12th Physics Paper Solutions Set 2 : CBSE All India Previous Year 2014

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.
Q1 :

A conducting loop is held above a current carrying wire PQ as shown in the figure. Depict the direction of the current induced in the loop when the current in the wire PQ is constantly increasing.

The increasing magnetic field in the loop due to wire PQ is out of the plane of the paper (perpendicular to the plane). So, the direction of the induced current in the loop will be such that it produces an inward magnetic field (perpendicular to the plane). Thus, the current induced in the loop is in clockwise direction (using the right-hand thumb rule).

Q2 :

Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current.

One ampere of current can be defined as the amount of current which when flowing (in same direction) through two infinitely long parallel wires separated by one metre produces an attractive force of 2 × 10−7 N/m. The wires must have negligible circular cross-section and they must be placed in vacuum.

Q3 :

Why is the use of A.C. voltage preferred over D.C. voltage ? Give two reasons.

The use of A.C. voltage is preferred over the use of D.C. voltage because of the following reasons:
(i) The loss energy in transmitting the A.C. voltage over long distances with the help of step up transformers is negligible as compared to D.C. voltage.
(ii) A.C. voltage can be stepped up and stepped down as per the requirement using a transformer.

Q4 :

Why do the electrostatic field lines not form closed loops?

Q5 :

A biconvex lens made of a transparent material of refractive index 1.5 is immersed in water of refractive index 1.33. Will the lens behave as a converging or a diverging lens? Give reason.

Q6 :

The graph shows the variation of stopping potential with frequency of incident radiation for two photosensitive metals A and B. Which one of the two has higher value of work-function? Justify your answer.

Q7 :

To which part of electromagnetic spectrum does a wave of frequency 3 × 1013 Hz belong?

Q8 :

Why is it found experimentally difficult to detect neutrinos in nuclear β-decay?

Q9 :

Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2.5 × 10−7 m2 carrying a current of 1.8 A. Assume the density of conduction electrons to be 9 × 1028 m−3.

Q10 :

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.

Q11 :

Using Rutherford's 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.

Q12 :

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 1.3 and 1.5. Trace the path of these rays after entering the prism.

Q13 :

Write the functions of the following in communication systems:

(i) Transmitter
(ii) Modulator

Q14 :

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?

Q15 :

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

Q16 :

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

Q17 :

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.

Q18 :

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.

Q19 :

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?

Q20 :

(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.

Q21 :

(a) Show, with the help of a diagram, how unpolarised sunlight gets polarised due to scattering.

(b) Two polaroids P1 and P2 are placed with their pass axes perpendicular to each other. An unpolarised light of intensity Io is incident on P1. A third polaroid P3 is kept in between P1 and P2 such that its pass axis makes an angle of 45° with that of P1. Determine the intensity of light transmitted through P1, P2 and P3.

Q22 :

Define the term self-inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self-inductance L to build up a current I through it.

Q23 :

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?

Q24 :

A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm at a distance of 50 cm apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.

Q25 :

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.

Q26 :

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?

Q27 :

Write any two distinguishing features between conductors, semiconductors and insulators on the basis of energy band diagrams.

Q28 :

(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.

Q29 :

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 p⃗  in the presence of a uniform electric field E⃗ .
(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 'εr' is introduced in the space inside S1 in place of air ? Deduce the necessary expression.

Q30 :

(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.