138

PHYSICS (Theory)

Time allowed : 3 hours Maximum Marks : 70

General Instructions:

(i) There are 26 questions in all. All questions are compulsory.

(ii) This question paper has five sections: Section A, Section B, Section C, Section

D and Section E.

(iii) Section A contains five questions of one mark each, Section B contains five

questions of two marks each, Section C contains twelve questions of three

marks each, Section D contains one value based question of four marks and

Section E contains three questions of five marks each.

(iv) There is no overall choice. However, an internal choice has been provided in

one question of two marks, one question of three marks and all the three

questions of five marks weightage. You have to attempt only one of the choices

in such questions.

(v) You may use the following values of physical constants wherever necessary:

c = 3 108 ms–1

h = 6.63 10–34 Js

e = 1.6 10–19 C

0 = 4 10–7 T mA–1

0 = 8.854 × 10–12 C2 N–1 m–2

04

1

= 9 109 N m2 C–2

me = 9.1 10–31 kg

139

QUESTION PAPER CODE 55/1/1/D

1. Define capacitative reactance. Write its S.I. units. 1

2. What is the electric flux through a cube of side 1 cm which encloses an electric

dipole? 1

3. A concave lens of refractive index 1.5 is immersed in a medium of refractive index

1.65. What is the nature of the lens ? 1

4. How are side bands produced ? 1

5. Graph showing the variation of current versus voltage for a material GaAs is shown

in the figure. Identify the region of

(i) negative resistance

(ii) where Ohm's law is obeyed. 1

mass of neutron = 1.675 × 10–27 kg

mass of proton = 1.673 × 10–27 kg

Avogadro's number = 6.023 × 1023 per gram mole

Boltzmann constant = 1.38 × 10–23 JK–1

140

Section-B

6. A proton and an a-particle have the same de-Broglie wavelength. Determine the

ratio of (i) their accelerating potentials and (ii) their speeds. 2

7. Show that the radius of the orbit in hydrogen atom varies as n2, where n is the

principal quantum number of the atom. 2

8. Distinguish between 'intrinsic' and 'extrinsic' semiconductors. 2

9. Use the mirror equation to show that an object placed between f and 2f of a concave

mirror produces a real image beyond 2f. 2

OR

Find an expression for intensity of transmitted light when a polaroid sheet is rotated

between two crossed polaroids. In which position of the polaroid sheet will the

transmitted intensity be maximum ?

10. Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone

bridge. 2

Section- C

11. Name the parts of the electromagnetic spectrum which is

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

(b) used to treat muscular strain.

(c) used as a diagnostic tool in medicine.

Write in brief, how these waves can be produced. 3

12. (i) A giant refracting telescope has an objective lens of focal length 15 m. If an

eye piece of focal length 1.0 cm is used, what is the angular magnification of

the telescope?

141

(ii) If this telescope is used to view the moon, what is the diameter of the image

of the moon formed by the objective lens? The diameter of the moon is

3.48 × 106 m and the radius of lunar orbit is 3.8 x 108 m. 3

13. Write Einstein's Photoelectric equation and mention which important features in

photoelectric effect can be explained with the help of this equation.

The maximum kinetic energy of the photoelectrons gets doubled when the wavelength

of light incident on the surface changes from 1 to

2. Derive the expressions for the

threshold wavelength 0 and work function for the metal surface. 3

14. In the study of Geiger-Marsdon experiment on scattering of particles by a thin

foil of gold, draw the trajectory of -particles in the Coulomb field of target

nucleus. Explain briefly how one gets the information on the size of the nucleus from

this study.

From the relation R = R0 A1/3, where R

0 is constant and A is the mass number of

the nucleus, show that nuclear matter density is independent of A. 3

OR

Distinguish between nuclear fission and fusion. Show how in both these processes

energy is released.

Calculate the energy release in MeV in the deuterium-tritium fusion reaction :

nHeHH 4

2

3

1

2

1

Using the data :

m( H2

1) = 2.014102 u

m( H3

1) = 3.016049 u

m( He4

2) = 4.002603 u

mn = 1.008665 u

l u = 931.5 MeV/c2

142

15. Draw a block diagram of a detector for AM signal and show, using necessary

processes and the waveforms, how the original message signal is detected from the

input AM wave. 3

16. A cell of emf 'E' and internal resistance 'r' is connected across a variable load

resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the

current I.

It is found that when R = 4 , the current is 1 A and when R is increased to 9 ,

the current reduces to 0.5 A. Find the values of the emf E and internal resistance r. 3

17. Two capacitors of unknown capacitances C1 and C

2 are connected first in series

and then in parallel across a battery of 100 V. If the energy stored in the two

combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C

2.

Also calculate the charge on each capacitor in parallel combination. 3

18. State the principle of working of a galvanometer.

A galvanometer of resistance G is converted into a voltmeter to measure upto V

volts by connecting a resistance R1 in series with the coil. If a resistance R

2 is connected

in series with it, then it can measure upto V/2 volts. Find the resistance, in terms of

R1 and R

2, required to be connected to convert it into a voltmeter that can read upto

2 V. Also find the resistance G of the galvanometer in terms of R1 and R

2. 3

19. With what considerations in view, a photodiode is fabricated ? State its working

with the help of a suitable diagram.

Eventhough the current in the forward bias is known to be more than in the reverse

bias, yet the photodiode works in reverse bias. What is the reason? 3

20. Draw a circuit diagram of a transistor amplifier in CE configuration.

Define the terms: (i) Input resistance and (ii) Current amplification factor. How are

these determined using typical input and output characteristics? 3

143

21. Answer the following questions:

(a) In a double slit experiment using light of wavelength 600 nm, the angular

width of the fringe formed on a distant screen is 0.1o. Find the spacing between

the two slits.

(b) Light of wavelength 5000 Å. propagating in air gets partly reflected from the

surface of water. How will the wavelengths and frequencies of the reflected

and refracted light be affected? 3

22. An inductor L of inductance XL is connected in series with a bulb B and an ac

source. How would brightness of the bulb change when (i) number of turns in the

inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of

reactance XC = X

L is inserted in series in the circuit. Justify your answer in each case. 3

Section -D

23. A group of students while coming from the school noticed a box marked "Danger

H.T. 2200 V" at a substation in the main street. They did not understand the utility of

such a high voltage, while they argued, the supply was only 220 V.They asked their

teacher this question the next day. The teacher thought it to be an important question

and therefore explained to the whole class.

Answer the following questions:

(i) What device is used to bring the high voltage down to low voltage of a.c.

current and what is the principle of its working?

(ii) Is it possible to use this device for bringing down the high d.c. voltage to the

low voltage ? Explain.

(iii) Write the values displayed by the students and the teacher. 4

144

Section-E

24. (a) State Ampere's circuital law. Use this law to obtain the expression for the

magnetic field inside an air cored toroid of average radius 'r' having 'n' turns

per unit length and carrying a steady current I.

(b) An observer to the left of a solenoid of N turns each of cross section area 'A'

observes that a steady current I in it flows in the clockwise direction. Depict

the magnetic field lines due to the solenoid specifying its polarity and show

that it acts as a bar magnet of magnetic moment m = NIA. 5

OR

(a) Define mutual inductance and write its S.I. unit.

(b) Derive an expression for the mutual inductance of two long co-axial solenoids

of same length wound one over the other.

(c) In an experiment, two coils c1 and c

2 are placed close to each other. Find out

the expression for the emf induced in the coil c1 due to a change in the current

through the coil c2. 5

25. (a) Using Huygens's construction of secondary wavelets explain how a diffraction

pattern is obtained on a screen due to a narrow slit on which a monochromatic

beam of light is incident normally.

(b) Show that the angular width of the first diffraction fringe is half that of the

central fringe.

145

(c) Explain why the maxima at = a

λ

2

1 n

become weaker and weaker with

increasing n. 5

OR

(a) A point object 'O' is kept in a medium of refractive index n1 in front of a

convex spherical surface of radius of curvature R which separates the second

medium of refractive index n2 from the first one, as shown in the figure.

Draw the ray diagram showing the image formation and deduce the relationship

between the object distance and the image distance in terms of n1, n

2 and R.

(b) When the image formed above acts as a virtual object for concave spherical,

surface separating the medium n2 from n

1 (n

2 > n

1), draw this ray diagram and

write the similar (similar to (a)) relation. Hence obtain the expression for the

lens maker's formula. 5

26. (a) An electric dipole of dipole moment p

consists of point charges +q and -q

separated by a distance 2a apart. Deduce the expression for the electric field

E

due to the dipole at a distance x from the centre of the dipole on its axial

line in terms of the dipole moment p

. Hence show that in the limit x >> a,

p2E / (40x3).

146

(b) Given the electric field in the region

i2E x , find the net electric flux through

the cube and the charge enclosed by it. 5

OR

(a) Explain, using suitable diagrams, the difference in the behaviour of a (i) conductor

and (ii) dielectric in the presence of an external electric field. Define the terms

polarization of a dielectric and write its relation with susceptibility.

(b) A thin metallic spherical shell of radius R carries a charge Q on its surface. A

point charge 2

Q is placed at its centre C and an other charge +2Q is placed

outside the shell at a distance x from the centre as shown in the figure. Find

(i) the force on the charge at the centre of shell and at the point A and (ii) the

electric flux through the shell.

A

2Qx

176

QUESTION PAPER CODE 55(B)

SECTION A

1. Where on the surface of Earth, is the vertical component of Earth's magnetic field

zero? 1

2. Define the term 'rms' value of the current. How is it related to the peak value? 1

3. Write the expression for the de Broglie wavelength associated with an electron

accelerated through a potential 'V'. 1

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

magnetic field. What is the direction of the magnetic field ? 1

5. Why is convex mirror used as a side view mirror in a car? 1

SECTION B

6. A point charge causes an electric flux of – 1 × 103 Nm2/C to pass through a

spherical Gaussian surface of 10·0 cm radius centred on the charge.

(a) What is the value of the point charge?

(b) If the radius of the Gaussian surface were doubled, how much flux would

pass through the surface? 2

7. State Lenz's law. Show that it is a consequence of the principle of conservation of

energy. 2

8. (i) What is the power of the lens whose focal length is 0·25 m?

(ii) The radii of curvature of the faces of a double convex lens are 20 cm and

25 cm. Its focal length is 20 cm. Calculate the refractive index of the material. 2

9. Define electrical resistivity of a given material. Why does resistivity of a metal

increase with the increase in temperature whereas in the case of a semiconductor

it decreases? 2

177

10. Write the functions of (i) transmitter and (ii) transducer in the context of communi-

cation system. 2

OR

Write two factors justifying the need of modulation for transmission of a signal. 2

SECTION C

11. (a) Describe briefly how an oscillating charge can produce an electromagnetic

wave propagating through space.

(b) Which part of the. electromagnetic spectrum is used in satellite communica-

tion ? 3

12. (a) In an unbiased p-n junction, why do holes from p-region diffuse to n -region?

(b) What is the effect of forward biasing on (i) barrier potential and (ii) depletion

layer, in a p-n junction diode? 3

13. Explain the terms (i) threshold frequency and (ii) stopping potential, using Einstein's

photoelectric equation.

State clearly one observed feature in photoelectric effect which cannot be explained

by wave nature of light. 3

14. Write two characteristic properties of nuclear force. How does one explain the

release of energy in the processes of nuclear fusion and nuclear fission ? 3

15. State the underlying principle of a cyclotron. Obtain the expression for cyclotron

frequency and explain how it is used to accelerate the charged particles. 3

16. Define the term 'linearly polarised light'. How does an unpolarised light get linearly

polarised when passed through a polaroid ? When does the intensity of transmitted

178

light become maximum when a polaroid sheet is rotated between two crossed

polaroids ? 3

17. Explain briefly how an n-p-n transistor is fabricated. Define the terms (i) input

resistance and (ii) current amplification factor (B) of a transistor, used in its CE

configuration. 3

OR

State the underlying principle of a full wave rectifier. Explain how it works. 3

18. (a) How is the electric field due to a charged parallel plate capacitor affected

when a dielectric slab is inserted between the plates fully occupying the

intervening space?

(b) A slab of material of dielectric constant K has the same area as the plates of a

parallel plate capacitor but has the thickness d/2, where'd' is the separation

between the plates. Find the expression for the capacitance when the slab is

inserted between the plates. 3

19. Explain the working of an astronomical telescope. The magnifying power of a

telescope in its normal adjustment is 20. If the length of the telescope is 105 cm in

this adjustment, find the focal lengths of both the lenses. 3

20. State Ampere's circuital law. Using this law, deduce the expression for the magnetic

field due to a thin straight infinitely long current carrying wire at a distance ' r' from

it. 3

21. The ground state energy of hydrogen atom is -13·6 eV. If an electron makes a

transition from an energy level - 0·85 eV to - 3·4 eV, calculate the wavelength of the

spectral line emitted. To which series of hydrogen spectrum does this wavelength

belong? 3

22. Consider a large spherical shell of radius 'R' on which a charge 'Q' is placed. If we

place a small sphere of radius ' r ' carrying a charge 'q' at the centre of the large

179

sphere, find out the expressions for the total potential on the surface of the outer

shell and inner sphere. Which one would be at a higher potential and why? 3

SECTION D

23. Anuj has the habit of talking on his mobile phone for a long span of time. One day,

when he was absent from the school, he contacted his friend and asked about the

homework. He then asked his friend how to solve these problems. His sister, Meena,

kept on watching him. She finally suggested to him that if he had to talk for such a

long time, it would be better if he used the land line. She explained how a prolonged

exposure and use of a mobile phone. over a long time could be harmful. Anuj got

convinced and accepted his sister's advice.

Based on the above paragraph, answer the following questions:

(a) What, according to you, are the values displayed by Meena?

(b) In what way could the use of mobile phone for a long time be harmful?

(c) Find out the range upto which electromagnetic waves can be transmitted

from an antenna of height 320 m. (Given: Radius of Earth = 6·4 × 106 m) 4

SECTION E

24. Explain briefly the principle and working of the device used for comparing the emfs

of two cells. Define the potential gradient and write its S.I. unit. How can the current

sensitivity of such a device be increased ? In what way is this method of comparing

the emfs of two cells different from the one using voltmeter? 5

OR

(a) Use Kirchhoff's rules to obtain the balance condition in terms of the values of

the four resistors in a Wheatstone bridge so as to obtain null deflection in the

galvanometer.

180

(b) Explain how the balance condition in Wheatstone bridge is used in meter

bridge to determine the value of unknown resistance. Under what condition is

the error in determining the unknown resistance minimized ? 5

25. (a) Derive the condition for resonance in a series LCR circuit connected to an

a.c. source of variable frequency.

(b) Define the following terms :

(i) Q- factor

(ii) Power factor

(iii) Wattless current 5

OR

(a) Explain the working principle of a step-up transformer. Deduce the expression

for the secondary to primary voltage in terms of the number of turns in the two

coils. In an ideal transformer, how is this ratio related to the currents in the

two coils?

(b) How are the transformers used in large scale transmission and distribution of

electrical energy over long distances? 5

26. (a) A parallel beam of monochromatic light falls normally on a narrow slit and the

light coming out of the slit is obtained on a screen kept parallel to the plane of

the slit. What kind of pattern do we observe on the screen and why ? How

does the (i) angular width and (ii) linear width of the principal maximum in this

pattern change when the source is moved parallel to itself away from the slit

plane?

(b) State two points of difference between this pattern and the interference pattern

observed in Young's double slit experiment. 5

181

OR

(a) What is meant by coherent sources. ? 'Why are they necessary for observing

a sustained interference pattern?

(b) Show that the superposition of the waves originating from two coherent sources

S1 and S

2 described by y

1 = a cos t and y

2 = a cos (t + ) at a point,

produces a resultant intensity

I = 4 a2 cos2 /2

Hence write the conditions for the appearance of dark and bright fringes. 5