Board Paper of Class 12-Science 2014 Physics (SET 2) - Solutions

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. VIEW SOLUTION

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

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?
Using Bohr's postulates of the atomic model, derive the expression for radius of n^th electron orbit. Hence obtain the expression for Bohr's radius. VIEW SOLUTION

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.
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Write the functions of the following in communication systems:

(i) Transmitter
(ii) Modulator VIEW SOLUTION

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

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

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

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

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

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

Answer the following:
(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?
 
A resistance of R Ω draws current from a potentiometer, as shown in the figure. The potentiometer has a total resistance R_o 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.
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(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 I_o 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. VIEW SOLUTION

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. VIEW SOLUTION

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

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. VIEW SOLUTION

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

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

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

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

(b) Answer the following:
(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

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.
(a) Deduce the expression for the torque acting on a dipole of dipole moment $\overrightarrow{\mathrm{p}}$ in the presence of a uniform electric field $\overrightarrow{\mathrm{E}}$.
(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.
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(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.
(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