Board Paper of Class 12-Science 2017 Physics (SET 2) - Solutions

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.

Question 1
At a place, the horizontal component of earth's magnetic field is B and angle of dip is 60°. What is the value of horizontal component of the earth's magnetic field at equator? VIEW SOLUTION

Question 2
Name the junction diode whose I-V characteristics are drawn below:

VIEW SOLUTION

Question 3
Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer. VIEW SOLUTION

Question 4
How is the speed of em-waves in vacuum determined by the electric and magnetic field? VIEW SOLUTION

Question 5
A long straight current carrying wire passes normally through the centre of circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify. VIEW SOLUTION

Question 6
Find the wavelength of the electron orbiting in the first excited state in hydrogen atom. VIEW SOLUTION

Question 7
Distinguish between a transducer and a repeater. VIEW SOLUTION

Question 8
How does Ampere-Maxwell law explain the flow of current through a capacitor when it is being charged by a battery? Write the expression for the displacement current in terms of the rate of change of electric flux. VIEW SOLUTION

Question 9
Define the distance of closest approach. An α-particle of kinetic energy 'K' is bombarded on a thin gold foil. The distance of the closest approach is 'r'. What will be the distance of closest approach for an α-particle of double the kinetic energy?

OR

Write two important limitations of Rutherford nuclear model of the atom. VIEW SOLUTION

Question 10
Why should the objective of a telescope have large focal length and large aperture? Justify your answer. VIEW SOLUTION

Question 11
A resistance of R draws current from a potentiometer. The potentiometer wire, AB, has a total resistance of R_o. 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 potentiometer wire.

VIEW SOLUTION

Question 12
In the study of a photoelectric effect the graph between the stopping potential V and frequency v of the incident radiation on two different metals P and Q is shown below :

(i) Which one of the two metals has higher threshold frequency?

(ii) Determine the work function of the metal which has greater value.

(iii) Find the maximum kinetic energy of electron emitted by light of frequency 8 × 10¹⁴ Hz for this metal. VIEW SOLUTION

Question 13
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor? If another capacitor of 6 pF is connected in series with it with the same battery connected across the combination, find the charge stored and the potential difference across each capacitor. VIEW SOLUTION

Question 14
(i) A ray of light incident on face AB of an equilateral glass prism, shows minimum deviation of 30°. Calculate the speed of light through the prism.

(ii) Find the angle of incidence at face AB so that the emergent ray grazes along the face AC. VIEW SOLUTION

Question 15
(i) A radioactive nucleus 'A' undergoes a series of decays as given below:
$A \overset{α}{\to} A_{1} \overset{β}{\to} A_{2} \overset{α}{\to} A_{3} \overset{γ}{\to} A_{4}$
The mass number and atomic number of A₂ are 176 and 71 respectively. Determine the mass and atomic numbers of A₄ and A.

(ii) Write the basic nuclear process underlying β⁺ and β^– decays. VIEW SOLUTION

Question 16
Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial magnetic field and (ii) a cylindrical soft iron core in a galvanometer? Write the expression for current sensitivity of the galvanometer. (3)

Can a galvanometer as such be used for measuring the current? Explain.

OR

(a) Define the term 'self-inductance' and write its S.I. unit.

(b) Obtain the expression for the the mutual inductance of two long co-axial solenoids S₁ and S₂ wound one over the other, each of length L and radii r₁ and r₂ and n₁ and n₂ number of turns per unit length, when a current I is set up in the outer solenoid S₂. VIEW SOLUTION

Question 17
For a CE-transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2 V. Given the current amplification factor of the transistor is 100, find the input signal voltage and base current, if the base resistance is 1 kΩ. VIEW SOLUTION

Question 18
A zener diode is fabricated by heavily doping both p- and n- sides of the junction. Explain, why? Briefly explain the use of zener diode as a de voltage regulator with the help of a circuit diagram. VIEW SOLUTION

Question 19
(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage ?

(ii) Without making any other change, find the value of the additional capacitor C₁, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

VIEW SOLUTION

Question 20
Define the term 'amplitude modulation'. Explain any two factors which justify the need for modulating a low frequency base-band signal. VIEW SOLUTION

Question 21
A electron of mass m_e revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as $\vec{μ} = - \frac{e}{2 m_{e}} \vec{L}, where \vec{L}$ is the orbital angular momentum of the electron. Give the significance of negative sign. VIEW SOLUTION

Question 22
(i) Derive the expression for the electric potential due to an electric dipole at a point on its axial line.

(ii) Depict the equipotential surfaces due to an electric dipole. VIEW SOLUTION

Question 24
(a) Distinguish between unpolarized light and linearly polarized light. How does one get linearly polarised light with the help of a polaroid?

(b) A narrow beam of unpolarised light of intensity I₀ is incident on a polaroid P₁. The light transmitted by it is then incident on a second polariod P₂ with its pass axis making angle of 60° relative to the pass axis of P₁. Find the intensity of the light transmitted by P₂.

OR

(a) Explain two features to distinguish between the interference pattern in Young's double slit experiment with the diffraction pattern obtained due to a single slit.

(b) A monochromatic light of wavelength 500 nm is incident normally on a single slit of width 0.2 mm to produce a diffraction pattern. Find the angular width of the central maximum obtained on the screen.

Estimate the number of fringes obtained in Young's double slit experiment with fringe width 0.5 mm, which can be accommodated within the region of total angular spread of the central maximum due to single slit. VIEW SOLUTION

Question 25

(i) Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm's law.

(ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts.

Which of the following quantities remain constant in the wire?
(a) drift speed
(b) current density
(c) electric current
(d) electric field

OR

(i) State the two Kirchhoff's laws. Explain briefly how these rules are justified.

(ii) The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for (i) the current draw from the cell and (ii) the power consumed in the network.

VIEW SOLUTION

Question 26
(a) Draw a labelled diagram of AC generator. Derive the expression for the instantaneous value of the emf induced in the coil.

(b) A circular coil of cross-sectional area 200 cm² and 20 turns is rotated about the vertical diameter with angular speed of 50 rad s⁻¹ in a uniform magnetic field of magnitude 3.0 × 10⁻²T. Calculate the maximum value of the current in the coil.

OR

(a) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turn and currents in the two coils.

(b) A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 300 turns. Find the number of turns in the secondary to get the power output at 220 V. VIEW SOLUTION

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