Board Paper of Class 12-Science 2019 Physics Abroad(Set 3) - Solutions

General Instructions:

1. All questions are compulsory. There are 27 questions in all.

2. This question paper has four sections: Section A, Section B, Section C and Section D.

3. Section A contains five questions of one mark each, Section B contains seven questions of two marks each, Section C contains twelve questions of three marks each, and Section D contains three questions of five marks each.

4. There is no overall choice. However, internal choices have been provided in two questions of one mark, two questions of two marks, four questions of three marks and three questions of five marks weightage. You have to attempt only one of the choices in such questions.

5. You may use the following values of physical constants wherever necessary.

c = 3 × 10⁸ m/s

h = 6.63 × 10^–34 Js

e = 1.6 × 10^–19 C

μ_o = 4π × 10^–7 T m A^–1

ε₀ = 8.854 × 10^–12 C² N^–1 m^–2

$fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction$ = 9 × 10⁹ N m² C^–2

m_e = 9.1 × 10^–31 kg

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

Question 1
Plot a graph of stopping potential (V₀) versus the frequency (v) of incident radiation in photoelectric emission. VIEW SOLUTION

Question 2
Name the charge carries for the flow of current in a (i) conductor and (ii) electrolyte. VIEW SOLUTION

Question 3
Why are the antennas in space wave mode of propagation generally mounted at heights of many wavelengths above the ground ? VIEW SOLUTION

Question 4
Two identical conducting balls A and B have charges −Q and +3Q respectively. They are brought in contact with each other and then separated by a distance d apart. Find the nature of the Coulomb force between them.

OR

A metallic spherical shell has an inner radius R₁ and outer radius R₂. A charge Q is placed at the center of the shell. What will be the surface charge density on the (i) inner surface, and (ii) outer surface of the shell?
VIEW SOLUTION

Question 5
The small ozone layer on top of the stratosphere is crucial for human survival. Why ?

OR

Illustrate by giving suitable examples, how you can show that electromagnetic waves carry energy and momentum.
VIEW SOLUTION

Question 6
Two long straight wires carrying currents of 2 A and 5 A in the same direction are kept parallel, 10 cm apart from each other. Calculate the force acting between them and write its nature VIEW SOLUTION

Question 7
A parallel plate capacitor of plate area A each and separation d, is being charged by an AC source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor. VIEW SOLUTION

Question 8
Apply Gauss's law to show that for charged spherical shell, the electric field outside the shell is, as if the entire charge were concentrated at the centre.

OR

Two large parallel plane sheets have uniform charge densities + σ and − σ. Determine the electric field (i) between the sheets, and (ii) outside the sheets.
VIEW SOLUTION

Question 9
Out of the two optical instruments, a microscope and a telescope, which one plays the role in magnifying the objects and in resolving the two objects kept close to each other? Explain, giving example. VIEW SOLUTION

Question 10
A beam of light converges at a point P. Now a convex lens is placed in the path of the convergent beam at 15 cm from P. At what point does a beam converge if the convex lens has a focal length 10 cm?

OR

An object is kept in from of a concave mirror of focal length 15 cm. The image formed is real and three times the size of the object. Calculate the distance of the object from the mirror.
VIEW SOLUTION

Question 11
For a CE transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2 V. If the current amplification factor of the transistor is 100, calculate the input signal voltage and the base current, given the base resistance as 1 kΩ. VIEW SOLUTION

Question 12

The figure shows a modified Young's double slit experimental set-up. Here SS₂ − SS₁ = λ/4.

(a) Write the condition for constructive interference.
(b) Obtain an expression for the fringe width. VIEW SOLUTION

Question 13
Use Bohr's postulates to derive the expressions for the potential and kinetic energy of the electron moving in the n^th orbit of the hydrogen atom. How is the total energy of the electron expressed in terms of its kinetic and potential energies? VIEW SOLUTION

Question 14
(a) Depict the magnetic field lines due to a circular current carrying loop showing the direction of field lines.
(b) A current I is flowing in a conductor placed along the x-axis as shown in the figure. Find the magnitude and direction of the magnetic field due to a small current element $\vec{d l}$ lying at the origin at points (i) (0,d,0) and (ii) (0,0,d).

VIEW SOLUTION

Question 15
Plot a graph showing the variation of number of undecayed nuclei in a radioisotope as a function of time. Hence define half life of a nucleus and obtain its relation with average life VIEW SOLUTION

Question 16

(a) For the circuit shown in the figure, how would the balancing length be affected, if
(i) R₁ is decreased
(ii) R₂ is increased
the other factors remaining the same in the circuit? Justify your answer in each case.

(b) Why is a potentiometer preferred over a voltmeter ? Give reason

OR

State the underlying principle of the meter bridge. Draw the circuit diagram and explain how the unknown resistance of a conductor can be determined by this method.
VIEW SOLUTION

Question 17
(a) Draw a graph showing the variation of current versus voltage in an electrolyte when an external resistance is also connected.

(b) (i) The graph between resistance (R) and temperature (T) for Hg is shown in figure (a). Explain the behavior of Hg near 4 K.

(ii) In which region of the graph shown in figure (b) is resistance negative and why?

VIEW SOLUTION

Question 18
(a) Briefly explain how a galvanometer is converted into an ammeter.
(b) A galvanometer coil has a resistance of 15 Ω and it shows full scale deflection for a current of 4 mA. Convert it into ammeter of range 0 to 6 A.

OR

(a) Briefly explain how a galvanometer is converted into a voltmeter.
(b) A voltmeter of a certain range is constructed by connecting a resistance of 980 Ω in series with a galvanometer. When the resistance of 470 Ω is connected in series, the range gets halved. Find the resistance of the galvanometer.
VIEW SOLUTION

Question 19

The figure shows a rectangular conducting frame MNOP of resistance R placed partly in a perpendicular magnetic field $\vec{B}$ and moved with velocity $\vec{v}$ as shown in the figure.

Obtain the expressions for the
(a) Force acting on the arm 'ON' and its direction, and
(b) power required to move the frame to get a steady emf induced between the arms MN and PO. VIEW SOLUTION

Question 20
Draw a ray diagram to show the image formation of a distant object by a refracting telescope. Write the expression for its angular magnification in terms of the focal lengths of the lenses used. State the important considerations required to achieve large resolution and their consequent limitations.

OR

(a) Plot a graph for angle of deviation as a function of angle of incidence for a triangular prism.
(b) Derive the relation for the refractive index of the prism in terms of the angle of minimum deviation and angle of prism.
VIEW SOLUTION

Question 21
Draw the energy band diagram of (i) n-type, and (ii) p-type semiconductors at temperature T > 0 K.
In the case of n-type Si-semiconductor, the donor energy level is slightly below the bottom of conduction band whereas in p-type semiconductor, the acceptor energy level is slightly above the top of the valence band. Explain, giving examples, what role do these energy levels play in conduction and valence bands. VIEW SOLUTION

Question 22
(a) State briefly, with what purpose was Davisson and Germer's experiment performed and what inference was drawn from this.
(b) Obtain an expression for the ratio of the accelerating potentials required to accelerate a proton and an α-particle to have the same de-Broglie wavelength associated with them.

OR

(a) An electron and a proton are accelerated through the same potential. Which one of the two has
(i) the greater value of de-Broglie wavelength associated with it, and

(ii) lesser momentum ?
Justify your answer in each case.
(b) How is the momentum of a particle related with its de-Broglie wavelength? Show the variation on a graph. VIEW SOLUTION

Question 23
(a) What is amplitude modulation ? Draw a diagram showing an amplitude modulated wave obtained by modulation of a carrier sinusoidal wave on a modulating signal.
(b) Define the terms (i) modulation index, and (ii) side bands. Mention the significance of side bands. VIEW SOLUTION

Question 24
How is Zener diode fabricated ? Draw its I-V characteristic and use this to explain the working of a Zener diode as a voltage regulator. VIEW SOLUTION

Question 25
(a) What do you understand by 'sharpness of resonance' for a series LCR resonant circuit ? How is it related with the quality factor 'Q' of the circuit ? Using the graphs given in the diagram, explain the factors which affect it. For which graph is the resistance (R) minimum ?

(b) A 2 μF capacitor, 100 Ω resistor, and 8 H inductor are connected in series with an ac source. Find the frequency of the ac source for which the current drawn in the circuit is maximum.
If the peak value of emf of the source is 200 V, calculate the (i) maximum current, and (ii) inductive and the capacitive reactance of the circuit at resonance.

OR

(a) Draw a schematic diagram of an ac generator. Explain its working and obtain the expression for the instantaneous value of the emf in terms of the magnetic field B, the number of turns N of the coil of area A rotating with angular frequency ω. Show how an alternating emf is generated by a loop of wire rotating in a magnetic field.
(b) A circular coil of radius 10 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s⁻¹ in a uniform horizontal magnetic field of 3⋅0 × 10⁻²T.
(i) Calculate the maximum and average emf induced in the coil.
(ii) If the coil forms a closed loop of resistance 10 Ω, calculate the maximum current in the coil and the average power loss due to Joule heating. VIEW SOLUTION

Question 26
(a) Using the ray diagram for a system of two lenses of focal lengths f₁ and f₂ in contact with each other, show that the two lens system can be regarded as equivalent to a single lens of focal length f, where
$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$ .
Also, write the relation for the equivalent power of the lens combination.

(b) Determine the position of the image formed by the lens combination given in the figure.

OR

(a) Explain, using a suitable diagram, how unpolarized light gets linearly polarized by scattering.

(b) Describe briefly the variation of the intensity of transmitted light when a polaroid sheet kept between two crossed polaroids is rotated. Draw the graph depicting the variation of intensity with the angle of rotation. How many maxima and minima would be observed when θ varies from 0 to π?
VIEW SOLUTION

Question 27
(a) When a parallel plate capacitor is connected across a dc battery, explain briefly how the capacitor gets charged.
(b) A parallel plate capacitor of capacitance 'C' is charged to 'V' volt by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant 1 < k < 2 is introduced to fill the space between the plates. How will the following be affected?
(i) The electric field between the plates of the capacitor.

(ii) The energy stored in the capacitor

Justify your answer in each case.

(c) The electric potential as a function of distance 'x' is shown in the figure. Draw a graph of the electric field E as a function of x.

OR

(a) Derive an expression for the potential energy of an electric dipole in a uniform electric field. Explain conditions for stable and unstable equilibrium.
(b) Is the electrostatic potential necessarily zero at a point where the electric field is zero ? Give an example to support your answer.
VIEW SOLUTION