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# Board Paper of Class 12-Science 2014 Physics (SET 1) - Solutions

General Instructions:
(i) All questions are compulsory.
(ii) There are 30 questions in total. Question Nos. 1 to 8 are very short answer type questions and carry one mark each.
(iii) Questions Nos. 9 to 18 carry two marks each. Questions Nos. 19 to 27 carry three marks each and questions Nos. 28 to 30 carry 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 three questions of five marks each. You have to attempt only one of the choices in such questions.
(v) Use of calculators is not permitted. However, you may use log tables if necessary.

• Question 1
Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current. VIEW SOLUTION

• Question 2
To which part of the electromagnetic spectrum does a wave of frequency 5 × 1019 Hz belong? VIEW SOLUTION

• Question 3
Two equal balls with 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? VIEW SOLUTION

• Question 4
Define intensity of radiation on the basis of photon picture of light. Write its S.I. unit. VIEW SOLUTION

• Question 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. VIEW SOLUTION

• Question 6
Why is it found experimentally difficult to detect neutrinos in nuclear β-decay? VIEW SOLUTION

• Question 7
Why is the use of A.C. voltage preferred over D.C. voltage ? Give two reasons. VIEW SOLUTION

• Question 8
A biconvex lens made of a transparent material of refractive index 1.25 is immersed in water of refractive index 1.33. Will the lens behave as a converging or a diverging lens? Give reason. VIEW SOLUTION

• Question 9
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?

OR

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. VIEW SOLUTION

• Question 10
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. VIEW SOLUTION

• Question 11
Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current. VIEW SOLUTION

• Question 12
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. VIEW SOLUTION

• Question 13
Explain, with the help of a circuit diagram, the working of a p-n junction diode as a half-wave rectifier. VIEW SOLUTION

• Question 14
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. VIEW SOLUTION

• Question 15
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 the prism. VIEW SOLUTION

• Question 16
Write the functions of the following in communication systems:

(i) Transducer
(ii) Repeater VIEW SOLUTION

• Question 17
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? VIEW SOLUTION

• Question 18
Draw a circuit diagram of n-p-n transistor amplifier in CE configuration. Under what condition does the transistor act as an amplifier? VIEW SOLUTION

• Question 19
(a) Using the phenomenon of polarisation, show how the transverse nature of light can be demonstrated.

(b) Two polaroids P1 and P2 are placed with their pass axes perpendicular to each other. An unpolarised light of intensity I0 is incident 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. VIEW SOLUTION

• Question 20
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. VIEW SOLUTION

• Question 21
(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?

OR

A resistance of R Ω draws current from a potentiometer, as shown in the figure. The potentiometer has a total resistance Ro Ω. 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. VIEW SOLUTION

• Question 22
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 apart. 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. VIEW SOLUTION

• Question 23
A voltage V = V0 sin ωt is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle.
Under what condition (i) no power is dissipated even though the current flows through the circuit, (ii) maximum power is dissipated in the circuit? VIEW SOLUTION

• Question 24
Write any two distinguishing features between conductors, semiconductors and insulators on the basis of energy band diagrams. VIEW SOLUTION

• Question 25
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? VIEW SOLUTION

• Question 26
Write two basic modes of communication. Explain the process of amplitude modulation. Draw a schematic sketch showing how amplitude modulated signal is obtained by superposing a modulating signal over a sinusoidal carrier wave. VIEW SOLUTION

• Question 27
An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie wavelength associated with the electrons. Taking other factors, such as numerical aperture etc. to be same, how does the resolving power of an electron microscope compare with that of an optical microscope which used yellow light? VIEW SOLUTION

• Question 28
Draw a labelled diagram of Van de Graaff generator. State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

OR

(a) Deduce the expression for the torque acting on a dipole of dipole moment $\stackrel{\to }{\mathrm{p}}$ in the presence of a uniform electric field $\stackrel{\to }{\mathrm{E}}$.
(b) Consider two hollow concentric spheres, S1 and S2, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere S1 change if a medium of dielectric constant '${\mathrm{\epsilon }}_{\mathrm{r}}$' is introduced in the space inside S1 in place of air ? Deduce the necessary expression. VIEW SOLUTION

• Question 29
(a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.
(b) The ratio of the intensities at minima to the maxima in the Young's double slit experiment is 9 : 25. Find the ratio of the widths of the two slits.

OR

(a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of secondary maxima and secondary minima.
(b) Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 × 10−6 m. The distance between the slit and the screen is 1·5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases. VIEW SOLUTION

• Question 30
(a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.

(b) Draw a schematic sketch of a cyclotron. Explain, giving the essential details of its construction, how it is used to accelerate the charged particles.

OR

(a) Draw a labelled diagram of a moving coil galvanometer. Describe briefly its principle and working.

(i) Why is it necessary to introduce a cylindrical soft iron core inside the coil of a galvanometer?
(ii) Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity. Explain, giving reason. VIEW SOLUTION
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