Useful for Railways, DRDO, BHEL, DMRC & Other Competitive Examinations.

By Dr. M. P. Sinha Deptt. of Physics

J. R. S. College Jamalpur, Munger–811214 (T. M. Bhagalpur University, Bhagalpur–812007 (Bihar) & Smt. Neetu Sinha Deptt. of Electronics & Communication S. College of Engineering, Barabanki (U. P.)

UPKAR PRAKASHAN, AGRA–2

© Publishers Publishers UPKAR PRAKASHAN (An ISO 9001 : 2000 Company)

2/11A, Swadeshi Bima Nagar, AGRA–282 002 Phone : 4053333, 2530966, 2531101 Fax : (0562) 4053330, 4031570 E-mail : [email protected] Website : www.upkar.in Branch Offices 4845, Ansari Road, Daryaganj, New Delhi–110 002 Phone : 011–23251844/66

● ●

●

1-8-1/B, R.R. Complex (Near Sundaraiah Park, Adjacent to Manasa Enclave Gate), Bagh Lingampally, Hyderabad–500 044 (A.P.), Phone : 040–66753330

The publishers have taken all possible precautions in publishing this book, yet if any mistake has crept in, the publishers shall not be responsible for the same. This book or any part thereof may not be reproduced in any form by Photographic, Mechanical, or any other method, for any use, without written permission from the Publishers. Only the courts at Agra shall have the jurisdiction for any legal dispute.

SBN : 978-93-5013-310-1

Code No. 1718

Printed at : Repro Knowledgecast Limited, Thane

Preface It is a matter of pleasure to present this book of UPKAR’S Objective Electronics & Telecommunication Engineering (Diploma Level) for recruitment test for Railways, DRDO, BHEL, DMRC and other competitive examinations of India. This book has been prepared for the candidates preparing on the basis of the new syllabus prescribed for Diploma Engineering. The aim of writing this book is to provide a self-oriented study style and covering the different aspects of examination in Electronics & Telecommunication Engineering (Diploma Level) for all those candidates who do not have the facilities of extra guidance for preparation. Selected important facts with definitions and formulae with diagram have been given first of all the nine chapters, then objective types questions and their answers. Each chapter has an important review of topics as a help to the memory of the candidates. All the necessary subject matter has been presented in a simple, lucid style and in an elaborate form which will help even a fresher in following the subject with a little effort and a forming clear mental concept. Neat and clean diagrams are used for explanations. It is earnestly hoped that this book will be found useful by the candidates appearing in various competitive examinations. Possible suggestions from the learned teachers for improvement of this book, are thankfully invited. Our thanks are also due to UPKAR PRAKASHAN for encouraging us to write this book and by whose interest and efforts this book could be brought out in time.

—Dr. M.P. Sinha & Smt. Neetu Sinha

CONTENTS 1. Applied Physics………………………………………………………… ● Objective Questions…………………………………………………

3–78 43

2. Basic Electricity …..…………………………………………………… ● Objective Questions…………………………………………………

79–124 103

3. Instrumentation and Measurements …………………………………… 125–164 ● Objective Questions………………………………………………… 144 4. Engineering Materials and Electronic Devices …...…………………… 165–205 ● Objective Questions………………………………………………… 183 5. Electronic Analog Circuits …………………………………………….. 206–248 ● Objective Questions………………………………………………… 234 6. Digital Techniques …………………………………………………….. 249–269 ● Objective Questions………………………………………………… 260 7. Communication and Television Engineering ………………………….. 270–314 ● Objective Questions………………………………………………… 301 8. Control Systems and Industrial Electronics …………………………… 315–335 ● Objective Questions………………………………………………… 323 9. Computer Science and Information Technology ………………………. 336–391 ● Objective Questions………………………………………………… 364

Electronics & Telecommunication

1 Applied Physics Important Definitions, Facts and Formulae 1. Physics Physics is that branch of science which deals with the nature and natural phenomena with interaction of energy or in which we study about matter, energy and their mutual interaction. There is a close relation between theory and experiment in physics. In earlier times, the methods of measurement in physics were of subjective nature. Some outstanding and spectacular work in physics has been done with quite simple and crude apparatus. Since information or conclusion obtained by subjective methods can be inaccurate and sometimes misleading also, the use of objective methods, i.e., scientific apparatus is made for taking observation in present day physics.

1. 2. 3. 4.

Scientific Principles/Laws Bernaulli's theorem. Newton’s second and third law of motion. Conversion of gravitational energy into electrical energy. Law of thermodynamics.

5. Electromagnetic induction. 6. Propagation of electromagnetic waves. 7. Motion of charged particle under electric and magnetic field. 8. Nuclear fission. 9. Amplification by a process called population inversion. 10. Digital logic of electronic circuits.

Technology/ Engineering Aeroplane Rocket propulsion. Hydro electric power. Heat engine and refrigerator. Electric generator. Radio and television. Cyclotron. Nuclear Reactor. Laser Calculators and

2. Physics in Relation to Technology/ computers. Engineering 3. Units for Measurement Technology/Engineering is the application of science in general and physics in particular for practical purposes. For example the discoveries of electro-magnetic induction by Faraday, can be regarded as one of those great scientific discoveries, which have not only benefited a common man but has formed the basis of the technology. The following tables gives a list of a few technologies and the scientific principles related to them—

Measurement of a physical quantity involves its comparison with a chosen standard of the same kind as the physical quantity. The chosen standard of same kind as reference to measure a physical quantity, is called the unit of that quantity. The unit of the physical quantity has to be stated along with the result of measurement. In general, measure of a physical quantity = numerical value of the quantity × size of its unit. Fundamental units—Fundamental units are those units, which can neither be derived from one

4 | Electronics & Telecommunication another, nor can they be further resolved into any other units. The units of physical quantities are expressed in terms of the fundamental units of mass, length and time. Derived units—The units of all physical quantity (mass, length and time) which are expressed in terms of the fundamental units of mass, length and time are called derived units. For examples, the unit of area, volume, speed, acceleration, momentum, force, work etc. are all derived units and they can be obtained by writing their defining equations in terms of fundamental physical quantities.

4. International System (S.I.) of Units The General Conference of Weights and Measurements held in 1960 and then in 1971 introduced a new and logical system of units known as International System of units. It is abbreviated as S.I. from the French name Le Systeme Internationale d units. It is based on the following seven basic and two supplementary units— Basic Physical Quantities 1. Length 2. Mass 3. Time 4. Temperature 5. Electric current 6. Luminous intensity 7. Quantity of matter Supplementary Physical Quantities 1. Plane angle 2. Solid angle

Units metre kilogram second kelvin ampere candela mole Units radian steradian

Symbols m kg s K A Cd mol Symbols rad Sr

Metre—On atomic standards metre is defined as to be equal to 165763·3 wavelengths in vacuum of the radiation emitted due to transition between the level 2p 10 and 5d5 of the isotope. of Krypton having mass number 86. Kr-86 emits light of several different wavelengths, due to transition between the levels 2p10 and 5d5. The light emitted is orange-red in colour and has wavelength 6057·8021 Å or 6·0578021 × 10–7 metre. The number of these wavelengths in one metre can be counted by using an optical interferometer which comes out to be 1·650763·3. 1 light year = 9·5 × 1015 metre 1 AU = 1·496 × 1011 metre 1 Parsec = 3·08 × 1016 metre Kilogram—Kilogram is the mass of a Platinum-iridium cylinder kept in the International

Bureau of Weights and Measures at Serves near Paris, France. 1 a.m.u. = 1·66 × 10–27 kilogram Second—Second is defined as to be equal to the duration of 9192631770 vibrations corresponding to the transition between two hyperfine levels of cesium – 133 atom in the ground state. 1 Kelvin—Kelvin is defined as th frac273·16 tion of the thermodynamic temperature at the triple point of water. Ampere—Ampere is defined as the current generating a force of 2 × 10–7 newton per metre between two straight parallel conductors of infinite length and negligible circular cross-section, when placed one metre apart in vacuum. Candela—Candela is the luminous intensity in a given direction due to a source which emits monochromatic radiation of frequency 540 × 10 12 Hzs. and of which the radiant intensity in that direction is 1/683 watt per steradian. Mole—Mole is the amount of substance containing same number of elementary units as there are atoms in 0·012 kg of carbon-12. Radian—Radian is the plane angle between the two radii of a circle which out off from the circumference, an arc equal to the length of the radius. Plane angle in radian = length of arc/radius. Steradian—Steradian is the solid angle with its apex at the centre of a sphere that cuts out an area on the surface of the sphere equal to the area of the square, whose sides are equal to the radius of the sphere. Solid angle in steradian = area cut out from the surface of sphere/radius2.

5. Dimensions The dimensions of a physical quantity are the powers to which the fundamental units of mass, length and time have to the raised to obtained its units. If units of mass, length and time are denoted by bracketed capital letters [M], [L] and [T], then for area = length × breadth, we have area = [L] × [L] = [L2]. It is represented as [M0L2 T0 ]. Similarly, for velocity = distance/time = [L]/[T] = [LT–1] = M0 LT–1]. In general dimensional equation is written as [X] = [MaLb Tc], where right hand side represents the dimensional formula of physical quantity X, whose dimensions in mass, length and time are a , b and c respectively.

Electronics & Telecommunication | 5

6. Table for the S. I. Units and Dimensional Formulae of Given Physical Quantities S. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.

Physical Quantities Area Volume Density Velocity Acceleration Momentum Force Pressure Work or energy Power Moment of force Gravitational constant Impulse Stress or coefficient of elasticity Surface tension Surface energy Velocity gradient Coefficient of viscosity Moment of inertia Angular velocity Angular acceleration Angular momentum Torque or couple Frequency Specific heat Latent heat Electric field intensity Electric potential or e.m.f. Electric dipole moment Capacity Resistance Universal gas constant/ Boltzmann coinstant Stefan’s constant Magnetisation Resistivity Inductance Magnetic field Magnetic dipole moment Permeability Permittivity Planck’s constant Thermal conductivity

S.I. Units metre2 metre3 kg metre–3 metre second–1 metre second–2 kg. metre second–1 newton newton metre–2 joule watt newton metre newton metre2 kg–2 newton second newton metre–2 newton metre–1 joule metre–2 second–1 deca poise kg. metre2 radian second–1 radian second–2 kg metre2 second–1 newton metre second–1 or hertz joule kg–1 K–1 joule kg–1 volt metre–1 volt coulomb metre farad ohm joule K–1

Dimensional Formulae [M0 L2T0] [M0 L3T0] [ML–3T0] [M0 LT–1] [M0 LT–2] [MLT–1] [MLT–2] [ML–1T–2] [ML2T–2] [ML2T–3] [ML2T–2] [M–1L3T–2] [MLT–1] [ML–1T–2] [ML0T–2] [ML0T–2] [M0 L0T–1] [ML–1T–1] [ML2T0] [M0 L0T–1] [M0 L0T–2] [ML2T–1] [ML2T–2] [M0 L0T–1] [M0 L2T–2K–1] [M0 L2T–2] [I–1MLT–3] [ML2I–1T–3] [M0 ILT] [M–1L–2I2 T–4] [ML2T–3I–2] [ML2T–2K–1]

joule metre–2 sec–1 K–4 [ML0T–3K–4] –1 ampere metre [M0 L–1T0I] ohm metre [I–2ML3T–3] henry [I–2ML2T–2] –2 tesla or weber m [I–2ML–2T0] –2 ampere metre [M0 IL2T0] –1 henry metre [I–2MLT–2] –1 farad metre [I2 M–1L–3T4] joule second [ML2T–1] joule metre–1 second–1 kelvin–1 or [MLT–3K–1] watt metre–1 kelvin–1 Strain, angle or same ratio for quantities Unitless Dimensionless

6 | Electronics & Telecommunication

7. Constant Errors

10. Absolute Errors

When the results of a series of observations are in error by the same amount, the error is said to be a constant errors. For example, in measuring the length of a cylinder by a vernier callipers, whose graduations are faulty, say one centimeter, the measured length is always greater than the true value by a constant amount. It is due to zero error, bench error etc. For its removal some standard is necessary. For example bench error is estimated with the help of standard index rod. If the instrumental error, error due to wrong adjustment or error due to observers prejudice be absent, it can be shown that possible error due to arithmetic mean. It is given by

The magnitude of the difference of true value and the measured value is called absolute error. Thus absolute error = true value – measured value. If we regard arithmetic mean as the true value then absolute error in the ith measurement is given by Δ ai = –a – ai The final absolute error is taken as the arithmetical mean of the absolute errors in various measurements. – |Δa1 | + |Δa2 | + |Δa3 | + … + |Δan| Thus Δa = n – 1 n or Δa = Σ | Δai | n i=1

E = ± 0·6745

S , n(n – 1)

11. Deviation, Standard Deviation and Root Mean Square Errors

Deviation—The difference of each reading from the arithmetic mean of all the observations where n = number of observations, S = δ1 + δ2 + for the measurement of a physical quantity, is 2 … δn and δ1 , δ2 , … δn are the differences of each called deviation. observation respectively from the arithmetic Standard deviation—It is the square root of mean. the mean of the squares of the individual deviations from the mean of the deviations. The 8. Systematic Errors standard deviation of the observations is deterA systematic error is one that always mined by the following equation— produces an error of the same sign. These are due S, to known causes and eliminated by detecting the σ = ± n source of the error and the rule governing this S = δ1 2 + δ2 2 + … δn 2 error. It may be subdivided into the following four where n = number of observations and δ1 , δ2 etc. are main types—(a) Instrument’s errors, (b) Observational or personal errors, (c) Errors due to respectively the difference of each deviation from external causes and (d) Errors due to imperfection. the arithmetic mean, and σ is root mean square error. 2

2

9. Random Errors

These errors are due to unknown causes and are sometimes termed on chance errors. In an experiment, even the same person repeating an observation may get different readings everytime. If we repeat the observation a number of times, the arithmetical mean of all the readings is found to the most accurate or very close to the most accurate reading for that observation. Let a1, a2 , a3 , … an be the n-different readings in an experiment, then their arithmetical mean is given by –a = a1 + a2 + a3 + … + an n n –a = 1 Σ a or n i=1 i

12. Scalar o r Dot Product of Two Vectors

→ The scalar or dot product of two vectors A → and B is defined as the product of the magnitudes → → of vectors A and B and the cosine of the smaller angle between them. →→ Mathematically, A · B = AB cos θ, where A → → and B are the modules of the vectors A and B respectively and θ is the angle between them.

13. Vector or Cross Product of two Vectors The vector or cross product of two vectors → → A × B is defined as the product of the magnitude

Electronics & Telecommunication | 7 → → of vectors A and B and sine of the smaller angle → → between them. The direction of vector A × B is → → at right angles to both A and B and points in the direction given by right handed screw rule or the right hand thumb rule. → → Mathematically, A × B = ^nAB sin θ, where → → A and B are the magnitude of vectors A and B , θ is the angle between them and ^n is its unit vector. The vector product of two vectors is also a vector.

insect crawling over the floor of a room; earth revolving round the sun etc. Three dimensional motion—The motion of an object is called three dimensional, if all the three co-ordinates specifying the position of the object change with respect to time. Such a motion is not restricted to a straight line or a plane but takes place in space. Examples—a flying kite or a bird, an aeroplane, random motion of gas molecules etc.

The position of an object in space in specified with the help of a co-ordinate frame as shown in the figure. Point P represents the initial position of an object, while Q represents its final position. Each of the two position of the object is fixed in the space with the help of a set of three distances along x-axis, y-axis and z-axis; called co-ordinates of the point. The change in the position of the object with the passage of time means the change in the values of x, y and z with the passage of time.

velocities of moving bodies along a straight line in the same direction. (b) v AB = v A + v B , where v AB is the relative velocity of A with respect to B, velocity vB has direction opposite to that of vA. (c) v = u + at is velocity time relation, which gives the velocity of an object at any time t, when moving with initial velocity u and uniform acceleration a. 1 (d) S = ut + a t2 is position time relation, 2 where S is the distance covered by an object in time t, in case of uniform acceleration a and initial velocity u. (e) v 2 – u2 = 2a s is velocity displacement relation. 1 (f) S n th = u + a (2n – 1), where Sn th is the 2 displacement of the particle in the nth second, u is initial velocity, a is uniform acceleration and n is the time. (g) For a freely falling body, following are the equation of motion— (i) v = u + gt 1 (ii) h = ut + gt2 2 2 2 (iii) v – u = 2gh or v2 = u2 + 2gh and 1 (iv) Snth = u + g(2n – 1), 2 where g is acceleration due to gravity = 9·8 m/sec2 and h is the height = distance covered vertically. (h) h = u2 /2g, where h is the maximum height reached. (i) u/g = time of ascent = time of descent.

15. Important Formulae 14. One Dimensional, Two Dimensional (a) vAB = v A – vB, where vAB is the relative and Three Dimensional Motions velocity of A with respect to B, vA and vB are the

Q (x2, y2, z2)

Z P(x1, y1, z1)

z1 x2

x1

z2 Y

O y1

X

y2

One dimensional motion—The motion of an object is called one dimensional, if only one of the three co-ordinates, specifying the position of the object; changes with respect to time. In such motion, the object moves along the straight line. Example—motion of a train along a straight railway track or a man walking on a level and narrow road, an object falling freely under gravity etc. Two dimensional motion—The motion of an object is called two dimensional, if two of the three co-ordinates specifying the position of the object change with respect to time. In such a motion, the object moves in a plane. Examples—a billiard ball moving over the billiard table, an

8 | Electronics & Telecommunication (j) Total time of flight = 2u/g. (k) For vertically upward motion g = –g and following are the equations of motion— (i) v = u – gt 1 (ii) h = ut – gt2 2 (iii) v2 = u2 – 2gh and 1 (iv) S n th = u – g (2n – 1) 2 (l) ω = θ /t or θ = ω t, where ω is angular velocity, θ is angular displacement and t is time. (m) v = ω, r, where v is linear velocity, ω is angular velocity and r is radius of the circular path.

16. Uniform Circular Motion When a body moves on a circular path with uniform velocity, its motion is said to be uniform circular motion. In this motion the magnitude of the velocity is constant but the direction of motion changes constantly. Hence its velocity is periodic.

17. Centripetal Force Centripetal force is that type of force which acts upon a body moving in circular path, which is always directed towards the centre. Without centripetal force, the motion on a circular path is not possible. Let m be the mass of the body moving on a circular path, then the magnitude of centripetal force is given by F=

mv2 , r

where v 2 /r is centripetal acceleration. The nature of the centripetal force may be different for different system. Examples–elastic force supplied to the stone through the string, moon encircling the earth by the gravitational pull of the earth, electron moving round the nucleus in a circular path, movement of a car along a curved path, banking of the rails, to rotate a bucket full of water etc.

18. Centrifugal Force Centrifugal force is that type of pseudo force and non-reactive force which acts upon a body moving in a circular path and is always directed outwards the centre. It acts on the body negotiating a curved path and according to Newton third law of motion, a reaction to this action, equal but opposite in direction acts upon the body. The

existence of centrifugal force is possible only in rotatory frame of reference. Example—Centrifugal drier, cream separator, speed governor, centrifugal pump, centrifugal blower etc.

19. Motion of a Cyclist Along a Curved Path A cyclist while moving round a curve has to lean inwards along with the cycle, i.e., towards the centre of curvature of the curved path in order to maintain his balance. Inclination angle to the vertical inward is given by θ = tan–1 (v 2 /rg), the value of θ increases with increase in v and decreases with the value of r. Maximum speed of a cyclist, so that it should not skid over a curved surface is given by v=⎯ √⎯⎯ μrg. If v > √ ⎯⎯μrg or tan θ >μ, then the cycle will skid.

20. Projectile Motion (a) The Equation of Trajectory of the Projectile 1 g x2. As 2 u2 cos2 θ u and g are constant, this equation has the form, y = bx + cx2 , the equation of parabola. Hence the trajectory of the projectile is parabola. It is given by y = x tan θ –

(b) Maximum Height of Projectile It is given by H = u2 sin2 θ/2g

21. Angle of Friction and Angle of Repose Angle of Friction is the angle which is the resultant of limiting friction and normal reaction makes with the normal reaction. Angle of friction is given by θ = tan–1 μ, where μ is coefficient of friction. Angle of Repose—Is the angle of inclination of the inclined plane to the horizontal at which a body on the surface of this plane just begins to slide down. Angle of repose is numerically equal to the angle of friction.

22. Lubricants Lubricants is viscous liquid introduced between the surfaces of two solids. It reduces the friction because the force of friction is due to inter locking of projections of one surface into the

Electronics & Telecommunication | 9 depressions of the other due to inter molecular forces and these forces are much weaker in liquids than those in solids.

23. Law of Conservation of Linear Momentum It states that “when no net external force acts on a system consisting of several particles, the total linear momentum of the system is conserved, the total linear momentum being the vector sum of the linear momentum of each particle in the system.”

24. Law of Conservation of Energy It states that “Energy can neither be created nor be destroyed but can be transformed from one form to an another form.” “The total energy in any system always remains constant.” The change of one form of energy into another form, is called transformation of energy. Examples—(i) In winding the clock, the energy spent is stored in the spring as potential energy. As clock works the spring is unwound, the potential energy is converted into kinetic energy of hand of clock. (ii) In a thermal power station, the chemical energy of coal is changed into heat energy which is further changed into electrical energy. (iii) In steam engine, the heat energy is converted into mechanical energy. (iv) At a hydroelectric power house, the potential energy of water is transformed into kinetic energy and then into electrical energy.

25. Different Forms of Energy (i) Potential Energy—Potential energy is the energy possessed by a body by virtue of its position. Examples—(a) The water at the top of water fall, (b) Wounded spring of watch, (c) Stretched bow and (d) Stretched rubber in a gulel. (ii) Kinetic Energy—The energy possessed by a body as a result of its motion, is called kinetic energy. Examples—(a) Running tram, (b) Fast moving stone, (c) A raised hammer on striking a nail, drives the nail into wood, and (d) Moving bullet. (iii) Internal Energy—An object possesses internal energy because of its temperature. Any object can be supposed to be made of molecules. The molecules possess potential energy due to

their locations against the intermolecular forces and possess kinetic energy because of motion. The sum of the kinetic energy and potential energy of all the molecules constituting the object, is called its internal energy. It depends upon its temperature. (iv) Heat Energy—An object possesses heat energy due to the disorderly motion of its molecules. It is also related to the internal energy of the object. Due to increase in temperature, the molecular motion and intermolecular distance of object increases. The changes result in the increase in kinetic and potential energy of the molecules and hence the internal energy of the molecules. (v) Chemical Energy—An object possesses chemical energy because of chemical binding of its atoms. Such an object may be preferably called as a chemical compound. A chemical compound has lesser energy than possessed by the part of which it is made. This difference in energy is called chemical energy. In chemical reaction, the chemical energy becomes available. (vi) Electrical Energy—Work has to be done in order to move an electric charge from one point to another in electric field or for the transverse motion of a current carrying conductor inside a magnetic field. This work done appears as the electrical energy of the system. (vii) Nuclear Energy—Nuclear energy is that energy when uranium ( 92U235) nucleus break up into lighter nuclei in being bombarded by a slow neutron. This phenomenon is called nuclear fission. It is found that in nuclear fission of 92U235, the mass of product nuclei is less than the mass of 235 nucleus. The nuclear energy becomes avail92U able due to conversion of this decrease in mass into energy in accordance with Einstein mass energy equivalence relation. Nuclear reactors and nuclear bombs are the sources of nuclear energy.

26. Important Formulae (a) Potential energy is given by P. E. = mgh, where m is the mass of body and h is distance moved by the body against gravity. (b) Kinetic energy is given by 1 K. E. = mv2 , where m is the mass of body 2 and v is the uniform velocity of body. (c) Potential energy of system of spring is given by

10 | Electronics & Telecommunication 1 2 kx , where k is spring constant, and 2 x is the distance from equilibrium position of spring. (d) Kinetic energy of S.H.M. is given by 1 K. E. = mω (a2 – y2), where a is amplitude, y is 2 displacement, ω is angular velocity = 2πn and m is the mass of the particles. (e) Potential energy of S.H.M. is given by 1 P. E. = mω2 y2 2 1 ∴ Total energy of S.H.M. = mω2 a2 2 (f) Kinetic energy due to the motion of electron is given by me 4 K. E. = , 8n2 h2 ε02 where m is the mass of electron, v is the velocity of electron. (g) Potential energy of electron lies in the electric field of positive nucleus is given by me 4 P. E. = – 2 2 2 4n h ε0 (h) Kinetic energy of a satellite is given by GMm Ek = . 2r (i) Total energy of a satellite is given by GMm ET = – . Negative value indicates that the 2r satellite is bound. (j) Binding energy is given by GMm B. E. = – E T = . 2r

Lissajous Figures—The resultant of two rectangular simple harmonic motions is represented by some figures, which are called Lissajous figures.

27. Simple Harmonic Motion (S.H.M.)

Keter pendulum is a special type of compound pendulum by which acceleration due to gravity is determined correctly. It is a bar of copper and steel. A heavy weight is fitted in it. Two knife edges are fitted an each side of centre of gravity and may be suspended on a rigid horizontal plate and the bar is thus suspended on the knife edges separately (one after another) and the time period is determined. Acceleration due to gravity ‘g’ determined by Bessel’s modification in Keter’s pendulum is given by 8π2 (l1 + l2) g = , T1 2 + T2 2

WP.E. =

When a particle moves right to left or up and down from a fixed point on a straight line in such a way that at any instant its acceleration is proportional to its displacement from the fixed point at that instant and is always directed towards the fixed point, then the motion of the particle is called simple harmonic motion. Equation of S. H. M. is given by— y = a sin ωt, where y is displacement, a amplitude and ωt 2π is its phase in which t is time and ω = 2πf = . T where f is frequency and T is time period.

28. Simple Pendulum Pendulum

&

Seconds

When a heavy bob suspended by a weightless and inextensible but flexible string from a rigid support so that it may oscillate without any friction, is called a simple pendulum. The pendulum having time period of two second is called seconds pendulum. Time period of simple pendulum is given by l , g where l is the effective length of simple pendulum and g is acceleration due to gravity. T = 2π

29. Compound Pendulum Compound pendulum is that rigid body which oscillates independently about an axis passing through itself. It is practical pendulum. Time period of compound pendulum is given by K2 /l + l , g where K is the radius of gyration, l is the distance between centre of suspension to centre of gravity and g is acceleration due to gravity. K2 + l = L, is called and equal to the l length of an equivalent simple pendulum. T = 2π

(

)

30. Keter Pendulum

Electronics & Telecommunication | 11 where l1 and l 2 are the distances of both knife edges from the centre of gravity respectively, and T1 and T2 are time periods about both knife edges respectively.

31. Newton’s Law of Gravitation Newton gave a universal law for attraction between two objects and it is known as Newton’s Law of Gravitation. Statement—“Every body in this universe attracts every other body with a force which is directly proportional to the product of two masses and inversely proportional to square of distance between their centres.” Force of attraction between two objects is given by mm mm F ∝ 12 2 or F = G 12 2 , r r where G is gravitational constant or universal constant, m 1 and m2 are the masses of both objects respectively and r is the distance between them.

32. Gravitational Constant It is defined as the force of attraction between two bodies each of unit mass and separated from each other by a unit distance. Its value is 6·673 × 10–11 newton metre2 kg –2.

33. Important Formulae (a) An acceleration due to gravity at the surface of earth is given by GM g = , R2 where G is gravitational constant, M is mass of earth and R is the radius of earth. (b) Mass of earth is given by M = gR 2 /G Knowing the value of g = 9·8 m/sec2 , gravitational constant, G = 6·67 × 10–11 newton metre2 kg–2 and radius of earth R = 6·38 × 106 metre, the mass of earth is calculated and found, M = 5·98 × 1024 kg. (c) Density of earth is given by 3g ρ = = 0·0055 kg m–3. 4πGR

34. Natural and Artificial Satellite A natural satellite is a heavenly body revolving around a planet in a close and stable

orbit. In solar system, the nine planets namely, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto revolving around are called the satellites of the sun. Except Mercury, Venus and Pluto, above planets too have got satellites revolving around them. Earth has one, Mars and Neptune two each, Uranus five, Saturn ten and Jupiter has twelve satellites. Thus, moon is a natural satellite of the earth. A man made satellite is called the artificial satellite. Since 4th October 1957, many artificial satellites of the earth have been put in their orbits. For examples—Sputnik–I, Laika, Appolo flights, Aryabhatta, Bhaskara I, SLV–3, Rohini–I, Bhaskara II, INSAT–IA, INSAT–IB etc. Orbital velocity of a satellite is the velocity required to put the satellite into its orbit. It is given by g R+x where x is the distance of orbiting satellite to the surface of earth. Time period of satellite is the time taken by it to go once around the earth. It is given by v = R

2π R

(R + x)3 g

= 2π

(R + x)3 GM

T =

35. Geostationary Satellite A satellite revolving around the earth at a height of 800 km above its surface completes a revolution around the earth in about 107 minutes. If such a satellite is put in a circular orbit concentric and co-planar with the equatorial plane of earth, the satellite appears to be moving with respect to the earth. However, such satellites stay over the same place on the earth and hence appears stationary, if the period of revolution of the satellite is synchronised to just 24 hours, because the earth takes 24 hours to make one complete rotation about its own axis. Such a satellite is called geostationary satellite. The height of satellite above the surface of earth which enables the satellite to have period of revolution in 24 hours and enabling it to appear as a geostationary satellite = 35930 km. Thus, a satellite appear stationary, if it revolves around earth in an orbit at a height of about

12 | Electronics & Telecommunication 36000 km above the surface of earth. Such an orbit is called geostationary orbit and the satellite revolving in this orbit, is called geostationary satellite. The orbital velocity of geostationary satellite is about 308 km/sec. Such satellite always appears to be over the same place relative to an observer in earth.

36. Escape Velocity Escape velocity is defined as the minimum velocity with which a body must be projected from the surface of earth in the atmosphere so that it escapes the gravitational pull of earth and never returns. It is given by 2GM = √ ⎯⎯⎯ 2gR , R where g is acceleration due to gravity, G is gravitational constant, M is mass of earth and R is radius of earth. ve =

37. Kepler’s Law of Planetary Motion First Law—Each planet revolves around the sun in an elliptical orbit with the sun as one focus of the ellipse. Second Law—The straight line joining the sun and the planet sweeps out equal area in equal time intervals. Third Law—The squares of the periodic times of the planets are proportional to the cubes of the semi-major axis of their orbits.

38. Weightlessness Weightlessness means absence of gravity and means a situation where a person feels that he is not being attracted by any force. When a spaceship revolves round the earth, all objects inside the spaceship are in a state of weightlessness. This is because the force of gravitational attraction between the spaceship and earth is completely used in providing the required force for revolution. The spaceship will always be in a state of free fall. Weightlessness is experienced in the artificial satellite also. If a satellite rotates near surface of the earth around it with the orbital velocity, the acting centripetal acceleration on the satellite is equal to the acceleration due to gravity. It may be inferred from this, that the satellite is like a free body. On a free body the acceleration due to gravity is always directed towards the centre of the earth and the apparent weight of a body kept in

the satellite is zero because the entire gravitational force acting upon it provides the centripetal force to rotate it. Hence the body kept in it including man is in the state of weightlessness.

39. Centre of Mass When a system of particles executing motion under the effect of some external forces acting on it, there is a point in the system, where whole mass of the system is concentrated, the system executes the same motion when the forces acting on the system are applied directly to this point. Such a point in the system is called centre of mass of the system. The equation of motion of the centre of mass of the system is given by → d2 → F = M 2 ( r ), dt → where F is the total external force on the system → → → → ( F = f1 + f2 + … + fn ), M is the total mass of N → the system (M = m 1 + m2 + … + mn), and r = ∑ → mi ri /M, in which N is the number of particles.

i=1

40. Torque The turning effect of a force about the axis of rotation is called moment of force or torque due the force. It is measured as the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation. It is denoted by τ (tou). Thus, torque, τ = Force × perpendicular distance from the axis of rotation. Its S. I. unit is newton metre and dimensional formula is [ML 2 T–2].

41. Moment of Inertia The moment of inertia of a rigid body about a given axis of rotation is the sum of the products of the masses of various particles and squares of their perpendicular distances from the axis of rotation. It is denoted by I and is given by N

I=

∑ miri2 , or I = MR2 i=1

Its S. I. unit is kilogram metre2 and its dimensional formula is [ML2 T0 ].

42. Radius of Gyration Radius of gyration is defined as the distance from the axis of rotation at which of whole mass

: 255.00 : 255.00 : 255.00