular region. A charged ring (charge = Q) of radius b, b > a and mass m lies in the x-y plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time Δt. Find the angular velocity ω of the ring after the field vanishes. 66. A metallic ring of mass m and radius l (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of magnetic field is Bz = Bo (1+λ z). If R is the resistance of the ring and if the ring falls with a velocity v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B, λ and acceleration due to gravity g. 67. A long solenoid ‘S’ has ‘n’ turns per meter, with diameter ‘a’. At the centre of this coil we place a smaller coil of ‘N’ turns and diameter ‘b’ (where b < a). If the current in the solenoid increases linearly, with time, what is the induced emf appearing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of mt2+C.

68.A Current ‘I’ flows along the length of an infinitely long straight thin walled pipe. What is the magnetic field at any point on the axis of pipe?

69.The Earth’s core contains iron but geologists do not regard this as a source of Magnetic Field, Why? 70. Is the Resistance of Voltmeter larger than or smaller than the resistance of Galvanometer from

which it is converted. 71. A Magnetic Field dipole placed in a Magnetic Field experiences a net force. What can you say about

the Nature of Magnetic Field? 72. Earth’s Magnetic Field does not affect working of moving

UNIT-4

ELECTROMAGNETIC INDUCTION AND AC CURRENT

1.The currents flowing in the two coils of self-inductance L1 16 mH and L2 12 mH are increasing at the same rate. If the power supplied to the two coils are equal, find the ratio of (i) induced voltages, (ii) the currents and

(iii) the energies stored in the two coils at a given instant.

2. Use Lenz’s law to determine the direction of the induced current when a rectangular conducting loop abcd is moved into a region of magnetic field which is directed normal to the plane of the loop away from the reader. 3. A toroidal solenoid with air core has an average radius of 15 cm, area of cross-section 12 cm2 and has 1200 turns. Calculate the self-inductance of the toroid. Assume the field to be uniform across the cross-section of the toroid.

4. Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2 (r2 r1). Total number of turns in the two solenoids are N1 and N2 respectively. 5. In a series LCR circuit with an ac source of effective voltage 50 V, frequency v 50 / Hz, R = 300 , C = 20 F and L = 1.0 H. Find the rms current in the circuit. 6. A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 and a capacitor of reactance 200 in series. An alternating emf of 150 2 V, 500/ Hz is applied across this series combination. Calculate the power dissipated in the resistor. 7. Why is the use of AC voltage preferred over DC voltage? Give two reasons. 8.When a coil is rotated in a uniform magnetic field at constant angular velocity, will the magnitude of

induced emf set up in the coil be constant? Why?

9.When an alternating current is passed through a moving coil galvanometer, it shows no deflection.

Why ?

10.What is the power dissipated in an ac circuit in which voltage and current are given by

and ?

11.A solenoid is connected to a battery so that steady current flows through it . If an iron core is

inserted into the solenoid, will the current increase or decrease?

12.Twelve wire of equal length are connected to form a skeleton cube which moves with a velocity v

parallel to the magnetic field B. What will be the induced emf in each arm of the cube .

13. Derive the energy stored in a inductor of inductance L.

14. Diagram shows a rectangular wire loop PQRS kept in a perpendicular magnetic field B. If the arm RS of length l is moved towards right with a velocity v.

(a) Find the expression for emf induced . (b) Which end of the rod RS is at higher potential? (c) What is the direction of induced current?

15.A flexible wire of irregular shape, abcd, as shown in the figure, turns into a circular shape when placed in a region of magnetic field which is directed normal to the plane of the loop away from the reader. Predict the direction of the induced current in the wire.

16. In a series LCR circuit, obtain the conditions under which (i) the impedance of the circuit is minimum, and (ii) wattless current flows in the circuit. 17. A voltage V V0 sin t is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition is (i) no power dissipated even though the current flows through the circuit, (ii) maximum power dissipated in the circuit?

18. A bulb and a capacitor are connected in series to an a.c source of variable frequency .How will the brightness of the bulb change on increasing the frequency of the a.c source? Give reason.

19. A conducting loop is held above a current carrying wire ‘PQ’ as shown in the figure. Depict the direction of the current induced in the loop when the current in the wire PQ is constantly increasing. 20. A current induced in coil c1 due to the motion of current carrying coil c2 (a) write any two ways by which a large deflection can obtained in the galvanometer G . (b) Suggest an alternative device to demonstrate the induced current in place of galvanometer. 21. Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’as

shown in the figure. Predict the polarity of the capacitor. 21. A square loop of side 12 cm with its sides parallel to X and Y-axes is moved with a velocity of 8

cm/s in positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of 10--3 T/cm along negative x-direction,. Find the emf and magnitude of the induced current in the loop if its resistance is 4.5 m Ω.

22. A metallic rod of length l is rotated at an angular speed ω ,normal to uniform magnetic field B. Derive expressions for the (i) emf induced in the rod

(ii) heat dissipation , if the resistance of the rod is R. . 23. An inductor `L’ of reactance XL, is connected in series with a bulb `B’ to an a.c. source. Briefly explain how does the brightness of the bulb change, when

(i) numbers of turns of the inductor is reduced and (ii) a capacitor of reactance XC= XL is included in series in the same circuit.

24.Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’as shown in the figure. Predict the polarity of the capacitor. 25. An inductor of unknown value, a capacitor of 100mF and a resistor of 10W are connected in series to a 200 V, 50 Hz a.c. source. It is found that the power factor of the circuit is unity. Calculate the inductance of the inductor and the current amplitude.

26. Show that the current leads the voltage in phase by /2 in an ac circuit containing an ideal capacitor. 27. The power factor of an a.c circuit is 0.5. What will be the phase difference between voltage and current in this circuit? 28. When a lamp is connected to an alternating voltage supply, it lights with the same brightness as when connected to a 12V DC battery .What is the peak value of alternating voltage source? 29. A current induced in coil c1 due to the motion of current carrying coil c2 (a) write any two ways by which a large deflection can obtained in the galvanometer G .(b) Suggest an alternative device to demonstrate the induced current in place of galvanometer. 30. Explain the principle in which a metal detector used at airports for security reasons works. 31. An inductor `L’ of reactance XL, is connected in series with a bulb `B’ to an a.c. source. Briefly explain how does the brightness of the bulb change, when (i) numbers of turns of the inductor is reduced and (ii) a capacitor of reactance XC= XL is included in series in the same circuit. 32. Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’as shown in the figure. Predict the polarity of the capacitor. 33. An inductor of unknown value, a capacitor of 100mF and a resistor of 10W are connected in series to a 200 V, 50 Hz a.c. source. It is found that the power factor of the circuit is unity. Calculate the inductance of the inductor and the current amplitude. 34. How is the mutual inductance of a pair of coils affected when: (i) separation between the coils is increased (ii) the number of turns of each coil is increased (iii) a thin iron sheet is inserted between the two coils ,other factors remaining the same. Explain your answer in each case. 35. Which physical quantity is called the INERTIA OF ELECTRICITY? Why is its called so? 36. Draw a plot showing the variation of the current I as a function of angular frequency ‘ω’ of the applied ac source for the two cases of a series combination of (i) inductance L1, capacitance C1 and resistance R1 and (ii) inductance L2, capacitance C2 and resistance R2 where R2 > R1. Write the relation between L1, C1 and L2, C2 at resonance. Which one, of the two, would be better suited for fine tuning in a receiver set? Give reason. 37. When an alternating voltage of 200V is applied across a device X, a current of 0.5A flows through the circuit and is in phase with the applied voltage. When the same voltage is applied across another device Y the same current flows through the circuit but it leads the applied voltage by π/2 rad. (a) Name the devices X and Y. (b) Calculate the current flowing in the circuit when same voltage is applied across the series combinations of X and Y. 38. When a lamp is connected to an alternating voltage supply, it lights with the same brightness as

when connected to a 12v DC battery .What is the peak value of alternating voltage source?

39. A bulb and a capacitor are connected in series to an a.c source of variable frequency .How will the

brightness of the bulb change on increasing the frequency of the a.c source? Give reason.

40. Define mutual inductance between two long co-axial solenoid .Find out the expression for the

mutual inductance of inner solenoid of length l having the radius r1 and r2 and the number of turns

n1 per unit length due to the second outer solenoid of same length and n2 number of turns per unit

length.

.

41. 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=Blv.

42. Explain with the help of labeled diagram the underlying principle and working of a step up

transformer. Why such a device cannot be used to step up d.c voltage.

43. What are eddy currents? How are these produced? In what sense are eddy currents considered

undesirable in transformer and how are these reduced in such device?

44. A coil of number of turns N , area A , is rotated at a constant angular speed Ω, in a uniform

magnetic field B, and resistor R .Deduce expression for ;(i) Maximum emf induced in the coil (ii)

power dissipation in the coil .

45. Derive an expression for impedance of a series LCR circuit connected to an a.c supply of variable

frequency. Plot the graph showing variation of current with the frequency of the applied voltage

.Explain briefly how the phenomenon of resonance in the circuit can be used in the tuning mechanism

of radio or TV set.

46.When a coil is rotated in a uniform magnetic field at constant angular velocity will the magniyude

of induced emf set up in the coil be constant ? Why

47. The magnetic flux threading a coil changes from 12x 10 -3 wb to 6x10-3wb in 0.01 s . Calculate the

induced emf

48. A wire in the form of tightly wound solenoid is connected to dc source , and carries a current . If

the coil is stretched so that there are gaps between successive elements of the spiral coil , will the

current increase or decrease?

49.Calculate the quality factor of a series LCR circuit with L=2H , C=2 Micro Farad and R

=10ohm.Mention the significance of quality factor in LCR circuit

50. The self –inductance of the motor of an electric fan is 10H in order to impart maximum power at

50Hz , Find the capacitance of the capacitor that should be connected across the inductor.

51.The currents flowing in the two coils of self-inductance L1 16 mH and L2 12 mH are increasing at the same rate. If the power supplied to the two coils are equal, find the ratio of (i) induced voltages, (ii) the currents and

(iii) the energies stored in the two coils at a given instant.

52. A toroidal solenoid with air core has an average radius of 15 cm, area of cross-section 12 cm2 and has 1200 turns. Calculate the self-inductance of the toroid. Assume the field to be uniform across the cross-section of the toroid.

53. Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r1 and r2 (r2 r1). Total number of turns in the two solenoids are N1 and N2 respectively. 54. In a series LCR circuit with an ac source of effective voltage 50 V, frequency v 50 / Hz, R = 300 , C = 20 F and L = 1.0 H. Find the rms current in the circuit.

55. A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 and a capacitor of reactance200 in series. An alternating emf of 150 2 V, 500/ Hz is applied across this series combination.Calculate the power dissipated in the resistor. 56. Diagram shows a rectangular wire loop PQRS kept in a perpendicular magnetic field B. If the arm RS of length l is moved towards right with a velocity v.

(a) Find the expression for emf induced . (b) Which end of the rod RS is at higher potential? (c) What is the direction of induced current?

57.A straight conductor is carrying a current I and a square loop of length L is placed on the plane

of the conductor such that its nearer side lies at a distance d from the straight conductor. Find out

their mutual inductance.

58.If a magnet falls through a solenoid then draw the emf vs time graph and explain the graph?

59.If an aeroplane is moving towards north with velocity V over a place where the strength of

magnetic field is B and angle of dip is ϴ , find out the emf induced across the two wings of the plane

whose length is l each?

60.A fully charged capacitor C is connected with an inductor L at t=0. Find the time after which the

energy stored will be equal on the inductor and capacitor?

61.An inductor an a bulb are connected in series with a source of E volt. If an iron rod is inserted in

between the inductor how the brightness of the bulb will be affected?

62- The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of what farad? 63- The phase difference between the alternating current and emf is π / 2. Which of the element cannot be the constituent of the circuit ? 64- A circuit has a resistance of 12 ohm and an impedance of 15 ohm. Find the power factor of the circuit ? 65- A coil of inductance 300 mH and resistance 2 Ω is connected to a source of voltage 2 V. The current reaches half of its steady state value in what time? 66- In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be what volt? 67-A 220 volt and 50 Hz ac source is connected with an inductance of 0.2 H and a resistance of 20 ohm

in series. Find the current through the circuit.

68-An inductor L and a resistor R are joined in series to a source of frequency w. F ind the power

dissipated in the circuit?

69-An alternating EMF of angular frequency w is applied across an inductance L. Find the

instantaneous power of the circuit?

70-A fully charged capacitor C is connected to an inductor L at t=0. Find the shortest time after

which the charge on the capacitor will be zero?

71-The voltage of an ac supply is given by V=120 Sin 100∏t Cos100∏t. Find the maximum voltage

and frequency of AC?

72.A circular coil of radius 10 cm, 500 turns and resistance 2 W is placed with its plane perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. Estimate the magnitudes of the emf and current induced in the coil. Horizontal component of the earth’s magnetic field at the place is 3.0 × 10–5 T. 73. A closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets? 74. A closed loop moves normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop (i) when it is wholly inside the region between the capacitor plates (ii) when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop. 75.(a) Obtain the expression for the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length l of the solenoid. (b) How does this magnetic energy compare with the electrostatic energy stored in a capacitor? 76. A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of earth’s magnetic field HE at a place. If HE = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? Note that 1 G = 10–4 T. 77. 1MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if (i) power is transmitted at 220V. Comment on the feasibility of Doing this. (ii) a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transfomer is used to bring voltage to 220 V. ( 1.7 10–8SI unit) Cu ρ 78. Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency. 79. Explain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage. 80.A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current. 81. Even though an electric field E exerts a force qE on a charged particle yet the electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain. 82. You are given a 2μF parallel plate capacitor. How would you establish an instantaneous displacement current of 1mA in the space between its plates? UNIT-5

ELECTROMAGNETIC WAVES 1. Arrange the following electromagnetic waves in order of decreasing frequency: X- -rays, microwaves and infrared rays. 2. To which part of the electromagnetic spectrum does a wave of frequency 5 × 1019 Hz belong? 4. Considering the case of a parallel plate capacitor being charged, show how one is required to generalise Ampere’s circuital law to include the term due to displacement current. 5. The electric field of a plane electromagnetic wave in vacuum is represented by Ex =0 ,

, Ez=0

i) What is the direction of propagation of electromagnetic wave?

ii) Determine the wavelength of the wave

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

By = (8×10-6) sin(2 ×1011t + 300 πx )T

(i) Calculate the wavelength of the electromagnetic wave

(ii) Write the expression of the oscillating electric field.

7. Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency.

8. A plane electromagnetic wave of frequency 25 MHz travels in a free space along the X- direction. At a particular point in space and time the electric field is E=6.3 J V/m .Calculate B at this point.

9. A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere’s circuital law is generalized incorporate the effect due to the displacement current.

10. Name the constituent radiation of electromagnetic spectrum which:

(i) Produce intense heating.

(ii) Is similar of the radiations emitted during decay of a radioactive nucleus,

(iii) Is absorbed from sunlight by ozone layer.

11.A variable frequency a.c source is connected to a capacitor. What will happen to the displacement

current with increase with frequency of a.c?

12.Calculate the displacement current between the squre plates of side 1.0 cm of a capacitor of electric

field between the plates is changing at the rate of 3 X 10 6 V/ms.

13.(a) How does oscillating charge produce electromagnetic waves? (b) Sketch a schematic diagram depicting oscillating electric and magnetic fields of an em wave propagating along + z-direction. 14.What is common between different types of e.m. radiations ?

15.When an ideal capacitor is charged by a dc battery, no current flows. However when an a.c. source

is used, the current flows continuously. How does one explain this, based on the concept of

displacement current?

16.Give reason of the following (i) The small ozone layer on top of the stratospheric is crucial for human survival. (ii) Long distance radio broadcasts use short wave bands (iii) Satellites are used for long distance TV transmission . 17. The oscillating electric field in a plane electromagnetic wave is given by EY= 30 sin (2×1011 t +300

π x ) V m-1 (i) Calculate the wavelength of the electromagnetic wave. (ii) Write down the expression

for the oscillating magnetic field.

18. Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency 19. Name the electromagnetic radiations which can be produced by klystron or a magnetron valve. 20. A plane electromagnetic wave of frequency 25 MHz travels in a free space along the X- direction. At a particular point in space and time the electric field is E=6.3 J V/m .Calculate B at this point. 21. How are radio waves produced ?

22. What is common between different types of e.m. radiations ?

23. A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere’s circuital law is generalized incorporate the effect due to the displacement current. 24. The oscillating electric field in a plane electromagnetic wave is given by EY= 30 sin (2×1011 t +300

π x ) V m-1 (i) Calculate the wavelength of the electromagnetic wave. (ii) Write down the expression

for the oscillating magnetic field.

25.How is X- rays produced.

26. Write the following radiations in ascending order in respect of their frequencies ; X-ray ,

microwave , UV raya and radio waves .

27. Name the electromagnetic radiations which can be produced by klystron or a magnetron valve.

28. Which part of electromagnetic spectrum is used in radar system?

29. How micro waves produced.

30. A plane electromagnetic wave of frequency 25Mhztravels in a free space along the X- direction . At

a particular point in space and time the electric field is E=6.3 J V/m .Calculate B at this point.

31. Draw sketch of a plane electromagnetic wave propagating along the z-direction .Depict clearly the

directions of electric and magnetic fields varying sinusoid ally with z.

32. Write order of frequency range and one use of each of the following electromagnetic radiations (i)

Micro waves (ii) Ultra –violet rays( iii)Gamma rays.

33. Give reason of the following

(i) Long distance radio broadcasts use short wave bands

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

(iii) Satellites are used for long distance TV transmission.

34.How is X- rays produced.

35. Write the following radiations in ascending order in respect of their frequencies ; X-ray ,

microwave , UV raya and radio waves .

37. Name the electromagnetic radiations which can be produced by klystron or a magnetron valve.

38. Which part of electromagnetic spectrum is used in radar system?

39. How micro waves produced.

40. A plane electromagnetic wave of frequency 25Mhztravels in a free space along the X- direction . At

a particular point in space and time the electric field is E=6.3 J V/m .Calculate B at this point.

41. Draw sketch of a plane electromagnetic wave propagating along the z-direction .Depict clearly the

directions of electric and magnetic fields varying sinusoid ally with z.

42. Write order of frequency range and one use of each of the following electromagnetic radiations (i)

Micro waves (ii) Ultra –violet rays( iii)Gamma rays.

43. Give reason of the following

(i) Long distance radio broadcasts use short wave bands

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

(iii) Satellites are used for long distance TV transmission.

44. Arrange the following electromagnetic waves in order of decreasing frequency: X- -rays, microwaves and infrared rays. 45. To which part of the electromagnetic spectrum does a wave of frequency 5 × 1019 Hz belong? 46. Considering the case of a parallel plate capacitor being charged, show how one is required to generalise Ampere’s circuital law to include the term due to displacement current.

47. The electric field of a plane electromagnetic wave in vacuum is represented by Ex =0 ,

, Ez=0

iii) What is the direction of propagation of electromagnetic wave?

iv) Determine the wavelength of the wave

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

By = (8×10-6) sin(2 ×1011t + 300 πx )T

(iii) Calculate the wavelength of the electromagnetic wave

(iv) Write the expression of the oscillating electric field.

49. Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency. nucleus, (iii) Is absorbed from sunlight by ozone layer.

50. The magnetic field in a plane electromagnetic wave is given by By = 2 × 10–7 sin (0.5×103x+1.5×1011t) T. (a) What is the wavelength and frequency of the wave? (b) Write an expression for the electric field. 51.A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength? 52. Answer the following questions: (a) Long distance radio broadcasts use short-wave bands. Why? (b) It is necessary to use satellites for long distance TV transmission. Why? (c) Optical and radiotelescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why? 53.The small ozone layer on top of the stratosphere is crucial for human survival. Why? (a) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now? (b ) Some scientists have predicted that a global nuclear war on the earth would be followed by a severe ‘nuclear winter’ with a devastating effect on life on earth. What might be the basis of this prediction? 54.Why is the quantity e0 dFE/dt called the displacement current? 55. Using a d.c. source, a capacitor has been fully charged. What are the magnitudes of

conduction and displacement currents? 56. What is the ratio of speed of infrared and ultraviolet rays in vacuum? 57. An electromagnetic wave consists of oscillating electric and magnetic fields. What is the phase relationship between these oscillations? 58. Radio waves diffract predominately around building while light waves, which are also

electromagnetic waves, do not. Why?

UNIT-6

OPTICS

1.A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if refractive index of the

material of the sphere is 3 .

2. Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays ‘1’ and ‘2’ are respectively 1.35 and 1.45. Trace the path of these rays after entering through the prism. 3.A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of Curvature 20 cm. The two are kept at 15 cm from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed. 4. When Puja, a student of 10th class, watched her mother washing clothes in the open, she observed coloured soap bubbles and was curious to know why the soap bubbles appear coloured. In the evenin when her father, an engineer by profession, came home, she asked him this question. Her father explained to her the basic phenomenon of physics due to which the soap bubbles appear coloured. (aba) What according to you are the values displayed by Puja and her father? (b) State the phenomenon of light involved in the formation of coloured soap bubbles.

5. (i) Distinguish between unpolarised and linearly polarised light. (ii) What does a polaroid consist of? How does it produce a linearly polarised light? (iii)Explain briefly how sunlight is polarised by scattering through atmospheric particles.

6.At what angle of incidence should a light beam strike a glass slab of refractive index √ , such that the

reflected and the refracted rays are perpendicular to each other?

7.A ray is to be deviated through 90o by a right angled isosceles prism . What should be the minimum

refractive index of the material of the prism.

8.Two Polaroid’s P1 and P2 are 90° to each other. A third Polaroid P3 is placed between P1 and P2

bisecting the angle between them. If the intensity of un Polaroid beam is I0 then find the intensity of

transmitted beam through P3 and P2.

9.In the figure given below, light rays of blue, green, red wavelengths

are incident on an isosceles right-angled prism.

Explain with reason, which ray of light

(i)will be transmitted through the face AC. The refractive index of the

(ii)prism for red, green, blue light is 1.39, 1.424, 1.476 respectively.

10. You are given three lenses L1, L2 and L3 each of focal length 10 cm.

An object is kept at 15 cm in front of L1, as shown.

The final real image is formed at the focus ‘I’ of L3. Find the separations between L1, L2 and L3.

11.A parallel beam of monochromatic light of wavelength 500 nm falls normally on a narrow slit and

the resulting diffraction pattern is obtained on a screen 1 m away. It is observed that the first

minimum is at a distance of 2.5 mm from the centre of the screen. Find

(a) the width of the slit.

(b) the distance of the second maximum from the centre of the screen.

(c) the width of the central maximum.

12.Two Polaroids are placed at 90 0 to each other and the transmitted intensity is zero.

a) What happens when one more Polaroid is placed between these two bisecting the angle between them

b) N-1 more polaroids are inserted between two crossed polaroids ( at 90 ) to each other). Their axes are equally spaced. How does the transmitted intensity behave for large N ?

13.Two coherent sources emit waves of amplitude a and 2a. They meet at a point P equidistant from the two sources. If the intensity of the first is I, What is the resultant intensity at point P ? 14.The ratio of intensity of maxima and minima in an interference pattern is 100 :64. Calculate the ratio of intensities of the coherent sources producing this pattern. 15.Sodium light has two wavelengths 1 = 589 nm and λ2 = 589.6 nm As the path difference increases, when is the visibility of the fringes a minimum? 16.Can two lamps of sodium light act as coherent sources? Give your reason? 17.Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f . 18.A jar of height h is filled with a transparent liquid of refractive index µ. At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of the disc , such that when placed on the top surface symmetrically the centre, the dot is invisible. 19.Why must both objective and the eyepiece of a compound microscope have short focal length?

20.Show that for a material with refractive index √ , light incident at any angle shall be guided along a length perpendicular to the incident face. 21.A lens of focal length f forms the image of aluminous object on a screen m time larger. Prove that the distance of the screen from the lens is (m + 1 )f. 22. Figure shows a ray of light passing through a prism. If the refracted ray QR is parallel to the base BC, show that

i) r1 = r2 = A/2, ii) angle of minimum deviation, Dm = 2i – A. 23. (a) Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main considerations required in selecting the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope. (b) A compound microscope has an objective of focal length 1.25 cm and eyepiece of focal length 5 cm. A small object is kept at 2.5 cm from the objective. If the final image formed is at infinity, find the distance between the objective and the eyepiece. 24. A biconvex lens made of a transparent material of refractive index 1.25 is immersed in water of refractive index . Will the lens behave as a converging lens? Give reason. 25.(a) Write three characteristic features to distinguish between the interference fringes in Young’s double slit experiment and the diffraction pattern obtained due to a narrow single slit. (b) A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is a distance of 2.5 mm away from the entre. Find the width of the slit. 26. (a) Using the phenomenon of polarisation, show how transverse nature of light can be demonstrated. (b) Two polaroids P1 and P2 are placed with their pass axes perpendicular to each other. Unpolarised light of intensity I 0 is indident on P1. A third polaroid P3 is kept in between P1 and P2 such that its pass axis makes an angle of 30° with that of P1. Determine the intensity of light transmitted through P1, P2 and P3 . 27.A concave lens of focal length -20 cm is cut into two identical plano concave lens . What is the focal length of each part? 28. Violet light is incident on a thin convex lens. If this light is replaced by red light, explain with the reason how the power of the lens would change? 29.Under what condition two rays will converge by a convex mirror ?

30.A person looking at a person wearing a shirt with a pattern comprising vertical and horizontal lines is able to see the vertical lines more distinctly than the horizontal lines .What is this defect due to ? How is such defect of vision corrected? 31. How does the angular separation of interference fringes change, in Young’s experiment, if the distance between the slits is increased? 32. A concave lens of focal length -20 cm is cut into two identical plano concave lens . What is the focal length of each part? 33. Violet light is incident on a thin convex lens. If this light is replaced by red light, explain with the reason how the power of the lens would change? 34. How does focal length of a lens change when red colour light incident on it is replaced by violet light ? Give reason for your answer. 35. Two Polaroid’s P1 and P2 are 90° to each other. A third Polaroid P3 is placed between P1 and P2 bisecting the angle between them. If the intensity of un Polaroid beam is I0 then find the intensity of transmitted beam through P3 and P2. 36. A concave lens of focal length 15 cm in air is immersed in water whose refractive index is 1.4. Find the apparent change in the focal length of the lens. 37.A ray is to be deviated through 90o by a right angled isosceles prism . What should be the minimum refractive index of the material of the prism. 38. In the figure given below, light rays of blue, green, red wavelengths are incident on an isosceles right-angled prism. Explain with reason, which ray of light will be transmitted through the face AC. The refractive index of the prism for red, green, blue light is 1.39, 1.424, 1.476 respectively.

39. Trace the path of a ray of light passing through a glass prism (ABC) as shown in the figure. If the refractive Index of glass is 3, find out of the value of the angle of emergence from the prism. . 40 (i) Analytically find the condition of maxima and minima when two wave from coherent source overlap with each other. (ii)find the ratio of intensities at two point on a screen in young’s double slit experiment when

waves from the two slits have a path difference wave (a) 0 and (b) λ

.

41. A biconvex lens made of transparent material of refractive index 1.5 is immersed in water of

refractive index 1.3 .Will the lens behave as a converging or diverging lens ? Give reason.

42. A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is

the nature shown by the lens?

43. You are given two converging lenses of focal length 1.25cm and 5cm to design a compound

microscope. if it is to desired to have a magnification of 30, find out the separation between the

objective and eyepiece.

44. A small telescope has an objective lens of focal length 150cm and eye piece of focal length 5cm

.what is magnifying power of the telescope is for viewing distant object in normal adjustment.

45. A convex lens made of material of refractive index n1 is kept in a medium of refractive index n2

.Parallel rays of light are incident on the lens .Complete the path of the rays of light emerging from the

convex lens if, (i) n1>n2 (ii) n1=n2 and (iii)n1<n2

46.Write the conditions for observing a rainbow .Show , by drawing suitable diagrams, to understand

the formation of a rainbow.

47.A convex lens is placed in contact with a plane mirror . A point object at a distance of 20cm on the

axis of this combination has it image coinciding with itself .What is the focal length.

48. What is the diffraction of light? Draw a graph sawing the variation of intensity with angle in 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 affected when?

a- The width of the slit decreases.

b- The monochromatic source of light is replaced by source of white light.

49. What are coherence source of light? State two conditions for two light sources to be coherent.

Derive a mathematical expression for the width of interference fringes obtained in Young’s Double Slit

experiment with the help of a suitable diagram.

50.How does the refractive index of a transparent medium depend on the wave length of incident

light used? Velocity of light is 2x10 +8 m/s and an air is 3x10+8 m/s .If the ray of light passes from

glass to air ,calculate the value of critical angel.

51.Light from a point source in air falls on a spherical glass surface n=1.5 and radius of curvature

20cm ,The distance of the light source from the glass surface is 100cm at what position the image is

formed .

52.What is the effect on interference fringe in young double slit experiment if one slit is covered

53.Red light of wavelength 6500 angstrom from a distance source falls on a slit .50 mm wide . what is

the distance between two dark bands on each side of the central bright band of the different pattern

observed on a screen placed .8 m from the slit

54.A convex lens of focal length 20cm is placed co-axially with a convex mirror of radius of curvature

20cm .The two are kept at 15cm from each other .A point object lies 60cm in front of the convex lens

.Draw the ray diagram to show the formation of the image by the combination .Determine the nature

and the position of the image formed

55.A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if refractive index of the material of

the sphere is 3 .

56. Two monochromatic rays of light are incident normally on the face AB of an isosceles

right-angled prism ABC. The refractive indices of the glass prism for the two rays ‘1’ and ‘2’ are respectively 1.35 and 1.45. Trace the path of these rays after entering through th prism.

57.A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of Curvature 20 cm. The two are kept at 15 cm from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed. 58. When Puja, a student of 10th class, watched her mother washing clothes in the open, she observed coloured soap bubbles and was curious to know why the soap bubbles appear coloured. In the evening when her father, an engineer by profession, came home, she asked him this question. Her father explained to her the basic phenomenon of physics due to which the soap bubbles appear coloured. (aba) What according to you are the values displayed by Puja and her father? (b) State the phenomenon of light involved in the formation of coloured soap bubbles.

59. (i) Distinguish between unpolarised and linearly polarised light. (ii) What does a polaroid consist of? How does it produce a linearly polarised light? (iii)Explain briefly how sunlight is polarised by scattering through atmospheric particles.

60.At what angle of incidence should a light beam strike a glass slab of refractive index √ , such that

the reflected and the refracted rays are perpendicular to each other?

61-A convex mirror of focal length f forms an image which is 1/n times the size of the object.Find the

distance of the object from the mirror?

62- Draw U vs V graph for a convex mirror and for a concave mirror?

63-A plano convex lens has aperture 6cm and thickness at its centre is 2 cm. If its refractive index is

1.5 find out its focal length?

64-In diffraction pattern if the intensity of the central bright fringe is I0 then find the intensity of

second order maxima.

65-Why the intensity of unpolarised light becomes half after passing through a polaroid?

66. (i) If f = 0.5 m for a glass lens, what is the power of the lens? (ii) The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. Its focal length is 12 cm. What is the refractive index of glass? (iii) A convex lens has 20 cm focal length in air. What is focal length in water? (Refractive index of air-water = 1.33, refractive index for air-glass = 1.5.) 66.A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.) 67.Use the mirror equation to deduce that: (a) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole. (b) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.6.4The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose? 68. A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. Determine the focal length of the lens. 69.What is the effect on the interference fringes in a Young’s double-slit experiment due to each of the following operations: (a) the screen is moved away from the plane of the slits; (b) the (monochromatic) source is replaced by another (monochromatic) source of shorter wavelength; (c) the separation between the two slits is increased;

(d) the source slit is moved closer to the double-slit plane; (e) the width of the source slit is increased; (f ) the monochromatic source is replaced by a source of white light? 70. Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids? 71. In Young’s double-slit experiment using monochromatic light of wavelength l, the intensity of light at a point on the screen where path difference is l, is K units. What is the intensity of light at a point where path difference is l/3? 72. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. (a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm. (b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide? 73. Show that for a material with refractive index μ ≥ 2 , light incident at any angle shall be guided along a length perpendicular to the incident face. 74. The mixture a pure liquid and a solution in a long vertical column (i.e, horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance d << h, the height of the column. 75. In many experimental set-ups the source and screen are fixed at a distance say D and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points. 76. A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take L <<|v - f|. 77. An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed? 78. To ensure almost 100 per cent transmittivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF2 (n = 1.38). What should the thickness of the film be so that at the center of the visible speetrum (5500 A) there is maximum transmission. 79. Can reflection result in plane polarised light if the light is incident on the interface from the side with higher refractive index? 80. For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of 5000A and electrons accelerated through 100V used as the illuminating surface. 81.Two points A and B are situated at the same distance from the source of light, but in opposite direction from it.What is the phase difference between the light waves passing through A

and B? 82.When the light is polarized by reflection , what is the angle between reflected and refracted rays. 83. For double refracting crystal the refractive indices , for the ordinary and extraordinary denoted by

μo and μe. What is the relation valid along the optical axis of the crystal. 84.What is the angle between planes of electric and magnetic field oscillation in case of light waves?

85.What is the colour of the interference fringe nearest to the white central maximum incase of white light?

86. What happens to the fringe pattern when YDS experiment is performed in water instead of air? 87. In which direction relative to the normal, does a ray of light bend, when it enters

obliquely a medium in which its speed is increased? 88. For the same angle of incidence, the angles of refraction in three different media A,B and C are 15°

,25° and 35°,respectively. In which medium will the velocity of light be minimum? 89. For what angle of incidence, the lateral shift produced by a parallel sided galss slab is maximum? 90. If a plane glass slab is placed on letters of different colours, the red coloured letters appear more

raised up. Why? 91. Does refraction in a water tank make apparent depth same throughout? 92. The critical angle for glass-air interface is ic. Will the critical angle for glass-water interface be

greater than or less than ic? 93. An air bubble in a jar of water shines brightly. Why? 94. What happens to the shining of diamond if it is dipped in a transparent oil? 95. What type of a lens is a tumbler filled with water? 96. What type of a lens is an air bubble inside water? Give reason also. 97.A lens immersed in a transparent liquid is not visible. Under what condition can this happen? 98.(b)Deduce Snell’s law of refraction using Huygens wave theory .

99.(c) If the Young’s apparatus is immersed in water, then what will be effect on the fringe width?

100.(d) In Young’s double slit experiment using monochromatic light of wavelength ,the intensity at

a point on the screen where path different is λ ,is k units .What is the intensity of light at a point

where path different is

?

101.(e) Can we get reflection result in plane polarization light, if the light is incident on the interface

from the side with higher refractive index ?

102.How will the angular separation and visibility of fringes in Young’s double slit experiment change when (i) screen is moved away from the plane of the slits, and (ii) width of the source slit is increased?

UNIT- 7

DUAL NATURE OF RADIATION AND MATTER

1. Draw the variation of photoelectric current with collector plate potential for different frequencies of incident radiation. 2. (a) A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic. (b) A student performs an experiment on Photoelectric effect, using two materials A and B. A plot of Vstop vs ν is given inFig. Which material A or B has a (i) higher work function (ii)higher threshold wavelength?

3. Derive an expression for the de-Broglie wavelength associated with an electron accelerated through a potential V. Draw a schematic diagram of a localised-wave describing the wave nature of the moving electron. 4. A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 × 10–4. Calculate the particle’s mass and indentify the particle. 5.Figure shows variation of stopping potential (V0 ) with the frequency (n) for two photosensitive materials M1 and M2 . (i) Why is the slope same for both lines? (ii) For which material will the emitted electrons have greater kinetic energy for the incident radiations of the same frequency ? Justify your answer. 6. A proton and an electron have same de-Broglie wavelength which of them moves fast and which

possesses more K.E. Justify your answer. 7. An electron and a proton are accelerated through the same potential. Which one of the two has

greater value of de-Broglie wavelength associated with it and less momentum? Justify your answer.

8.Ultraviolet radiations of different frequencies ν1 and ν2 are incident on two photosensitive materials having work functions Ф1 and Ф2 (Ф1>Ф2) respectively. The KE of the emitted photoelectrons are same in both cases. Which of the two will be of higher frequency?

9.What happen to the wavelength of a photon after it collides with an electron? 10.The de Broglie wavelength of a particle of kinetic energy K is λ. What would be the wavelength of the particle , if its kinetic energy were K/4? 11.Find out the work function of the metal, If the kinetic energies of the photo electrons are E1 and E2 with wavelength of incident light λ1 and λ2. 12.When a surface 1 cm thick is illuminated with light of wavelength λ, the stopping potential is V0, But when the same surface is illuminated by light of wavelength 3 λ, the stopping potential is V0/6. Find the threshold wavelength for metallic surface? 13.The wavelength of light from from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which an electron and proton would have the same de Broglie wavelength. 14. In photoelectric effect, why should the photoelectric current increase as the intensity of monochromatic radiation incident on a photosensitive surface is increased? Explain 15. (a) Describe briefly how Davisson – Germer experiment demonstrated the wave nature of electrons. (b) An electron is accelerated from rest through a potential V. Obtain the expression for the de-Broglie wavelength associated with it. 16. Plot a graph showing variation of photoelectric current with collector plate potential at a given frequency and intensity of incident radiation. What does the intercept of the graph with potential axis signify? 17. Plot a graph showing the variation of photoelectric current with collector plate potential at a given frequency but for two different intensities I 1 and I 2 , where I 2 > I 1.

18.Define intensity of radiation. 19.The given graph shows the variation of photoelectric current with applied voltage for two different

materials and for two different intensities of the incident radiation. Identify the pair of curves

corresponding to different materials but same intensity of incident radiation.

20.Two lines A and B shown in the graph represent the de Broglie wavelength (λ ) as a function of

1/√ V (V is the accelerating potential) for two particles having the same charge. Which of the

two represents the particle of smaller mass?

21.Sketch a graph between frequency of incident radiation and stopping potential for given

photosensitive material. What information can we obtain from the value of the intercept on the

potential axis? A Source of light of frequency greater than threshold frequency is placed at a distance

of 1 m from the cathode of a photocell. The stopping potential is found to be V. if the distance of the

light source from the cathode is reduced, explain giving reason, what change will you observe in the

(i) photoelectric current (ii) stopping potential.

22. The graph shows variation of stopping potential V0 versus frequency of incident radiation v for two photosensitive metals A and B. Which of the two metals has higher threshold frequency and why? 23.Two metals A and B have work functions 4 e V and 2 e V respectively. Which of them has lower threshold wavelength? 24. Can non metals show photoelectric effect? 25. If the intensity of incident radiation on a photosensitive surface is doubled, how does the kinetic energy of the emitted electrons get affected. 26. An electron and alpha particle have the same de Broglie wavelength associated with them. How are their kinetic energies related to each other ? 27. The given graph shows the variation of photo-electric current (I) versus applied voltage (V) for two different photosensitive materials and for two different intensities of the incident radiation. Identify the pairs of curves that correspond to different materials but same intensity radiation.

λ

1/ √V

A

B

1

3

2 4

I

V

28. The graph shows variation of stopping potential V0 versus frequency of incident radiation v for two photosensitive metals A and B. Which of the two metals has higher threshold frequency and why? 29. With what purpose was famous Davisson-Germer experiment with electrons performed?

30. An electron and alpha particle have the same kinetic energy. How is the de Broglie wavelength

associated with them related?

31. Show graphically how the stopping potential for a given photosensitive surface varies with the

frequency of incident radiations.

32. An electron is accelerated through a potential difference of 100volt .What is the DE Broglie

wavelength associated with it? To which part electromagnetic spectrum does this value of wave

length correspond?

33. Write an Einstein’s photoelectric equation. State clearly the three silent features observed in

photoelectric effect, which can be explained on the basis of the above equation?

34. An electron and a proton have the same kinetic energy. Which of the two has a greater

wavelength? Explain.

35. An electron and a photon each have wavelength of 2nm find (i) their momenta (ii) energy of th

photon (iii) the kinetic energy of the electron

36. A proton and alpha particle are accelerated through the same potential .Which one of the two has

(i) greater value of the De-Broglie wavelength associated with it and (ii) less kinetic energy? Justify

37.The de-Broglie wavelength of body moving with speed v is x . On it way it loses some of its mass

and gains twice the speed .Kinetic energy also increase to twice of its initial value .What will be the

new value of the de Broglie wavelength.

38.Ulterviolet light of wavelength 2271 angstrom from 100W mercury source irradiates a photocell

made of molybdenum metal .If the stopping potential is -1.3V estimate the work function of the metal

.How would the photocell respond when the source is replaced by another source of high intensity

red light of wavelength 6328 angstrom .

39.An electron and proton , each have de- Broglie wavelength of 1nm (i) Find the ratio of their

momenta (ii) Compare the kinetic energy of the proton with that of electron.

40. Apartcle A with amass m1 is moving with velocity v and hits a particle B m2 at rest . Find the

change in the de-Broglie wavelenghtof the particle A .Treat the collision as elastic.

41. When a surface 1cm thick is illuminated with light of wavelength √, The stopping potential is V,

but when the same surface is illuminated by light of wavelength 3√ ,the stopping potential is V/6

.Find the threshold wave length of the metallic surface.

42. Draw the variation of photoelectric current with collector plate potential for different frequencies of incident radiation. 43. (a) A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic. (b) A student performs an experiment on Photoelectric effect, using two materials A and B. A plot of Vstop vs ν is given inFig. Which material A or B has a (i) higher work function (ii)higher threshold wavelength? 44. Derive an expression for the de-Broglie wavelength associated with an electron accelerated through a potential V. Draw a schematic diagram of a localised-wave describing the wave nature of the moving electron. 45. A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 × 10–4. Calculate the particle’s mass and indentify the particle. 46.Figure shows variation of stopping potential (V0 ) with the frequency (n) for two photosensitive materials M1 and M2 . (i) Why is the slope same for both lines? (ii) For which material will the emitted electrons have greater kinetic energy for the incident radiations of the same frequency ? Justify your answer. 47. A proton and an electron have same de-Broglie wavelength which of them moves fast and which

possesses more K.E. Justify your answer. 48-A small plane perfectly reflecting mirror of area A and mass M is hanging vertically with the help of

a massless string of length L . Light of intensity I is incident normally on it .Find the angle made by the

string with the vertical?

49-What is the angular momentum of an electron in Bohrs hydrogen atom whose energy is -3.4ev.

50-If the kinetic energy of an electron is increased by 100% then by what % its Debroglie wave length

changes?

51-If the stopping potentials for a metal surface are V1 and V2respectively for two light waves having

wave length λ1 and λ 2 respectively then express it work function in terms of above parameters?

52-The frequency of incident light is doubled. Prove that the kinetic energy of emitted electrons will be more than the twice

53.The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let the de-

54.The kinetic energy of electron and proton is J 32 10 -Broglie wavelengths. 55. Find the number of photons of wavelength 540 nm emitted per second by an electric bulb of power 100W (taking 34 6 10 h J-sec).

56. An electron and photon possessing same K.E. Which one will have greater wavelength? 57. In Davisson – Germer experiment if the angle of diffraction is 520 find Glancing angle? 58. What is the energy associated with a photon of wavelength 6000 A0 ? 59. What is the effect on the velocity photo electrons, if the wavelength of incident light is decreased? 60. Show graphically how the stopping potential for a given metal varies with a frequency of the

incident radiation. 61. To work functions 2ev and 5ev for two metals x and y respectively. Which metal will emit electrons,

when it is irradiated with light and wave length 400nm and why? 62. A photon and an electron have same de-broglie wavelength. Which has greater total

energy.Explain? 63. The de-broglie wave length of a photon is same as the wave length of electron. Show that K.E. of a

photon is 2mc ג/h times K.E. of electron. Where ‘m’ is mass of electron,c is velocity of light. 64. Derive the expression of de-broglie wave length in terms of energy of energy and temperature? 65. Light from bulb falls on a wodden table but no photon electrons are emitted why ?

66.The wavelength of light in the visible region is about 390 nm for violet colour, about 550 nm (average wavelength) for yellow green colour and about 760 nm for red colour. (a) What are the energies of photons in (eV) at the (i) violet end, (ii) average wavelength, yellow-green colour, and (iii) red end of the visible spectrum? (Take h = 6.63×10–34 J s and 1 eV = 1.6×10 –19J.) (b) From which of the photosensitive materials with work functions listed in Table 11.1 and using the results of (i), (ii) and (iii) of (a), can you build a photoelectric device that operates with visible light? 67.Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon). 68. Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates 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 a high intensity (~105 W m–2) red light of wavelength 6328 Å produced by a He-Ne laser? 69.An electron and a photon each have a wavelength of 1.00 nm. Find (a) their momenta, (b) the energy of the photon, and (c) the kinetic energy of electron. 70.The energy flux of sunlight reaching the surface of the earth is 1.388 × 103 W/m2. How many photons (nearly) per square metre are incident on the Earth per second? Assume that the photons in the sunlight have an average wavelength of 550 nm. 71.The given graph shows the variation of photoelectric current with applied voltage for two different

materials and for two different intensities of the incident radiation. Identify the pair of curves

corresponding to different materials but same intensity of incident radiation.

72.Two lines A and B shown in the graph represent the de Broglie wavelength (λ ) as a function of

1/√ V (V is the accelerating potential) for two particles having the same charge. Which of the two

represents the particle of smaller mass?

73.Sketch a graph between frequency of incident radiation and stopping potential for given

photosensitive material. What information can we obtain from the value of the intercept on the

potential axis? A Source of light of frequency greater than threshold frequency is placed at a

distance of 1 m from the cathode of a photocell. The stopping potential is found to be V. if the

distance of the light source from the cathode is reduced, explain giving reason, what change will

you observe in the (i) photoelectric current (ii) stopping potential.

74. Calculate the momentum and de Broglie wavelength of the electrons accelerated through a potential difference of 56 V. 75. An alpha particle and a proton are accelerated from rest by the same potential. Find the ratio of their de-Broglie wavelength. 76. Light of wavelength 2500A0 falls on a metal surface of work function 3.5 e v. What is the K.E of (i) Fastest and (ii) slowest electro from the surface n emitted 77. Electrons are emitted from a photosensitive material 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 (ii) Blue light? Explain

λ

1/ √V

A

B

1

3

2 4

I

V

UNIT-8

ATOM & NUCLEI 1. (a) Using Bohr’s postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom. (b) Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.

2. Why is it found experimentally difficult to detect neutrinos in nuclear -decay? 3. For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour. (a) What, according to you, are the values displayed by Aarti? (b) How can radioisotopes help a doctor to diagnose brain tumour? 4. Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron

in hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf).When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2, 1, identify the spectral series to which the emission lines belong.

5.A radioactive sample can decay by two different processes. The Half life for the first processes T1

and that for the second process is T2. Show that the effective half life of T of the nucleus is given by

1/T = 1/T1 + 1/ T2.

6.Two radioactive nuclei X and Y initially contaion an equal number of atoms. Their half life is 1 hr and

2 hr. Calculate the ratio of their rates of disintegration after two hours.

8.The second member of Layman series in hydrogen spectrum has wavelength 5400 Ao . Find the

wavelength of first member?

9.In a given sample two radioactive nuclei , A and B are initially present in the ratio of 4:1. The half

lives of A and B are respectively 25 yrs and 50 yrs . Find the time after which the amounts of A and B

become equal.

10. Using Rutherford model of the atom, derive the expression for the total energy of the electron in

hydrogen atom. What is the significance of total negative energy possessed by the electron?

11.Using Bohr’s postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr’s radius.

12. In both decay processes, the mass number of a nucleus remains same whereas the atomic number Z increases by one in decay and decreases by one in decay. Explain, giving reason. 13.(a) Define the terms (i) half-life (T1/2) and (ii) average life ( ). Find out their relationships with the decay constant ( ). (b) A radioactive nucleus has a decay constant 0.3465 (day)–1. How long would it take the nucleus to decay to 75% of its initial amount? 14.(a) Use binding energy per nucleon (BE/A) graph to explain the release of energy in both the processes of nuclear fusion and fission. (b) Write the basic nuclear process of neutron undergoing β-decay. Why is the detection of neutrinos found very difficult? 15. Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two

important conclusions. Which you can draw regarding the nature of nuclear forces? 16. If the nucleons bound in a nucleus are separated apart from each other , the sum of their masses is

greater than the mass of the nucleus. Where does this difference come from ? Explain briefly . 17. After a certain lapse of time, the fraction of radioactive polonium undecayed is found to be 4.625%

of its initial quantity. What is the duration of this time lapse if the half life of polonium is 138 days?

18.If the total number of protons and neutrons in a nuclear reaction is conserved, how then is the energy absorbed or evolved in the reaction? Explain.

19.The half life of a given radioactive nuclide is 1338.6 days. What is the mean life of this nuclide? After how much time will a given sample of this radioactive nuclide get reduced to only 12.5% of its initial value?

21.The energy levels of an element X are shown in the figure. A hoton of wavelength 620 nm is

emitted and this corresponds to which of the transition A, B, C, D or E?

22. The activity of a radioactive material drops to 1/14 th of its value in 24 hours. Calculate the half-life and the decay constant? 23. Is the mass of electrons obtained by all sources equal? 24. Why is the mass of nucleus always less than the sum of the masses of its constituents, neutrons and protons? 25. A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme :

The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A 4 ? 26.How will the distance of closest approach change when(i) the K.E. of the projectile is doubled (ii) velocity of the projectile is halved ? 27.How will the distance of closest approach change when(i) the K.E. of the projectile is doubled (ii) velocity of the projectile is halved ? . 28. The energy of the electron in the ground state of hydrogen atom is – 13. 6 eV .How much energy is required to take an electron in this atom from the ground state to the first excited state? 29. After a certain lapse of time, the fraction of radioactive polonium undecayed is found to be 4.625% of its initial quantity. What is the duration of this time lapse if the half life of polonium is 138 days? 30. The half life of a given radioactive nuclide is 1338.6 days. What is the mean life of this nuclide? After how much time will a given sample of this radioactive nuclide get reduced to only 12.5% of its initial value?

31. The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength 102.7 nm. 32. A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme :

0 A B C

-1 eV D

E

-3 eV

-10 eV

The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A 4 ? 33. The half life of 612C is 5700 years. What does it mean? Two radioactive nuclei P and Q initially contain an equal number of atoms. Their half life is 1 hour and 2 hours respectively. Calculate the ratio of their rates of disintegration after two hours. 34. Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states can be expressed as the sum of kinetic energy (K) and potential energy(U) , where U= -2K. 35.A star converts all its hydrogen to helium achieving 100% helium composition. It then converts helium to carbon via the reaction:

324He → 212C + 7.27 MeV

The mass of the star is 5.0 x 1030 kg and it generates energy at the rate of 5 x 1030 watt. How long will it take to convert all its helium to carbon? 36. How is the mean life of radioactive sample related to its half-life?

37. Write expression for Bohr’s a radius in hydrogen atom.

38. Define the term activity of a radionuclide? Write its S,I unit.

39. Draw a plot of potential energy of a pair of nucleons as a function of their separations .write two

important conclusion which you can draw regarding the nature of nuclear forces

40. Using the curve for the binding energy per nucleon as a function of mass number A, state clearly

how the release in energy in the process of nuclear fusion can be explained.

41. State two characteristics of nuclear force .Why do the binding energy per nucleon decrease with

increase in mass number of heavy nuclei like 235U

42. Explain with example, whether the neutron to proton ratio increase or decrease during (i) alpha

decay (ii) beta decay.

43. The ground state energy of hydrogen atom is -13.6 ev . If an electron makes an transition from an

energy level -0.85ev to -3.4 ev , calculate the wave length of the spectral line emitted . two which

series hydrogen spectrum does this wave length belong.

44. Draw plot of potential energy of pair of nucleon as function of their separations. Mark the region s

where the nuclear force is (i) attractive and (ii) repulsive .Write any two characteristics feature of

nuclear forces .

45.Using the postulates of Bohr’s model of hydrogen atom , obtain expression for the frequency of

radiation emitted when the atom makes a transitions from the higher energy state with quantum

number nitwo the lower energy state with quantum number nf. .(ni<nf)

46. Why is the mass of the nucleus always less than the sum of the masses of its constituents ,

neutrons and protns ? If the total number of neutron and protons in a nuclear reaction is conserved ,

hoe then is the energy absorbed or evolved in the reaction .Explain .

47.a) Using Bohr’s postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom. (b) Using Rydberg formula, calculate the wavelengths of the spectral lines of the first member of the Lyman series and of the Balmer series.

48. Why is it found experimentally difficult to detect neutrinos in nuclear -decay? 49. For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour. (a) What, according to you, are the values displayed by Aarti? (b) How can radioisotopes help a doctor to diagnose brain tumour? 50. Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when

electron in hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf).When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2, 1, identify the spectral series to which the emission lines belong.

51.A radioactive sample can decay by two different processes. The Half life for the first processes T1

and that for the second process is T2. Show that the effective half life of T of the nucleus is given by

1/T = 1/T1 + 1/ T2.

52.Two radioactive nuclei X and Y initially contaion an equal number of atoms. Their half life is 1 hr

and 2 hr. Calculate the ratio of their rates of disintegration after two hours.

53-The energy released in the fission of one nucleus is 200Mev. Find the no of nuclei required per

second to operate a power plant of 16 Kw?

54-N atoms of a radio active element emit n alpha particles per second. Find the half life of the

element?

55-After 280 days , the activity of a radio active sample is 6000 dps. The activity reduces to 3000dps

after another 14 days. Find the initial activity of the sample?

56-The half life of Radon is 3.8 days. After how many days will only one twentieth of Radon sample be

left over?

57-If T is the half life of a radioactive sample then what fraction would remain after time T/2.

58.In a Geiger -Marsden experiment, what is the distance of closest approach to the nucleus of a 7.7 MeV α-particle before it comes momentarily to rest and reverses its direction? 59.The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV. (a) What is the kinetic energy of the electron in this state? (b) What is the potential energy of the electron in this state? (c) Which of the answers above would change if the choice of the zero of potential energy is changed? 60.The half-life of 238 92U undergoing a-decay is 4.5 × 109 years.What is the activity of 1g sample of

U238

92 ?

61.A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted? 62. A nuclide 1 is said to be the mirror isobar of nuclide 2 if Z1 =N2 and Z2 =N1 . (a) What nuclide is a

mirror isobar of Na23

11 ? (b) Which nuclide out of the two mirror isobars have greater binding energy

and why?

63.The energy levels of an element X are shown in the figure. A hoton of wavelength 620 nm is

emitted and this corresponds to which of the transition A, B, C, D or E?

64.A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV.

65. Define ionization energy. How would the ionization energy change when electron in hydrogen

atom is replaced by a particle of mass 200 times that of the electron but having the same charge?

66. Calculate the shortest wavelength of the spectral lines emitted in Balmer series.

[Given: Rydberg constant, R = 107: m‒1]

67. Calculate the de-Broglie wavelength of the electron orbiting in the n = 2 state of hydrogen atom.

68.A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglic wavelength of the particle A. Treat the collision as elastic. 69. Consider a thin target (10–2m square, 10–3m thickness) of sodium, which produces a photocurrent of 100μA when a light of intensity 100W/m2 (λ = 660nm) falls on it. Find the probability that a photoelectron is produced when a photons strikes a sodium atom. [Take density of Na = 0.97 kg/m3]. 70. Consider a metal exposed to light of wavelength 600 nm. The maximum energy of the electron doubles when light of wavelength 400 snm is used. Find the work function in eV. 71. Two particles A and B of de Broglie wavelengths λ1 and λ2 combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional). 72. If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1Å, and (ii) R = 10 Å. 73. In the Auger process an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition. 74. Show that the first few frequencies of light that is emitted when electrons fall to the nth level from levels higher than n, are approximate harmonics (i.e. in the ratio 1 : 2: 3...) when n >>1.

0 A B C

-1 eV D

E

-3 eV

-10 eV

75. What is the minimum energy that must be given to a H atom in ground state so that it can emit an Hγ line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such Hγ photon? 76. Deuteron is a bound state of a neutron and a proton with a binding energy B = 2.2 MeV. A γ -ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident γ-ray. If E = B, show that this cannot happen. Hence calculate how much bigger than B must E be for such a process to happen. 77. Are the nucleons fundamental particles, or do they consist of still smaller parts? One way to find out is to probe a nucleon just as Rutherford probed an atom. What should be the kinetic energy of an electron for it to be able to probe a nucleon? Assume the diameter of a nucleon to be approximately 10–15 m. 78. A nuclide 1 is said to be the mirror isobar of nuclide 2 if Z1 =N2 and Z2 =N1 . (a) What nuclide is a mirror isobar of 11 Na 23 ? (b) Which nuclide out of the two mirror isobars have greater binding energy and why? 79. Calculate the longest and shortest wavelength of Lyman series. Given R =10967700 m-1. (911.6 A0, 1215 A0) 80. The wavelength of second line of the Balmer series in hydrogen spectrum is 4861 A0. Calculate the

wavelength of first line. (6562 A0)

81. Which state of the triply ionized beryllium atom (Be +3) has the same orbital radius as that of the ground state of hydrogen atom? rn µ n2 /Z

82. Which level of double ionized lithium (Li +2) has same energy as the ground state energy of hydrogen atom? Compare the orbital radius of two levels. En µ Z2 / n2)

83. Calculate the frequency of photon, which can excite the electron to – 3.4eV from – 13.6 eV. (2.47 ´ 1015 Hz) 84.Show that the shortest wavelength lines in Lyman, Balmer and Paschen series have their

wavelength ratio 1: 4: 9. 85.The potential energy of the electron in ground state is –27 eV, what is its potential and kinetic

energies? 86.Show that the wavelength of electromagnetic radiation is equal to the de

Broglie wavelength of its photon.

87.Two Cu64 nuclei touch each other. Find the electrostatics repulsive energy of the system.

88.The half-life of 215At is 100 s. Find the time taken for the radioactivity of a sample of 215At to

decay to 1/16th.

89.At any instant the ratio of the amount of radioactive substances is 2 : 1. If their half lives be

respectively 12 and 16 hours, then after two days, what will be the ratio of the substances?

90.nucleus of mass number A, originally at rest, emits an -particle with speed v. What will be the

daughter nucleus recoils with a speed.

91.A atomic power reactor furnace can deliver 300 MW. The energy released due to fission of each

ofuranium atom 238 U is 170 MeV. Compute the number of uranium atoms fissioned per hour.

UNIT-9 ELECTRONIC DEVICES

1. Identify the gate equivalent to the circuit shown in the figure. Write its truth table.

2. Identify the gate equivalent to the circuit shown in the figure. Write its truth table.

3. Distinguish between a metal and an insulator on the basis of energy band diagrams.

4. (a) Why is zener diode fabricated by heavily doping both p-and n-sides of the junction? (b) Draw the circuit diagram of zener diode as a voltage regulator and briefly explain its working. 5. (a) How is photodiode fabricated? (b) Briefly explain its working. Draw its V–I characteristics for two different intensities illumination.

6. Draw the circuit diagram of an illuminated photodiode In reverse bias. How is photodiode used to

measure light intensity?

8. Draw a circuit diagram showing the biasing of an LED. State the factor which controls (i) Wavelength of light (ii) Intensity of light emitted by the diode. 11.(a) Draw the circuit diagram of a p-n junction diode in (i) forward bias , (ii) reverse bias. How are these circuits used to study the characteristics of a silicon diode ? Draw a typical V-I characteristics . 12. Explain briefly why the output and input signals of a common-emmiter amplifier differ in phase by

180 0.

13.In a p-n-p transistor circuit, the collector current is 10 mA. If 90 % of the holes reach the collector,

find emitter and base current.

14.The circuit shown in figure uses a zener diode of 12 V as a voltage regulator to run a 12 V ,

6W tape recorder on 110 V dc line . What should be the value of the resistor R if

the dc supply varies from 102 V -115V ?

(i)Write the truth table of the given combination.

(ii)Three photo diodes D1, D2,and D3 are made of semiconductors having

band gaps of 2.5 eV , 2eVand 3eV, respectively . Which one will be able todetect light

of wavelength 6000A o.

15. Explain, with the help of a circuit diagram, the working of a p-n junction diode as a half-wave rectifier. 16. Draw a circuit diagram of n-p-n transistor amplifier in CE configuration. Under what condition does the transistor act as an amplifier? 17.Write any two distinguishing features between conductors, semiconductors and insulators on the basis of energy band diagrams.

18. Identify the equivalent gate represented by the circuit shown in the figure. Draw its logic symbol and write the truth table.

19. Draw energy band diagrams of an n-type and p-type semiconductor at temperature T > 0 K. Mark the donor and acceptor energy levels with their energies. 20.A logic gate is obtained by applying output of AND gate to a NOT gate. Name the gate so formed. Write the symbol and truth table of this gate. 21. Draw the output wave form at X, using the given inputs A, B for the logic circuit shown below.Also identify the gate. 22.. C, Si and Ge have the same lattice structure. Why is C insulator while Si and Ge intrinsic semiconductor 23. For a CE- transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2V. Suppose the current amplification factor of the transistor is 100, find the input signal voltage and base current , if the base resistance is 1 kΩ.

. 24.The figure adjoining shows the V-I characteristics of a semiconductor diode (i) Identify the semiconductor diode used (ii) Draw the circuit diagram to obtain the given characteristic of this device. (iii) Briefly explain how this diode can be used as a voltage regulator. 25. What happens to the width of depletion player of a p-n junction when it is (i) forward biased, (ii) reverse biased? 26. What is LDR? How it is used for measurement of Intensity of light. 75. Name the semiconductor device that can be used to regulate an unregulated dc power supply. With the help of I-V characteristics of this device, explain its working principle. 27. A logic gate is obtained by applying output of AND gate to a NOT gate. Name the gate so formed. Write the symbol and truth table of this gate. 28. Draw the output wave form at X, using the given inputs A, B for the logic circuit shown below.Also identify the gate. .

29. For a CE- transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2V. Suppose the current amplification factor of the transistor is 100, find the input signal voltage and base current , if the base resistance is 1 kΩ. . 30.Why should a photodiode be operated at reverse bias? 31. Give logic symbol of NAND gate.

32. Draw energy band diagram of p-type semiconductor.

33. Name the type of biasing of p-n junction diode so that junction offers very high resistance.

34. Give logic symbol of NOR gate.

35.Descibe the briefly whit the help of a circuit diagram , the paths of current carriers in an n-p-n

transistor with emitter –base junction forward biased and base collector junction reverse biased.

36. Write two characteristic features to distinguish between n-type and p-type semiconductor.

37.If the output of two input NOR gate fed as both input A and B two another NOR gate ,Write down a

truth table to find the final output for all combinations of A and B.

38. Show the biasing of a photodiode with the help of a circuit diagram .Draw the graphs to show

variations in reverse bias currents for different illuminations intensities.

39. Explain briefly with the help of a circuitdiagram, the working principle of a transistor as an

amplifier .

40. On the basis of the energy band diagram distinguish between metals, insulators and

semiconductors.

41. What is an intrinsic semiconductor? How can this material be converted (i) p- type semiconductor

(ii) n- type semiconductor? Explain with help of energy band diagram.

42. (i) Describe the working of light emitting diode (LED) (ii) What semiconductors are preferred to

make LED diode

(iii) Give two advantages of using LED over conventional incandescent low power lamps.

43. Identify the gate equivalent to the circuit shown in the figure. Write its truth table.

44. Identify the gate equivalent to the circuit shown in the figure. Write its truth table.

45. Distinguish between a metal and an insulator on the basis of energy band diagrams.

46. (a) Why is zener diode fabricated by heavily doping both p-and n-sides of the junction? (b) Draw the circuit diagram of zener diode as a voltage regulator and briefly explain its working. 47. (a) How is photodiode fabricated? (b) Briefly explain its working. Draw its V–I characteristics for two different intensities of

illumination.

48. Draw the circuit diagram of an illuminated photodiode In reverse bias. How is photodiode used to

measure light intensity?

49. In a common base amplifier, what is the phase difference between the input signal voltage and output voltage? 50.In a full wave rectifier, circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be how many Hz? 51. For a transistor amplifier in common emitter configuration for load impedance of 1 KΩ ( hfe = 50 and hoe = 25 μA / V ), find the current gain. 52.- The menifestation of band structure in solids is due to ( a ) Heisenberg’s uncertainty principle ( b ) Pauli’s exclusion principle ( c ) Bohr’s correspondence principle ( d ) Boltzmann’s law 53. When p-n junction diode is forward biased, then ( a ) the depletion region is reduced and barrier eight is increased ( b ) the depletion region is widened and barrier height is reduced ( c ) both the depletion region and barrier height are reduced ( d ) both the depletion region and barrier height are increased 54. The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in ( a ) type of bonding ( b ) crystal structure ( c ) scattering mechanism with temperature ( d ) no. of charge carriers with temp. 55. In the middle of the depletion layer of a reverse biased p-n junction, the ( a ) the potential is zero ( b ) electric field is zero ( c ) potential is maximum ( d ) electric field is maximum 56. In a p-n junction, the depletion layer consists of ( a ) electrons ( b ) protons ( c ) mobile ions ( d ) immobile ions 57. In forward bias, the width of otential barrier in p-n junction diode ( a ) increases OR ( b ) decreases 58. Draw the output waveform across the resistor (Fig.) 59. If each diode in Fig. 14.13 has a forward bias resistance of 25Ωand infinite resistance in reverse bias, what will be the values of the current I1, I2, I3 and I4?

60. Suppose a pure Si crystal has 5 × 1028 atoms m–3. It is doped by 1 ppm concentration of pentavalent As. Calculate the number of electrons and holes. Given that ni =1.5 × 1016 m–3. 61.(a) The current in the forward bias is known to be more (~mA) than the current in the reverse bias (~μA). What is the reason then to operate the photodiodes in reverse bias? (b)Why are Si and GaAs are preferred materials for solar cells? 62. In half-wave rectification, what is the output frequency if the input frequency is 50 Hz. What is the output frequency of a full-wave rectifier for the same input frequency. 63.Distinguish between an intrinsic semiconductor and P-type semiconductor. Give reason, why a P-

type semiconductor crystal is electrically neutral, although nh >> ne?

64In the given diagram, is the diode D forward or reversed biased? 65.Name the logic gate realized using p-n junction diodes in the given diagram. Give its logic symbol. 66.A semiconductor has equal electron and hole concentrations of 2 x 108/m3. On doping with a certain impurity, the hole concentration increases to 4 x 1010/m3. (i) What type of semiconductor is obtained on doping? (ii) Calculate the new electron hole concentration of the semiconductor. (iii) How does the energy gap vary with doping?

67.In a transistor, the base current is changed by 30 μA. This results in a change of 0.03 V in base to emitter voltage and a change of 3 mA in the collector current. (i) Find (a) current gain ‘βac‘ and (b) transconductance ‘gm’, (ii) If this transistor is used as an amplifier with the load resistance 7.5 kΩ, calculate voltage gain of amplifier.

68.The input resistance of a silicon transistor is 665 Ω. Its base current is changed by 15 μA which results in change of collector current by 2 mA. This transistor is used as a common emitter amplifier with a load resistance of 5 k Ω. Calculate(i) current gain ‘βa.c.’, (ii) trans-conductance ‘gm‘, and (iii) voltage gain ‘Av’ of the amplifier.

69. In a transistor a change of base current by 20 μA, results in a change of 0.02V in base emitter voltage and a change of 2mA in the collector current, Find (i) current gain ‘βa.c.’, (ii) trans-conductance ‘gm‘. Also calculate the voltage gain of this transistor when used as a common emitter amplifier with a load resistance of 5 kΩ.

70. How a pn junction can be used as a (a) half wave rectifier (b) full-wave rectifier?

71. What is a pn junction? Explain with the help of a diagram, how depletion layer is formed near the junction. Explain also what happens to this layer when the junction is (i) forward biased and (ii) reverse biased.

72. What do you understand by the term “holes” in a semiconductor. Discuss how they move under the influence of electric field.

73.What is a pn junction? How is a pn junction made? How potential barrier is caused into it?

74.By drawing a labeled circuit diagram, explain how a NPN transistor can be used as an amplifier in common base configuration. Find its current gain, voltage gain and power gain.

75. Define the terms “potential barrier” and ‘depletion region’ for a pn junction. Explain with the help of a circuit diagram, the use of a pn junction as a full wave rectifier. Draw the input and output waveforms.

76. .The ratio of number of free electrons to holes ne/nh for two different materials A and B are 1 and <1 respectively. Name the type of semi conductor to which A and B belongs.

77. In half wave rectification , what is the output frequency if the input frequency is 50 hz.What is the output frequency of a full wave rectification for the same input frequency.

78. How can you relate drift velocity and mobility of an electron? 79. Show by the graph how does the current vary with the voltage change for a junction diode. 80. Why do semiconductors obey OHM’S law for only low fields? 81. Mention the factors upon which Tranconductance of a transistor depend. 82. For faster action which transistor is used and why? 83. How would you set up a circuit to obtain NOT gate using a transistor? 84. Explain why elemental semiconductor cannot be used to make visible LEDs. 85. Suppose a ‘n’-type wafer is created by doping Si crystal having 5 × 1028 atoms/m3 with 1ppm concentration of As. On the surface 200 ppm Boron is added to create ‘P’ region in this wafer. Considering ni = 1.5 × 1016 m–3, (i) Calculate the densities of the charge carriers in the n & p regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when diode is reverse biased. 86. Three photo diodes D1, D2 and D3 are made of semiconductors having band gaps of 2.5eV, 2eV and 3eV, respectively. Which ones will be able to detect light of wavelength 6000A ?

UNIT-10 COMMUNICATIONS. 1. (a) State briefly any two reasons explaining the need for modulating a signal. (b) Draw a labelled block diagram of a simple modulator for obtaining an AM signal. 2.(a) An amplitude modulated wave is as shown in Fig.

Calculate (i) peak carrier voltage .

(ii) the percentage modulation. (b) Why is a AM signal likely to be more noisy than a FM signal upon transmission through a channel? 3. Describe briefly, by drawing suitable diagrams, the (i) sky wave and (ii) space wave modes of propagation. Mention the frequency range of the waves in these modes of propagation. 4. Write the functions of the following in communication systems: (i) Transducer (ii) Repeater

5.Give the expression for bandwidth in FM Modulation

6.How does the effective power radiated by an antenna vary with wavelength

7.An audio signal of amplitude one half the carrier amplitude is employed in amplitude modulation.

What is themodulation index.

8.A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving

antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS

mode?

9.What is role of band pass filter in amplitude modulation?

10. Distinguish with the help of suitable diagrams between ground wave and sky wave modes of propagation. Mention the frequency range of the waves in these modes of propagation. 11.Explain, with the help of a suitable diagram, the space wave mode of propagation. Give two examples in communication system where this mode is used. What is the frequency range of these waves? Give reason for using this range of frequency. 12.Write the functions of the following in communication systems: (i) Transducer (ii) Repeater 13.Why is the amplitude of modulating signal kept less than the amplitude of the carrier wave ? 14.In the block diagram of a simple modulator for obtaining an AM signal, shown in the figure, identify the boxes A and B. Write their functions. 15.In the given block diagram of receiver, identify the boxes labeled as and Y and write their functions. 16.A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving

antenna is 49 m. What is the maximum distance between them, for satisfactory communication in the LOS mode ?

(Radius of earth = 6400 km). 18.A schematic arrangement for transmitting a message signal (20 Hz to 20 KHz) is given below: Give two drawbacks from which this arrangement suffers.

Describe briefly with the help of a block diagram the alternative arrangement for the transmission and reception of the message signal.

19.Why do we need carrier waves of very high frequency in the modulation of signals? A carrier wave of peak voltage 20 V is used to transmit a message signal. What should be the peak voltage of the modulating signal, in order to have a modulation index of 80%?

20. In the given block diagram of receiver, identify the boxes labelled as X and Y and write their functions.

21.Why ground wave transmission signal is is restricted to only 1500 KHz. 22.. What is meant by LOS mode of communication ? 23.Ground receiver station is receiving a signal at (i) 5 MHz and (ii )100 MHz transmitted from a ground transmitter at a height of 300 m, located at a distance of 100 km from the receiver station. Identify whether the signal is coming via space wave or sky wave propagation or satellite transponder. Radius of earth = 6.4 x 106 m. Nmax of the Ionosphere = 1012/ m3..

24 .Why should transmitters broadcasting programmes use different carrier frequencies? 25. What is modulation index ? How does it affect modulation ? 26. A T.V tower has a height of 500 m at a given place. Calculate its coverage range if the radius of the earth is 6400 Km. 27. A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is the maximum distance between them, for satisfactory communication in the LOS mode ? (Radius of earth = 6400 km). 28. A schematic arrangement for transmitting a message signal (20 Hz to 20 KHz) is given below: Give two drawbacks from which this arrangement suffers. Describe briefly with the help of a block diagram the alternative arrangement for the transmission and reception of the message signal. 29. A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS mode? Given radius of earth 6.4 × 106 m. 30. A message signal of frequency 10 kHz and peak voltage of 10 volts is used to modulate a carrier of frequency 1 MHz and peak voltage of 20 volts. Determine (a) modulation index, (b) the side bands produced. 31. Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81m tall. How much service area can it cover if the receiving antenna is at the ground level? 32. A carrier wave of peak voltage 12V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 75%? 33. For an amplitude modulated wave, the maximum amplitude is found to be 10V while the minimum amplitude is found to be 2V. Determine the modulation index, μ. What would be the value of μ if the minimum amplitude is zero volt? 34.In the block diagram of a simple modulator for obtaining an AM signal, shown in the figure, identify the boxes A and B. Write their functions. 35.Ground receiver station is receiving a signal at (i) 5 MHz and (ii )100 MHz transmitted from a ground transmitter at a height of 300 m, located at a distance of 100 km from the receiver station. Identify whether the signal is coming via space wave or sky wave propagation or satellite transponder. Radius of earth = 6.4 x 106 m. Nmax of the Ionosphere = 1012/ m3. [3] 36.Why do we need carrier waves of very high frequency in the modulation of signals? A carrier wave of peak voltage 20 V is used to transmit a message signal. What should be the peak voltage of the modulating signal, in order to have a modulation index of 80%? 37. An audio signal is modulated by a carrier wave of 20MHz such that the bandwidth required for modulation is 3kHz. Could this wave be demodulated by a diode detector which has the values of R and C as (i) R = 1 kΩ, C = 0.01μF. (ii) R = 10 kΩ, C = 0.01μF.

(iii) R = 10 kΩ, C = 0.1μF. 38. A 50 MHz sky wave takes 4.04 ms to reach a receiver via re-transmission from a satellite 600 km above earth’s surface. Assuming re-transmission time by satellite negligible, find the distance between source and receiver. If communication between the two was to be done by Line of Sight (LOS) method, what should size and placement of receiving and transmitting antenna be? 39. A TV transmission tower antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) at ground level, (ii) at a height of 25 m? Calculate the percentage increase in area covered in case (ii) relative to case (i). 40. If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earths radius? 41.Why the transmission of signal is not possible for frequency greater than 20Mhz . 42.How does the effective power radiated by the antenna vary with wavelength? 43.what should be the length of the dipole antenna for a carrier wave of 5 X 10 8hz ? 44.By how much should the height of the antenna be increased to double the coverage range R= 6400

Km. 45. A TV. tower has a height of lOOm . How much population is covered by the TV.

broadcaste if the average population density around the tower is 1000/km2

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