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REGIONAL OFFICE, RAIPUR STUDY cum SUPPORT MATERIAL PHYSICS CLASS XII SESSION 2016-17 SYLLABUS-2016-17 (THEORY) One Paper Time: 3 hrs. Max Marks: 70 UNIT NAME OF CHAPTER Unit I Electrostatics Unit II Current Electricity Unit III Magnetic Effect of Current and Magnetism Unit IV Electromagnetic Induction and Alternating Current MARKS 15 16 Unit V Electromagnetic Waves Unit VI Optics Unit VII Dual Nature of Matter Unit VIII Atoms and Nuclei Unit IX Electronic Devices Unit X Communication Systems 17 10 12 TOTAL 70 Unit I: Electrostatics Electric Charges; Conservation of charge, Coulomb's law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Unit II: Current Electricity Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm's law, electrical resistance, V-I characteristics (linear and nonlinear),electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colorcode for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff's laws and simple applications. Wheatstone bridge, meter bridge. Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell. Unit III: Magnetic Effects of Current and Magnetism Concept of magnetic field, Oersted's experiment. Biot - Savart law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long straight wire. Straight and toroidal solenoids, force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel currentcarrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth's magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets. Unit IV: Electromagnetic Induction and Alternating Currents Electromagnetic induction; Faraday's laws, induced EMF and current; Lenz's Law, Eddy currents. Self and mutual induction. Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer. Unit V: Electromagnetic waves Need for displacement current, Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses. Unit VI: Optics Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens maker's formula. Magnification, power of a lens, combination of thin lenses in contact, combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of light - blue color of sky and reddish appearance of the sun at sunrise and sunset. Optical instruments : Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Wave optics: Wave front and Huygens’s principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’s principle. Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescope. Polarization, plane polarized light, Brewster's law, uses of plane polarized light and Polaroids. Unit VII: Dual Nature of Matter and Radiation Dual nature of radiation. Photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained). Unit VIII: Atoms and Nuclei Alpha-particle scattering experiment; Rutherford's model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion. Unit IX: Electronic Device Energy bands in solids (Qualitative ideas only) conductor, insulator and semiconductor; semiconductor diode - I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor, transistor as an amplifier (common emitter configuration). Logic gates (OR, AND, NOT, NAND and NOR). Unit X: Communication Systems Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave. Marking Pattern in CBSE Board TYPE OF QUESTION Very Short Answer Question Short Answer Question-1 Short Answer Question –II Value Based Questions Long Answer Question GRAND TOTAL MARKS ON EACH QUESTION 1 NO OF QUESTIONs TOTAL MARKS 5 5 2 5 10 3 12 36 4 1 4 5 3 15 26 70 UNIT I ELECTROSTATICS WEIGHTAGE:8m 1. Charge: It is something possessed by material objects that makes it possible for them to exert electrical force and to respond to electrical force. 2. Properties of charges: (a) Quantisation of charge: It is property by virtue of which all free charges are integral multiple of a basic unit of charge of an electron. = ± where e=1.6x10-19 (b) Additive nature of charge: It is property by virtue of which total charge of a system is obtained by simply adding algebraically all charges present any where on the system. = 1 + 2 + 3−−−−−− + (c) Conservation of charge: It is property by virtue of which total charge of an isolated system always remains constant. 3. Coulombs law: The force of interaction between two point charges is directly proportional to the product of charges and inversely proportional to square of distance between them. ∝ and ∝ Where k is a constant which depends on system of measurement and nature of medium. = = ∈ = 9 × 109 Nm2/kg2 4. Unit of charge: SI unit of charge is one coulomb which is that charge which when placed at a distance of 1m from an equal charge and similar charge in vacuum would repel it by a force of 9x109newtons. CGS unit is 1 statcoulomb or 1 electrostatic unit 1coulomb = 3x109 stat coulomb 5. Electric field: Due to a given charge is the place space around a given charge in which force of attraction or repulsion due to the charge can be experienced by any other charge. 6. Electric field intensity: At any point is the strength of field at that point. It is defined as the force experienced by unit positive charge placed at that point. ⃗E = ⃗F q0 0 →0 0 ⃗ = lim 7. Electric field intensity due to a point charge: ⃗⃗⃗ = 8. Unit of electric field intensity: The SI unit of electric field is newton per coulomb. 9. Electric field intensity due to multiple charges: Electric field intensity at a point due to a group of charges is equal to the vector sum of the electric field intensity due to individual charges at the same point. ⃗⃗⃗ = ⃗1 + ⃗2 … … … + ⃗ ⃗ = ∑ =1 ̂ 2 10. Electric field lines: It is the path straight or curved in electric field, such that tangent at any point of it gives direction of electric field at that point. Properties of electric field lines: 1. Electric field lines are discontinuous curves. They start from positive charge and end at negative charge. 2. Tangent to electric field line at any point gives direction of electric field at that point. 3. No two lines of force can intersect each other because at the point of intersection , there will be two possible direction of electric field which is not possible. Hence the lines do not cross each other. 4. The electric field lines are always normal to the surface of conductor. 5. The electric field lines contract longitudinally, on account of attraction between unlike charges. 6. The electric field lines exert a lateral pressure on account of repulsion between like charges. 11. Electric dipole: It is a system of equal and opposite charges separated by a small distance. 12. Dipole moment: It is given by product of magnitude of either charge and distance between the two charges. = (2) The of dipole moment is from is from positive to negative charge 13. Field intensity on axial line of dipole; The axial line of a dipole is the line passing through the positive and negative charges of the electric dipole. Electric field at P (EB) due to +q Electric field at P due to -q (EA) Net field at P is given by Simplifying, we get As a special case : 14. Field intensity at a point on the equatorial line of dipole: Let P be a point Consider a point P on the equatorial line. The resultant intensity is the vector sum of the intensities along PA and PB. EA and EB can be resolved into vertical and horizontal components. The vertical components of EASinθ and EBSinθ cancel each other as they are equal and oppositely directed. It is the horizontal components which add up to give the resultant field. E = 2EA cos As 2qa = p As a special case, 15. Torque on a dipole in uniform electric field: Force on +q charge=qE along direction of E Force on –q charge =qE opposite to E Fnet=qE-qE =0 The forces are equal in magnitude, opposite in direction acting at different points, therefore they form a couple which rotates the dipole. Torque = × . = × = × = () [ = ⃗⃗ = × ⃗ ] 16. Electric flux: It is represented by electric field passing normally through a given surface. SI unit of flux is newton m2/coulomb. It is a scalar quantity. ∆∅ = ⃗. ⃗⃗⃗⃗⃗⃗ ∆ = ∆ 17. Gauss’s Law: ‘Electric flux over a closed surface is 1/ε0 times the charge enclosed by it.’ ∅= ∈0 18. Electric field due to a an infinite long uniformly charged wire: Gaussian surface is a cylinder with wire as axis, radius r and length l The field is radial everywhere and hence the electric flux crosses only through the curved surface of the cylinder. If E is the electric field intensity at P, then the electric flux through the Gaussian surface is ∅ = × 2 According to gauss theorem electric flux is ∅= ∈0 = ∈0 Hence × 2 = ∈0 [∴ = ] ∈ 19. Electric field due to a uniformly charged spherical shell: Let R be the radius of uniformly charged shell with charge density′′. Case (i)r>R At points outside the sphere the electric field is radial every where because of spherical symmetry. Total electric flux∅ = × 4 2 According to gauss theorem electric flux is ∅= ∈0 × 4 2 = ∈ 0 hence [ = 4∈0 2 ]Electric field due to charged shell is same as that due to a point charge q placed at the centre of shell Case (ii)r=R When point P lies on the surface of the shell or sphere, r = R hence × 4 2 = ∈ 0 [ = = ] 4 ∈0 2 ∈0 Case (iii)r<R The gaussian surface does not enclose any charge, (charge resides on the surface of the shell) 0 × 4 2 = ∈ 0 hence [E=0] 20. Electric field at a distance r when r›R = r=R = r‹ R E=0 2 2 = ∈0 21. Electric field due to a thin infinite plane sheet of charge: Let σ be the surface charge density on the sheet. E.F is independent of the distance from the plane sheet. = 2 ∈0 22. Electric field due to two thin parallel sheet of charge: Electric field between the plates is = ∈0 and in the region on either side of the plates = 0 23. Electrostatic potential difference: P.D between two points in electric field is defined as the amount of work done to move a test charge without acceleration from one point to another. SI unit of PD is volt. ∆ = 24. Electrostatic potential: Electrostatic potential at any point in electric field is the amount of work done in moving a unit positive charge from infinity to the point. = ∞ = Potential is a scalar quantity measured in volts. 25. Electrostatic potential at any point due to a dipole: Potential at a distance r from the centre of dipole at an angle θ with the axis of dipole is =k p cos θ r 2 − a2 = 2 − 2 At a point on the axis of dipole θ=0 At a point on the equatorial line of dipole θ=90 = 0 90 = 0 26. Equipotential surface: It is the surface at every point of which the potential is same. 27. Properties of equipotential surface: 1. No work is done in moving a charge from one point of equipotential surface to the other 2. For any charge configuration, equipotential surface through a point is normal to the electric field at that point. 3. Where electric field is large the distance between electric field is small and vice versa. 28. Potential energy of system of charges: It is defined as the amount of work done in bringing the various charges to their respective positions from infinitely large mutual separations. 29. Expression for potential energy for a system of charges: n n qi qj 1 = k∑∑ 2 rij j=1 i=1 i≠j 30. Electrostatics of a conductors: 1. Electric field inside a conductor is zero 2. The interior of a conductor can have no excess charge in static situations. 3. Electric field just outside the conductor is normal to the surface of the conductor. 4. Electrostatic potential is constant throughout the volume of the conductor and has the same value as on its surface. 5. Electric field at the surface of conductor is = ∈0 31. Relation between electric potential and electric intensity: dV E=− dr 32. Electrical capacitance: It is ability to store charge. It is numerically the charge required to raise the potential by unity. = SI unit of capacity is Farad 1 1 = 1 = [−1 −2 4 2 ] 33. Capacity of isolated spherical conductor: Let R be the radius of spherical conductor. C = 4π ∈0 R 34. Capacity of a parallel plate capacitor: Let the surface charge density on the plates be σ Such that = Electric field between the plates is given by = + = 2 ∈0 2 ∈0 ∈0 Potential difference between the plates is V=Ed V= Capacity of a capacitor = = /∈0 = ∈0 ∈0 [ = ∈0 ] Capacity of a parallel plate capacitor with dielectric: Let the surface charge density on the plates be σ Such that = Electric field between the plates is given by ⃗⃗⃗⃗ = ⃗⃗⃗ = ∈0 ∈0 where E0 is electric field in air and Ei is electric field in dielectric. Potential difference between the plates is given by = ⃗⃗⃗⃗⃗ ( − ) + ⃗⃗⃗⃗ = ( − ) + = ( − + ) ∈0 ∈0 ∈0 Capacity of a capacitor = [ = ∈0 1 − (1 − ) = (−+) ∈0 = ∈0 (−+) ] ∈ If d=t then[ = 0 ] = 0 35. Grouping of capacitors: Parallel combination: = + ± − − − − − − + Series combination: = + + ⋯……..+ 36. Energy stored in capacitor: Consider a parallel plate capacitor of capacity C. Let at any instant the charge on the capacitor be Q’. Then potential difference between the plates will be Suppose the charge on the plates increases by d Q’. The work done will be = ′ ′ = ′ ′ ′ 2 ′ The total work done is = ∫0 = [2 ] This work done is stored as electrical potential energy. [∴ = 2 1 2 1 = = ] 2 2 2 Energy density of parallel plate capacitor: Capacity of a parallel plate capacitor is = ∈0 1 ∈0 2 2 1∈ = 2 0 2 = 2 [ = 1 = 2 ∈0 () 2 = ∈ ] Energy is stored in the dielectric medium between the plates of capacitor 1 1 2 1 = 2 = = QV 2 2 2 When a dielectric is inserted between the plates of capacitor and the battery remains connected 1 1 = () 2 = = 2 = 0 2 2 Total energy is additive in series and parallel combination. = 1 + 2 + 3 S0ME IMPORTANT QUESTIONS AND ANSWERS 1. Define dipole moment of an electric dipole. Is it a scalar or a vector? Electric dipole moment of an electric dipole is equal to the product of either charge and distance between the two charges. = × where p is dipole moment. It is a scalar quantity. 2. Why must electrostatic field be normal to the surface at every point of a charged conduction? The component of electric field along the tangent to the surface of the conductor must be zero. = where θ is angle between and tangent to the surface. ≠ , ∴ = = hence E is perpendicular to the surface 3. Why do the electric field lines not form closed loop? No electric field exist from negative to positive charge , hence electric field lines do not form closed loop. 4. In which orientation a dipole placed in a uniform electric field is in a) Stable, b)UnstableEquilibrium? (a) For stable equilibrium the angle between p and E must be 00 (b) For unstable equilibrium the angle between p and E must be 1800 5. Two point charges having equal charge are separated by 1m distance experience a force of 8N. What will be the force if they are held in water at the same distance? (Given kwater = 80) = ∴ = = = 6. A dipole, of dipole movement p is present in a uniform electric field E. Write the value of angle between p and E for which the torque experienced by the dipole is minimum. = for the torque to be minimum = ∴ = = 7. A charge q is placed at the centre of a cube of side l. What is the flux passing through each face of the cube? According to gauss theorem electric flux linked with a closed surface is∅ = ∈ The flux is symmetrically distributed through all the six faces ∴ ∅ = ∈ 8. Figure shows three pouint charges +2q, -q and +3q. What is the flux through the closed surface S? Electric flux through the surface S ∅= ∑ ∈ = +− ∈ = ∈ 9. If the radius of Gaussian surface is halved, how will the flux through the Gaussian surface change? Even if the radius of the surface is halved, the charge enclosed by the surface does not change hence the flux remains constant. 10. A hollow metal sphere of radius 5 cms is charged such that potential on its surface is 5 V. What is the potential at the centre of the sphere? In side a hollow sphere potential is constant and same as that on its surface. Hence = = 11. Name a physical quantity whose SI unit is J/C. Is it a scalar or a vector quantity? J/C is unit of electric potential.It is a scalar quantity. 12. What is the work done to move a test charge q through a distance of 1 cm along the equatorial axis of dipole? Potential at any point on the equatorial line is 0. Hence work done W = q∆V =0 as ∆V=0 13. The following graph shows variation of charge Q with voltage V for two capacitors K and L. In which capacitor is more energy stored ? Q L K V The slope of straight line represents capacitances. Therefore capacity of L will be more. Energy stored in a capacitor = 14. Draw a plot showing variation of a) Electric field E and b) Electric potential V with distance r due to a point charge Q. 15. Calculate amount of work done in turning an electric dipole ofdipole moment 3x10-8 C-m from position of unstable equilibrium to the position of stable equilibrium in a uniform electric field of intensity 103 N/C For unstable equilibrium θ=1800and for stable equilibrium θ=00Required work done = ( − ) +F I 1/r2 = × − × ( − ) = − × − 2 -F 16. Plot a graph showing the variation of Coulomb’s force (F) versus 1/r2 where r is the distance between the two charges of each pair of charge(1µC,2µC) and (1µC,-3µC). For given pair of charge ∝ 17. Magnitude of q1q2 is higher and negative in second case Two point charges 4µC and -2µC are separated by a distance of 1m. At what point on the line joining the two charges is the electric potential zero. Let the potential be zero at a point P at a distance x from the charge 4µC. At P V1+V2=0 + = A 4µC B P × − × − − = − = ( − ) = − = = Potential is zero at a distance of from 4µC charge SOME QUESTIONS FOR PRACTISE LEVEL-I 1. What is the charge acquired by a body when 1 million electrons are transferred to it? 2. An attractive force of 5N is acting between two charges of +2.0 μC & -2.0 μC placed at some distance. If the charges are mutually touched and placed again at the same distance, what will be the new force between them? 3. A charge of +3.0 x 10-6 C is 0.25 m away from a charge of -6.0 x 10-6C. a. What is the force on the 3.0 x 10-6 C charge? b. What is the force on the -6.0 x 10-6 C charge? 4. An electric dipole consist of a positive and a negative charge of 4µC each placed at a distance of 5mm. Calculate dipole moment. 5. Three capacitors of capacitances 2µF, 3µF and 4µF are connected in parallel. What is the equivalent capacitance of the combination? Determine charge on each capacitor, if the combination is connected to 100V supply? 6. An electric dipole with dipole moment 4x10-9C-m is aligned at 300 with direction of electric field of magnitude 5x104N/C. Calculate the magnitude of the torque acting on the dipole. 7. A point charge of 2µC is at the centre of cubic Gaussian surface 9.0 cm in edge. What is the net electric flux through the surface? 8. What is the amount of work done in moving a 200nC charge between two points 5 cm apart on an equipotential surface? 9. How much work must be done to charge a 24 μF capacitor, when the potential difference between the plates is 500 V? 10.What is the equivalent capacity of the network given below? 1µC LEVEL II 1. What is the work done in moving a charge of 100μC through a distance of 1cm along the equatorial line of dipole? 2. The given graph shows that variation of charge q versus potential difference V for two capacitors C1 and C2. The two capacitors have same plate separation but the plate area of C2 is double than that of C1. Which of the lines in the graph correspond to C1 and C2 and why? – 4 µC are separated by a distance of 1 m in air. At what point on the line joining the charges is the electric potential zero? 4. Two charges +5µC and +20µC are placed 15 cm apart. At what point on the line joining the two charges is the electric field zero? 5. Two charges +16µC and −9µC are placed 8 cm apart. At what point on the line joining the two charges is the electric field zero? 6. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected and from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process. 7. Keeping the voltage of the charging source constant, what will be the percentage change in the energy stored in a parallel plate capacitor if the separation between its plates were to be decreased by 10%. 8. Four charges are placed at the vertices of a square of side d as shown in the figure.(i) Find the work done to put together this arrangement. (ii) A charge q0is brought to the center E of the square, the four charges being held fixed at its corners. How much extra work is needed to do this? 3. Two point charges 5µC and 9. If S1 and S2 are two hollow spheres enclosing charges Q and 2Q respectively as shown in the figure (i) What is the ratio of the electric flux through S1 and S2? (ii) How will the flux through the sphere S1 change, if a medium of dielectric constant 5 is filled in the space inside S1. 10. A charge of 24μC is given to a hollow sphere of radius 0.2m. Find the potential (i) at the surface of the sphere, and (ii) at a distance of 0.1 cm from the centre of the sphere. LEVEL III 1. A slab of material of dielectric constant has the same area as the plates of a parallel plate capacitor but has a thickness 3d / 4, where d is the separation of the plates. How is the capacitance changed when the slab is inserted between the plates? 2. A parallel plate capacitor with air between the plates has a capacitance of 8µF. What will be the capacitance if the distance between the plates is doubled and the space between them is filled with a substance of dielectric constant K=6? 3. Two dipoles, made from charges ±q and ±Q, respectively, have equal dipole moments. Give the (i) ratio between the ‘separations’ of these two pairs of charges (ii) angle between the dipole axis of these two dipoles. 4. The capacitors C1, and C2, having plates of area A each, are connected in series, as shown. Compare the capacitance of this combination with the capacitor C3, again having plates of area A each, but ‘made up’ as shown in the figure. 5. A point charge +10μC is at a distance 5cm directly above the centre of a square of side 10cm as shown in fig. What is the magnitude of flux through the square? 6. Two identical charges ,Q each are kept at a distance r from each other. A third charge q is placed on the line joining the two charges such that all the three charges are in equilibrium. What is magnitude, sign and position of the charge q? 7. ABCD is a square of side 5m. Charges of +50C, -50C and +50C are placed at A,C and D respectively . Find the magnitude of resultant electric field at B. 8. A cube with each side a is kept in electric field given by E = Cx as shown in the figure where C is a positive dimensional constant. Find (i) The electric flux through the cube, and (ii) The net charge inside the cube. 10. Two parallel plate capacitor X and Y have same area of plates and same separation between them. X has air between the plates whereas Y has a dielectric of constant k=4 (i) Calculate capacitance of each capacitor if equivalent capacitance is4 μF. (ii) Calculate potential difference between the plates of X and Y. (iii) What is the ratio of electrostatic energy stored in X and Y. UNIT: I ELECTROSTATICS ANSWERS LEVEL I -13 1. Q = Ne 1.6 x10 C 2. F=0 3. FAB = FBA=2.736N 4. P=2x10-8 C-m 5. 6. 10-4Nm 7. 2,26x105Nm2/C 8. W=0 9. W=3J 10. C=15µF LEVEL II 1. 2. 3. 4. 5. 6. 7. 0 A 5 from 5µC charge 9 5 cm from 5 µC charge 24cm from -9 µC charge 6x10-6 J 11.11% 8. 2 4∈0 (4 − √2) , 0 9. 1: 3, ∅ = 5∈0 6 10. (i) 1.08x10 V (ii) 1.08x106V LEVEL III 4 1. +3 0 2. 3. 4. 5. 24 µF q a=Q A or a/A=Q/q θ = 0 C3= Ceq 1.88x105Nm2/C 6. 200 3 ,100 V, 50V, 50V, 200V,10-8C, 10-8C, 10-8C,2x10-8 C 7. Q/4, Positive, r/2 8. 2.7x1010N/C 9. a3C N-m2/C, a3C0 Coulombs. 10. Cx=5μF Cy= 20μF CURRENT ELECTRICITY The flow of charge through a conductor is called electric current. I= It is scalar quantity and its SI unit is Ampere OHMS LAW It states that current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor provided physical conditions like temperature and pressure remains constant. V∝I V=IR RESISTANCE It is the obstruction to the flow of current. Resistance of a conductor is directly proportional to length and inversely proportional to its area of cross-section. ∝ = Where is the resistivity of the material of the conductor It is defined resistance per unit length per unit area of cross section. SI unit is ohm m. It depends on nature of material and temperature’ DRIFT VELOCITY It is the average velocity with which electrons move through the conductor in presence of external electric field. In absence of electric field the elwctrons are in random motion nd the average thermal velocity is =0 F= = = From I equation of motion = + = + = = = – Relaxation time – it is the average time between 2 successive collisions. CURRENT IN TERMS OF DRIFT VELOCITY n – no.of elecrtrrons per unit volume - volume of the conductor – total no. of electrons – total charge = = = CURRENT DENSITY & RESISTIVITY = = = 2 = = = = = Comparing above equations 2 VARIATION OF RESISTIVITY WITH TEMPERATURE CONDUCTORS Resistivity increases with increase in temperature ALLOYS Variation of resistivity is very less hence the alloys are used in making standard resistance. SEMICONDUCTORS Resistivity decreases with increase in temperature. COMBINATION OF RESISTANCE SERIES COMBINATION = + + = + + = + + Using Ohm’s law PARALLEL COMBINATION = + + Using Ohm’s law = 1 + COMBINATION OF CELLS SERIES COMBINATION = + + − = ( − ) + ( − ) = + = + 2 + 3 or 1 = 1 1 + 1 2 + 1 3 PARALLEL COMBINATION = + + − − − = + On solving = + = + + COLOUR CODE FOR CARBON RESISTORS: The first two rings from the end give the first two significant figures of resistance in ohm. The third ring indicates the decimal multiplier. The last ring indicates the tolerance in per cent about the indicated value AB x 10C ± D % ohm Eg. Letter Colour Number Colour Tolerance B Black 0 Gold 5% B Brown 1 Silver 10% R Red 2 No colour 20% O Orange 3 Y Yellow 4 G Green 5 B Blue 6 V Violet 7 G Grey 8 W 9 KIRCHHOFF’S LAWS: I Law or Current Law or Junction Rule: (∑I=0 ) The algebraic sum of electric currents meeting at a junction in any electrical network is always zero. I1 - I2 - I3 + I4 - I5 = 0 II Law or Voltage Law or Loop Rule:( ∑∆V=0) The algebraic sum of all the potential drops and emf’s along any closed path in an electrical network is always zero. Loop ABCA: - E1 + I1.R1 + (I1 + I2).R2 = 0 Loop ACDA: - (I1 + I2).R2 - I2.R3 + E2 = 0 Sign Conventions: The emf is taken negative when we traverse from positive to negative terminal of the cell through the electrolyte. The emf is taken positive when we traverse from negative to positive terminal of the cell through the electrolyte. The potential falls along the direction of current in a current path and it rises along the direction opposite to the current path. The potential fall is taken negative. The potential rise is taken positive. Note: The path can be traversed in clockwise or anticlockwise direction of the loop. WHEAT STONE BRIDGE: If no current flows through galvanometer ( VB=VD) = In the loop ABDA I1P + IgG – (I – I1)R = 0________________(1) In the loop BCDA (I1-Ig)Q – (I-I1+Ig)S - IgG = 0____________(2) Solving equation (1) & (2) = METRE BRIDGE: It works on the principle of Wheatstone bridge. = − = = − POTENTIOMETER: It is a device used to measure emf of a cell. PRINCIPLE: The potential drop or fall of potential across any portion of the wire is directly proportional to the of the wire provided the wire is of uniform area and current flowing through it is constant. V=IR = = kL Where, k – potential gradient = = NOTE:-For better Sensitivity of Potentiometer k should be less. COMPARISON OF EMF’S USING POTENTIOMETER: = INTERNAL RESISTANCE OF A CELL = ( − ) = ( − ) CURRENT ELECTRICITY PREVIOUS YEAR FOR PRACTICE 1. Two wires of equal length, one of copper and the other of manganin have the same resistance. Which wire is thicker? ANS- Manganin 2. Define drift velocity and relaxation time. Derive the expression for resistivity in terms of number density of electrons and relaxation time. 3. 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. 4. Answer the following : (a) Why are the connections between the resistors in a meter bridge made of thick copper strips ? (b) Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire ? (c) Which material is used for the meter bridge wire and why ? 5. Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with each other across an external resistance R. What is the current through this resistance? 6. Write principle of potentiometer. Draw the circuit diagram to compare emf of two primary cells. Write the formula used. 7. Calculate the value of the resistance R in the circuit shown in the figure so that the current in the circuit is 0.2 A. What would be the potential difference between points B and E? ANS- VBE=1V 8. In the meter bridge experiment, balance point was observed at J with AJ = l. (i) The values of R and X were doubled and then interchanged. What would be the new position of balance point? (ii) If the galvanometer and battery are interchanged at the balance position, how will the balance point get affected? 10. Two conducting wires X and Y of same diameter but different materials are joined in series across a battery. If the number density of electrons in X is twice that in Y, find the ratio of drift velocity of electrons in the two wires. 11. State Kirchhoff’s rules. Use these rules to write the expressions for the currents I1, I 2 and I 3 in the circuit diagram shown. ANS- I1=2/13,I2=7/13,I3=9/13 12. Calculate the current drawn from the battery in the given network. ANS- I=2A 13. The following graph shows the variation of terminal potential difference V, across a combination of three cells in series to a resistor, versus the current, i: (i) Calculate the emf of each cell. (ii) For what current i will the power dissipation of the circuit be maximum? ANS- emf of each cell is 2V and I=1A 14. Two wires X, Y have the same resistivity, but their cross-sectional areas are in the ratio 2 : 3 and lengths in the ratio 1 : 2. They are first connected in series and then in parallel to a d.c. source. Find out the ratio of the drift speeds of the electrons in the two wires for the two cases. ANS (a) Vdx/vdy=3/2 (b)vdx/vdy=2/1 MAGNETIC EFFECTS OF CURRENT & MAGNETISM 1 MARK QUESTIONS 1. A vector needs three quantities for its specification.name three independent quantities needed to completely specify the earth’s magnetic field at appoint on the earth’s surface? Ans. These are(i) angle of declination (ii) angle of dip or inclination (iii)horizontal component of the earth’s magnetic field. 2. Why should a voltmeter have high resistance? Ans. A voltmeter is always connected in parallel. When connected in parallel, it should drawleast current, otherwise the potential difference which it has to measure will change. 3. What is the direction of the force acting on a charge particle q, moving with a velocity , will cange.v in a uniform magnetic field B Ans: Force, to both velocity v and magnetic field B. 2. Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why? Ans: Magnetic field lines can be entirely confined within the core of a toroid because toroid has no ends. A solenoid is open ended and the field lines inside it which is parallel to the length of the solenoid, cannot form closed curved inside the solenoid. 3. An electron does not suffer any deflection while passing through a region of uniform magnetic field. What is the direction of the magnetic field? Ans: Magnetic field is parallel or antiparallel to velocity of electron i.e., angle between v and B is 0° or 180°. 4. A beam of a particles projected along +x-axis, experiences a force due to a magnetic field along the +y-axis. What is the direction of the magnetic field? Ans: 5. Ans: 6. Ans: 7. Ans: 9. By Fleming’s left hand rule magnetic field must be along negative Z-axis What is the characteristic property of a diamagnetic material? These are the substances in which feeble magnetism is produced in a direction opposite to the applied magnetic field. These substances are repelled by a strong magnet. These substances have small negative values of susceptibility and positive low value of relative permeability. The permeability of a magnetic material is 0.9983. Name the type of magnetic materials it represents. As permeability < 1, so magnetic material is diamagnetic. Where on the surface of Earth is the angle of dip zero? Angle of dip is zero at equator of earth’s surface. A narrow beam of protons and deuterons, each having the same momentum, enters a region of uniform magnetic field directed perpendicular to their direction of momentum. What would be the ratio of the circular paths described by them? Ans. As r=mv/qB i.e., => r∝ 1/q so, rp:rd =1:1 10. Mention the two characteristic properties of the material suitable for making core of a transformer. Ans: Two characteristic properties: (i) Low hysteresis loss (ii) Low coercivity. 11. An electron is moving along positive x axis in the presence of uniform magnetic field along positive y axis. What is the direction of the force acting on it? Ans: 12. negative z direction. Why should the spring or suspension wire in a moving coil galvanometer have low torsional constant? Ans: Sensitivity of a moving coil galvanometer is inversely proportional to the torsional constant. 13. Steel is preferred for making permanent magnets whereas soft iron is preferred for making electromagnets .Give one reason. Ans: steel-- high retentivity, high coercivity Soft iron-- high permeability and low retentivity. 14. Where on the surface of the earth is the vertical component of earth’s magnetic fieldzero? Ans: At equator. TWO MARKS QUESTIONS 1. Define magnetic susceptibility of a material. Name two elements, one having positive susceptibility and the other having negative susceptibility. What does negative susceptibility signify ? Ans: Magnetic susceptibility: It is defined as the intensity of magnetisation per unit magnetising field, It has no unit. Iron has positive susceptibility while copper has negative susceptibility. Negative susceptibility of a substance signifies that the substance will be repelled by a strong magnet or opposite feeble magnetism induced in the substance. 2. Define the term magnetic dipole moment of a current loop. Write the expression for the magnetic moment when an electron revolves at a speed ‘v’, around an orbit of radius ‘ r’ in hydrogen atom. Ans: Magnetic moment of a current loop: M = NIA i.e., magnetic moment of a current loop is the product of number of turns, current flowing in the loop and area of loop. Its direction is perpendicular to the plane of the loop. Magnetic moment of Revolving Electron, M=evr/2 3. Define current sensitivity and voltage sensitivity of a galvanometer. Increasing the current sensitivity may not necessarily increase the voltage sensitivity of a galvanometer. Justify. Ans: Current sensitivity :It is defined as the deflection of coil per unit current flowing in it.Current Sensitivity, S=NAB/ k Voltage sensitivity :It is defined on the deflection of coil per unit potential difference across ends. Voltage Sensitivty, SV=NAB/GC where G is resistance of galvanometer. Justification: When number of turnsNis doubled, then the current sensitivity (µN) isdoubled; but at the same time, the resistance of galvanometer coil (G) will also be doubled, so voltage sensitivity S will remain unchanged; hence inreasing current sensitivity does not necessarily increase the voltage sensitivity. 4. A wire of length L is bent round in the form of a coil having N turns of same radius. If a steady current I flows through it in a clockwise direction, find the magnitude and direction of the magnetic field produced at its centre. Ans: = × 2 => = 2 0 0 2 = = 2 5. A point charge is moving with a constant velocity perpendicular to a uniform magnetic field as shown in the figure. What should be the magnitude and direction of the electric field so that the particle moves undeviated along the same path? Ans: Magnitude of electric field is vB and its direction is along positive Y-axis. 6. (i) Write two characteristics of a material used for making permanent magnets. (ii) Why is core of an electromagnet made of ferromagnetic materials? Ans: (i) For permanent magnet the material must have high retentivity and high coercivity (e.g.,steel). (ii) Ferromagnetic material has high retentivity, so when current is passed in ferromagnetic material it gains sufficient magnesium immediately on passing a current through it. 7. Draw magnetic field lines when a (i) diamagnetic, (ii) paramagnetic substance is placed in an external magnetic field. Which magnetic property distinguishes this behaviour of the field lines due to the two substances? Ans: 8. Ans: The magnetic susceptibility of diamagnetic substance is small and negative but that of paramagnetic substance is small and positive. Deduce the expression for the magnetic dipole moment of an electron orbiting around the central nucleus. Consider an electron revolving around a nucleus (N) in circular path of radius r with Area of current loop (electron orbit), A = p r2 Magnetic moment due to orbital motion, M= IA=evr/2 9. A circular coil of ‘N’ turns and diameter ‘d’ carries a current ‘I’. It is unwound and rewound to make another coil of diameter ‘2d’, current ‘I’ remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. Ans: Magnetic moment (M) = NIA=NIπd2/4 = NIπR2 Length of wire remains same, so NB = NA/2, R=2R On solving MA/MB = 2/1 10. Which one of the two, an ammeter or a milliammeter, has a higher resistance and why? Ans: As the shunt resistance is connected in parallel with the galvanometer, so the milliammeter will have a higher resistance than the ammeter. 11. The following figure shows the variation of intensity of magnetization I versus the applied magnetic field intensity H for two magnetic materials A and B. (1) Identify the materials A and B (2) Draw the variation of susceptibility with temperature for B. Ans: 1) A is paramagnetic material. 2) B is diamagnetic material. THREE MARKS QUESTIONS Q.1Distinguish between diamagnetic, paramagnetic and ferromagnetic substances. Ans. Property Effects of magnets Susceptibility(Xm) Relative permeability value(µr) Permeability value(µ) Effect of temperature Examples Diamagnetic They are feebly repelled by magnets. -1=< Xm<0 0=<µr <1 µ< µ0 Independent temperature. Paramagnetic They are feebly attracted by magnets. 0<Xm<ε 1<µr<1+ε Ferromagnetic They are strongly attracted by magnets. Xm>1000 µr>1000 µ> µ0 of Susceptibility is inversely proportional to temperature. µ>> µ0 Susceptibility decreases with temperature in a complex manner. Bi ,Pb,Cu Hints: for distinguishing them, use the formula µr=1+Xm. Q 2. Discuss the motion of a charged particle in a uniform magnetic field with initial velocity (i) parallel to the field, (ii) perpendicular to the magnetic field and (iii) at an arbitrary angle with the field direction. Ans. When a charged particle having charge q and velocity v enter a magnetic field B it experiences a force F = qv B sinθ The direction of this force is perpendicular to both v and B. Following three cases are possible: 1. When the initial velocity is parallel to the magnetic field: Here θ=0 , So F = qvB sin0 = 0. Thus the parallel magnetic field does not exert any force on the moving charged particle. The charged particle will continue to move along the line of force. 2. When the initial velocity is perpendicular to the magnetic field: The particle will move along circular path. Centripetal force = magnetic force mv2/r = qvB or r = mv / qB 3. When the initial velocity makes an arbitrary angle with the field direction: In this case particle will move along helical path with velocity vCosθ along the direction of magnetic field m(vSinθ)2/r = qvSinθB r = mvSinθ / qB Q.3 . State the factors on which the force acting on a charge moving in a magnetic field depends. Write the expression for this force. When is this force minimum and maximum? Ans: Factors on which the force acting on a charge moving in a magnetic field depends are 1. Magnitude of charge’q’ 2. Intensity of magnetic field ‘B’ 3. Velocity of the particle’v’ 4. Angle between ‘v’ and ‘B’ – θ F = qvBSinθ For Maximum force θ = 900 then F = qvB For Minimum force θ = 00 then F = 0 Q4. State Biot-Savart law for magnetic field produced at a point due to a small current element. And express it in vector form. Derive the expression for magnetic field at the centre of current carrying circular loop. Ans According to Biot Savart Law the Magnetic field dB due to small current element is 1. directly proportional to the current I 2. directly proportional to the current dl 3. directly proportional to the current Sinθ 4. directly proportional to the current 1/r2 Hence dB α 2 or dB = k dB = 2 0 2 4 Vector form of Biot Savart Law ⃗⃗⃗⃗ 0 × ⃗⃗⃗⃗⃗ = 3 4 2 According to Biot Savart Law dB = 40 θ= 900 hence dB = Total field B = 0 4 2 0 2 = 20 4 2 Q. 5. Derive a mathematical expression for the force acting on a current carrying straight conductor kept in a magnetic field. Under what conditions is this force (i) zero and (ii) maximum? Ans. Let ‘n’ be the no. of electrons per unit volume of the conductor. Total no. of electrons = nAl Charge q= enAl Force F =qvBSinθ = enAlvBSinθ = IlBSinθ ⃗ = × For Maximum force θ = 900 then F = IlB For Minimum force θ = 00 then F = 0 Q. 6. Define current sensitivity and voltage sensitivity of a galvanometer. State the factors on which the sensitivity of a moving coil galvanometer depends. Ans. Current sensitivity: It is the deflection produced in the galvanometer when a unit current flows through it. Voltage sensitivity: It is the deflection produced in the galvanometer when a unit potential difference is applied across its ends. Voltage sensitivity, Vs=α/V=NBA/k RG Q.7. State ampere’s circuital law connecting the line integral of B over a closed path to the net current crossing the area bounded by the path. Use the law to derive the formula for the magnetic field due to an infinitely long straight current carrying wire. Q. 8. A long solenoid with closely wound turns has n turns per unit of its length. A steady current I flow through this solenoid. Use Ampere’s circuital law to obtain an expression for the magnetic field at a point on its axis and close to its mid point. Ans. The magnetic field along the axis of solenoid is uniform and outside the solenoid the magnetic field is zero. Q. 9. How will you convert a galvanometer into an ammeter of range 0 - I amperes? What is the effective resistance of an ammeter? To convert a galvanometer into an ammeter a small resistance shunt ‘S’ is connected in parallel with the galvanometer. Ig G= (I - Ig)S Or S = IgG/((I - Ig)) Effective resistance R= SG/(S+G) Q. 10. How can a galvanometer be converted into a voltmeter to read a maximum potential difference V? Discuss with related mathematical expression. Ans. A voltmeter is connected in parallel with a circuit element. So it must draw a very small current, otherwise the voltage to be measured would decrease. To convert a galvanometer into a voltmeter large resistance ‘R’ is connected in series with the galvanometer. Let RG be the resistance of galvanometer and Ig be the current with which galvanometer gives full scale deflection. To measure a maximum potential difference V, a high resistance R is connected in series with it. Total resistance of the device = R + RG Therefore by Ohm’s law Q 11. How will you select materials for making permanent magnets, electromagnets and cores of transformers? Ans. A. Permanent magnets- The material used for making permanent magnets must have the following characteristics: 1. High retentivity 2. High coercivity 3.High permeability. B. Electromagnets- The material used for making cores of electromagnets must have the following characteristics: 1. High initial permeability 2. Low retentivity C. Transformer cores- The material used for making cores of transformers must havethe following characteristics: 1. High initial permeability 2. Low hysteresis loss 3. Low resistivity Q12. Define the terms, (i) Magnetisation, (ii) Relative permeability and (iii) magnetic susceptibility. Give their S I unit, if any Ans. (i)Magnetisation or intensity of magnetization - It is the magnetic moment developed per unit volume of a material when placed in a magnetising field. It is a vector quantity. It’s SI unit is Am-1. (ii)Relative permeability - It is the ratio of permeability of the medium to thepermeability of free space. It is unit less quantity. (iii)Magnetic susceptibility - Magnetic susceptibility measures the ability of a substanceto take up magnetisation when placed in a magnetic field. It is the ratio of the intensity of magnetisafion M to the magnetising field inteitsity H. As magnetic susceptibility is the ratio of two quantities having the same units, so it has no unit. FIVE MARKS QUESTIONS Q.1(a)Using Biot-Savart law, deduce an expression for the magnetic field on the axis of a circular current loop. Hence obtain the expression for the magnetic field at the centre of the loop. (b)Two circular coils of equal radius and carrying equal current are placed such that their centers coincide and their axis are perpendicular to each other. Find the net magnetic field at the common center. Ans. Consider a circular loop of wire of radius a and carrying current I, as shown in figure. Let the plane of the loop be perpendicular to the plane of paper. We wish to find field at an axial point P at a distance r from the centre C. Consider a current element dl at the top of the loop. It has an outward coming current. 0 According to Biot Savart Law ⃗⃗⃗⃗⃗ = θ= 900 hence ⃗⃗⃗⃗⃗ = 0 4 2 4 2 The magnetic field is resolved into its components, the cos component being equal and opposite cancel out and total field is given by sum of sin components 0 (b) Magnetic field at the centre B1 = B2 = 2 B2 = B12 + B22 B=√2 √20 B= 2 Q. 2. With the help of a labeled diagram, explain the principle, construction, theory and working of a cyclotron. Ans. It is a device used to accelerate charged particles like protons, deuterons, α- particles, etc., to very high energies. Principle: A charged particle can be accelerated to very high energies by making it pass through alternating electric field and strong magnetic field perpendicular to each other, by making it cross the same electric field time and again. Q3. Derive an expression for the torque on a rectangular coil of area A, carrying a current I and placed in a magnetic field B. The angle between the direction of B and vector perpendicular to the plane of the coil is θ. Ans. Consider a rectangular coil PQRS suspended in a uniform magnetic field B , with its axis perpendicular to the field. Let I be the current flowing through the coil PQRS, a and b be the sides of the coil PQRS, A =ab= area of the coil and is the angle between the direction of B and normal to the plane of the coil. According to Fleming’s left hand rule, the magnetic forces on sides PS and QR are equal, opposite and collinear (along the axis of the loop),so their resultant is zero. The side PQ experiences a normal inward force equal to IbB while the side RS experiences an equal normal outward force. These two forces form a couple which exerts a torque given by = Force x perpendicular distance = IbBx asinθ = IBAsinθ If the rectangular loop has N turns, the torque increases N times i.e., = NIBAsinθ But NIA = m, the magnetic moment of the loop, so =mBsinθ In vector notation torque is represented as ⃗⃗ × ⃗ ⃗ ⃗ = ⃗ The direction of the torque t is such that it rotates the loop clockwise about the axis of suspension. Q. 4. With the help of a neat and labeled diagram, explain the underlying principle, construction and working of a moving coil galvanometer. What is the function of (i) uniform radial field (ii) soft iron core in such a device? Ans. A galvanometer is a device to detect current in a circuit, the magnitude of which depends on the strength of current. Construction: A pivoted-type galvanometer consists of a rectangular coil of fineinsulated copper wire wound on a light aluminium frame. The motion of the coil is controlled by a pair of hair springs of phosphor-bronze. The springs provide the restoring torque. A light aluminium pointer attached to the coil measures its deflection on a suitable scale. The coil is placed symmetrically between the concave poles of a permanent horse-shoe magnet. There is a cylindrical soft iron core which not only makes the field radial but also increases the strength of the magnetic field. Theory and working: As the field is radial, the plane of the coil always remains parallel to the field B . When a current flows through the coil, a torque acts on it. It is = Force x perpendicular distance = NIbB x a sin 90 = NIB (ab) = NIBA Here ϴ =90 , because the normal to the plane of coil remains perpendicular to the field in all positions. The torque deflects the coil through an angle θ. A restoring torque is set up in the coil due to the elasticity of the springs such that = Where k is the torsion constant of the springs i.e., torque required to produce unit angular twist. In equilibrium position, Restoring torque = Deflecting torque kα = NIBA α = NIBA/k Thus the deflection produced in the galvanometer coil is proportional to the current flowing through it. Functions: (i) A uniform magnetic field provides a linear current scale. (ii) A soft iron core makes the field radial. It also increases the strength of the magnetic field and hence increases the sensitivity of the galvanometer. Q5. Derive a mathematical expression for the force per unit length acting on each of the two straight parallel metallic conductors carrying current in the same direction and kept near each other. Hence define an ampere. Why do such current carrying conductors attract each other? Ans. AB and CD are two parallel conductors carrying currents I1 and I2 respectively separated by distance‘r’. The currents in the same direction force is attractive force currents in opposite directions, force is repulsive. The magnetic field produced by current I1 at any point on wire AB is B1= µ0I1/2πr According to Flemings Left Hand Rule the field acts perpendicular to the wire CD and points into the plane of paper. The force on current carrying wire RS. F2=µ0I1I2l/2πr Force per unit length, F2 / l=µ0I1I2/2πr Similarly force on AB due to magnetic field produced by CD is F1 / l=µ0I1I2/2πr According to Fleming’s left hand rule, this force acts at right angles to CD, towards AB in the plane of the paper. Similarly, an equal and opposite force is exerted on the wire AB by the field of wire CD. Thus when the currents in the two wires are in the same direction, the forces between them are attractive. Definition of ampere: One ampere is that value of steady current, which on flowing in each of the two parallel infinitely long conductors of negligible cross-section placed in vacuum at a distance of 1 m from each other, produces between them a force of 2 X 10-7 newton per meter of their length. VALUE BASED QUESTION MAGNETIC EFFECTS OF ELECTRIC CURRENT AND MAGNETISM 1. Mr Narasimham , a 65 year old person often complained of neck pain. One day his grandson Akash, suggested that magnetic therapy is very effective in reducing such pains. He said that the permanent magnet/electromagnet ,used in the device will help to produce Joule’s heating effects in the blood stream, which helps the blood flow better. He immediately contacted his friend in Chennai, who was running Magnetic Therapy Clinic. a.What two values did Akash exhibit towards his grandfather? Mention any two. Ans.Responsible behaviour, concern and awareness b. What is the SI unit of magnetic induction and define it? Ans. Tesla (defn) 2. Ms Rajyam joined a PG course in Nanotechnology lab in IIT Chennai. The first day, when she went to the lab, she met Mr. Antonio, the lab assistant.He greeted her and advised her not to touch the wires which were suspended from the roof at every part of the lab as they were from high voltage lines. He also told her not to bring any of the two wires closer to each other during any experimental applications. He helped her in understanding about the precautions that has to be taken in the lab. a.What value did Mr. Antonio exhibit towards Ms. Rajyam? Mention any two (Responsible behaviour, sensitivity, concern for others and alerting the people) b.Why two high voltage power transmission lines should not be close to each other? c.Give an expression for the magnetic force that acts between the wires? 3. In the birthday party of Bharat, a class 7student, his parents gave big slinkys to all his friends as return gifts. The next day, during the physics class Mr Mohan, the teacher explained them about the production of magnetic fields using current carrying coil and also said that they can make permanent magnets, using such coils by passing high currents through them. That night Suman, a friend of Bharat, asked his father about the coils, and their shape. His father asked him to bring the slinky, that his friend gave and explained the uses of toroid and solenoid. a.What value did Suman’s father exhibit towards his son? (Responsibility, makes his child to understand the concepts and to generate interest in the subjects) b.What is the difference in the fields produced by the solenoid and Toroid? The magnetic field lines in a toroid is concentric circles whereas in solenoid it is straight within the turns. 4. Ms Anita found that her son could not hear properly. The specialist prescribed hearing aid for her son. Hearing aids consist of electromagnets in the loudspeakers used in the device. a.What two values does Ms Anita exhibit towards her son and students?Mention any two. (caring attitude, sensitive towards society, concern for others b.What is an electromagnet? In what way its hysteresis curve is different from that used for permanent magnets? Ans. Electromagnet- temporary magnet.Hysteresis curve has small are,small coercivity, small retentivity. 5. Ms Gomathy wife of Mr Varadan complained about the non availability of gas cylinders and explained to him to look out for alternate methods for cooking.Mr Varadan bought an induction stove to overcome the fuel problem. The next day Gomathy used her copper bottom cooker and kept it on the induction stove. But even after using it for half an hour she found that the cooker was not hot and food not cooked. As she was not aware of the method to use the induction stove, she asked her elder daughter Tanya, studying first year engineering about it. She told her, that some vessels can not be used on this stove. She took the instruction manual and explained to her mother, that the stove works on magnetic induction, and copper being a dia magnetic material, will not respond to it. a.What values did Mr varadan and Tanya exhibit towards Ms Gomathy? Mention any two (awareness, concern for conservation of energy and fossil fuels, sharing the knowledge) b.Give few examples of diamagnetic materials and explain how their suceptiblity varies with temperature? Ans.Susceptibility is independent of temperature as they have no permanent dipoles. 6. Hari and Rama class X students, were assigned a project based on magnetism. In their project work, they had calculated the value of earth’s magnetic field. When they submitted their project for verification. Mr Satish, their physics teacher, corrected the mistakes. He also suggested few books which could be of use to them. a.What values did Mr Satish exhibit towards his students? Mention any Two. Ans. (Honesty, helpfulness, responsible behaviour towards students, concern for the student to create interest in the subject) b.Mention the three magnetic elements required to calculate the value of earth and draw a neat diagram to explain them. Ans. Magnetic declination, magnetic inclination and horizontal component of earth’s magnetic field. 7. Mr Sairam the chief development officer, in southern railway went on anofficial tour to attend a seminar on fast moving trains. He met his friend on tosaki in Tokyo after he finished his seminar there. His friend explained to Sairam, how Japanese people are concentrating on energy conservation and saving of fossil fuels using Maglev trains. Mr sairam travelled from Tokyo to Osaka in maglev train and found that sound is less, traveliing is smooth and understood in what way we are lagging behind Japanese in mass transporting systems. a. What values did Mr sairam found from Ontosaki? Mention any two. (awareness about new technology, concern for energy conservation, decrease of noise pollution and air pollution i.e, concern for environment) b.What is Meisner’s effect? Ans.When a superconduc tor is cooled in a magnetic field below its critical temperature the magnetic field lines are expelled showing diamagnetic property. This is called Meissner effect. 8. Ms Ramani a house wife aged 42 years complained of stomach ache one day. Her husband Mr Srinivas took her to a nearby hospital. The doctor observed her and found something wrong near her liver and suspected malignancy. There after checking her MRI scan, a team of doctors advised her to go through Carbon radio therapy which is very safe. They said using cyclotron, high speed ions can be generated that directly attach the cancerous tissues and destroy them. 1. What values did Mr srinivas and the doctor have exhibited? Mention any two. Ans. Concern for others, helpfulness, presence of mind, responsible citizen. 2.What are the role played by Electric field and magnetic fielding Cyclotron? Ans. The charged particles are accelerated by the electric field with the magnetic field bringing them again and again to the electric field that is the region between the Dees. ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT Gist of the lesson (including basic concepts and important formulae) 1. Magnetic Flux:- The no. of magnetic field lines passing through an area inside a magnetic field region is known as magnetic flux passing through that area. The magnetic flux through a plane surface placed inside a uniform magnetic field is given by ϕ = B A BA cos The magnetic flus passing any surface placed inside a magnetic field (uniform of non-uniform) is given by ϕ = B dA 2. 3. 4. 5. 6. The SI unit of magnetic flux is Tm2 or Wb. It is a Scalar quantity. The dimension of magnetic flux is [ML2T-2A-1]. Electromagnetic Induction:- “Whenever there is change in magnetic flux linked with a conductor or conducting coil, an emf is induced in the conductor or coil. The emf induced lasts so long as the magnetic flux linked with conductor or coil changes. This phenomenon is called EMI.” Faraday’s Law of Electromagnetic Induction:- “The magnitude of the induced emfin a circuit is proportional to the time rate of change of magnetic flux through the circuit.” d dt Lenz’s Law:-“ The polarity of induced emf is such that it tends to tends to produce a current which opposes the change in magnetic flux that produces it.”It is based of law of conservation of energy. Mathematically, Faraday’s & Lenz’s laws are combined in the following expression d dt Induced current and induced charge:- If a coil is closed and has resistance R, then current induced in the coil, N d i ampere, R R dt and the induced charge, N Total flux linkange q = i∆t = = R Resistance Motional emf:(a) The emf induced in a straight conductor moving inside a uniform magnetic field with a velocity perpendicular to its length as well as the magnetic field induction ɛ = Bvl (b) The emf induced in a disc rotating inside a uniform magnetic field directed parallel to the axis of rotation of disc/ the emf induced in a straight conductor rotating about its one end inside a uniform magnetic field directed parallel to the axis of rotation ɛ= Bvl Bwl 2 2 2 7. Eddy Currents:- “When bulk pieces of conductors are subjected to changing magnetic flux, induced currents are produced in them due to electromagnetic induction. The flow pattern of these currents resemble swirling water, so these are known as eddy currents or whirlpool currents.” Eddy currents are undesirable in many devices such as transformers, electric motors etc. since they heat up the core and dissipate electrical energy in the form of heat. Eddy currents are minimised by using laminations of metal to make a metal core. The laminations are separated by an insulating material like lacquer. The plane of the laminations must be arranged parallel to the magnetic field, so that they cut across the eddy current paths. This arrangement reduces the strength of the eddy currents. 8. Applications of eddy currents:(i) Magnetic braking in trains: (ii) Electromagnetic damping: (iii) Induction furnace: (iv) Electric power meters: 9. Self-Induction:- “When the current in a coil is changed, a back emf is induced in the coil that opposes the change in the current. This phenomenon is known as self induction or electrical inertia.” 10. Self-Inductance L :This quantity is the measure of self-induction of a coil. It is a scalar quantity. SI unit of this quantity is Henry and the dimension is [ML2T-2A-2]. This quantity is also known as ‘coefficient of selfinduction’. Self-inductance of a coil is defined numerically equal to, “the back emf induced in the coil when the current flowing through its turns changes at the rate of 1 A/s.” OR “the magnetic flux linked with the coil when the current flowing through its turns is unity.” The formula for the self-inductance of any coil is L or L I dI dt 11. Self-inductance of a long solenoid is L = μrμ0n2Al 12. Mutual-Induction:-“When two coils are placed nearby and the current in one coil is changed, an emf is induced in the neighbouring coil due to the change in magnetic flux linked with it. This phenomenon is known as mutual induction.” 13. Mutual-Inductance M12:- the mutual induction between two coils is given mathematically by quantity ‘Mutual-Inductance’ or ‘coefficient of mutual induction’. Mutual inductance of two coils is defined as the “Magnetic flux linked with one coil due to the unit amonut of current flowing in the neighbouring coil”. OR “the back emf induced in one coil due the unit rate of change of current in the neighbouring coil”. M 12 2 I1 or M 12 2 dI 1 dt Mutual-Inductance of two coils depends on the linkage of magnetic field lines between them apart from other factors. If the magnetic fields lines of one coil are completely linked with the neighbouring coil then they are called perfectly coupled. For two perfectly coupled co-axial solenoids, mutual-inductance is given by M12 = μ0n1 n2 πr2l where r is the radius of inner coil. OR, M12 = √³L1L2´ where L1 and L2 are the self-inductances of the two coils. 14. The magnetic energy stored in a current carrying solenoid:U = ½ LI2 15. Alternating emf and alternating current:- The emf/ current whose polarity/ direction reverses after a regular interval of time periods is called an alternating emf/ alternating current. The alternating emf / alternating current produced by an a.c. generator is a sinusoidally varying alternating emf/ current. The instantaneous magnetic flux associated with coil is NBA cos(t ) or NBA sin( t ) The instantaneous emf and instantaneous current is e =E0 sin (ɷt+ϕ) or e = E0cos (ɷt+ϕ) i = I0 sin (ɷt+ϕ) or i = I0cos (ɷt+ϕ) The peak value or amplitude of the emf/ current is E0 = NBA and I 0 = NBA / R 16. The average value of alternating emf / alternating current is ‘zero’ for full cycle. 2V 2I 0 17. The average value of alternating emf / alternating current for the ‘half’ cycle is 0 or 18. RMS value / Effective value / Virtual value of the alternating current:- It is the value of alternating emf/ current that is measured by a.c. metres which are based on heating effect of current. RMS value of the current is numerically equal to that value of constant (D.C.) current which when flows through a resistor for a certain time period produces the same amount of heat as is produced by the alternating current in the same time period for same resistor. Irms = Io/√2 = 0.707 I0 and Erms = Eo/√2 = 0.707 E0 19. Phase difference between the alternating current and alternating voltage:The potential difference across resistor remains in phase with the alternating current. The potential difference across inductor leads the alternating current with a phase angle π/2. The potential difference across capacitor lags behind the alternating current by a phase angle π/2. (a) Phasor diagram and a wave diagram for a resistor v =Vm sin ɷt1 and i = Im sin ɷt1 (b) Phasor diagram and a wave diagram for a inductor v =Vm sin ɷt1 and i = Im sin (ɷt1-π/2) (c) Phasor diagram and a wave diagram for a capacitor v =Vm sin ɷt1 and i = Im sin (ɷt1+π/2) 20. L-C-R series circuit:- 21. Impedance and reactance:- “The obstruction offered by the pure inductance or pure capacitance to the flow of a.c. which is frequency dependent and has the dimension of resistance but is not a source of power dissipation is called reactance.” “The obstruction offered by a circuit to the flow of a.c. that comprises of a frequency dependent component as well as frequency independent component is called impedance of the circuit. It has a dimension of resistance.” The SI unit of reactance and impedance is Ω. Reactance of an Inductor (or Inductive Reactance) XL = ѡL Reactance of a Capacitor (or Capacitive Reactance) XC = 1/ѡC Impedance of a series L-C-R circuit Z = √{(XL – XC)2 + R2} and voltage V = √{(VL – VC)2 + VR2} 22. Phasor diagram for a series L-C-R circuit with an a.c. source:- 23. Phase difference between voltage and current for a series L-C-R circuit: X XC V VC When the source frequency f >fr tan 1 L or tan 1 L R VR X XL V VL When the source frequency f<fr tan 1 C or tan 1 C R VR 24. Graphs of Reactance Vs frequency and Impedance Vs frequency for a.c. circuits:- 25. Graph of current Vs frequency for a series L-C-R circuit:- 26. Resonance in a series L-C-R circuit:“The a.c. current flowing in the series L-C-R circuit is maximum for a certain frequency of the a.c. source when the impedance of the circuit is minimum. This phenomenon is called resonance. And the corresponding frequency when the impedance is minimum is called the resonance frequency.” 27. The resonance frequency is:At resonance XL = XC Angular resonance frequency r 1 and resonance frequency f r 1 2 LC LC 28. Quality factor of series L-C-R circuit:The mathematical factor that is measure the sharpness of resonance of L-C-R circuit is called the quality factor of the series L-C-R circuit. The Q-factor of L-C-R circuit is defined as “the ratio of voltage drop across inductor (or capacitor) to the voltage drop resistor at resonance.” OR “the ratio of resonance frequency to the frequency band width of the resonant curve.” 1 L r L = = r R C 2 R 29. Power dissipation in a.c. circuit:The average power dissipation in a.c. circuit depends upon the phase difference between current and voltage. For pure inductive or capacitive circuit, where the phase difference between current and voltage is π/2, the average power dissipation is zero as for one half of the cycle the electrical energy is Q= transformed into magnetic/ electrostatic energy and in the next half cycle the magnetic energy/ electrostatic energy is retransformed into electrical energy. The power dissipation in an a.c. circuit is <P> = ErmsIrmscosϕ R The factor ‘cosϕ’ is called power factor. cos Z The power factor is maximum at resonance and is zero for pure capacitive or pure inductive circuit. 30. Watt-less current:- the component of current phasor that is at π/2 phase difference with the voltage is called watt-less current as it is not source of any power dissipation. The watt-less current is given by expression Irmscos ϕ 31. Transformer:It is a device used for converting low alternating voltage at high current into high voltage at low current and vice-versa. Principle: It works on the principle of mutual induction i.e. if two coils are inductively coupled and when current or magnetic flux is changed through one of the two coils, then induced emf is produced in the other coil. • According to Faradays law, the emf induced in secondary If the current in the secondary is very small The emf induced in primary As the primary has negligible resistance From equation (i) and (ii) Transformers are of two types:1. Step – up transformer The transformer having more number of turns in the secondary coil than primary coil (i.e.NS>NP) and used to convert low voltage at high current to high voltage at low current. 2. Step – down transformer The transformer having more number of turns in the primary coil than secondary coil (i.e.NS<NP) and used to convert high voltage at low current to low voltage at high current. Transformation Ratio:“The output to input voltage ratio of transformer is equal to the ratio of no. of turns in the secondary to the primary of transformer. This ratio is called the transformation ratio of the of the transformer.” vS N S = vP N P v I P Efficiency of Transformer:- η = s s 0 v p I p Pi 100% efficient transformer is called an ideal transformer as there is no energy loss in this transformer For an ideal transformer;a) The windings of transformer should have no resistance. b) The output of transformer should be in open circuit. c) There should be no flux leakage. d) There should be no hysteresis loss or any other loss. The various sources of energy loss in transformer are:1. Flux losses:- The coupling of the two coils of transformer is not perfect. As a result, whole of the magnetic flux linked to the primary coil can not be linked to the secondary coil. 2. Copper losses:- Some electrical energy is always converted into heat energy in the resistance of the copper wire used in the winding of the coil. 3. Iron losses:- The changing magnetic flux leads to production of induced emf in the iron core of the transformer which also leads to loss of some electric energy in the eddy current produced in the iron core. It is minimized using laminated iron core. It is prepared by joining two similar iron strips together after coating with varnish. As a single iron strip is very thin so its resistance becomes large which leads to production of very small eddy currents in it and in this way only a small amount of heat is produced in the core. 4. Hysteresis losses:- Due to alternating current flowing through the coil, the iron core is magnetised and demagnetised again and again. During each cycle of magnetisation and demagnetisation, some energy is lost due to Hysteresis. It can be minimized by selecting a material for iron core whose area of hysteresis loop is very small. 5. Humming losses:- Due to passage of AC current, the core of the transformer starts vibrating and produces humming sound in which some part of the electrical energy is lost in the form of sound. Uses of transformer:1. 2. 3. 4. Transformers are used for voltage regulators and stabilized power supplies. Small transformers are used in radio sets, televisions, telephones, loud speakers etc. A step-up transformer is used in the production of X-rays. A step-down transformer is used for obtaining large current for electric welding or in the induction furnace for melting metals. VERY SHORT ANSWER QUESTION S (1 marks) Q1. An electric lamp, connected in series with a capacitor and an a.c. source is glowing with certain brightness. How does the brightness of bulb changes on reducing the capacitance? Ans. On reducing the capacitance, capacitive reactance increases which reduce brightness of lamp. Q2. If the speed of rotation of armature is increased twice how would it affect the (a) maximum e.m.f produced (b) frequency of the e.m.f? (e=NBAω ;f=ω/2Π) A choke coil and a bulb are connected in series to a d.c. source. The bulb shines brightly. How does the brightness changes when an iron core is inserted in the choke coil? Ans. Q3. Ans. Brightness of bulb will not change because at steady d.c. , the choke coil has no inductive reactance. Q4. The current in the wire PQ is increasing. In which direction does the induced current flows in the current loop. Ans. Clockwise Q5. Give the direction in which the induced current flows in the wire loop, when the magnet moves towards it as shown in figure. P Q N S Ans. Clockwise when looked from magnet side of the loop. Q6. Why a transformer cannot be used to step up d.c. voltage? Ans. D.C. cannot produce varying field for secondary winding, therefore induced emf cannot be produced in it. Q7. What is the phase difference between the the voltage across an inductor and a capacitor in an a.c. circuit. Ans. 1800 Q8. Give the phase difference between applied a.c. voltage and current in a LCR circuit at resonance. Ans. 00 i.e. in phase Q9. What is the power consumed in (i) purely inductive and (II) purely capacitive a.c. circuits? Ans. Zero Q10. What is the power dissipation of an a.c. circuit in which voltage and current are given by : V = 300 sin (ωt –π/2) and I = 10 sin ωt ? Ans. Power in a.c. circuit is ,P = VI cosφ Here φ = π/2 and cosπ/2 = 0 Thus P = 0 Q11. In series LCR circuit, when voltage and current are in same phase? Ans. At resonance Q12. What is the power factor of an LCR series circuit at resonance. Ans. Unity. Q13. If number of turns of a solenoid is doubled, keeping the other factors constant, how does self inductance of the solenoid changes? Ans. As L α N2thus Lˈα 4 N2 Hence self inductance increases to four times. Q14. Ans. A plot of magnetic flux (φ) versus current is shown in figure for two inductors A & B. which of the two has larger value of self inductance? L = φ/I A B Φ For given I, A has larger value of φ, so A has larger self inductance. I Q15. Why is a.c. more dangerous than d.c. for same voltage? Ans. A.c. of same r.m.s. voltage as that of d.c. will have higher value of maximum voltage given as Vmax = √2 Vrms This increases the value of a.c. which makes it more dangerous. SHORT ANSWER QUESTION (2 or 3 marks) Q1. State faraday's laws of electromagnetic induction (EMI). Ans. 1stlaw: When magnetic flux linking with a coil changes, an e.m.f. is induced in the coil. This induced e.m.f. lasts so long as the change in magnetic flux continues. 2nd law: the magnitude of the induced e.m.f. produced in a coil is directly proportional to the rate of change of magnetic flux dφ/dt linked with it. I.e. I e I = dφ /dt Q2. State Lenz’s law. Show that this law follows the principle of conservation energy. Ans. Lenz’s law states that induced e.m.f. opposes the cause that produces this e.m.f. In the arrangement shown in the figure, direction of the induced current is such that it produces magnetic field which opposes the movement of magnet towards the coil. Deflection of Galvanometer indicates the presence of electrical energy. Some work has to be done to move the magnet which results into electrical energy. Electrical energy produced in the coil is basically due to the mechanical energy applied to move the magnet towards the coil. Hence Lenz’s law follows from the principle of energy conservation. Q3. How are eddy currents produced? Give two applications of eddy currents. Ans. Eddy current are circulating currents produced in a metal itself due to EMI when it is placed in changing magnetic flux in accordance with faradays laws of EMI. Eddy currents are useful in induction furnaces and dead beat galvanometer. Non-uniform magnetic field Eddy current Metal Q4. Define self-inductance. Write its unit. Give expression for self-inductance of a long solenoid having N turns. Ans. It is defined as the induced as the induced e.m.f. produced in the coil through which the rate of decrease of current is unity. OR It is defined as the magnetic flux linked with a coil when unit current flows through it. Its S.I. unit is henry. Self-inductance of long solenoid is given by L= μ0μrN2A/l . Q.5 Define mutual inductance. Write its S.I. unit. Give two factors on which the coefficient of mutual inductance between a pair of coils depends. Ans. Mutual induction of the two coils or circuits can be defined as the magnetic flux linked with the secondary coil due to the flow of unit current in the primary coil. Its S.I. unit is henry. It depends upon number of turns of both the coils, area of cross-section of primary coil and length of coil. Q.6 Draw a labeled diagram of a step down transformer. Mention two sources of energy loss in a transformer. Ans. Losses in a transformer are mainly because of (i) iron loss in the core of the transformer and (ii) copper loss i.e. I2R loss in windings of the transformer. Q7. How do R, XL and XC get affected when the frequency of applied AC is doubled? Ans: a) R remains unaffected b) XL=2πfL, so doubled c) XC=1/2πfC, so halved Q8. An electric lamp connected in series with a capacitor and an AC source is glowing with certain brightness. How does the brightness of the lamp change on reducing the capacitance? Ans: Brightness decreases. (As C decreases, XC increases. Hence Z increases and I decreases.) Q9. The peak value of an AC is 5A and its frequency is 60Hz. Find its rms value. How long will the current take to reach the peak value starting from zero? Ans: Irms= 3.5A . Time period T=(1/60)s . The current takes one fourth of the time period to reach the peak value starting from zero. t =T/4 =(1/240)s. Q10. Ans: Q11. Ans: Q12 Ans: When an AC source is connected to a capacitor with a dielectric slab between its plates, will The rms current increase or decrease or remain constant? The capacitance increases, decreasing the reactance Xc. Therefore the rms current increases. In an AC circuit V and I are given by V=100Sin100t volts and I= 100 Sin(100t+π/3)ma respectively. What is the power dissipated in the circuit? V0=100V I0=100A Ф= π/3 P=VrmsIrmsCos Ф=2500W The natural frequency of an LC circuit is 1,25,000 Hz. Then the capacitor C is replaced by another capacitor with a dielectric medium k, which decreases the frequency by 25 KHz. What is the value of k? υ1=1/2π√LC υ2=1/2π√kLC k=( υ1/ υ 2)2=(1.25)2=1.56. Q13.Obtain the resonant frequency and Q factor of a series LCR circuit with L= 3H, C= 27μF and R= 7.4 Ώ. Write two different ways to improve quality factor of a series LCR circuit Ans: Q=45,ω0=111rad/s Q14. An ac generator consists of a coil of 50 turns and an area of 2.5m2 rotating at an angular speed of 60 rad/s in a uniform magnetic field of B= 0.3T between two fixed pole pieces. The resistance of the circuit including that of the coil is 500Ώ (i) What is the maximum current drawn from the generator? (ii)What is the flux through the coil when current is zero? (iii)What is the flux when current is maximum? (4.5A, 375Wb, zero) Q15. For given a.c. circuit, distinguish among resistance, reactance and impedance. Ans. S.No. Resistance (R) Inductive Reactance (XL) Capacitive Reactance (XC) Impedance (Z) 1. It is opposition to the flow of any type of current. It opposes the flow of variable current. It opposes direct current. It is the total opposition offered to current (Due to resistance, inductive reactance and capacitive reactance.) 2. It is independent of frequency of source of supply. It depends directly on the frequency of source. It depends inversely on the frequency of source. It depends on the frequency of the source. 3. It is given by, It is given by It is given by It is given by, R = ρ I/a XL =2 πνL XC = 1/2 πνC Z = √[R2+(XL-XC)2] Long Answer Questions (5 Marks) Q.1.(a) Derive the phase relation between current and voltage for a series LCR circuit using phasor diagram. (b)Obtain the resonance frequency. Draw a plot showing the variation of the peak current (i0) with frequency of the a.c. source used. Ans.(a) Across resistance current and voltage are in same phase Across inductance the voltage leads current by 900 Across capacitance the voltage lags current by 900 Therefore V = √{(VL – VC)2 + VR2} V=I Z, VR= I R, VL= I XL , VC= I XC Z = √[R2+(XL-XC)2] XL XC R tan 1 I = V /Z (b) Clearly I will be maximum when Z is minimum. i.e. for electrical resonance (XL - XC) = 0 Or XL = XC i.e. ωL = 1/ωC i.e. ω = 1/√(LC), where ω is the angular frequency of the circuit. i.e. νm= 1/2π√(LC), Q.2. Ans. Draw a schematic diagram of a step-up transformer. Explain its working principle. Deduce the expression for the secondary to primary voltage in terms of the number of turns in the two coils. In an ideal transformer, how is this ratio related to the currents in the two coils? For figure refer to NCERT text book part 1 fig. 7.20. page no. 260. Principle : It is based on the principle of mutual induction. It is a phenomena of inducing e.m.f. in coil due to rate of change of current in near by coil. Primary e.m.f. Ep= -Npdφ/dt = VP ( Resistance of Primary is very small) Secondary e.m.f. Es = -Nsdφ/dt = VS (Resistance of Secondary is very high) Thus Es/Ep = Vs/Vp = Ns/Np In ideal transformer, input power = output power i.e.ipVp = isVs i.e. Us/Up=Ns/Np=is/ip NUMERICAL PROBLEMS Q1. Ans. The electric mains in a house are marked 220 V, 50 Hz. Write down the equation for instantaneous voltage. Given Vrms= 220 V and ν = 50 Hz V0 = √2 Vrms = 1.414 × 220 = 311 V And ω = 2πν = 2× 3.14 × 50 = 314 rad-1 Equation for instantaneous voltage, e = 311 sin 314 t Q2. An alternating voltage E = 200 sin 300 t is applied across a series combination of R = 10 Ω and an Inductor of 800 mH. Calculate (i) impedance of circuit (ii) peak value of current in circuit (iii) powerfactor of the circuit. Ans.(i) Impedance, Z = √(R2 + ω2 L2 ) Here ω = 300 rad-1 Z = √[102 + (300 × 0.8)2] On solving Z = 240.2 Ω (ii) peak value of current, I0 = E0/Z = 200/240.2 = 0.83 A (iii) Power factor, cosφ = R/Z = 10/ 240.2 = 0.042 Q3. A series LCR circuit with L = 5 H, C = 80 μF, R = 40 Ω is connected to a variable frequency source of 230 V (i) determine resonance frequency of the circuit (ii) obtain impedance of circuit and amplitude of current at resonance. Ans.Given :Vrms = 230 V (i) Resonance frequency, ω = 1/√(LC) = 1/ √(5 × 80 ×10-6) = 50 rad-1 (ii) At resonance, impedance ,Z = R = 40 Ω And Amplitude, I0 = V0/Z = (230 ×√2)/ 40 { V0 = Vrms√2} = 8.13 A Q4.The output voltage of an ideal transformer connected to a 240 V a.c. mains is 24 V. When this transformer is used to light a bulb with rating 24 V, 24 W. calculate current in primary coil of the circuit. Ans. Since V1/V2 = I2/I1 I1 = I2× V2/ V1 I2 = W/V2 = 24/24 = 1A Thus I1 = 1 × 24/240 = 0.1 A Q.5 Prove that the average power over a complete cycle of a.c. through an ideal inductor is zero. Ans. For inductor current lags voltage by 900 Average power over a full cycle, PL = average of PL Average of sin 2ωt for full cycle = <P>= < VI >=<VOSin ωt IO Cos ωt > 1 1 <P>= 2 0IO <2Sin ωt Cos ωt >=2 0 IO <Sin2 ωt > = 0 ( because <Sin2 ωt > = O) Previous year questions 1 mark questions 1. State Lenz’s law. A metallic rod horizontally along east-west direction is allowed to fall under gravity. Will there be an emf induced at its ends? Justify your answer. 2. Predict the direction of induced current in metal rings 1 and 2 when current I in the wire is steadily decreasing? 1 I 3. 4. 5. 6. 7. 2 How does the mutual inductance of a pair of coils change when (i) distance between the coils is increased and (ii) number of turns in the coils is increased? How can the self- inductance of a given coil having N number of turns area of cross-section A and length l be increased? Define self-inductance of a coil. Write its SI unit. Mention any two useful applications of eddy current A graph of magnetic flux (ø) versus current (I) is shown in the figure for two inductors A and B. Which of the two has larger value of selfinductance? 8. In the given figure a bar magnet is quickly moved towards a conducting loop having a capacitor. Predict the polarity of the plates A and B of the capacitor. S N 2 marks questions 9. A metallic rod of length L is rotated with angular frequency of ω with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius L about an axis passing through the centre and perpendicular to the plane of the ring. A constant and uniform magnetic field B parallel to the axis is presents everywhere. Deduce the expression for the emf between the centre and the metallic ring. 10. A current is induced in coil C1 due to the motion of current carrying coil C2. (i) Write any two ways by which a large deflection can be obtained in the galvanometer G. (ii) Suggest an alternative device to demonstrate the induced current in place of a galvanometer. 11. Predict the polarity of the capacitor in the situation described by adjoining figure. Explain the reason too. S N S N 12. Two identical loops one of copper and the other of aluminium are rotated with the same angular speed in the same magnetic field. Compare (i) the induced emf and (ii) The current produced in the two coils. Justify your answer. 13. (i) When primary coil P is moved towards secondary coil S (as shown in figure below) the galvanometer shows momentary deflection. What can be done to have larger deflection in the galvanometer with the same battery?(ii) State the related law. S P 14. A coil B is connected to low voltage bulb B and placed near another coil A as shown in the figure. Give reasons to explain the following observations (i) The bulb B lights (ii) Bulb gets dimmer if the coil Q is moved towards left. 15. A conducting rod of length l is moved in a magnetic field of magnitude B with velocity v such that the arrangement is mutually perpendicular. Prove that the emf induced in the rod is || = Blv. 16. A rectangular coil of area A having number of turns N is rotated at f revolutions per second in a uniform magnetic field B the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2πfNBA. 17. An alternating voltage given by V = 70 sin 100 πt is connected across a pure resistor 25 Ω. Find (i) the frequency of the source (ii) the rms current through the resistor. 18. i) The graphs (I) and (II) represent the variation of the opposition offered by the circuit element to the flow of alternating current with frequency of the applied emf corresponding to each graph. (ii) Write the expression for the impedance Offered by the series combination of the above two elements connected across the AC source. Which will be ahead in phase in this circuit voltage or current? O Frequency (I) O Frequency (II) 3 marks questions 19. (i) State faraday’s law of electromagnetic induction. (ii) A jet plane is travelling towards west at a speed of 1800 km/h. what is the voltage difference developed between the ends of the wing having a span of 25m if the earth’s magnetic field at the location has magnitude of 5x10-4 T and the dip angle is 30o? 20. (i) State the law that gives the polarity of the induced emf. (ii) A 1.5 μF capacitor is connected to 220 V , 50 Hz source. Find the capacitive reactance and the rms current. 21. A coil of number of turns N area A is rotated at a constant speed ω in a uniform magnetic field B and connected to a resistor R. Deduce expressions for (i) maximum emf induced in the coil (ii) power dissipation in the coil. 22. An AC voltage V = Vo sin ωt is applied across a pure inductor L. Obtain an expression for the current I in the circuit and hence obtain the (i) inductive reactance of the circuit and (ii) the phase of the current flowing with respect to the applied voltage. 23. An AC voltage V = Vo sin ωt is applied across a pure capacitor C. Obtain an expression for the current I in the circuit and hence obtain the (i) capacitive reactance of the circuit and (ii) the phase of the current flowing with respect to the applied voltage. 5 marks questions 24. State Faraday’s law of electromagnetic induction. Figure shows a rectangular conductor PQRS in which the conductor PQ is free to move in a uniform magnetic field B perpendicular to the plane of paper. The field extends from x=0 to x=b and is zero for x > b. Assume that only the arm PQ possesses resistance r. When the arm PQ is pulled outward from x = 0 to x = 2b and is then moved backward to x = 0 with constant speed v obtain the expression for the flux and the induced emf. Sketch the variation of these quantities with distance 0 ≤ x ≤ 2b. (All India 2010) ● S ● ● ● ● ● ● P ● ● ● ● ● ● ● Q● ● R● ● ● X=0 x=b x = 2b 25. (i)State Lenz’s law. Give one example to illustrate this law. The Lenz’s law is a consequence of the principle of conservation of energy. Justify this statement. (ii) Deduce an expression for the mutual induction of two long coaxial solenoids but having different radii and different number of turns. 26. (i) What are eddy currents? Write their two applications. (ii) Figure shows a rectangular conducting loop PQR in which arm RS of length l is movable. The loop is kept in a uniform magnetic field B directed downward perpendicular to the plane of loop. The arm RS is moved with a uniform speed v. Deduce an expression for (a) the emf induced across the arm RS (b) the external force required to move the arm and (c) the power dissipated as heat. ELECTROMAGNETIC WAVES 1. Concept of displacement current Displacement current is that current which appears in a region in which the electric field (and hence electric flux) is changing with time. Note- We have ID = ε0 dΦ/dt = ε0d(EA) /dt = ε0d[(q/ ε0A)A] /dt = dq /dt = I 2. Modified Ampere’s circuital Law ∮B.dl = µ0 (I + ε0 dΦ/dt ) 3. Learn only one order either increasing wavelength or frequency .other calculated by c= ν λ ,velocity of light c=3x108m/s S.No Name Frequency Wavelengt Production Uses . h Range (Hz) Range 1. Gamma rays 1019 – 1023 10-11 to 1014 m Emitted by radioactive nuclei, Produced in nuclear reaction In medicine, to destroy cancer cells. 2. X – rays 1016 - 1020 10-8 to 1012 m 3. Ultraviolet rays 1015 – 1017 (4 × 10-7 to Produced by special lamps & 6 × 10-10) m very hot bodies (sun). For eye surgery, to kill germs in water purifiers. 4. Visible rays 4 × 1014 – 7 × 1014 700 – 400 nm Jumping of electrons in higher orbits Provide us information about the world. 5. Infrared rays (heat waves) 1012 - 1014 1mm - 700 nm Produced by hot bodies and molecules. Infrared detectors used in earth satellite, used in green house to keep plants warm. 6. microwave s 1010 - 1012 0.1 – 1 mm Produced by special vacuum tubes (klystrons, gun diode & magnetrons) Microwave oven, for radar system in aircraft navigation. 7. Radio waves 10 - 109 > 0.1 m Produced by accelerated motion of charges in conducting wires. In radio & television communication system, in cellular phones to transmit voice communication. Generated by bombarding a metal target by high energy electron Question Answer related to this topic Used as diagnostic tool in medicine, to study crystal structures Q.1 What is the ratio of speed of infrared rays and ultra violet rays in vacuum? (1 mark) 1:1 Q.2 Write the following radiations in ascending order in respect of their frequencies X-ray, microwaves, radio waves. (1 mark) radio wave, microwave , X-ray. Q.3 Name the electromagnetic radiation to which waves of wavelength in the range 10-2 m belong. Give one use of this part of Em spectrum. (1 mark) Infrared, used in remote control. Q.4 Which part of the electromagnetic spectrum has the largest penetrating power? (1 mark) Gama rays Q.5 Give a reason to show that microwaves are better carrier of signal for long range transmission. (1 mark) As high frequency wave reduces size of transmitting antenna. Q.6 Name the EM waves used for studying crystal structure of solids. (1 mark) X-rays Q.7 Name the EM waves used for treatment of cancer tumors. mark) (1 Y-rays Q.8 Name the electromagnetic radiation used for viewing objects through haze and fog. (1 mark) I.R. Q.9 Identify the electromagnetic radiations as given : frequency = 1020 HZ. (1 mark) X – rays Q.10 Write the expression for the velocity of e.m. waves in terms of permittivity and permeability. (1 mark) Q.11 Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave propagating along z-direction. (2 marks) Q.12 The oscillating magnetic field in a plane electromagnetic wave is given by B Y=8 x 106 sin(20 x 1011t + 300πx)T. Calculate the wavelength of e.m. wave. Write down the expression for oscillating electric field. (2 marks) As B = Bo sin(wt + bx) BY = 8 x 10-6 sin(2 x 1011t + 300πx) ω = 2 x 1011rad/s and K = 300π = 2π/λ λ = 2π/300 = 1/150m = 0.006m EZ = E0 sin(wt + kx) Where E0 = CBO = 3 x 108 x 8 x 10-6 = 2400N/C EZ = 2400 sin(2 x 1011t + 300πx) Q.13 The oscillating electric field of an electromagnetic wave is given by E Y=30 sin(2 x 1011t + 300πx) Vm-1. Find the dirn of propagation of wave and write down the expression for magnetic field ? (2 marks) EY = 30 sin(21 x 1011t + 300πx) Comparing with EY = E0 sin(wt + kx) dirn of propagation is –x direction & BZ = B0 sin( 2 x 1011t + 300πx) Where B0 = E0/C = 10-7 T Q.14 Find the wave length of e.m. waves of frequency 5 x 1019 Hz. Give its two applications. (2 marks) Gamma rays, use (i) To detect flaws in metal castings (ii) Medicinal uses Q.15 Mention four properties of em waves. (2 marks) (i) They are produced by accelerating or oscillating charge. (ii) They do not require material medium for propagation. (iii) They follow the law of super position. (iv) They propagate with speed of light in vacuum irrespective of their wavelength. Q.16 Why are infrared radiations referred to as heat waves also? Name the radiations which are next to these radiations in spectrum having (i) shorter wavelength and (ii) longer wavelength. (2 marks) I.R. waves get produced by molecules of hot bodies. (i) Visible (ii) Microwaves. Q.17 From the following, identify the e.m. waves having (i) maximum (ii) Minimum frequency. (2 marks) (a) Radio waves (b)Gamma rays (c)Visible light (d)Microwaves (e)U.V.rays (f)I.R.rays Maximum frequency – Gamma rays Minimum frequency – Radio waves Q.18 Electromagnetic radiations with wavelength (i) λ1 are used to kill germs in water (ii) λ2 are used in T.V communication (iii) λ2 plays an important role in maintaining the earth’s warmth. purifiers system Name the part of e.m. spectrum to which these radiation belong. Arrange these radiation in decreasing order of wavelength. (2 marks) (i) U.V. (ii) Radio waves (iii) I.R radiation Radio waves I.R, U.V. Q.19 Draw a sketch of a plane e.m. wave propagating along x axis. Depict clearly the directions of electric and magnetic field varying sinusoidally. (2 marks) Q.20 Arrange the following electromagnetic radiation in ascending order of their frequencies. (a)Microwaves (b)Radio waves (c)X-rays (d) Gamma rays Write two uses any one of this. (2 marks) (R M I V U X Y) Radio wave , micro wave , x rays, gamma rays Uses – X-rays (i) radiography (ii) Crystal structure Q.21 The magnitude of magnetic field in a plane e.m. wave is given as BX=0, BY=2 x107 sin(0.5 x 103 x + 1.5 x 1011t)T. (3 marks) (a) Determine the wavelength (b) Write an expression for the electric field. BY = BO sin (1.5 x 1011t + 0.5 x 103x)T BO = 2 x 10-7 T, ω = 2πν = 1.5 x 1011 ω = 1.5 x 1011 K = 0.5 x 103 ⇒ and frequency of wave. EX = 0 , EY = 0, EZ = CBO sin (1.5 x 1011t + 0.5 x 103x) EZ = 60 sin (1.5x 1011t + 0.5 x 103x) Q.22 Identify the following e.m. radiation as per wave length given below. Write one application of each. (3marks) -3 -3 (i)10 nm (ii)10 m (iii)1nm (i) Infrared – used in remotes (ii) Microwave – used in Radar (iii) U.V. rays – In water purifier. Q.23 Give two uses each of (i) radio waves (ii) Microwaves. (3 marks) Radio waves – used in (a) Cellular phones communication (b) T.V. communication Microwaves – used in (a) RADAR (b) Microwave ovens Q.24 Identify the following electromagnetic radiations as given below Write one application of each ? (3 marks) (a) 1nm (b)10-12m (c)10-8m (a) U.V rays – In water purifier. (b) γ rays – medicinal use (c) X rays – studying crystal structure Q.25 Name the constituent radiation of e.m. spectrum which (i) is used in satellite communication (ii) is used for studying crystal structure (iii) is similar to radiation emitted during decay of nuclei (iv) has wavelength b/w 390nm and 770nm (v) is absorbed from sunlight by ozone layer (vi) produces intense heating effect (i) Radio wave (ii) X – ray (iii) Γ – ray (iv) Visible (v) U.V.ray (vi) I.R.rays Q.26 Name the following constituent radiation of electromagnetic radiation which is suitable for (a) Radar system used in aircraft navigation (b) Treatment of cancer tumors Write two application of each of them. (3 marks) (a) Microwaves – Uses in automobiles as speed determination microwave ovens. (b) γ-rays uses (i) To detect flaws in metal (ii) Sterilization castings Q.27 A plane electromagnetic wave of frequency 25MHz travels in free space along the xdirection at a particular point in space and time time. (3 marks) Q.28 . Determine the at this Write the order of frequency range and one use each of the following e.m. radiation (i) Micro waves (ii) U.V rays (iii) Gamma rays ? (3 marks) (i) 1010Hz use :- Micro wave ovens (ii) 1015Hz use :- In water purifier (iii) 1022Hz use :- Medicinal use Q.29 The electric field of plane an wave is given Ex=0 , Ey=0, Ez=0.5cos{2π x 108(t-4c)} (i) What is dirn of propagation of wave? (ii) Compute the components of magnetic fields. (3 marks) (i) dirn = xdirn/x-axis (ii) Bx = 0 , By = Bo cos{2π x 108(t-x/c)} T Bz = 0 Where Bo = 0.5 x 3 x 108 T Q.30 Value based questions 1. A woman and her daughter of class XII in KV were in the kitchen, preparing a feast for visitors using the new microwave oven purchased last evening. Suddenly, the daughter noticed sparks inside the oven and unplugs the connection after switching it off. She found that inside the microwave oven a metallic container had been kept to cook vegetable. She informs her mother that no metallic object must be used while cooking in microwave oven and explains the reasons for the same. a) What attitude of the daughter inspires you? b) Give another use of a microwave oven c) The frequency of microwave is 3 x 1011 Hz. Calculate its wavelength. ANS:a) Presence of mind, Knowledge of subject; b) Used in telecommunication; & c) λ= ʋ /c = (3 x 1011))/ (3 x 108). = 10-3.m 2. Two persons were playing and one of them got injured as he fell from the top of a tree. He was taken to the Hospital where, he was admitted for a fracture after X-ray. The boy’s mother, who on hearing the above incident rushed to the hospital, was worried and restless; the other boy consoled her and the doctor who, overheard them, informed her about the latest developments in the Medicine field and assured a speedy recovery of her son. a) How would you rate the qualities of the boy who consoled his friend’s mother? b) How X-ray is produced? c) Mention the fields where X-ray is used. (ANS: caring for others, giving timely assistance, positive attitude; b) & c) Refer NCERT Text book) 3. Gopal visits his friend Naresh. In his house Naresh was playing with his kid sister and in spite of the broad day light, Gopal notices the tube light burning and advises him to save electricity; He also claims that the heat inside the room increases which would lead to global warming. a) What are the values associated with the decision saving electricity? b) Which electromagnetic wave is responsible for increase in the average temperature of the earth? Give other applications of the electromagnetic wave. ANS: a) concern for society/nation, awareness about global warming, c) Infrared waves; applications- to treat muscular strain, solar water heaters & cookers) 4. Two friends were passing through the market. They saw two welders using the welding machine. One welder was using the goggles face mask with window in order to protect his face. The other one was welding with naked eyes. They went to the welder who was not using face mask and explained him the advantages of using goggles and face masks. Next day, the welder bought asset of goggles and began to do his work fearlessly. a. What values were displaced by two friends? b. Why do welders wear glass goggles or face masks with glass windows while carrying out welding? Ans- a. Knowledge, creating awareness and social responsibilities. b. Welder wear special glass goggles or face mask with glass windows to protect their eyes from large amount of harmful UV radiation produced by welding arc. 5. Many people like to watch CID programme on a TV channel. In this programme, a murder mystery is shown. This murder mystery is solved by CID team. Each member of the team works with full dedication. They collect information and evidences from all possible sources and then tend to lead the correct conclusion. Sometimes they also use ultraviolet rays in the forensic laboratory. Some people get surprised to know the advantages of ultraviolet rays because they only aware of the fact that ultraviolet rays coming from the sun produce harmful effects. a. What values were displayed by the members of CID team? b. What is the use of ultraviolet rays in forensic laboratory? Ans. (a). Team spirit, sense of responsibilities and,(b). UV rays are used in the detection of forged documents, finger prints, etc RAY OPTICS AND OPTICAL INSTRUMENTS GIST OF THE LESSON Light is a form of energy that gives sense of vision to our eyes. Light waves are electromagnetic waves, whose nature is transverse. The speed of light in vacuum is 3 x 108mls but it is different in different media. The speed and wavelength of light change when it travels from one medium to another but its frequency remains unchanged. Reflection of Light The ray of light is turned back into the same medium on striking a highly polished surface such as a mirror, this phenomenon is called reflection of light. Laws of Reflection There are two laws of reflection. (i) The angle of incidence (i) is always equal to the angle of reflection (r). (ii) The incident ray, the reflected ray and the normal at the point of incidence all three lie in the same plane. Different properties of image formed by plane mirror Size of image = Size of object Magnification = Unity Distance of image = Distance of object A plane mirror may form a virtual image. A man may see his full image in a mirror of half height of man. To see complete wall behind himself a person requires a plane mirror of at least one third the height of wall. It should be noted that person is standing in the middle of the room. Sign Convention for Spherical Mirrors 1. All distances are measured from the pole of the mirror. 2. Distances measured in the direction of incident light rays are taken as positive. 3. Distances measured in opposite direction to the incident light rays are taken as negative. 4. Distances measured above the principal axis are positive. 5. Distances measured below the principal axis are negative. Focal length of spherical mirrors Rays parallel to principal axis after reflection from a concave/ convex mirror meet at a point or appear to diverge from a point on principal axis called focus. Focal Length The distance between the pole and focus is called focal length (f). Relation between focal length and radius of curvature is given by f = r/2 Image formation by a spherical mirror: (i) The ray from the point which is parallel to the principal axis. The reflected ray goes through the focus of the mirror. (ii) The ray passing through the centre of curvature of a concave mirror or appearing to pass through it for a convex mirror. The reflected ray simply retraces the path. (iii) The ray passing through (or directed towards) the focus of the concave mirror or appearing to pass through (or directed towards) the focus of a convex mirror. The reflected ray is parallel to the principal axis. (iv) The ray incident at any angle at the pole. The reflected ray follows laws of reflection. The mirror equation Mirror formula is the relationship between object distance (u), image distance (v) and focal length. 1 1 1 = + f v u Linear Magnification The ratio of height of image (I) formed by a mirror to the height of the object (O) is called linear magnification (m). Linear magnification (m) = I/O = -v/u Refraction of Light The deviation of light rays from its path when it travels from one transparent medium to another transparent medium is called refraction of light. Snell experimentally obtained the following laws of refraction: (i) The incident ray, the refracted ray and the normal to the interface at the point of incidence, all lie in the same plane. (ii) The ratio of the sine of the angle of incidence to the sine of angle of refraction is constant. sin i n21 = sin r where n21 is a constant, called the refractive index of the second medium with respect to the first medium . If n21 is the refractive index of medium 2 with respect to medium 1 and n12 the refractive index of medium 1 with respect to medium 2,then it should be clear that 1 n21 = n12 Refractive Index: The ratio of speed of light in c vacuum (c) to the speed of light in any medium (u) is called refractive index of the medium . n21 = v The refraction of light through the atmosphere is responsible for many interesting phenomena. The sun is visible a little before the actual sunrise and until a little after the actual sunset due to refraction of light through the atmosphere. Refraction by the atmosphere makes the sun oval. Twinkling of stars is caused by the passing of light through different layers of a turbulent atmosphere. Critical Angle The angle of incidence in a denser medium for which the angle of refraction in rarer medium becomes 90°. is called critical angle (C). Critical angle for glass = 42° Critical angle for water = 48° Critical angle increases with temperature Total Internal Reflection (TIR) When a light ray travelling from a denser medium towards a rarer medium is incident at the interface at an angle of incidence greater than critical angle, then light rays reflected back in to the denser medium. This phenomenon is called TIR. Conditions necessary for TIR Total internal reflection occurs if angle of incidence in denser medium exceeds critical angle. a ray of light enters from a denser medium to a rarer medium. Relation between critical angle and refractive index 1 n12 = sin C. Total internal reflection in nature and its technological applications MIRAGE (a) A tree is seen by an observer at its place when the air above the ground is at uniform temperature, (b) When the layers of air close to the ground have varying temperature with hottest layers near the ground, light from a distant tree may undergo total internal reflection, and the apparent image of the tree may create an illusion to the observer that the tree is near a pool of water. Prisms designed to bend rays by90º and 180º or to invert image without changing its size make use of total internal reflection Optical fibres Optical fibres are fabricated with high quality composite glass/quartz fibres. Each fibre consists of a core and cladding. The refractive index of the material of the core is higher than that of the cladding. Optical fibres are extensively used for transmitting and receiving electrical signals which converted to light by suitable transducers. Optical fibres can also be used for transmission of optical signals. For example, these are used as a ‘light pipe’ to facilitate visual examination of internal organ like esophagus, stomach and intestines. It is available in decorative lamp with fine plastic fibres with their free ends forming a fountain like structure. REFRACTION AT SPHERICAL SURFACES: n2 n1 n2 − n1 − = v u R Refraction through a lens 1 n2 1 1 [ = ( − 1) ( − )] f n1 R1 R 2 Magnification (m) produced by a lens is defined, as the ratio of the size of the image to that of the object. When we apply the sign convention, we see that, for erect (and virtual) image formed by a convex or concave lens, m is positive, while for an inverted (and real) image, m is negative. Linear magnification (m) = I/O = v/u Power of a lens The power P of a lens is defined as the tangent of the angle by which it converges or diverges a beam of light falling at unit distant from the optical centre. 1 tan δ = f 1 P= f The SI unit for power of a lens is dioptre (D): 1D = 1m–1. The power of a lens of focal length of 1 metre is one dioptre. Power of a lens is positive for a converging lens and negative for a diverging lens Combination of thin lenses in contact: Two lenses A and B of focal length f1 and f2 placed in contact with each other. The effective focal length f of their combination is given by 1 1 1 = + f f1 f2 The effective power P of their combination is given by P = P1 + P2 The total magnification m of the combination is m = m1 × m2 If lens of refractive index n2 is placed in a medium of refractive index n1. A convex lens will behave as convex if n2> n1 A concave lens will behave as concave if n2> n1 A convex lens will behave as concave if n2 < n1 A concave lens will behave as convex if n2 < n1 A convex lens will behave as plane glass sheet if n2 = n1( no refraction will occur) A concave lens will behave as plane glass sheet if n2 = n1( no refraction will occur) Refraction through prism Prism is uniform transparent medium bounded between two refracting surfaces, inclined at an angle. Angle of Deviation The angle sub tended between the direction of incident light ray and emergent light ray from a prism is called angle of deviation (δ). Prism Formula A+δm ⌈n21 = sin ( 2 A sin 2 ) ⌉ DISPERSION BY A PRISM When a narrow beam of sunlight, usually called white light, is incident on a glass prism, the emergent light is seen to be consisting of several colours violet, indigo, blue, green, yellow, orange and red (given by the acronym VIBGYOR). The red light bends the least, while the violet light bends the most. The phenomenon of splitting of light into its component colours is known as dispersion. The pattern of colour components of light is called the spectrum of light. Red light is at the long wavelength end (~700 nm) while the violet light is at the short wavelength end (~ 400 nm). Dispersion takes place because the refractive index of medium for different wavelengths (colours) is different. Red light travels faster than violet light in a glass prism. Scattering of light Blue colour of sky: As sunlight travels through the earth’s atmosphere, it gets scattered (changes its direction) by the atmospheric particles. Light of shorter wavelengths is scattered much more than light of longer wavelengths. The amount of scattering is inversely proportional to the fourth power of the wavelength. This is known as Rayleigh scattering. Hence, the bluish colour predominates in a clear sky, since blue has a shorter wavelength than red and is scattered much more strongly. Clouds are generally white Clouds have droplets of water with a >> λ large scattering objects (for example, raindrops, large dust or ice) all wavelengths are scattered nearly equally. Hence clouds are generally white Reddish appearance of the sun and full moon near the horizon. At sunset or sunrise, the sun’s rays have to pass through a larger distance in the atmosphere Most of the blue and other shorter wavelengths are removed by scattering. The least scattered light reaching our eyes, therefore, the sun looks reddish. Optical instruments Simple Microscope It is used for observing magnified images of objects. It is consists of a converging lens of small focal length. Magnifying Power (i) When final image is formed at least distance of distinct vision (d) then = 1+ where, f= focal length of the lens. (ii) When final image is formed at infinity, then M = d/f Compound Microscope It is a combination of two convex lenses called objective lens and eye piece separated by a distance. Both lenses are of small focal lengths but fo < fe, where fo and fe are focal lengths of objective lens and eye piece respectively. Astronomical(refracting telescope) Telescope The telescope is used to provide angular magnification of distant objects. It also has an objective and an eyepiece. But here, the objective has a large focal length and a much larger aperture than the eyepiece. Magnifying power When final image is formed at infinity, = Length of telescope tube is = 0 + Aberration of Lenses The image formed by the lens suffer from following two drawbacks (i) Spherical Aberration Aberration of the lens due to which the rays passes through the lens are not focussed at a single and the image of a point object placed on the axis is blurred called spherical aberration. (ii) Chromatic Aberration Image of a white object formed by lens is usually coloured and blurred. This defect of the image produced by lens is called chromatic aberration. Reflecting telescope Telescopes with mirror objectives are called reflecting telescopes. They have several advantages. First, there is no chromatic aberration in a mirror. Second, if a parabolic reflecting surface is chosen, spherical aberration is also removed. WAVE OPTICS Wavefront: A wave front is the locus of points having the same phase of oscillation. Rays are the lines perpendicular to the wavefront, which show the direction of propagation of energy. The time taken for light to travel from one wavefront to another is the same along any ray. Huygens’ Principle. According to Huygens’ (a) Each point on the given wave front (called primary wave front) acts as a fresh source of new disturbance, called secondary wavelet, which travels in all directions with the velocity of light in the medium (b) A surface touching these secondary wavelets, tangentially in the forward direction at any instant gives the new wavefront at that instant. This is called secondary wave front. Doppler effect Doppler effect is the shift in frequency of light when there is a relative motion between the source and the observer. The effect can be used to measure the speed of an approaching or receding object. = 0 Coherent and Incoherent Addition of Waves. Two sources are coherent if they have the same frequency and a stable phase difference. Two sodium lamps illuminating two pinholes we will not observe any interference fringes. This is because of the fact that the light wave emitted from an ordinary source (like a sodium lamp) undergoes abrupt phase changes in times of the order of 10–10 seconds. Thus the light waves coming out from two independent sources of light will not have any fixed phase relationship and would be incoherent, The interference term averaged over many cycles is zero if (a) The sources have different frequencies; or (b) The sources have the same frequency but no stable phase difference. Diffraction Diffraction refers to light spreading out from narrow holes and slits, and bending around corners and obstacles. Different parts of the wavefront at the slit act as secondary sources: diffraction pattern is the result of interference of waves from these sources. Diffraction is a general characteristic exhibited by all types of waves, be it sound waves, light waves, water waves or matter waves. Since the wavelength of light is much smaller than the dimensions of most obstacles; we do not encounter diffraction effects of light in everyday observations. Resolving Power The ability of an optical instrument to produce separate and clear images of two nearby objects, is called its resolving power Limit of Resolution The minimum distance between two nearby objects which can be just resolved by the instrument, is called its limit of resolution (d). Resolving power of a microscope = 1/d = 2 n sin θ / λ Where, d = limit of resolution, λ = wavelength of light used. μ = refractive index of the medium between the objects and objective lens and θ = half of the cone angle. Resolving power of a telescope = 1/dθ = d/1.22 λ where, dθ = limit of resolution, A = wavelength of light used and d = diameter of aperture of objective Polarisation: The phenomenon of restricting the vibrations of light in a particular direction, perpendicular to direction of wave motion is called polarisation The plane ABCD in which vibrations are present is called plane of vibration and plane EFGH which is perpendicular to plane of vibration is called plane of polarization. Law of Malus: When a beam of completely plane polarized is incident on an analyser, the resultant intensity of light transmitted through the analyser is given by = 0 2 θ where θ is the angle between plane of transmission of analyser and polarizer. Polarisation by scattering: Polarisation of the blue scattered light from the sky.The incident sunlight is unpolarised (dots and arrows). A typical molecule is shown. It scatters light by 90º polarised normal to the plane of the paper (dots only). Polarisation by reflection: When unpolarised light is incident on the boundary between two transparent media, the reflected light is polarised with its electric vector perpendicular to the plane of incidence when the refracted and reflected rays make a right angle with each other. The angle of incidence in this case is called Brewster’s angle and is denoted by ip. We can see that ip is related to the refractive index of the denser medium. Since we have ip+r = π/2, we get from Snell’s law 21 = if i=ip r = 90-ip 21 = (90 − ) = 21 = tan (BREWESTER’S LAW) IMPORTANTDERIVATIONS Mirror formula. The figure shows an object AB at a distance u from the pole of a concave mirror. The image A1B1 is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram. But ED = AB From equations (1) and (2) If D is very close to P then EF = PF But PC = R, PB = u, PB1 = v, PF = f By sign convention PC = -R, PB = -u, PF = -f and PB1 = -v Equation (3) can be written as R= 2 f Dividing equation (4) throughout by uvf we get Relation between critical angle and refracive index of the medium. Ray of light is travelling from denser(water) to rarer (air)medium. According to Snells law 12 = If angle of incidence i =C Then r= 900 1 12 = ⌊21 = ⌋ 90 Refraction at spherical surface O : Point object, OP = u = Object Distance P : Pole, C : centre of curvature, PC = R = Radius of curvature I : Point Image, PI = v = Image distance i, r, α, β and γ are small enough for sin i= i= tan i to hold . n1 and n2 refractive indices of rarer & denser media (with respect to vacuum or air as incidence medium) ; 2 1 2 = = = 1 21 = 21 1 = 2 In triangle MOC = + In triangle MCI = + 1 ( + ) = 2 ( − ) _______________________(1) Where = , = and = Substituting values of α, β and γ in eq. (1) 1 ( + ) = 2 ( − )_____________________(2) Where PO = - u, PI = -v and PC = R Substituting these values in eq.(2) 2 1 2 − 1 ⌈ − = ⌉ Lens Makers formula for a thin convex lens Consider a convex lens (or concave lens) of absolute refractive index n 2 to be placed in a rarer medium of absolute refractive index n1. Considering the refraction of a point object on the surface the image is formed at I1 which is at a distance ′ and object distance is u. CI1= P1I1 = ′ (as the lens is thin) CC1 = P1C1 = R1 CO = P1O = u It follows from the refraction due to convex spherical surface XP1Y 2 ′ − 1 = 2 −1 1 ____________________________(1) The refracted ray from A suffers a second refraction on the surface XP2Y and emerges along BI. Here the object distance is ′ and image distance is Therefore I is the final real image of O. CI1= P2I1 = ′ (as the lens is thin) CC2 = P2C2 = R2 CI = P2I = 1 − 2′ = 1 −2 2 ______________________________(2) Adding (1) & (2) 1 − 1 1 1 = (2 − 1 ) ( − ) ____________________(3) 1 1 1 2 1 But = − 1 1 1 Hence[ = (2 − 1) ( − )] 1 1 2 XP1Y, Refraction through prism The passage of light incident from air into a glass prism is deviated due to refraction occurring twice, once at the boundary separating air-class and next at the boundary separating glass-air as shown in fig According to Snells Law 21 = _________________(1) In cyclic quadrilateral ALOM A + LOM = 180º ___________________________(2) From the triangle LOM r1 + r + LOM = 180º _____________________(3) Hence A = 2r ⌈ = 2 ⌉ __________________(4) Comparing these two equations, we get 1 + 2 = In minimum deviation position r1 = r = r ⌈ = 2 ⌉________________________________(5) The total deviation δ is the sum of deviations at the two faces, δ = (i – r1 ) + (e – r ) that is, δ =i + e – A In minimum deviation position = & i = e Hence = 2i –A + =( 2 )_________________________________(6) Substituting values of i and r in eq. (1) + ⌈21 = ( 2 2 ) ⌉ HUYGENS PRINCIPLE Each point of the wave front is the source of a secondary disturbance and the wavelets emanating from these points spread out in all direction with the speed of wave. These wavelets are referred to as secondary wavelets. The common tangent to the secondary wavelets gives new position of wave front at a later time. Reflection on the basis of Wave Theory Let t be the time in which the incident wave front reach from Q to P’ in the same time the reflected wave front starting from P reaches Q’ QP’=PQ’=v t In triangle PQP’ and triangle PQ’P’ Angle PQP’= Angle PQ’P’= 90 PP’ is the common side QP’=PQ’=v t Triangle PQP’≈ Triangle PQ’P’ AngleQPP’ = AngleQ’PP’ i = r Refraction on the basis of wave theory Let t be the time in which the incident wave front reach from Q to P’ in the same time the refracted wave front starting from P reaches Q’ such that QP’=C1t and PQ’=C2t In triangle PQP’ = In triangle ′ 1 = _________(1) ′ ′ = ′ 12 = __________(2) ′ ′ Hence from eq. (1) and (2) [ 1 2 = = = 21 ] 2 1 INTERFERENCE OF LIGHT CONDITION FORCONSTRUCTIVE AND DESTRUCTIVE INTERFERENCE OF LIGHT Let the waves from two coherent source of light be represented by 1 = __________________(1) 2 = ( + ∅)______________(2) According to principal of superposition, resultant displacement is given by y = y1 + y2 = a[ + ( + ∅] = 2 a cos∅ cos (ωt + ∅/2) The amplitude of the resultant displacement is 2a cos (∅/2) and therefore the intensity at that point will be = 42 2 ∅ /2) = 4I0 ∅ /2)_________________(3) Where ∅ = 0, ±2, ±4 … … ..corresponds to constructive interference leading to maximum intensity. Hence condition for constructive interference ∅ = 2_____________(4) Where ∅ = ±, ±3 … … ..corresponds to destructive interference leading to minimum intensity. (2+1) Hence condition for destructive interference ∅ = _________(5) 2 Young’s double slit experiment and fringe width Light from the two coherent sources (S1&S2) superimpose to produce interference pattern on the screen placed at a distance D from the plane of the slit. The intensity of light reaching at P depends on path difference between the waves reaching at the point. The path difference between the waves reaching at P = 2 − 1 2 2 (2 )2 − (1 )2 = 2 + ( + ) − 2 − ( − ) = 2 2 2 2 − 1 = 2 2 = 2 + 1 2 path difference ∆ = = = for constructive interference = , , , … …position of bright band path difference ∆ = = (+) = (2+1) 2 for destructive interference = , , … …position of dark band Distance between two consecutive dark bands or two consecutive bright bands is called fringe width (β). = − − = Diffraction at single slit The phenomenon of bending of light around the corners of an obstacles or aperture. Condition for Diffraction – The size of obstacle or aperture should be of the order of the wavelength of thelight. Condition for secondary Minima asinθn = nλ a -Size of aperture, n –order of minima, λ –wavelength of light used. Condition for secondary Maxima – asinθn = (2n +1)λ/2 a -Size of aperture, n –order of minima, λ –wavelength of light used. Width of fringes = β = Dλ/a Width of central Bright fringe = 2 β = 2 Dλ/a QUESTIONS 1Mark Questions 1. Write the relation between angle of incidence I, angle of prism A and angle of minimum deviation for a glass prism. Ans: 2i = A + 2. A concave mirror, of aperture 4cm, has a point object placed on its principal axis at a distance of 10cm from the mirror. The image, formed by the mirror, is not likely to be a sharp image. State the likely reason for the same. Ans: The incident rays are not likely to be paraxial. 3. How does power of lens vary when incident red light is replaced by blue light? Ans: Wavelength decreases hence power increases 4. An object is held at the principal focus of a concave lens of focal length f. Where is the image formed? Ans: That is image will be formed between optical centre and focus of lens; towards the side of the object. 5. What is the geometrical shape of the wavefront when a plane wave passes through a convex lens? Ans: The wavefront is spherical of decreasing radius. 6. What is the angle between the plane of polariser and analyser, in order that the intensity of transmitted through analyser reduces to half? Ans: 450 7. A diverging lens of focal length ‘F’ is cut into two identical parts each forming a plano-concave lens. What is the focal length of each part? Ans: Focal length of each half part will be twice the focal length of initial diverging lens. 8. How the angular separation of interference fringes in Young’s double slit experiment change when the distance between the slits and screen is doubled? Ans: Angular separation between fringes, θ = λ/d where λ = wavelength, d = separation between coherent sources. So, θ is independent of distance between the slits and screen. So angular separation (θ ) will remain unchanged. 9. Two thin lenses of power +6 D and – 2 D are in contact. What is the focal length of the combination? Ans: Net power of lens combination P = P1 + P2 = + 6 D - 2 D = + 4 D ∴ Focal length, f = 1/P = ¼ m = 25 cm 10. How does the angular separation between fringes in single-slit diffraction experiment change when the distance of separation between the slit and screen is doubled? Ans: Angular separation is θ = β / D = λ / d Since θ is independent of D, angular separation would remain same. 12. How does the fringe width, in Young’s double-slit experiment, change when the distance of separation between the slits and screen is doubled? Ans: The fringe width is, β = D λ / d If D (distance between slits and screen) is doubled, then fringe width will be doubled. 13. When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a decrease in the energy carried by the light wave? Justify your answer. Ans: No; when light travels from a rarer to denser medium, its frequency remains unchanged. According to quantum theory, the energy of a light beam depends on frequency and not on speed. 14. For the same value of angle incidence, the angles of refraction in three media A, B and C are 15°, 25° and 35° respectively. In which medium would the velocity of light be minimum? Ans: From Snell's law, n = sin i/sin r = c/v For given i, v α sin r ; r is minimum in medium A, so velocity of light is minimum in medium A. 15. How does resolving power of telescope change if the incident yellow light is replaced by blue light? Ans: Resolving power = D / 1.22 λ < Hence RP decreases 16. When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the samefrequency as the incident frequency. Explain why? Ans: Reflection and refraction arise through interaction of incident light with the atomic constituents of matter. Atoms may be viewed as oscillators, which take up the frequency incident light. Thus, the frequency of scattered light equals the frequency of incident light. 17. Unpolarised light is incident on a plane glass surface. What should be the angle of incidence so that the reflected and refracted rays are perpendicular to each other? Ans:For i + r to be equal to /2, we should have tan iB This gives iB = 57°. This is the Brewster’s angle for air to glass interface. 18. In a single-slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? Ans: In single slit diffraction experiment fringe width is, β = 2Dλ / d If d is doubled, the width of central maxima is halved. Thus size of central maxima is reduced to half. Intensity of diffraction pattern varies square of slit width. So, when the slit gets double, it makes the intensity four times. 19. Under what condition does a convex lens of glass having certain refractive index, acts as a plane glass sheet? Ans: When refractive index of lens is equal to refractive index of liquid. 20. You are given following three lenses. Which two lens you will use to make objective and eyepiece of an astronomical telescope? LENS POWER APERTURE L1 3D 8cm L2 6D 1cm L3 10D 1cm Ans: L1 as objective. L3 as eyepiece 21. The line AB in the ray diagram represents a lens. State whether the lens is convex or concave? Ans: AB represents concave lens. 22. A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens? Ans: Since image coincides with object, it implies that ray must be falling normally on the plane mirror. This implies that the ray after passing through lens becomes parallel. So, object must be at the focus of lens. So, focal length of lens = 20 cm. 23.‘Two independent monochromatic sources of light cannot produce a sustained interference pattern’. Give reason. Ans:In independent monochromatic sources phase difference changes at a rate of 108 Hz. Hence, the interference pattern obtained also fluctuates with 108 Hz and therefore, it is not sustainable as result of persistence of vision. Q24. A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens? Ans: Since for lens. <for surrounding. It behaves like converging lens. 2 Mark Questions 1. An object AB is kept in front of a concave mirror as shown in the fig. (i) Draw ray diagram showing image formation by the concave mirror (ii) How will the position and intensity of the image be affected if the lower half of the mirror’s reflecting surface is painted black? Ans: (i) Image formed will be inverted diminished between C and F. (iii) No change in position of image and its intensity will get reduced. 2. Draw a labeled ray diagram to show the image formation in a refracting type astronomical telescope. Why should the diameter of the objective of a telescope be large? Ans: For large light gathering power and higher resolution, the diameter of the objective should be large. 3. Define resolving power of a compound microscope. How does resolving power of a compound microscope change when the (i) Refractive index of the medium between the object and objective lens increases? (ii) Wavelength of the radiation used is increased? Ans: Resolving power of a microscope is defined as the reciprocal of the minimum separation of two points seen distinctly. Resolving power = 2 n sinθ / 1.22 λ 232 (i) Increase in the refractive index (n) of the medium increases resolving power because RP α n (ii) On increasing the wavelength of the radiation, resolving power decreases because RP α 1/λ 4. Define resolving power of a telescope. How does it get affected on (i) Increasing the aperture of the objective lens? (ii) Increasing the focal length of the objective lens? Ans: Resolving power of a telescope is defined as the reciprocal of the smallest angular separation between two distant objects. Resolving power = D / 1.22 λ where is aperture of the objective lens (i) Resolving power increases on increasing the aperture of the objective lens, since RP α D. (ii) Resolving power does not get affected on increasing the focal length of objective lens, since RP is independent of focal length. 5. How will the angular separation and visibility of fringes in Young’s double slit experiment change when (i) screen is moved away from the plane of the slits, and (ii) width of the source slit is increased? Ans. (i) Angular separation = β / D = λ/d It is independent of D; β = D λ/d increases, so visibility of fringes increases. (ii) Remains unchanged but fringes becomes less and less sharp; so visibility of fringes decreases. If the condition s/S =λ/d is not satisfied, the interference pattern disappears. 6. In single slit diffraction pattern a slit of width‘d’ is illuminated with red light of wavelength 650nm. For what value of‘d’ will (i) The first minima fall at an angle of diffraction of 300. (ii) The first maxima fall at an angle of diffraction of 300. Ans. For first minima = Substituting value of and λ , d = 1300nm For first maxima = Substituting value of and λ , d = 1950nm 7. Two convex lens of same focal length but of aperture A1 and A2 (A2<A1), are used as objective lenses in two astronomical telescopes having identical lenses. What is the ratio of their resolving power? Which telescope will you prefer and why? Ans R=1.22 1 1 = 2 2 A1 because it has greater resolving power 8. A convex lens of focal length 10 cm is placed co-axially 5cm away from a concave lens of focal length 10cm. If an object is placed 30cm in front of the convex lens, find the position of the final image formed by the combined system. AnsFor convex lens u1=-30cm, f1= +10cm 1 1 1 = − 1 1 1 V1=15cm U2= 15 - 5=10cm,f2=-10cm Hence v2= ∞ (on the left of second lens) 9. (i) State the principle on which the working of an optical fiber is based. (ii) What are the necessary conditions for this phenomenon to occur? Ans: (i) The working of optical fiber is based on total internal reflection. Statement: When a light ray goes from denser to rarer medium at an angle greater than critical angle, the ray is totally reflected in first (denser) medium. This phenomenon is called total internal reflection. (ii) Conditions: (a) Ray of light must go from denser medium to rarer medium. (b) Angle of incidence must be greater than critical angle (i. e., i > C). 10. Draw a labelled ray diagram of a reflecting telescope. Mention its two advantages over the refracting telescope. Ans: Ray Diagram Advantages: (i) It is free from chromatic and spherical aberrations. (ii) Its resolving power is greater than refracting telescope due to larger aperture of mirror. 11. Write down the conditions to obtain the sustained interference fringe pattern of light. What is the effect on the interference fringes in Young’s double slit experiment, when monochromatic source is replaced by a source of white light? Ans: Conditions for sustained interference (i) The two sources of light must be coherent to emit light of constant phase difference. (ii) The amplitude of electric field vector of interfering wave should be equal to have greater contrast between intensity of constructive and destructive interference. When monochromatic light is replaced by white light, then coloured fringe pattern is obtained on the screen. 12. State briefly two features which can distinguish the characteristic features of an interference pattern from those observed in diffraction pattern. Ans: S.No Interference Pattern Diffraction Pattern 1. All the bright bands are of same Bright bands are not of same intensity. intensity. 2. Intensity of minima is very small or zero. The intensity of minima is never zero. There There is a good contrast between bright is poor contrast between bright and dark and dark bands. bands. 13. Draw a ray diagram of compound microscope. Write the expression for its magnifying power. 1+ Ans: = ( ) 5 Mark Questions Q1. (i)Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism. Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation. (ii)Explain briefly how the phenomenon of total internal reflection is used in fibre optics. Q2. Trace the rays of light showing the formation of an image due to a point object placed on the axis of a spherical surface separating the two media of refractive indices n1 and n2 .Establish the relation between the distance of the object, the distance of image and the radius of curvature from the central point of spherical surface. Hence, derive the expression of the lens maker’s formula. Q3. (i) Draw a ray diagram for formation of image of a point object by a thin double convex lens having radii of curvatures R1 and R2 and hence, derive lens maker’s formula. (ii)Define power of a lens and give its SI units. If a convex lens of length 50 cm is placed in contact coaxially with a concave lens of focal length 20 cm, what is the power of the combination? Q4. (i) Use Huygens geometrical construction to show how a plane wave front at t=0 propagates and produces a wave front at a later time. (ii) Verify, using Huygens principle, snell’s law of refraction of a plane wave propagating from a denser to a rarer medium. (iii) When monochromatic light is incident on a surface separation two media, the reflected and refracted light both have the same frequency. Explain why? Q5. (i) What are coherent sources? Why they are necessary for observing sustained coherent sources obtained in the Young’s double slit experiment? (ii) Show that the superposition of the waves originating from the two coherent sources,S1 and S2 having displament,Y1=a cost and Y2 = a cos(t+Ø)at a point produce a resultant intensity, Hence, write the conditions for the appearance of dark and bright fringes. Q7. In a Young’s double slit experiment, (i) Deduce the conditions for constructive and destructive interference. Hence, write the expression for the distance between two consecutive bright or dark fringes. (ii) What change in the interferences pattern do you observe, if the two slits, S1and S2 are taken as point sources? (iii) Plot a graph of the intensity distribution vs. path difference in this experiment. Compare this with the intensity distribution of fringes due to difference do you observe? (i) How does an unpolarised light incident on a Polaroid gets polarized? Q8. Describe briefly, with the help of a necessary diagram, the polarization of light by reflection from a transparent medium. (ii) Two Polaroid’s, A and B are kept in crossed positions. How a third Polaroid, C should be placed between them so that the intensity of polarized light transmitted by Polaroid reduce to 1/8th of the intensity of unpolarised light incident on A? Q9. (i) Obtain the conditions for the bright and dark fringes in diffraction pattern due to a single narrow slit illuminated by monochromatic source. Explain Cleary why the secondary maxima go on becoming weaker with increasing order? (ii)When the width of the slit is made double, how would this affect the size and intensity of the central diffraction band? Justify your answer. Q10. (i) Draw the ray diagram for the formation of image of an object by a convex mirror and use it (along with the sign convention) to derive the mirror formula. (ii)Use the mirror formula to show that for an object, kept between the pole and focus of a concave mirror, the image appears to be formed behind the mirror. Value Based Questions With Answers (Unit – Optics) 1. Shweta’s grandmother often complains of headache. Shweta asked her to visit an eye specialist for a check up, but she refused saying that her eye sight is O.K. Some other day, her grandmother asked Shweta to thread a needle. Shweta understood her problem and took her to the eye specialist who prescribed her spectacles of suitable power. Read the above passage and answer the following questions: What could Shweta make out? Can you guess the nature of lens prescribed? What values are displayed by Shweta? Answer: a) Shweta could make out that her grandmother is suffering from hypermetropia have difficulty in viewing nearby objects. b) Yes, the eye specialist must have prescribed a convex lens of suitable power. c) Shweta has displayed concern for the health of her grandmother in particular and senior citizens in general. Like kids, elderly people must be provided care with love. 2. Mona and Anushka are friends, both studying in class 12. Mona is in Science stream and Anushka is in Arts stream. Both of them go to market to purchase sunglasses. Anushka feels that any coloured glasses with fancy look are good enough. Mona tells her to look for UV protection glasses, Polaroid glasses and photo sensitive glasses. Read the above passage and answer the following questions: a) What are UV protection glasses, Polaroid glasses and photo sensitive glasses? b) What values are displayed by Mona? Answer: a) UV protection glasses are those which filter ultra-violet rays that are harmful to our eyes. Polaroid glasses help in reducing the glare. Photo-sensitive glasses get darker in strong day light. They protect our eyes from strong sunlight especially at noon. b) Mona has displayed concern for her friend. She has put to use the knowledge she acquired in her science classes. Mugging up things for examinations is of no use. What we are taught in class room must be used in practice. 3. The rays of light falling on a convex lens in a direction parallel to principal axis of the lens, get refracted through the lens and meet actually at a single point F on the principal axis of the lens. This point is called principal focus of the lens. Read the above passage and answer the following questions: a) Is principal focus of a convex lens, a real point? Is the same true for a concave lens? b) A distinct image of a distant tree is obtained on a screen held at 40cm from a convex lens. What is its focal length? c) Our teachers and parents advise us to stay focused. What does it imply? Answer: a) Yes, the principal focus of a convex lens is a real point. This is because rays refracted through convex lens meet actually at this point. b) F=distance of screen from the lens = 40cm c) It implies that we concentrate all out energies/efforts at a single point/problem so that we can resolve the same easily. Staying focused means that we do not divert our energies and attention to several things at a time. This would lead us nowhere. Thus, the secret of success is to stay focussed. 4. The formula governing reflection of light from a spherical mirror is : 1 1 1 = + This is known as mirror formula and is applicable equally to concave mirror and convex mirror. The linear magnification of the mirror is given by (m) = I/O = -v/u Read the above passage and answer the following questions: a) An object is held at a distance of 30cm in front of a concave mirror of radius of curvature 40cm. Calculate distance of the image from the object? What is linear magnification of the mirror? b) The object is moved to a distance of 40cm in front of the mirror. How is focal length of mirror affected? c) What values of life do you learn from the mirror formula? Answer: a) Here, u = - 30cm, R = - 40cm, v ? Substituting in mirror formula v = 60-30=30cm, on the same side as object. Magnification, m = -2 (negative sign for inverted image) b) Focal length (f) of mirror remains unaffected. On changing u; v changes and not f. c) Mirror formula reveals that f depends only on R, and not on ‘u’ pr ‘v’. In fact on changing ‘u’, v changes, but’ f’ remains constant. In day to day life, ‘u’ corresponds to a situation that arises and ‘v’ corresponds to our responses to the situation. We are like a mirror. Our nature/curvature determines our focal length. The mirror formula implies that our nature is not affected by the situation that comes up. Response to a particular situation will depend on our nature. 5. During summer vacation Ravi and Rohit decided to go for a 3-D film (movie). They have heard about this film through their friends. They were asked buy special glasses to view the film. Before they go for a movie, they approached their Physics teacher to know about these glasses. Physics teacher explained when two polarizers are kept perpendicular to each other (crossed polarizers) the left eye sees only the image from the left end of the projector and the right eye sees only the image from the right lens. The two images have the approximate perspectives that the left and right eyes would see in reality the brain combine the images to produce a realistic 3-D effect. Read the above passage and answer the following questions: (a)What qualities do these boys possess? (b)What do you mean by Polarization? (c) Mention the other applications of polarization. Answer: a) Curiosity to learn, approaching the teacher to learn new things, inquisitiveness. b) The phenomenon of restricting the oscillations of a light wave (electric vector) in a particular direction is called polarization of light. c) In Sun glasses, Liquid Crystal Displays, CD players etc. ************************************ DUAL NATURE OF MATTER AND RADIATION IMPORTANT CONCEPTS Work function-The minimum amount of energy required by an electron to just escape from the metal surface is known as work function of the metal. One Electron Volt (1eV)-It is the kinetic energy gained by an electron when it is accelerated through a potential difference of 1 volt. 1eV = 1.6X10-19J Photon-According to Planck's quantum theory of radiation, an electromagnetic wave travels in the form of discrete packets of energy called quanta. One quantum of light radiation is called a photon. The main features of photons are as follows:(i) A photon travels with the speed of light. (ii) The rest mass of a photon is zero i.e., a photon cannot exist at rest. (iii) Energy of a photon, E = hν (iv) Momentum of a photon, p =mc Photoelectric Effect: -The phenomenon of emission of electrons from a metallic surface when light of appropriate frequency (above threshold frequency) is incident on it, known as photoelectric effect. Photoelectric Effect experimental setup- Factors which Effect Photoelectric Effect:(i) Effect of potential on photoelectric current: It is can be shown in fig. potential v/s photoelectric current. (ii) Effect of intensity of incident radiations on photoelectric current: For frequency of radiations as constant. (iii) Effect of frequency of the incident radiations on stopping potential: For constant intensity. The stopping potential Vo depends on(i) The frequency of incident light and (ii) the nature of emitter material. For a given frequency of incident light, the stopping potential is independent of its intensity. eVo =(1/2)mv2max=Kmax From this graph between frequency ν, stopping potential Plank's constant (h) can be determined Intercept on x- axis- Threshold frequency Intercept on y-axis- Work function/ electron Slope= tan = ℎ Intercept on x- axis- Threshold frequency Intercept on y-axis- Work function Slope= tan = ℎ De-Broglie HypothesisAccording to de Broglie, every moving particle is associated with a wave which controls the particle in every respect. The wave associated with a particle is called matter wave or de Broglie wave. λ =h/p = h/mv This is known as de-Broglie equation. de-Broglie wavelength of an electron of kinetic energy Kℎ ℎ 1.227 = = = √2 √2 √ Davisson and Germer experimentThis experiment proves the existence of de-Broglie waves.It establishes the wave nature of electron particle. Theory-A sharp diffraction is observed in the electron distribution at an accelerating voltage of 54 V and scattering angle 50°. The maximum of intensity obtained in a particular direction is due to constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystal. Questions/Answers related to this topic Q.1 The frequency of incident radiation is greater than threshold frequency 0 in a photocell .How will the stopping potential vary if frequency is increased. (1 mark) Q.2 If the intensity of the incident radiation in a photocell is increased. How does the stopping potential vary? (1 mark) No effect. Q.3 Two metals P and Q have work function 2ev and 4ev respectively. Which of the two metal have smaller threshold wavelength. (1 mark) Q.4 The stopping potential in an experiment in Photoelectric effect is 1.5 eV. What is the maximum kinetic energy of the photoelectron? (1 mark) Kmax = 1.5 eV Q.5 In an experiment on photoelectric effect, the following graph were obtained. Name the characteristics of incident radiation that was kept constant. (1 mark) frequency Q.6 State Einstein’s Photoelectric equation. E=h =h Q.7 0 (1 mark) + Kmax How does the maximum kinetic energy of photoelectrons vary with work function of metal? (1 mark) Decreases. Q.8 With what purpose was famous Davisson - Germer experiment with electrons per formed? (1 mark) To proves the existence of de-Broglie waves Q.9 An electron and a proton have same De broglie wavelength associated with them. How are their Kinetic energies related to each other? Q.10 Ultra violet light of wavelength 2271 Ao is incident on two photo sensitive material having work function W1 and W2 (W1 >> W2). In which case will the kinetic energy of emitted electrons be greater? (1 mark) For W2 metal .11 Two lines A and B in the plot given below show the variation of De Broglie wavelength λ versus 1/ . Where V is the accelerating potential difference for two particles carrying the same charge .Which one represents a particles of smaller mass. (2 marks) Q.12 Derive an expression for the de Broglie Wavelength of an electron moving under potential difference of V volt. (2 marks) Let an electron be accelerated by applying a potential difference V volt. Then W=Qv= Q.13 A particle of mass M at decays into two particle of masses m1 and m2having velocity v1 and v2 respectively .Find the ratio of de Broglie wavelength of two particles. (2 marks) Q.14 The wavelength λ of a photon and De Broglie wavelength is of an electron have the same value .Show that energy of photon is 2 λ mc/n times the energy of the electron. (2 marks) Q.15 For a photosensitive surface threshold wavelength is λ0 .Does photo emission occur if wavelength (λ) of incident radiation is more than λ0 , less than λ0. Justify your answer. (2 marks) (i) No, as work function Energy if incident radiation Decreases. (ii) Yes, Energy of incident radiation increases. Q.16 When a monochromatic yellow colored light beam is incident an a given photosensitive surface, photo electrons are not ejected to green colored monochromatic beam. What will happen if the same surface is exposed to (i) violet and (ii) red colored monochromatic beam of light. (2 marks) λv <λy , λR > λy (i) For violet, color, Photo emission will take place as Energy increases. (ii) For Red color, No emission of electrons. Q.17 A Source of light is placed at a distance of 50 c.m from a photocell and cut –off potential is found to be Vo .If the distance b/w source and photocell is made 25 c.m. What will be new cut –off potential? (2 marks) Same, as intensity increases and stopping potential remains same. Q.18 Show the graphical variation of stopping potential with the frequency of incident radiation .How do we determine the Planck’s constant using Graph. (2 marks) Q.19 Explain the effect of increase of intensity and potential difference on photoelectrons kinetic energy. Due to increase in Intensity , No effect on kinetic energy of Photo electrons as well as on Potential Difference. As due to increase in Intensity , there is only an increase in the number of Photons per unit area , and not the energy incident. Q.20 Calculate the number of photons emitted per second by transmitter of 10 KW power; radio waves of frequency 6×105 Hz. (2 marks) Q.22 The following graph shows the variation of stopping potential Vo with the frequency of the incident radiation for two Photosensitive metals X and Y. (i) Explain which metal has smaller threshold wavelength . (ii) Explain giving reason, which metal emits photoelectrons having smaller kinetic energy. marks) (3 Y as Y as K = h - Φo Work function of Y will be more as compared to X. Q.23 A proton and an alpha particle are accelerated through the same potential .Which one them has Higher De Broglie wave length. (3 marks) as mα =4mp and qα =2qp Q.24 Show the graphical variation of photocurrent with intensity of incident radiation at constant potential difference b/w electrons and the graphical variation of photocurrent of incident radiation. (3 marks) Q.25 State the laws of Photoelectric effect. Explain it on the basis of Einstein equation. (3 marks) Laws : (i) It is an instantaneous process (ii) No Photo emission takes place below threshold frequency of material, no matter how intense the incident beam. (iii) The maximum photo current (saturation current ) does not depends upon stopping potential or frequency but depends on intensity of incident radiation. (iv) Stopping potential is independent on intensity of incident radiation. Q.26 Draw a schematic diagram of the experimental arrangement used by Davisson &Germer to establish wave nature of electrons .Explain briefly how the De Broglie relation was verified experimentally. (3 marks) Q.27 An electromagnetic wave of wave length λ is incident on a photosensitive surface of negligible work function .if photoelectrons emitted from this surface have the De Broglie wavelength λ1 them show that . (3 marks) E = h = Φo + Kmax Q.28 X-rays of wavelength λ fall on the photosensitive surface emitting electrons. Assuming that the work function of the surface can be neglected, Show that De Broglie wave length of electrons emitted will be . (5 marks) As E= h = Φo + K Q.29 IF the frequency of incident radiation and photocell is doubled for same intensity, what charges will you observe in (3 marks) (i) Kinetic energy of photo electrons (ii) Photoelectric current (iii) Stopping potential. (i) Kinetic energy will be increased (ii) No effect. (iii) Will increase. Q.30 Sketch a graph b/w of incident radiation and stopping potential for a given photosensitive material. What information can be drawn from the value of intercept on the potential axis? marks) E = h = Φo + eVo Q.21 Radition of frequency 1015 Hz are in incident on two photosensitive surfaces A and B. Following observations are recorded: Surface A: No photoemission takes place. Surface B: photoemission takes place but photoelectrons hace zero energy. Explain the above observations on the basis of Einstein’s photo electric equation. For ‘A’, Energy incident is less than work function. For ‘B’, Energy incident is equal to work function of metal. (3 marks) (5 UNIT—VIII- ATOMS & NUCLEI 1. Rutherford’s -Particle scattering experiment (Geiger – Marsden experiment) Scattering of -particles by heavy nuclei is in accordance with coulomb’s law. Rutherford observed that number of -particles scattered is given by 1 N ∝ 4 ⁄2 2. Distance of closest approach : Estimation of size of nucleus 1 2 0 = 4 1 2 0 2 m 3. Bohr’s atomic model Radius of orbit = v = 2 2 (40 )ℎ (40 )2 ℎ2 4 2 2 X= Frequency Where = 2 2 (40 )ℎ v= 1 = 137 2 2 (40 )ℎ is called fine structure constant 4. Energy of electron En = − ( ) Rydberg constant. . En = − eV Formula – En = − 4 R = 82 ℎ3 = 1.097 X 107 m-1 and is called 0 1 1 1 2 ̅ = [ 2 − 2 ] where ̅ is called wave number. K.E. = - ( Total Energy ) P.E.= - 2 K.E. 5. Spectral Series of Hydrogen Atom 6. Energy level diagram for hydrogen atom We know that for hydrogen atom, energy of an electron in nth orbit is given by 13.6 En = − 2 eV 7. Atomic Mass Unit (amu) 1 One atomic mass unit is defined as 12th of the actual mass of c-12 atom. 1 1 1 u = 12 X mass of C-12 atom = 12 X 1.992678 X 10-26 kg = 1.66 X 10-27 kg. 8. Electron Volt (eV) It is the energy acquired by an electron when it is accelerated through a potential difference of 1 volt. 1 eV = 1.6 X 10-19 J & 1 MeV = 1.6 X 10-13 J 9. Relation Between amu & MeV Einstein ‘s Mass Energy Equivalence Relation is E =mc2 1amu =1u =931 MeV 10. Nuclear Density () =2.3 X 1017 Kg/m3 obviously, nuclear density is independent of mass number A. 11. Properties of nuclear Forces (i) Nuclear forces are very short range attractive forces. (ii) Nuclear forces are charge independent. (iii) Nuclear forces are non-central forces. (iv) Nuclear forces do not obey inverse square law. 12. Nuclear force as a separation between two nucleons 13. Potential energy of a pair of nucleons as a separation between two nucleons 14. Nucleus consist of protons and neutrons. Nucleus of protons in a nucleus zXA is Z and number of neutrons ,N =A-Z 15. Radius of Nucleus :- R= R0A1/3 where R0 = 1.2 x 10-15m 16. Mass Defect (∆) ∆ = [Z mp + (A – Z) Mn ] − MN 17. Packing fraction (P.F.) It is defined as the mass defect per nucleon. ∆ i,e, P.F. = Nucleus is stable if P.F.>1 & unstable if P.F.< 1 18. Binding Energy (B.E.) The binding energy of a nucleus may be defined as the energy required to break up a nucleus in to its constituent protons and neutrons and to separate them to such a large distance that they may not interact with each other. It is equivalent energy of mass defect. i,e, B.E. = ∆ X c2 ⇨ B.E. = [{Z mp + (A – Z) Mn} −MN ] x c2 .. 19. Binding Energy per nucleonB.E. per nucleon = 20. Einstein ‘s Mass Energy Equivalence Relation is E =mc2 1amu =1u =931 MeV 21. Rutherford –Soddy formula :(i) Number of atoms un-decayed after time t N=N0e-λt (ii) N/N0 =[1/2]n Where n = t\T is number of half lives. 22. Relation between half –life (T) mean life ( ) and disintegration constant (λ ) is =1/λ and T = 0.693 = 0.693/λ 23. Displacement Laws: (i) For α -particle zXA z-2YA-4 + 2He4 (ii) For β - particle zXA A z+1Y + -1β 0 + ν (iii) For gamma– ray ( zXA)* (Excited State) zXA (Ground state) + γ 24. In nuclear fission a heavy nucleus break into lighter nuclei .Nearly 0.1 % mass is converted into energy .In each fission of 92 U 235 with slow neutron 200 MeV energy is released 25. In nuclear fusion two lighter nuclei combine to form a heavy and 0.7 % mass is converted into energy 1 MARK QUESTION Qn1.What is the ratio of the radii of orbits corresponding to first excited state and ground state in hydrogen atom? Ans:- r2 / r1 = (n2 /n1 )2 = (2/1) 2 = 4: 1 Qn2. Two nuclei have mass numbers in the ratio 1: 8. Find the ratio of their nuclear radii and nuclear densities. Ans;- R1 / R2 = ( A1/ A2) 1/3 = ( 1/ 8 ) 1/3 = 1 / 2 , d1/ d2 = 1:1 Density does not depends on mass (same) Qn3. What is the ground state energy of electron in case of 3Li 7 ? Ans:- E n = - 13.6 Z 2 / n2eV Putting Z= 3 , n = 2 E n = - 30.4 eV Qn4.Find first excitation energy and excitation potential of hydrogen atom. Ans:- E = E2 – E1 = -3.4 – ( - 13.6 ) eV = 10.2 eV and Potential = 10.2 Volt Qn5.Find ionisation energy and ionisation potential of hydrogen atom. Ans:- E n = - 13.6 Z 2 / n2eV , put Z =1 , n=1 E n = - 13.6 eV Hence ionisation energy = + 13.6 eV, ionisation potential = 13.6 V Qn6. Tritium has half-life of 12.5 years against β decay. What fraction of the sample will remain undecayed after 25 years ? Ans:- N/ N0 = (1/2 ) t/ T = (1/2 )25/12.5 = 1/4 2 MARKS QUESTION Qn1. With the help of an example explain how the neutron to proton ratio changes during α – decay of nucleus. Ans:- 92U238 →92Th234+2α4 238−92 146 N to P ratio before α-decay= 92 = 92 =1.59 N to P ratio after α-decay= 234−90 144 90 = 90 =1.60 146 144 < 92 90 This show that the N to P ratio increases during α-decay of a nucleus Qn2. A radioactive isotope has half-life of 5 years after how much time is its activity reduces to 3.125% of its original activity? Ans:- We know that 0= ( 1 n ) 2 =3.125/100 = 1/ 32 = (1/2)5 0 n=5 and n=t/T or t= n x T = 5x5=25years. Qn3. A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV. Ans:- Total energy of nucleus X = 240 × 7.6 = 1824 MeV Total energy of nucleus Y = 110 × 8.5 = 935 MeV Total energy of nucleus Z = 130 × 8.5 = 1105 MeV Therefore, energy released from fission, Q = 935 + 1105 − 1824 = 216 MeV Qn4. The ground state energy of hydrogen atom is -13.6eV.What is the K.E& P.E of the electron in this state? Ans:- K.E= - ( Total Energy ) =13.6 eV, P.E=-2K.E=-27.2 eV Qn5.At a given instant there are 25% un-decayed radioactive nuclei in a sample. After 10 seconds the number of un-decayed nuclei reduces to 12.5 %.calculate the i) mean life of the nuclei ii) the time in which the number of the un-decayed nuclei will further reduce to 6.25 % of the reduced number. Ans:- T =10s, λ=.0693/ T , τ=1/λ= 1.44 T = 14.43 sec N=1/16(N0/8) →t= n x T =4x10=40sec Qn 6.A radioactive nucleus ‘A’ decays as given below: Β α A A1 A2 If the mass number & atomic number of A1 are 180 & 73 respectively, find the mass number & atomic number of A &A2 Ans:- For A— 180 & 72, For A2—176 & 71 Q7. What is the shortest wavelength present in the Paschen series of hydrogen spectrum? (R = 1.097 x 10 7 m-1 ) 1 1 Ans:- 1/λ = R ⌊2 − 2 ⌋ 1 put n1=3, n2=∞ , λ=9/R=8204Ǻ 2 Qn8. Calculate the frequency of the photon which can excite an electron to -3.4 eV from -13.6 eV. Ans:- E = E2 – E1 , = -3.4 – ( - 13.6 ) eV , = 10.2 eV = 10.2 x 1.6 x 10 -19 J E = h ν = 10.2 x 1.6 x 10 -19 J , ν = 10.2 x 1.6 x 10 -19 / 6.6 x 10 -34 , = 2.5x1015Hz Q9. The energy levels of an atom are as shown below. a) Which of them will result in the transition of a photon of wavelength 275 nm? b) Which transition corresponds to the emission of radiation maximum wavelength? Ans:- (a) E=hc/λ = 6.6 x 10 -34 x 3x 10 8 / 275 x10 -9 x 1.6 x10 -19 , =4.5eV , transition B (b) Eα 1/λ transition A provides minimum energy of 2 eV , Hence maximum wavelength 3 MARKS QUESTION Qn1. Draw the graph showing the variation of binding energy per nucleon with the mass number.What are the main inferences from the graph? Explain with the help of this plot the release of energy in the processes of nuclear fission and fusion . Ans The variation of binding energy per nucleon versus mass number is shown in figure:- Inferences from graph 1. The nuclei having mass number below 20 and above 180 have relatively small binding energy and hence they are unstable . 2. The nuclei having mass number 56b and about 56 have maximum binding energy -5.8 MeV and so they are not stable. 3 Some nuclei have peaks ,e. g 2 He4 , 6C12 ,8O16 ; this indicates that theses are relatively more stable than their neighbours . Explanation : - When a heavy nucleus (A ≥ 235 say ) break into two lighter nuclei (nuclear fission ), the binding energy per nucleon increase i.e nucleons get more tightly bound .This implies that energy would be released in nuclear fission . When Two very light nuclei (A ≤ 10) join to from a heavy nucleus ,the binding is energy per nucleon of fused heavier nuclear more than the binding energy per nucleon of lighter nuclei,so again energy would be released in nuclear fusion . Q:2 Define half -life of a radioactive sample .which of the following radiations : α –rays ,β –rays and γ-rays (i) (ii) (iii) (iv) Are similar to X-rays Are easily absorbed by matter Travel with the greatest speed Are similar in nature to cathode rays ? Ans Half –life : The half –life of a radioactive sample is defined as the time in which the mass of sample is left one half of the original mass. (i) (ii) (iii) (iv) γ-rays are similar to X-rays α –rays are easily absorbed by matter γ-rays travel with greatest speed β –rays are similar to cathode rays . Q:-3 Define the term ‘ Activity ‘ of a radioactive substance .State its SI unit .Give plot of activity of a radioactive species versus time. Ans The activity of a radioactive elements at any instant is equal to its rate of decay at that instant S.I unit of activity is Becquerel . (=1 disintegration /second ). The plot is shown is figure . Q:-4 How does the size of nucleus depend on its mass number ? Hence explain why the density of nuclear matter in independent of the size of nucleus? Ans The radius (size) R of nuclear is related to its mass number (A) as R=R0 A1/3 where R0 =1.1 x 10- 15m If m is the average mass of a nucleon ,then mass of nucleus =mA ,where A is mass number . Volume of nucleus = (4/3) π R3 = (4/3) π R 0 3 A Density of nucleus = Mass / Volume = 3m / 4 π R 0 3 ∴ Nuclear density is independent of mass number . Q:-5 A radioactive nucleus A undergoes a series of decay according to following scheme: A α A1 β-1 A2 α A3 γ A4 The mass number and atomic number of A are 180 and 72 respectively .What are these numbers for A4? Ans The decay scheme may completely be represented as 180 72A α 76 70A β-1 176 71A α 69A3 172 γ 69A4 172 Clearly ,mass number of A4 is 172 and atomic number is 69. Q:-6 You are given two nuclides 3X7 and 3Y4 (i) (ii) Are they isotopes of the same element ? Why ? Which one of the two is likely to be more stable? Ans (i) The two nuclides are isotopes of the same elements because they have the same Z. (2) The nuclide 3Y4 is more stable because is has less neutron to proton ratio . Q:- 7 Derive the relation Nt = N0e-λt . Or Use basic law of radioactive decay to show that radioactive nuclei follow an exponential decay law? Or State the law of radioactive decay .If No is the number of radioactive nuclei at some initial time t 0 ,find out the relation to determine the number N present at a subsequent time . Ans Radioactive decay Law:- The rate of decay of radioactive nuclei is directly proportional to the number of undecayed nuclei at that time . = −λ N Where λ .is the decay constant . Suppose initially the number of atoms in radioactive elements is N 0 and the number of atoms after time t . According to Rutherford and Soddy law . = −λ N where λ disintegration constant . = −λ dt Integration loge N = λ t +C here c is a constant of integration . If N0 is initial number of radioactive nuclei ,then at t = 0,N= N0 ; so Loge N0 =0 + C⇒C = loge N0 Substituting this equation in (1) ,we get Loge N – loge N0 = λt Loge N / loge N0 = λt N=N0e—λt Q:8 Define half life of radioactive substance .Establish its relation with the decay constant ? Or Define – life of a radioactive sample .Using exponential decay law obtain the formula for the half –life of a radioactive in terms of its disintegration constant/ Ans Half-life of a radioactive elements is define as the time in which number of radioactive nuclei becomes half of its initial value Expression for half time :-time radioactive decay equation is N = N0e—λt When t = T,N = 0 2 Substituting and solving Or e-λt = 1/2 Taking log of both sides Or λT = loge 2 = 0.693 **************************************** ELECTRONIC DEVICES Electronics is a branch of physics which deals with flow of current through inert gases, vacuum or semiconductors. Types of metals on the basis of conductivity(i) Conductor :-low resistivity & high conductivity (ii) Insulator:- high resistivity & low conductivity (iii)Semiconductor:- resistivity & conductivity lies between them Energy Bands in Solids: Valence band(VB):- energy level Completely filled by valence electron Conduction band(CB):- Energy level either empty or partially filled by valence electron Forbidden Energy gap :- Energy gap between VB & CB For Germanium the forbidden energy gap is 0.7ev while it in 1.1ev silicon. Types of metals on the basis of Energy bands(i) Conductor :-CB & VB are overlap to each other so electron easily available in conduction band. (ii) Insulator:- Much energy gap between CB & VB so no electron easily available in conduction band. (iii)Semiconductor:- energy gap between CB & VB are less so electron can jump in conduction band. (i) Elemental semiconductors: Si and Ge (ii) Compound semiconductors: Examples are: CdS, GaAs, CdSe, InP, etc. 1) Semiconductors are the basic materials used in present solid state devices like diode, transistor, ICs ,etc. TYPES OF SEMICONDUCTORS 1) Pure semiconductors are called intrinsic. Semiconductors, ne= nh ie no. of electrons is equal to no. of holes. Holes are electron vacancies with aneffective positive charge. 2) Impure semiconductors are called extrinsic The number of charge carriers can be changed by doping. Such semiconductors are called extrinsic semiconductors TYPES OF EXTRINSIC SEMICONDUCTORS (i) N-type Semiconductor:- It is obtained by doping Si or Ge with pentavalent atomic(donors) like As, Sb, P etc, (ne >> nh ) (ii) P-type:- Semiconductor:- It is obtained by doping Si or Ge with trivalent atoms(acceptors) like B, Al, In, etc. (nh >> ne ) P-N junction:Arrow shows the direction of conventional current. Depletion layer: - Formation of p-n junction produces a depletion layer consisting of immobile ion cores devoid of charge carriers with a width of 10-3 mm. This layer is formed due to diffusion of majority carrier across the junction Potential barrier:- Potential difference due to negative immobile ions on p-side and positive immobile ions on n-side is called potential barrier which is produced about 0.7 V for a silicon p-n junction and 0.3V for Germanium p-n junction. Biasing of Diode :- p-n junction diode join with external battery. Forward biasing:-When positive terminal of battery join with p-region & negative terminal of battery join with n-region. Such biasing is called forward biasing (short P-Positive & N-Negative) Reversed biasing:-When positive terminal of battery join with n-region & negative terminal of battery join with p-region. Such biasing is called reversed biasing (short P-Negative) NOTE;-(i) In forward bias ,the barrier is decreased while ,it increases in reverse bias. Hence forward current is more (mA) while it is very small (µA) in reverse bias. (ii) Diodes can be used for rectifying ac voltage. With the help of a capacitor or suitable filter ,a dc voltage can be obtained. (iii) (iv) There are some special purpose diodes. Zener diode is used as a voltage regulator. p-n junctions have been used to obtain many photonic or optoelectronics devices. Eg- photodiodes , Solar cells, LED and diode LASER Identification of important topics /concepts 1) Difference between insulator ,conductor and semiconductor on the basis of Energy band diagram. 2) Difference between n-type and p-type semiconductor on the basis of doping and energy band diagram. 3) Definition of important terms like depletion layer, forward bias, and reverse bias, barrier potential, doping. 4) Graph forward Bias and reverse bias of a p-n junction diode. 5) Diode as rectifier-working and circuit diagram with graph. 6) Use of Zener diode as a voltage regulator 7) CE Amplifier circuit with working and graph. 8) Logic gates-AND,OR, NAND,NOR,NOT, with symbols and truth tables. 9) Some simple digital circuits with combination of gates IMPORTANT DERIVATIONS COVERING WHOLE UNIT (3 & 5 Marks) Que1. What is semiconductor diode . How a diode can be made forward and reverse bias. Draw its V-I characteristic curve . Ans. A semiconductor diode is basically a p-n junction with metallic contacts provided at the ends for external voltage. Forward bias: In forward bias, the p-type is connected with the positive terminal and the n-type is connected with the negative terminal. Reverse bias : In reverse bias , the p-type is connected with the negative terminal and the n-type is connected with the positive terminal. Que2. What is zener diode. Draw V-I characteristic curve of zener diode. Explain its use as an voltage regulator with circuit diagram. Ans. It is designed to operate in the reverse breakdown voltage region continuously without being damaged. A zener diode has unique feature that voltage drop across it , is independent of current through it. The resistor, RS is connected in series with the zener diode to limit the current flow through the diode Any increase or decrease in voltage appears across the series resistance RS and t6he voltage across zener diode remains constant Que 3. What is junction transistor. Write its types with symbol. Giving circuit diagram of p-n-p transistor in CE draw input & output characteristic curve. Ans. A junction transistor is a three terminal solid state device obtained by growing a thin layer of one type semiconductor in between two thick layers of other similar type semiconductor Transistor are of two types1. n-p-n transistors- it consist of a thin section p-type semiconductor sandwiched between two thicker section of n-type semiconductor. 2. p-n-p transistor-it consist of a thin section of n-type semiconductor Que 4 What is amplifier? Discuss use of n-p-n transistor as an amplifier with circuit diagram. What is phase relation between input & output waveform. Ans. A device which increases the amplitude of the input signal is called amplifier. In common emitter amplifier, input signal to be amplified is applied between base-emitter circuit and the output amplified signal is taken across the load resistance in emitter- collector circuit. There is a phase difference of π between input and output signal. Que 5. From the diagram shown below identify whether the diode is forward or reverse biased . Ans. (a) Forward bias (b) Reverse bias. Que 6. What is meant by rectifier? Discuss working of full wave rectifier with circuit diagram. Draw its input & output wave forms. Ans. Rectifier is a device which convert ac signal to dc. Working:-When the diode rectifies whole of the AC wave, it is called ‘full wave rectifier’ .During the positive half cycle of the input ac signal, the diode D1 conducts and current is through BA. During the negative half cycle, the diode D2 conducts and current is through BA. Que 7 What is half wave rectifier. Giving circuit diagram & input-output waveform explain its working. Ans. Half wave rectifier is a device which changes half cycle of ac to dc. Working:- In first half cycle of ac the diode is forward bias & conduct but in second half cycle the diode is reverse bias & hence not conduct. Hence it gives half dc Que 8. (a) Draw transfer characteristic curve of Base-biased C-E transistor. (b) Mention the region where the transistor used as switch & where as Amplifier. . (a) Active- Amplifier ((b) Switch- ON Switch- saturation region OFF-Switch-cut off region Amplifier – active region Que 9. You are given two circuits as shown in Fig. Giving truth table identify the logic operation carried out by the two circuits Electronic Devices Que 10. What is logic gate. Name the basic gates. Give symbol, Boolean expression & truth table for AND gate. Ans. A logic gate is a digital circuit that follows certain logical relationship betweenthe input and output voltage. Que11. What is a solar cell? How does it works? Give its one use. Ans: Solar cell is device for converting solar energy into electricity. It is basically a p-n junction operating in a photovoltaic mode without external bias. Working: When light photons fall at the junction electron-hole pairs are generated. those more in opposite direction due to junction field. These charges accumulate at the two sides of the junction and photo voltage is developed. Use: It is used in calculators etc. SOME IMPORTANT QUESTIONS FROM PREVIOUS YEAR PAPERS Q1.In a semiconductor the concentration of electrons is 8x1013cm-3 and that of holes is 5x1012cm-3. Is a p-type or n-type semiconductor? Ans : As concentration of electrons is more than holes, the given extrinsic semi conductor is n-type. Q2.The energy gaps in the energy band diagrams of a conductor, semiconductor and insulator are E1, E2 and E3. Arrange them in increasing order. Ans: The energy gap in a conductor is zero, in a semiconductor is ≈ 1eV and in an insulator is ≥ 3eV. E1=0, E2=1eV, E3≥3eV . E1 < E2 < E3. Q3. Find the truth table of following gates Q6.The current gain (α) of a transister in common base configuration is 0.98. What does It physically mean? Ans :The current gain α=0.98 means that 98% of charge carriers of an emitter reach the collector and constitute the collector current Q8.Name the gate obtained from the combination of gates shown if figure. Draw the logic symbol. Give the truth table of the combination. Ans : The gate is NOR gate the logic symbol is shown in figTruth table of NOR gate Q 9.Name the logic gate shown in fig. and write its truth table. Ans : . The given logic gate is NAND gate Truth table of NAND gate Q10. Show the output waveforms(Y) for the following inputs A and B of(i) OR gate (ii) NAND gate Ans : Q11. For CE transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2V. Suppose the current amplification factor of the transistor is 100,find the input signal voltage voltage and base current if the base resistance is 1kΩ. Ans : Given Rc=2kΩ, RB=1k Ω, V0=2V, Input voltage Vi=? β = IC/IB=100 V0= ICx Rc=2V IC=2/ Rc=10-3A Base current= IB= IC/β=10μA Base resistance, RB=VBB/IB Therefore Vi(VBB)= RBx IB = 0.01V Q12.Two amplifiers are connected one after another in series (cascaded). The first amplifier has a voltage gain of 10 and the second has a voltage gain of 20. If the input signal is 0.01 volt, calculate the output signal. Ans : Total voltage gain AV=A1X A2= 200 Voltage gain AV=Output Voltage/ Input Voltage Output Voltage V0= AVX Vi = 2V Q13.In a common emitter mode of a transister, the dc current gain is 20, the emitter curent is 7mA. Calculate (i)base current and (ii)collector curent. Ans : Given β=20, iE=7mA (i) β=iC/iB= iE-iB/ iB iB= ie/(1+ β) =1/3 mA (ii) iC = iE-iB= 20/3 mA Q14.A semiconductor has equal electron and hole concentration of 6X108/m3. On doping with certain impurity, electron concentration increases to 9X1012/m3. (i) Identify the new semiconductor obtained after doping. (ii) Calculate the new hole concentration. Ans : (i) The doped semiconductor is n-type. (ii) ne nh = ni2 hence nh = ni2/ ne=4x104m-3 Q 15. How does a light emitting diode (LED) works? Give two advantages of LED’s over the conventional incandescent lamps. Ans: Working of LED :- LED works in forward bias at the junction when majority charge carrier recombine with minority charge carriers, which grow in number due to diffusion of charges across the junctions, energy is released in the form of photons. Advanteges:- (i)Low operational voltage and (ii) Fast on-off switches capability Q 16. Draw a circuit diagram to slow how a photo diode is viewed. Draw its characteristics curres for three different illumination intensities. Ans: Q 17. Identify the logic gates marked P and Q in the given logic circuit. Write down the output at X for the inputs (i) A = 0, B = 0 and (ii) A = 1, B = 1. A Q P B X Ans: P→ NOR gate Q → AND gate A 0 1 B 0 1 A+B 0 1 + 1 0 + B 0 0 Q 18. In half wave rectification, What is the output frequency if the input frequency is 50 Hz. What is the output frequency of a full wave rectifier for the same input frequency. Ans: 50 Hz for half wave , 100 Hz for full wave. COMMUNICATION SYSTEMS Every communication system has three essential elements-transmitter, medium/channel and receiver. The block diagram shown in Fig. depicts the general form of a communication system. • • • • • • • • • • • • • TRANSDUCER: Any device that converts one form of energy into another can be termed as transducer. SIGNAL: Information converted in electrical form and suitable for transmission is called a signal. Signals can be either analog or digital. NOISE: Noise refers to the unwanted signals that tend to disturb the transmission and processing of message signals in a communication system. TRANSMITTER: A transmitter processes the incoming message signals so as to make it suitable for transmission through a channel and subsequent reception. RECEIVER: A receiver extracts the desired message signals from the received signals at the channel output. ATTENUATION: The loss of strength of a signal while propagating through a medium is known as a attenuation. AMPLIFICATION: It is the process of increasing the amplitude (and consequently the strength) of a signal using an electronic circuit called the amplifier. Amplification is necessary to compensate for the attenuation of signal in communication systems. RANGE: It is the largest distance between a source and destination up to which the signal is received with sufficient strength. BANDWIDTH: Bandwidth refers to the frequency range over which an equipment operates or the portion of the spectrum occupied by the signal. MODULATION: The original low frequency message/information signal cannot be transmitted to long distances. The low frequency message signal is superimposed on a high frequency wave, which acts as a carrier of the information. This process is known as modulation. DEMODULATION: The process of retrieval of information from the carrier wave at the receiver is termed modulation. This is the reverse process of modulation. REPEATER: A repeater is a combination of a receiver and a transmitter. A repeater picks up the signal from the transmitter, amplifies and retransmits it to the receiver sometimes with a change in carrier frequency. Repeaters are used to extend the range of a communication system. BANDWIDTH OF SIGNALS In a communication system, the message signal can be voice, music, and picture or computer data. Each of these signals has different ranges of frequencies. For speech signals, frequency range 300 Hz to 3100 Hz. Therefore speech signal requires a bandwidth of 2800 Hz (3100 Hz – 300 Hz) for commercial telephonic communication. To transmit music, an approximate bandwidth of 20 kHz is required because of the high frequencies produced by the musical instruments. The audible range of frequencies extends from 20 Hz to 20 kHz. Video signals for transmission of pictures require about 4.2 MHz of bandwidth. A TV signal contains both voice and picture and is usually allocated 6 MHz of bandwidth for transmission. BANDWIDTH OF TRANSMISSION MEDIUM Coaxial cable is a widely used wire medium, which offers a bandwidth of approximately 750 MHz. Such cables are normally operated below 18 GHz. Communication through free space using radio waves takes place over a very wide range of frequencies: from a few hundreds of kHz to a few GHz. Optical communication using fibers is performed in the frequency range of 1 THz to 1000 THz(microwaves to ultraviolet). An optical fiber can offer a transmission bandwidth in excess of100GHz. MODE OF COMMUNICATION OF ELECTRO MAGNETIC WAVES: GROUND WAVE PROPAGATION (up to few MHz) The antennas should have a size comparable to the wavelength λ of the signal (at least ~ λ/4). At longer wavelengths (i.e., at lower frequencies), the antennas have large physical size and they are located on or very near to the ground. The wave glides over the surface of the earth. A wave induces current in the ground over which it passes and it is attenuated as a result of absorption of energy by the earth. The attenuation of surface waves increases very rapidly with increase in frequency. The maximum range of coverage depends on the transmitted power and frequency (less than a few MHz) SKY WAVE PROPAGATION (Frequency range from a few MHz up to 30-40 MHz) • Communication can be achieved by ionospheric reflection of radio waves back towards the earth. • Ionosphere extends from a height of ~ 65 Km to about 400 Km above the earth’s surface. • The ionospheric layer acts as a reflector for a certain range of frequencies (3 to 30 MHz). • Electromagnetic waves of frequencies higher than 30 MHz penetrate the ionosphere and escape. SPACE WAVE PROPAGATION (Frequency greater than 40MHz) A space wave travels in a straight line from transmitting antenna to the receiving antenna. Space waves are used for line-of-sight (LOS) communication as well as satellite communication A space wave travels in a straight line from transmitting antenna to the receiving antenna. At these frequencies, the antennas are relatively smaller and can be placed at heights of many wavelengths above the ground. If the transmitting antenna is at a height hT ,then you can show that the distance to the horizon ddT is given as dt = √2RhT the maximum line-of-sight distance dM between the two antennas having heights hT and hR above the earth is given by MODULATION NEED OF MODULATION Size of the antenna or aerial For transmitting a signal, antenna should have a size comparable to the wavelength of the signal (at least L=λ/4 ) that the antenna properly senses the time variation of the signal. For an electromagnetic wave of frequency 20 kHz, the wavelength L is 15 km. Obviously, such a long antenna is not possible to construct and operate. If transmission frequency is high (for example, if ν is 1 MHz, then L is 300 m). Hence to decrease the size of antenna modulation is done. Effective power radiated by an antenna • A theoretical study of radiation from a linear antenna (length L) shows that the power radiated is proportional to () • • The power radiated increases with decreasing L, i.e., increasing frequency. For a good transmission, we need high powers and hence this also points out to the need of using high frequency transmission. Mixing up of signals from different transmitters To avoid mixing up of signals there is a need for translating the original low frequency baseband message or information signal into high frequency wave before transmission TYPES OF MODULATION • There are three types of modulations (i) Amplitude modulation (AM), (ii) Frequency modulation (FM) and (iii) Phase modulation (PM), • • • • • • AMPLITUDE MODULATED WAVE Amplitude modulation is the process in which the amplitude of the carrier wave changes in accordance with the instantaneous value of the message signal. Let () = sin t m() = sin t ()= ( + sin t) sin t ()= sin t + sin t sin t µ = Am/Ac is the modulation index; in practice,µ is kept ≤1 to avoid distortion. ()= sin t+ 2 cos( − )t+ 2 cos( + ) • Here ( − ) and ( + ) are respectively called the lower side and upper side frequency. PRODUCTION OF AM WAVE INPUT OF SQUARE LAW DEVICE () = () + () = sin t + sin OUTPUT OF SQUARE LAW DEVICe () = () + 2 () • The output of square law device is passed through a band pass filter which rejects dc and the sinusoids of frequencies ωm , 2ωm and 2 ωc and retains the frequencies ωc , (ωc –ωm) and (ωc + ωm) . The output of the band pass filter therefore is of the same form as obtained earlier and is therefore an AM wave. • BLOCK DIAGRAM OF TRANSMITTER BLOCK DIAGRAM OF RECEIVER DETECTION OR DEMODULATION It is the process of retrieval of message signal from the amplitude modulated wave 1. 2. 3. 4. 5. 6. 7. 8. SOME IMPORTANT QUESTIONS FOR PRACTISE Explain ground wave, Sky wave and space wave and ground wave propagation with suitable example. What is the function of following in communication system? (a) Reateter (b) Transducer Define modulation index. Why the amplitude of modulating signal kept less than amplitude of carrier wave? Distinguish between point to point and broadcast communication modes with example. What is meant by demodulation? With the help of block diagram explain the process of demodulation. For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is 2 V. Determine the value of modulation index. What would be the value of modulation index if the minimum amplitude is zero volts? Why is modulation index generally kept less than 1. A carrier wave of frequency 1·5 MHz and amplitude 50 V is modulated by a sinusoidal wave of frequency 10 kHz producing 50% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of the side bands produced. Block diagram of receiver is shown in the fig. Identify X and Y and write its functions 9. Define amplitude modulation and draw amplitude modulated and frequency modulated wave. 10. A transmitting antenna at the top of tower has a height of 36m and the height of receiving antenna is 49m. What is the maximum distance between them for satisfactory communication in the LOS mode? (radius of earth = 6400Km.) 11. Draw block diagram of simple modulator to produce amplitude modulated wave. 12. A schematic arrangement for transmitting a message signal (20 Hz to 20KHz) is given below Write two drawbacks from which the arrangement suffers and draw the correct diagram.,