Subject: Physics
Class XII
Time Allowed: 3 hours
Max. Marks: 70
General Instructions:
(1) There are 35 questions in all. All questions are compulsory
(2) This question paper has five sections: Section A, Section B, Section C, Section D and Section E. All the sections are compulsory.
(3) Section A contains eighteen MCQ of 1 mark each, Section B contains seven questions of two marks each, Section C contains five questions of three marks each, section D contains three long questions of five marks each and Section E contains two case study-based questions of 4 marks each.
(4) There is no overall choice. However, an internal choice has been provided in section B, C, D and E. You have to attempt only one of the choices in such questions.
(5) Use of calculators is not allowed.
SECTION A
1. Two large vertical and parallel metal plates having a separation of 1 cm are connected to a dc voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 450 to the vertical just after release. Then X is nearly
(a) 1×10-5 V
(b) 1x 10-7 V
(c) 1×10-9 V
(d) 1x 10-10 V
2. The electric flux for Gaussian surface A that encloses the charged particles in free space is (Given q1=-14nC, q2=78.85 n C, q3=-56nC)
(a) 103 Nm²C-1
(b) 103 CN-1m-2
(c) 6.32 x 103 Nm² C-1
(d) 6.32 x 103 CN-1m-2
3. Two capacitors of capacitances C1 and C2 are connected in parallel. If a charge q is given to the assembly, the charge gets shared. The ratio of the charge on the capacitor C1, to the charge that on C2, is
(a) C1/ C2
(b) C2/C1
(c) C1C2
(d) 1/C1C2
4. The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter, the change in the resistance of the wire will be
(a) 200%
(b) 100%
(c) 50%
(d) 300%
5. An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be
(a) 3
(b) 1/3
(c) 8/9
(d) 2
6. The magnetic field at a distance r from a long wire carrying current I is 0.4 tesla. The magnetic field at a distance
(a) 0.1 tesla
(b) 0.2 tesla
(c) 0.8 tesla
(d) 1.6 tesla
7. Two circular coils 1 and 2 are made from the same wire but the radius of the first coil is twice that of the second coil. What ratio of the potential difference (in volt) should be applied across them, so that the magnetic field at their centres is the same?
(a) 2
(b) 3
(c) 4
(d) 6
8. The variation of magnetic susceptibility with the temperature of a ferromagnetic material can be plotted as
Ans. (b) Susceptibility of a ferromagnetic material decreases with the increase in temperature and above the Curie temperature TC, it becomes paramagnetic
9. A coil having n turns and resistance R Ω is connected with a galvanometer of resistance 4R Ω. This combination is moved in time t seconds from a magnetic flux ɸ1 weber to, ɸ2 weber. The induced current in the circuit is
(a) (ɸ1-ɸ2)/5 R n t
(b) -n(ɸ1-ɸ2)/5Rt
(c) -( ɸ1-ɸ2)/R n \]t
(d) -n(ɸ1-ɸ2)/Rt
10. In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
(a) 4L
(b) 2L
(c) L/2
(d) L/4
11. An electromagnetic wave of frequency 3 MHz passes from vacuum into a dielectric medium with permittivity ε= 4. Then,
(a) wavelength and frequency both remain unchanged.
(b) wavelength is doubled and the frequency remains unchanged.
(c) wavelength is doubled and the frequency becomes half.
(d) wavelength is halved and the frequency remains unchanged.
12. If wavelength of light in air is 2400 x 10-10 m, then what will the wavelength of light in glass (µ = 1.5)?
(a) 1600 Å
(b) 7200 Å
(c) 1080 Å
(d) none of these
13. The threshold frequency for photoelectric effect on sodium corresponds to a wavelength of 5000 Å. Its work function is
(a) 4× 10-19 J
(b)1 J
(c) 2 × 10-19 J
(d) 3 x 10-19 J
14. The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true?
(a) Its kinetic energy increases and its potential and total energies decrease.
(b) Its kinetic energy decreases, potential energy increases and its total energy remains the same
(c) Its kinetic and total energies decrease and its potential energy increases
(d) Its kinetic, potential and total energies decrease
15. If the binding energy per nucleon in 3Li7 and 2He4 nuclei are 5.60 MeV and 7.06 MeV respectively, then in reaction 1H1+ 3Li7 → 2 2He4 energy of proton must be
(a) 28.24 MeV
(b) 17.28 MeV
(c)1.46 MeV
(d) 39.2 MeV
16. Two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true and R is NOT the correct explanation of A
c) A is true but R is false
d) A is false and R is also false
Assertion: It is not possible to have interference between the waves produced by two violins.
Reason: For interference of two waves the phase difference between the waves must remain constant.
Ans. The waves produced by the two violins are not coherent
17. Two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true and R is NOT the correct explanation of A 1
c) A is true but R is false
d) A is false and R is also false
Assertion: The resistivity of a semiconductor increases with temperature.
Reason: The atoms of a semiconductor vibrate with larger amplitudes at higher temperatures thereby increasing its resistivity.
Ans. Resistivity of a semiconductor decreases with temperature. Larger amplitudes of atoms at higher temperatures increase conductivity of a semiconductor.
18. Two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true and R is NOT the correct explanation of A 1
c) A is true but R is false
d) A is false and R is also false
Assertion: In photoelectron emission, the velocity of electron ejected from near the surface is larger than that coming from interior of metal.
Reason: The velocity of ejected electron will be zero
Ans. For an incident photon of given energy, velocity of photoelectron ejected from near the surface is larger than that coming from the interior of the metal because less energy is required to eject an electron from the surface than from the interior. The velocity of ejected electron may not be zero.
SECTION B
19. Name the constituent radiation of electromagnetic spectrum which is
a. used to study crystal structure
Ans. X rays – Used as a diagnostic tool in medicine
b. suitable for radar systems used in aircraft navigation.
Ans. Micro wave – Used in micro wave oven
Write one another application of each of these radiations.
20. Two similar bars, made from two different materials P and Q, are placed one by one, in a non-uniform magnetic field. It is observed that
a) bar P tends to move from the weak to the strong field region.
Ans.
b) bar Q tends to move from the strong to the weak field region. Identify the magnetic material used for making these two bars. Show with the help of diagrams, the behaviour of the field lines, due to an external magnetic field, near each of these two bars.
Ans.
21. Find the ratio between the wavelengths of the ‘most energetic’ spectral lines in the Balmer and Paschen series of the hydrogen spectrum.
Ans. Balmer, ni = α and nf = 2
Paschen, ni = α and nf = 3
1/ λ = R (1/nf 2 – 1/ni 2)
ΛB / λP = 4/9
OR
The Bohr radius of Hydrogen atom is 5.3 x 10-11 m. Find its radius in the first excited state. Also calculate the total energy in this state.
Ans. For first excited state, n = 2
r2 = n2 a0 = 22 x 5.3 x 10-11 = 21.2 x 10-11 m
Total energy = – 13.6/ n2 eV = -13.6/ 4 = -3.4Ev
22. Use the mirror equation to show that an object placed between F and 2F of a concave mirror produces a real image beyond 2F.
Ans. From mirror formula,1/v = 1/f – 1/u , Now for a concave mirror, f < 0 and for an object at u < 0, 2f<u 1/u >1/f
1/2f < 1/v < 0
This implies that v < 0 so that image is formed on left.
Also the above inequality implies 2f>v OR I2 f 1<|v| [2f and v are negative] i.e., the real image is formed beyond 2f.
23. Two material bars A and B of equal area of cross-section are connected in series to a dc supply. A is made of usual resistance wire and B of an n-type semiconductor. In which bar is the drift speed of free electrons greater? Why?
Ans. Drift speed in B is higher. Since the two bars are connected in series, the current through both same. I = neAvd , vd α 1/n. Since n is much lower in semiconductors, drift velocity will be more.
OR
Draw the energy band diagram of an n-type semiconductor. How does the energy gap of an intrinsic semiconductor vary with increase in temperature?
Ans.
The energy gap does not change with temperature
24. Determine the angular separation between central maximum and first order maximum of the diffraction pattern due to a single slit of width 0.25mm when light of wavelength 5890 Å is incident on it normally.
Ans. λ = 5890 x 10-10m, a= 0.25 x 10-3m
Angular separation Ɵ= 3λ/ 2a = 3.534 x 10-3 radian
25. 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.
Ans. Energy stored in the capacitor = ½ CV2
When it is connected to another uncharged capacitor, common potential
V’ = V/2
Energy stored in the combined system = ½ (C+ C) x (V/2)2 = 1/4 c v2
Required ratio = 1/2
SECTION C
26. State Ampere’s circuital law. Use this law to obtain the expression for magnetic field at a normal distance ‘r’ from an infinitely long current carrying straight wire. How will the magnetic field intensity at the centre of a current carrying circular coil change, if the current through the coil is doubled and the radius of the coil is halved?
Ans. Statement of Ampere’s law
Expression for magnetic field
Magnetic field at the centre B = μ0 I/2a
If I = 2I and a= a/2, B’ = 4B
27. An inductor L of reactance XL is connected in series with a bulb B and an AC source. How would the brightness of the bulb change when
a) The number of turns in the inductor is reduced
Ans. As n decreases, L= μ 0 n 2 Al decreases, XL = Lω decreases, brightness increases
b) An iron rod is inserted in the inductor and
Ans. When an iron rod is inserted, L increases, XL = Lω increases, brightness decreases
c) A capacitor of reactance Xc = XL is inserted in series in the circuit. Justify your answer in each case.
Ans. When a capacitor is introduced, since XL = Xc, impedance = R, minimum, hence brightness increases.
OR
A capacitor of unknown capacitance, a resistor of 100Ω and an inductor of self-inductance L= 4/π2 henry are connected in series to an ac source of 200V and 50Hz. Calculate the value of the capacitance and impedance of the circuit when the current is in phase with the voltage.
Ans. R = 100Ω, L= 4/π2 H, Vrms = 200V, v = 50Hz
At resonance, Impedance Z = R = 100Ω
Lω = 1/ Cω, C = 1/ ω2 L
ω = 2πv = 2π x 50 = 100π
C= 1/400 farad
28. a) State Faraday’s laws of electromagnetic induction.
b) A metallic rod of 1m length is rotated with a frequency of 50 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius1m, about an axis passing through the centre and perpendicular to the plane of the ring. A constant uniform magnetic field of 1T parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?
Ans. Emf induced = ½ BR2ω
B = 1T, R = L = 1m, ω = 2πv = 2π x 50 = 100π
Emf = ½ x 1x 12 x 2π x 50 = 50π = 157V
29. Draw a graph between the frequency of incident radiation (ϒ) and the maximum kinetic energy of the electrons emitted from the surface of a photo sensitive material. State clearly how this graph can be used to find a) Planck’s constant and b) work function of the material.
Ans.
K max = hv – Ф0
Slope of the graph gives the value of Planck’s constant
Intercept on the negative Y axis gives the value of work function
OR
The work function of Caesium metal is 2.14eV. When light of frequency 6x 1014Hz is incident on the metal surface, photoemission of electrons occurs. What is
a) maximum kinetic energy of the emitted electron
b) stopping potential and
c) maximum speed of the emitted photoelectrons
Ans. Ф0 = 2.14eV, v = 6 x 1014Hz
1.K max = hv – Ф0 = 0.34eV
2.Kmax = eV0
V 0 = 0.34V
3.Kmax = ½ m v2 max
v 2 max = 345.8 x 103 m/s
30. Draw a schematic arrangement of Geiger- Marsden experiment. Calculate the distance of closest approach when a 7.7MeV α-particle approaches a gold nucleus (Z = 79)
K = 7.7MeV = 7.7 x 106 x 1.6 x 10-19
K = Ze x 2e / 4πϵ0 r0
Substituting, r0 = 30fm
SECTION D
31. a) Derive an expression for the electric field ‘E’ due to a dipole of length ‘2a’ at a point, distant ‘r’, from the centre of the dipole, on the axial line.
b) Draw a graph of E varies ‘r’ for r>>a.
Ans.
c) Four equal point charges each 16µC are placed on the four corners of a square of side 0.2m. Calculate the force on any one of the charges
Ans. F = q1 q2 / 4πϵ0r 2
F1 = 57.6N along AD produced
F2 = 28.8N along BD produced
F3 = 57.6N along CD produced
Resultant of F1 and F3 is 81.5N
Total force on q4 = 28.8 + 81.5 =110.3 N along BD produced
OR
a) Using Gauss’ law, deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius ‘R’ at a point
i) outside and
ii) inside the shell.
b) Two charges of magnitude -2Q and +Q are located at point (a,o) and (4a, o) respectively. Find the electric flux due to these charges through a sphere of radius 3a with its centre at the origin.
Ans. ФE = Net charge enclosed / ϵ0 = -2Q/ ϵ0
32. a) Draw a ray diagram to show the image formation by a combination of two thin convex lenses in contact.
b) Obtain the expression for power of the combination in terms of focal length of the lenses.
c) You are given the following three lenses. Which two lenses will you use as an eye piece and as an objective to construct an astronomical telescope? Give reason.
Ans. Ans. m = f0/ fe, P = 1/f
To increase magnification, focal length of objective maximum and focal length of eye piece minimum. To increase the light gathering power, aperture of objective must be maximum. Hence objective is L1 and eyepiece is L3
OR
a) Define a wave front.
b) Use Huygen’s geometrical construction to show the propagation of plane wavefront from a rarer medium to a denser medium.
Hence derive Snell’s law of refraction.
c) What is the effect on the interference fringes in Young’s double slit experiment, if the separation between the two slits is decreased? Justify your answer.
33. Define relaxation time of free electrons drifting in a conductor. How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for electrical resistivity of the material.
What is the effect of temperature on the relaxation time of electrons in a metal?
Ans. Drift velocity vd = eEԎ/m
Derivation of the expression Resistivity = m/ne2 Ԏ
In metals, as temperature increases, relaxation time decreases
OR
a) State the two Kirchhoff’s rules
b) Obtain the balancing condition in a Wheatstone bridge
c) Using Kirchohoff’s rules, calculate the values of I1, I2 and I3
Ans. Applying Kirchhoff’s rules, I1 + I2 = I3
For the loop ABEFA, 2I3 + 5I1 = 12
For the loop BCDEB, -2I3 – 3I2 = -6
Solving the above equations, I1 = 48/31 A, I2 = 18/ 31 A, I3 = 66/31 A
SECTION E
34. Case Study: Read the following paragraph and answer the questions.
Two sources of light which continuously emit light waves of same frequency (or wavelength) with a zero or constant phase difference between them, are called coherent sources. Two independent sources of light cannot act as coherent sources, they have to be derived from the same parent source.In Young’s double slit experiment, two identical narrow slits S1 and S2 are placed symmetrically with respect to narrow slit S illuminated with monochromatic light. The interference pattern is obtained on an observation screen placed at large distance D from S1 and S2.
a) Mention any 2 conditions for sustained interference.
b) In the Young’s double slit experiment using a monochromatic light of wavelength λ, what is the path difference (in terms of an integer n) corresponding to any point having half the peak intensity?
c) Calculate the ratio of the fringe width for bright and dark fringes in YDS experiment.
OR
c) In Young’s double slit experiment, while using a source of light of wavelength 4500 Å, the fringe width obtained is 0.4 cm. If the distance between the slits and the screen is reduced to half, calculate the new fringe width.
35. Case Study: Read the following paragraph and answer the questions.
A p-n junction is a single crystal of Ge or Si doped in such a manner that one half portion of it acts as p-type semiconductor and other half functions as n-type semiconductor. As soon as junction is formed, the holes from the p-region diffuse into the n-region and electrons from -region diffuse into p-region. This results in the development of potential barrier VB across the junction which opposes the further diffusion of electrons and holes through the junction. The small region in the vicinity of the junction which is depleted of free charge carriers and has only immobile ions is called the depletion region.
a) Why is germanium preferred over silicon for making semiconductor devices?
b) Which type of biasing results in a very high resistance of a p n junction diode. Draw a diagram showing this bias.
c) How does the width of the depletion region of a pn junction vary, if the reverse bias applied to it decreases.
OR
(c) Name the 2 important processes involved in the formation of a p n junction.