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

Physics [All India Set 1]
Date: March 2014

 1

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

Concept: Force Between Two Parallel Currents, the Ampere
Chapter: [0.05] Moving Charges and Magnetism
 2

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

Concept: Electromagnetic Spectrum
Chapter: [0.08] Electromagnetic Waves
 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?

Concept: Coulomb’s Law - Force Between Two Point Charges
Chapter: [0.02] Electric Charges and Fields
 4

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

Concept: Experimental Study of Photoelectric Effect
Chapter: [0.11] Dual Nature of Radiation and Matter

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

Concept: Einstein’s Equation - Particle Nature of Light
Chapter: [0.11] Dual Nature of Radiation and Matter
 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. Concept: Magnetic Force
Chapter: [0.05] Moving Charges and Magnetism
 6

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

Chapter: [0.12] Nuclei
 7

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

Concept: Alternating Currents and Direct Currents
Chapter: [0.06] Alternating Current
 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.

Concept: Lenses
Chapter: [0.09] Ray Optics and Optical Instruments
 9 | Attempt Any One
 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?

Concept: Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom
Chapter: [0.13] Atoms
 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.

Concept: Bohr’s Model for Hydrogen Atom
Chapter: [0.13] Atoms
 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.

Concept: Capacitors and Capacitance
Chapter: [0.01] Electrostatic Potential and Capacitance
 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.

Concept: The Parallel Plate Capacitor
Chapter: [0.01] Electrostatic Potential and Capacitance
 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.

Concept: Cells, Emf, Internal Resistance
Chapter: [0.03] Current Electricity
 13

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

Concept: Application of Junction Diode as a Rectifier
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
 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

Concept: Drift of Electrons and the Origin of Resistivity
Chapter: [0.03] Current Electricity
 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. Concept: Refraction of Monochromatic Light
Chapter: [0.1] Wave Optics
 16

Write the functions of the following in communication systems:

Transducer

Concept: Basic Terminology Used in Electronic Communication Systems
Chapter: [0.15] Communication Systems

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

Concept: Basic Terminology Used in Electronic Communication Systems
Chapter: [0.15] Communication Systems
 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?

Concept: Magnetic Properties of Materials
Chapter: [0.04] Magnetism and Matter
 18

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

Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits

Under what condition does the transistor act as an amplifier?

Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
 19

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

Concept: Polarisation
Chapter: [0.1] Wave Optics

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

Concept: Polarisation
Chapter: [0.1] Wave Optics
 20

Define mutual inductance.

Concept: Inductance - Mutual Inductance
Chapter: [0.07] Electromagnetic Induction

Write the S.I. unit of mutual inductance.

Concept: Inductance - Mutual Inductance
Chapter: [0.07] Electromagnetic Induction

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.

Concept: Solenoid and the Toroid - the Solenoid
Chapter: [0.05] Moving Charges and Magnetism
 21 | Attempt Any One
 21.1 | Answer the following:

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

Concept: Metre Bridge
Chapter: [0.03] Current Electricity

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

Concept: Metre Bridge
Chapter: [0.03] Current Electricity

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

Concept: Metre Bridge
Chapter: [0.03] Current Electricity
 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. Concept: Metre Bridge
Chapter: [0.03] Current Electricity
 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

Concept: Lenses
Chapter: [0.09] Ray Optics and Optical Instruments
 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?

Concept: Different Types of AC Circuits: AC Voltage Applied to a Series LCR Circuit
Chapter: [0.06] Alternating Current
 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.

Concept: Energy Bands in Conductors, Semiconductors and Insulators
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
 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: [0.12] Nuclei
 26

Write two basic modes of communication

Concept: Elements of a Communication System
Chapter: [0.15] Communication Systems

Explain the process of amplitude modulation.

Concept: Amplitude Modulation (AM)
Chapter: [0.15] Communication Systems

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

Concept: Amplitude Modulation (AM)
Chapter: [0.15] Communication Systems
 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?

Concept: Davisson and Germer Experiment
Chapter: [0.11] Dual Nature of Radiation and Matter
 28 | Attempt Any One
 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.

Concept: Electric Potential Difference
Chapter: [0.01] Electrostatic Potential and Capacitance
 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

Concept: Dipole in a Uniform External Field
Chapter: [0.02] Electric Charges and Fields [0.04] Magnetism and Matter

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 Concept: Electric Flux
Chapter: [0.02] Electric Charges and Fields
 29 | Attempt Any One
 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.

Concept: Interference of Light Waves and Young’s Experiment
Chapter: [0.1] Wave Optics

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.

Concept: Interference of Light Waves and Young’s Experiment
Chapter: [0.1] Wave Optics
 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.

Concept: Fraunhofer Diffraction Due to a Single Slit
Chapter: [0.1] Wave Optics

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.

Concept: Fraunhofer Diffraction Due to a Single Slit
Chapter: [0.1] Wave Optics
 30 | Attempt Any One
 30.1
 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.

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
Chapter: [0.05] Moving Charges and Magnetism
 30.1.2

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

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
Chapter: [0.05] Moving Charges and Magnetism
 30.2
 30.2.1

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

Concept: Moving Coil Galvanometer
Chapter: [0.05] Moving Charges and Magnetism
 30.2.2 | Answer the following:
 30.2.2.1

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

Concept: Moving Coil Galvanometer
Chapter: [0.05] Moving Charges and Magnetism
 30.2.2.2

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

Concept: Moving Coil Galvanometer
Chapter: [0.05] Moving Charges and Magnetism

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