Board Paper of Class 12-Science 2008 Physics (SET 1) - Solutions

What is the direction of the force acting on a charged particle q, moving with a velocity in a uniform magnetic field ?

Name the part of the electromagnetic spectrum of wavelength 10⁻² m and mention its one application.

An electron and alpha particle have the same de−Broglie wavelength associated with them. How are their kinetic energies related to each other?

A glass lens of refractive index 1.5 is placed in a trough of liquid. What must be the refractive index of the liquid in order to make the lens disappear?

A 500 μC charge is at the centre of a square of side 10 cm. Find the work done in moving a charge of 10 μC between two diagonally opposite points on the square.

State the reason, why heavy water is generally used as a moderator in a nuclear reactor.

How does the fringe width of interference fringes change, upon the whole apparatus of Young’s experiment is kept in a liquid of refractive index 1.3?

The plot of the variation of potential difference across a combination of three identical cells in series versus current is as shown below. What is the emf of each cell?

Derive the expression for the electric potential at any point along the axial line of an electric dipole?

Define magnetic susceptibility of a material. Name two elements, one having positive susceptibility and the other having negative susceptibility. What does negative susceptibility signify?

The oscillating magnetic field in a plane electromagnetic wave is given by

(i) Calculate the wavelength of the electromagnetic wave.

(ii) Write down the expression for the oscillating electric field.

Prove that an ideal capacitor, in an a.c. circuit does not dissipate power.

OR

Derive an expression of the impedance of an ac circuit consisting of an inductor and a resistor.

A nucleus undergoes β⁻ decay and becomes . Calculate the maximum kinetic energy of electrons emitted assuming that the daughter nucleus and anti − neutrino carry negligible kinetic energy.

Distinguish between an intrinsic semiconductor and p-type semiconductor. Give reason, why a p-type semiconductor crystal is electrically neutral, although n_h >> n_e?

Draw a ray diagram of a reflecting type telescope. State two advantages of this telescope over a refracting telescope.

A ray of light passing through an equilateral triangular glass prism from air undergoes minimum deviation when angle of incidence is of the angle of prism. Calculate the speed of light in the prism.

The given inputs A, B are fed to a 2-input NAND gate. Draw the output wave form of the gate.

A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is the maximum distance between them, for satisfactory communication in the LOS mode? (Radius of earth = 6400 km)

How is a wavefront defined? Using Huygen’s construction draw a figure showing the propagation of a plane wave refracting at a plane surface separating two media. Hence verify Snell’s law of refraction.

A metallic rod of length l is rotated at a constant angular speed ω, normal to a uniform magnetic field B. Derive an expression for the current induced in the rod, if the resistance of the rod is R.

The figure below shows the V-I characteristic of a semiconductor diode.

(i) Identify the semiconductor diode used.

(ii) Draw the circuit diagram to obtain the given characteristic of this device.

(iii) Briefly explain how this diode can be used as a voltage regulator.

An inductor 200 mH, a capacitor 500 μF and a resistor 10 Ω are connected in series with a 100 V variable frequency a.c. source. Calculate the

(i) frequency at which the power factor of the circuit is unity.

(ii) current amplitude at this frequency.

(iii) Q-factor.

Prove that the current density of a metallic conductor is directly proportional to the drift speed of electrons.

OR

A number of identical cells, n, each of emf E, internal resistance r connected in series are charged by a d.c. source of emf E′, using a resistor R.

(i) Draw the circuit arrangement.

(ii) Deduce the expressions for (a) the changing current and (b) the potential difference across the combination of the cells.

A potentiometer wire of length 1 m is connected to a driver cell of emf 3 V as shown in the figure. When a cell of 1.5 V emf is used in the secondary circuit, the balance point is found to be 60 cm. On replacing this cell and using a cell of unknown emf, the balance point shifts to 80 cm.

(i) Calculate unknown emf of the cell.

(ii) Explain with reason, whether the circuit works, if the driver cell is replaced with a cell of emf 1 V.

(iii) Does the high resistance R, used in the secondary circuit affect the balance point? Justify your answer.

An electromagnetic wave of wavelength λ is incident on a photosensitive surface of negligible work function. If the photo-electrons emitted from this surface have the de-Broglie wavelength λ₁, prove that.

The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength 102.7 nm.

Draw a plot of the variation of amplitude versus ω for an amplitude modulated wave. Define modulation index. State its importance for effective amplitude modulation.

(a) Using Biot-Savart’s law, derive an expression for the magnetic field at the centre of a circular coil of radius R, number of turns N, carrying current i.

(b) Two small identical circular coils marked 1, 2 carry equal currents and are placed with their geometric axes perpendicular to each other as shown in the figure. Derive an expression for the resultant magnetic field at O.

OR

Draw a schematic diagram of a cyclotron. Explain its underlying principle and working, stating clearly the function of the electric and magnetic fields applied on charged particle.

Deduce an expression for the period of revolution and show that it does not depend on the speed of the charged particle.

(a) For a ray of light travelling from a denser medium of refractive index n₁ to a rarer medium of refractive index n₂, prove that where i_c is the critical angle of incidence for the media.

(b) Explain with the help of a diagram, how the above principle is used for transmission of video signals using optical fibres.

OR

(a) What is plane polarized light? Two Polaroid are placed at 90° to each other and the transmitted intensity is zero. What happens when one more Polaroid is placed between these two, bisecting the angle between them? How will the intensity of transmitted light vary on further rotating the third Polaroid?

(b) If a light beam shows no intensity variation when transmitted through a Polaroid which is rotated, does it mean that the light is un-polarized? Explain briefly.

(a) Using Gauss’ law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density σ C/m². Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative.

(b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 μC/m². Calculate the

(i) Charge on the sphere

(ii) Total electric flux passing through the sphere

OR

(a) Derive an expression for the torque experienced by an electric dipole kept in a uniform electric field.

(b) Calculate the work done to dissociate the system of three charges placed on the vertices of a triangle as shown.

Here q = 1.6 × 10⁻¹⁰C