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Physics All India Set 1 2013-2014 CBSE (Science) Class 12 Question Paper Solution

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Physics
All India Set 1
2013-2014 March
Marks: 70

[1]1

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

Chapter: [3.02] Moving Charges and Magnetism
Concept: Force Between Two Parallel Currents, the Ampere
[1]2

To which part of the electromagnetic spectrum does a wave of frequency 5 × 1019 Hz belong?

Chapter: [5.01] Electromagnetic Waves
Concept: Electromagnetic Spectrum
[1]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?

Chapter: [1.02] Electric Charges and Fields
Concept: Coulomb’s Law
[1]4

Define the term 'intensity of radiation' in terms of photon picture of light.

Chapter: [7.01] Dual Nature of Radiation and Matter
Concept: Experimental Study of Photoelectric Effect

Write its S.I. unit of (intensity of radiation)

Chapter: [7.01] Dual Nature of Radiation and Matter
Concept: Einstein’s Equation - Particle Nature of Light
[1]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.

Chapter: [3.02] Moving Charges and Magnetism
Concept: Magnetic Force
[1]6

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

Chapter: [8.01] Nuclei
Concept: Radioactivity - Law of Radioactive Decay
[1]7

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

Chapter: [4.01] Alternating Current
Concept: Alternating Currents and Direct Currents
[1]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.

Chapter: [6.01] Ray Optics and Optical Instruments
Concept: Lenses
[2]9 | Attempt Any One
[2]9.1

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?

Chapter: [8.02] Atoms
Concept: Alpha-particle Scattering and Rutherford’S Nuclear Model of Atom
[2]9.2

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.

Chapter: [8.02] Atoms
Concept: Bohr'S Model for Hydrogen Atom
[2]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.

Chapter: [1.01] Electrostatic Potential and Capacitance
Concept: Capacitors and Capacitance
[2]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.

Chapter: [1.01] Electrostatic Potential and Capacitance
Concept: The Parallel Plate Capacitor
[2]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.

Chapter: [2.01] Current Electricity
Concept: Cells, Emf, Internal Resistance
[2]13

Draw the circuit diagram of a half wave rectifier and explain its working.

Chapter: [9.01] Semiconductor Electronics - Materials, Devices and Simple Circuits
Concept: Application of Junction Diode as a Rectifier
[2]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

Chapter: [2.01] Current Electricity
Concept: Drift of Electrons and the Origin of Resistivity
[2]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.

Chapter: [6.02] Wave Optics
Concept: Refraction of Monochromatic Light
[2]16

Write the functions of the following in communication systems:

Transducer

Chapter: [10.01] Communication Systems
Concept: Basic Terminology Used in Electronic Communication Systems

What is the function of a 'Repeater' used in communication system?

Chapter: [10.01] Communication Systems
Concept: Basic Terminology Used in Electronic Communication Systems
[2]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?

Chapter: [3.01] Magnetism and Matter
Concept: Magnetic Properties of Materials
[2]18

Draw a circuit diagram of a transistor amplifier in CE configuration.

Chapter: [9.01] Semiconductor Electronics - Materials, Devices and Simple Circuits
Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)

Under what condition does the transistor act as an amplifier?

Chapter: [9.01] Semiconductor Electronics - Materials, Devices and Simple Circuits
Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)
[3]19

Using the phenomenon of polarisation, show how the transverse nature of light can be demonstrated.

Chapter: [6.02] Wave Optics
Concept: Polarisation

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

Chapter: [6.02] Wave Optics
Concept: Polarisation
[3]20

Define mutual inductance and write its S.I. units

Chapter: [4.02] Electromagnetic Induction
Concept: Inductance - Mutual Inductance

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.

Chapter: [3.02] Moving Charges and Magnetism
Concept: Solenoid and the Toroid - the Solenoid
[3]21 | Attempt Any One
[3]21.1 | Answer the following:

Why are the connections between the resistors in a meter bridge made of thick copper strips?

Chapter: [2.01] Current Electricity
Concept: Metre Bridge

Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire?

Chapter: [2.01] Current Electricity
Concept: Metre Bridge

Which material is used for the meter bridge wire and why?

Chapter: [2.01] Current Electricity
Concept: Metre Bridge
[3]21.2

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.

Chapter: [2.01] Current Electricity
Concept: Metre Bridge
[3]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

Chapter: [6.01] Ray Optics and Optical Instruments
Concept: Lenses
[3]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?

Chapter: [4.01] Alternating Current
Concept: Ac Voltage Applied to a Series Lcr Circuit
[3]24

Draw the necessary energy band diagrams to distinguish between conductors, semiconductors and insulators.
How does the change in temperature affect the behaviour of these materials ? Explain briefly.

Chapter: [9.01] Semiconductor Electronics - Materials, Devices and Simple Circuits
Concept: Energy Bands in Conductors, Semiconductors and Insulators
[3]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?

Chapter: [8.01] Nuclei
Concept: Radioactivity - Introduction of Radioactivity
[3]26

Write two basic modes of communication

Chapter: [10.01] Communication Systems
Concept: Elements of a Communication System

Explain the process of amplitude modulation.

Chapter: [10.01] Communication Systems
Concept: Amplitude Modulation

Draw a schematic sketch showing how amplitude modulated signal is obtained by superposing a modulating signal over a sinusoidal carrier wave.

Chapter: [10.01] Communication Systems
Concept: Amplitude Modulation
[3]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?

Chapter: [7.01] Dual Nature of Radiation and Matter
Concept: Davisson-Germer Experiment
[5]28 | Attempt Any One
[5]28.1

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.

Chapter: [1.01] Electrostatic Potential and Capacitance
Concept: Electric Potential Difference
[5]28.2

Deduce the expression for the torque acting on a dipole of dipole moment `vecp` in the presence of a uniform electric field `vecE`

Chapter: [3.01] Magnetism and Matter
Concept: Dipole in a Uniform External Field

Deduce the expression for the torque acting on a dipole of dipole moment `vecp` in the presence of a uniform electric field `vecE`

Chapter: [1.02] Electric Charges and Fields
Concept: Dipole in a Uniform External Field

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

Chapter: [1.02] Electric Charges and Fields
Concept: Electric Flux
[5]29 | Attempt Any One
[5]29.1

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.

Chapter: [6.02] Wave Optics
Concept: Interference of Light Waves and Young’S Experiment

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.

Chapter: [6.02] Wave Optics
Concept: Interference of Light Waves and Young’S Experiment
[5]29.2

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.

Chapter: [6.02] Wave Optics
Concept: Fraunhofer Diffraction Due to a Single Slit

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.

Chapter: [6.02] Wave Optics
Concept: Fraunhofer Diffraction Due to a Single Slit
[5]30 | Attempt Any One
[5]30.1
[3]30.1.1

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.

Chapter: [3.02] Moving Charges and Magnetism
Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
[2]30.1.2

State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies

Chapter: [3.02] Moving Charges and Magnetism
Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
[5]30.2
[3]30.2.1

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

Chapter: [3.02] Moving Charges and Magnetism
Concept: Moving Coil Galvanometer
[2]30.2.2 | Answer the following:
[1]30.2.2.1

Why is it necessary to introduce a cylindrical soft iron core inside the coil of a galvanometer?

Chapter: [3.02] Moving Charges and Magnetism
Concept: Moving Coil Galvanometer
[1]30.2.2.2

Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity. Explain, giving reason.

Chapter: [3.02] Moving Charges and Magnetism
Concept: Moving Coil Galvanometer

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