# Physics 55/1/1 2018-2019 CBSE (Science) Class 12 Question Paper Solution

Physics [55/1/1]
Date & Time: 5th March 2019, 2:30 pm
Duration: 3h
• All questions are compulsory. There are 27 questions in all.
• This question paper has four sections: Section A, Section B, Section C and Section D.
• Section A contains five questions of one mark each. Section B contains seven questions of two marks each, Section C contains twelve questions of three marks each, and Section D contains three questions of five marks each.
• There is no overall choice. However, internal choices have been provided in two questions of one mark, two questions of two marks, four questions of three marks and three questions of five marks weightage. You have to attempt only one of the choices in such questions.
• You may use the following values of physical constants wherever necessary.
• c = 3 × 109 m/s
• h = 6.63 × 10-34 Js
• e = 1.6 × 10-19 C
• μ= 4π × 10-7 TmA-1
• 1/4πε0 = 9 × 109 Nm2C-2
• me = 9 × 10-31 kg
• mass of neutron = 1.675 × 10-27 kg
• mass of proton = 1.673 × 10-27 kg
• Avagedro's number = 6.023 × 1023 per gram mole
• Boltmann constant = 1.38 × 10-23 JK-1

Section A
[1] 1

Draw the pattern of electric field lines, when a point charge –Q is kept near an uncharged conducting plate.

Concept: Electric Field Lines
Chapter: [0.02] Electric Charges and Fields
[1] 2

How does the mobility of electrons in a conductor change, if the potential difference applied across the conductor is doubled, keeping the length and temperature of the conductor constant?

Concept: Electric Current
Chapter: [0.03] Current Electricity
[1] 3
[1] 3.a

Define the term "Threshold frequency", in the context of photoelectric emission.

Concept: Electron Emission
Chapter: [0.11] Dual Nature of Radiation and Matter
OR
[1] 3.b

Define the term "Intensity" in the photon picture of electromagnetic radiation.

Concept: Electromagnetic Spectrum
Chapter: [0.08] Electromagnetic Waves
[1] 4

What is the speed of light in a denser medium of polarizing angle 30?

Concept: Speed of Light
Chapter: [0.1] Wave Optics
[1] 5
[1] 5.a

In sky wave mode of propagation, why is the frequency range of transmitting signals restricted to less than 30 MHz?

Concept: Propagation of Electromagnetic Waves
Chapter: [0.15] Communication Systems
OR
[1] 5.b

On what factors does the range of coverage in ground wave propagation depend?

Concept: Propagation of Electromagnetic Waves
Chapter: [0.15] Communication Systems
Section B
[2] 6

Two bulbs are rated (P1, V) and (P2, V). If they are connected (i) in series and (ii) in parallel across a supply V, find the power dissipated in the two combinations in terms of P1 and P2.

Concept: Combination of Cells in Series and in Parallel
Chapter: [0.03] Current Electricity
[2] 7
[2] 7.a

Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium of refractive index 1.4, to have a power of -5D?

Concept: Lenses
Chapter: [0.09] Ray Optics and Optical Instruments
OR
[2] 7.b

An equilateral glass prism has a refractive index 1.6 in the air. Calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index 4sqrt(2)"/"5.

Concept: Dispersion by a Prism
Chapter: [0.09] Ray Optics and Optical Instruments
[2] 8

An a-particle and a proton of the same kinetic energy are in turn allowed to pass through a magnetic field vec"B", acting normal to the direction of motion of the particles. Calculate the ratio of radii of the circular paths described by them.

Concept: Introduction of Magnetism
Chapter: [0.04] Magnetism and Matter
[2] 9
[2] 9.a

State Bohr's quantization condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum it belongs.

Concept: De Broglie’S Explanation of Bohr’S Second Postulate of Quantisation
Chapter: [0.13] Atoms
OR
[2] 9.b

Calculate the orbital period of the electron in the first excited state of the hydrogen atom.

Concept: Bohr’s Model for Hydrogen Atom
Chapter: [0.13] Atoms
[2] 10

Why a signal transmitted from a TV tower cannot be received beyond a certain distance? Write the expression for the optimum separation between the receiving and the transmitting antenna.

Concept: Modulation and Its Necessity
Chapter: [0.15] Communication Systems
[2] 11

Why is the wave theory of electromagnetic radiation not able to explain the photoelectric effect? How does a photon picture resolve this problem?

Concept: Photoelectric Effect and Wave Theory of Light
Chapter: [0.11] Dual Nature of Radiation and Matter
[2] 12

Plot a graph showing the variation of de Broglie wavelength (X) associated with a charged a particle of mass m, versus  1/sqrtV where V is the potential difference through which the particle is accelerated. How does this graph give us information regarding the magnitude of the charge of the particle?

Concept: De Broglie’S Explanation of Bohr’S Second Postulate of Quantisation
Chapter: [0.13] Atoms
Section C
[3] 13
[1.5] 13.a

Draw equipotential surfaces corresponding to a uniform electric field in the z-directions.

Concept: Electric Field - Introduction of Electric Field
Chapter: [0.02] Electric Charges and Fields
[1.5] 13.b

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

Concept: Potential Due to an Electric Dipole
Chapter: [0.01] Electrostatic Potential and Capacitance
[3] 14
[1.5] 14.a

Solve the following question.
Using Kirchhoff’s rules, calculate the current through the 40 Ω and 20 Ω  resistors in the following circuit.

Concept: Kirchhoff’s Rules
Chapter: [0.03] Current Electricity
OR
[1.5] 14.b

What is the end error in a meter bridge? How is it overcome? The resistances in the two arms of the metre bridge are R = Ω and S respectively.  When the resistance S is shunted with equal resistance, the new balance length found to be 1.5 l1, where l2 is the initial balancing length. calculate the value of s.

Concept: Cells, Emf, Internal Resistance
Chapter: [0.03] Current Electricity
[3] 15
[1.5] 15.a

Identify the part of the electromagnetic spectrum used in (i) radar and (ii) eye surgery. Write their frequency range.

Concept: Electromagnetic Spectrum
Chapter: [0.08] Electromagnetic Waves
[1.5] 15.b

Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field.

Concept: Electric Field - Introduction of Electric Field
Chapter: [0.02] Electric Charges and Fields
[3] 16
[1.5] 16.a

Define the term wavefront. Using Huygen’s wave theory, verify the law of reflection.

Concept: Huygens' Principle
Chapter: [0.1] Wave Optics
[1.5] 16.b

Define the term, “refractive index” of a medium. Verify Snell’s law of refraction when a plane wavefront is propagating from a denser to a rarer medium. Solution

Concept: Snell’s Law
Chapter: [0.09] Ray Optics and Optical Instruments
[3] 17
[1.5] 17.a

Define mutual inductance and write its S.I. units

Concept: Inductance - Mutual Inductance
Chapter: [0.07] Electromagnetic Induction
[1.5] 17.b

A square loop of side 'a' carrying a current I2 is kept at distance x from an infinitely long straight wire carrying a current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Concept: Torque on Current Loop, Magnetic Dipole - Torque on a Rectangular Current Loop in a Uniform Magnetic Field
Chapter: [0.05] Moving Charges and Magnetism
[3] 18
[1.5] 18.a

Derive the expression for the torque acting on a current-carrying loop placed in a magnetic field.

Concept: Torque on a Current Loop in Magnetic Field
Chapter: [0.05] Moving Charges and Magnetism
[1.5] 18.b

Explain the significance of a radial magnetic field when a current-carrying coil is kept in it.

Concept: Moving Coil Galvanometer
Chapter: [0.05] Moving Charges and Magnetism
[3] 19

Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is 3.48 xx 10^6m, and the radius of the lunar orbit is 3.48 xx 10^8m.

Concept: Optical Instruments - Telescope
Chapter: [0.09] Ray Optics and Optical Instruments
[3] 20
[1.5] 20.a

State Gauss’s law for magnetism. Explain its significance.

Concept: Gauss’s Law
Chapter: [0.02] Electric Charges and Fields
[1.5] 20.b

Write the four important properties of the magnetic field lines due to a bar magnet.

Concept: The Bar Magnet
Chapter: [0.04] Magnetism and Matter
OR
[3] 20.c

Write three points of differences between para-, dia- and ferromagnetic materials, giving one example for each.

Concept: Magnetic Properties of Materials
Chapter: [0.04] Magnetism and Matter
[3] 21

Define the term 'decay constant' of a radioactive sample. The rate of disintegration of a given radioactive nucleus is 10000 disintegrations/s and 5,000 disintegrations/s after 20 hr. and 30 hr. respectively from start. Calculate the half-life and the initial number of nuclei at t= 0.

Chapter: [0.12] Nuclei
[3] 22
[1.5] 22.a

Three photodiodes D1, D2, and D3 are made of semiconductors having band gaps of 2.5 eV, 2 eV, and 3 eV respectively. Which of them will not be able to detect light of wavelength 600 nm?

Concept: Classification of Metals, Conductors and Semiconductors
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
[1.5] 22.b

Why photodiodes are required to operate in reverse bias? Explain.

Concept: Semiconductor Diode
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
[3] 23
[1.5] 23.a

Describe briefly the functions of the three segments of the n-p-n transistor.

Concept: Junction Transistor - Transistor: Structure and Action
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
[1.5] 23.b

Draw the circuit arrangement for studying the output characteristics of n-p-n transistor in CE configuration. Explain how the output characteristics are obtained.

Concept: Transistor Action
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
OR
[3] 23.c

Draw the circuit diagram of a full-wave rectifier and explain its working. Also, give the input and output waveforms.

Concept: Diode as a Rectifier
Chapter: [0.14] Semiconductor Electronics - Materials, Devices and Simple Circuits
[3] 24
[1.5] 24.a

If A and B represent the maximum and minimum amplitudes of an amplitude-modulated wave, write the expression for the modulation index in terms of A and B.

Concept: Amplitude Modulation (AM)
Chapter: [0.15] Communication Systems
[1.5] 24.b

Solve the following question.
A message signal of frequency 20 kHz and peak voltage 10 V is used to modulate a carrier of frequency 2 MHz and peak voltage of 15 V. Calculate the modulation index. Why the modulation index is generally kept less than one?

Concept: Amplitude Modulation (AM)
Chapter: [0.15] Communication Systems
Section D
[5] 25
[2] 25.a

In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.

Concept: AC Voltage Applied to a Series LCR Circuit
Chapter: [0.06] Alternating Current
[1.5] 25.b

What is the phase difference between the voltages across the inductor and the capacitor at resonance in the LCR circuit?

Concept: AC Voltage Applied to a Series LCR Circuit
Chapter: [0.06] Alternating Current
[1.5] 25.c

When an inductor is connected to a 200 V dc voltage, a current at 1A flows through it. When the same inductor is connected to a 200 V, 50 Hz ac source, only 0.5 A current flows. Explain, why? Also, calculate the self-inductance of the inductor.

Concept: Inductance - Self Inductance
Chapter: [0.07] Electromagnetic Induction
OR
[2.5] 25.d

Draw the diagram of a device that is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.

Concept: AC Voltage Applied to a Series LCR Circuit
Chapter: [0.06] Alternating Current
[2.5] 25.e

A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two wirelines carrying power is 0.5 Ω per km. The town gets the power from the line through a 4000-220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat.

Concept: Peak and Rms Value of Alternating Current Or Voltage
Chapter: [0.06] Alternating Current
[5] 26
[2.5] 26.a

Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double-slit experiment.

Concept: Interference
Chapter: [0.1] Wave Optics
[2.5] 26.b

In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.

Concept: Refraction of Monochromatic Light
Chapter: [0.1] Wave Optics
OR
[2.5] 26.c

Under what conditions is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.

Concept: Reflection of Light by Spherical Mirrors
Chapter: [0.09] Ray Optics and Optical Instruments
[2.5] 26.d

Three lenses of focal length +10 cm, —10 cm and +30 cm are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.

Concept: Reflection of Light by Spherical Mirrors
Chapter: [0.09] Ray Optics and Optical Instruments
[5] 27
[2.5] 27.a

Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.

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

Solve the following question.
A parallel plate capacitor is charged by a battery to a potential difference V. It is disconnected from the battery and then connected to another uncharged capacitor of the same capacitance. Calculate the ratio of the energy stored in the combination to the initial energy on the single capacitor.

Concept: The Parallel Plate Capacitor
Chapter: [0.01] Electrostatic Potential and Capacitance
OR
[2.5] 27.c

Derive an expression for the electric field at any point on the equatorial line of an electric dipole.

Concept: Electric Dipole
Chapter: [0.02] Electric Charges and Fields
[2.5] 27.d

Two identical point charges, q each, are kept 2m apart in the air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.

Concept: Equipotential Surfaces
Chapter: [0.01] Electrostatic Potential and Capacitance

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