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 EMTL Question Bank II / IV B. Tech. ECE II Semester Unit I Syllabus: Review of Coordinate Systems, Vector Calculus: Coulomb’s Law, Electric Field Intensity – Fields due to Different Charge Distributions, E lectric Flux Density, Gauss Law and Applications, Electric Potential, Relations Between E and V, Maxwell’s Two Equations f or Electrostatic Fields, Energy Density, Related Problems. 1. State the Coulomb’s law in SI units and indicate the pa rameters used in the equations with the aid of a diagram. (Set No. 1Apr  / May 2008 Supply) 2. Point charges Q 1 and Q 2 are respectively located at (4, 0, -3) and (2, 0, 1). If Q 2 = 4 nC, find Q 1 such that. (Set No. 1 Apr  / May 2008 Supply) i. The E at (5, 0, 6) has no Z-component. ii. The force on a test charge at (5, 0, 6) has no X- component. 3 .  A charge Q1 is at point ( 0,-1,0)m. Another charge Q2 is at the point (0,2,0)m. Find the ratio Q2=Q1 resulting in zero force on a test charge at the origin. Q1;Q2 and the test charge are all of the same sign. (RR May 2010) 4. State Gauss’s law. Using divergen ce theorem and Gauss’s law, relate the displacement density D to the volume charge density ρυ. (Set No. 2 Apr  / May 2008 Supply) 5. A sphere of radius “a” is filled with a uniform charge density of ρ v c  / m 3 . Determine the electric field inside and outside the sphere. (Set No. 2 Apr  / May 2008 Supply) 6. Derive the boundary conditions for the tangential and normal components of Electrostatic fields at the boundary betwee n two  perf ect dielectrics. (Set No. 3 Apr  / May 2008 Supply) 7. x-z-plane is a boundary betwee n two  die lectrics. Region y < 0 contains dielectric material ε r1 = 2.5 while region y > 0 has dielectric with ε r2 = 4.0. If E = 30a x +50a y +70a z v  / m, find normal and tangential components of the E field on both sides of the boundary. (Set No. 3 Apr  / May 2008 Supply) 8. Explain the following terms: i. Homogeneous and isotropic medium and ii. Line, surface and volume charge dis tributions. (Set No. 4 Apr  / May 2008 Supply) 9. A circular ring of radius ‘a’ carries uniform charge ρ L C  / m and is in xy-plane. Find the Electric Field at Point (0, 0, 2) along its axis. (Set No. 4Apr  / May 2008 Supply) 10. State and Prove Gauss’s law. List the limitations of Gauss’s law. (Set No. 3 Aug/Sep 2008 Supply) (Set No. 1 Apr  / May 2008 Reg.) 11. Derive an expression for the electric field strength due to a circular ring of radius ‘a’ and uniform charge density, ρ L C  / m, using Gauss’s law. Obtain the value of height ‘h’ along z-axis at which the net electric field becomes zero. Assume the ring to be placed in x-y plane. (Set No. 1 Apr  / May 2008 Reg.) (Set No. 3 Aug/Sep 2008 Supply) 12. Define Electric potential. (Set No. 3 Aug/Sep 2008 Supply) (Set No. 1 Apr  / May 2008 Reg.) 13. State and prove Gauss’s law. Express Gauss’s law in both integral and differential f orms. (Set No. 2 Apr  / May 2008 Reg.) 14. Discuss the salient f eatures and limitations of Gauss’s law. (Set No. 2 Apr  / May 2008 Reg.) 15. Define conductivity of a material. (Set No. 3 Apr  / May 2008 Reg.) (Set No. 1, 2, 4 Aug / Sep 2 0 0 8 Supply) 16.  Apply Gauss’s law to derive the boundary conditions at a conductor-dielectric interf ace. (Set No. 3 Apr  / May 2008 Reg.) (Set No. 1 Aug / Sep 2 0 0 8 Supply)  17. In a cylindrical conductor of radius 2mm, the current density varies with distance f rom the axis according to J = 10 3 e 400r A/m 2 . Find the total current I. (Set No. 3 Apr  / May 2008 Reg.) 18. Using Gauss’s law derive expressions for electric field intensity and electric flux density due to an infinite sheet of conductor of charge density ρ C  / cm (Set No. 4 Apr  / May 2008 Reg.) 19. A parallel plate capacitance has 500mm side plates of square shape separated by 10mm distance. A sulphur sla b of 6mm thickness with r = 4 is kept on the lower plate find the capacitance of the setup. If a voltage of 100 volts is applied across the capacitor, calculate the voltages at both the regions of the capacitor betwee n the plates. (Set No. 4 Apr  / May 2008 Reg.) 20. In a cylindrical conductor of radius 2mm, the current density varies with distance from the axis according to J = 103e400rA/m2. Find the total current I.  (Set No. 1 Aug / Sep 2 0 0 8 Supply)  21. Apply Gauss’s law to derive the boundary conditions at a conductor-dielectric interface. (Set No. 4 Aug / Sep 2 0 0 8 Supply)  22. In a cylindrical conductor of radius 2mm, the current density varies with distance from the axis according to J = 103e400rA/m2. Find the total current I. (Set No. 4 Aug / Sep 2 0 0 8 Supply)  

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  • EMTL Question Bank II / IV B. Tech. ECE II Semester

    Unit I Syllabus: Review of Coordinate Systems, Vector Calculus:

    Coulombs Law, Electric Field Intensity Fields due to Different Charge Distributions, Electric Flux Density, Gauss Law and Applications, Electric Potential, Relations Between E and V, Maxwells Two Equations for Electrostatic Fields, Energy Density, Related Problems.

    1. State the Coulombs law in SI units and indicate the parameters used in the equations with the aid of a diagram. (Set No. 1 Apr/May 2008 Supply)

    2. Point charges Q1 and Q2 are respectively located at (4, 0, -3) and (2, 0, 1). If Q2 = 4 nC, find Q1 such that. (Set No. 1 Apr/May 2008 Supply)

    i. The E at (5, 0, 6) has no Z-component. ii. The force on a test charge at (5, 0, 6) has no X-component.

    3. A charge Q1 is at point (0,-1,0)m. Another charge Q2 is at the point (0,2,0)m. Find the ratio Q2=Q1 resulting in zero force on a test charge at the origin. Q1;Q2 and the test charge are all of the same sign. (RR May 2010)

    4. State Gausss law. Using divergence theorem and Gausss law, relate the displacement density D to the volume charge density . (Set No. 2 Apr/May 2008 Supply)

    5. A sphere of radius a is filled with a uniform charge density of v c/m3. Determine the electric field inside and outside the sphere. (Set No. 2 Apr/May 2008 Supply)

    6. Derive the boundary conditions for the tangential and normal components of Electrostatic fields at the boundary between two perfect dielectrics. (Set No. 3 Apr/May 2008 Supply)

    7. x-z-plane is a boundary between two dielectrics. Region y < 0 contains dielectric material r1 = 2.5 while region y > 0 has dielectric with r2 = 4.0. If E = 30ax +50ay +70az v/m, find normal and tangential components of the E field on both sides of the boundary. (Set No. 3 Apr/May 2008 Supply)

    8. Explain the following terms: i. Homogeneous and isotropic medium and ii. Line, surface and volume charge distributions. (Set No. 4 Apr/May 2008 Supply)

    9. A circular ring of radius a carries uniform charge L C/m and is in xy-plane. Find the Electric Field at Point (0, 0, 2) along its axis. (Set No. 4 Apr/May 2008 Supply)

    10. State and Prove Gausss law. List the limitations of Gausss law. (Set No. 3 Aug/Sep 2008 Supply) (Set No. 1 Apr/May 2008 Reg.)

    11. Derive an expression for the electric field strength due to a circular ring of radius a and uniform charge density, L C/m, using Gausss law. Obtain the value of height h along z-axis at which the net electric field becomes zero. Assume the ring to be placed in x-y plane. (Set No. 1 Apr/May 2008 Reg.)

    (Set No. 3 Aug/Sep 2008 Supply) 12. Define Electric potential. (Set No. 3 Aug/Sep 2008 Supply)

    (Set No. 1 Apr/May 2008 Reg.) 13. State and prove Gausss law. Express Gausss law in both integral and differential forms.

    (Set No. 2 Apr/May 2008 Reg.) 14. Discuss the salient features and limitations of Gausss law. (Set No. 2 Apr/May 2008 Reg.) 15. Define conductivity of a material. (Set No. 3 Apr/May 2008

    Reg.) (Set No. 1, 2, 4 Aug / Sep 2 0 0 8 Supply)

    16. Apply Gausss law to derive the boundary conditions at a conductor-dielectric interface. (Set No. 3 Apr/May 2008 Reg.)

    (Set No. 1 Aug / Sep 2 0 0 8 Supply) 17. In a cylindrical conductor of radius 2mm, the current density varies with distance from the axis according to J =

    103e400r A/m2. Find the total current I. (Set No. 3 Apr/May 2008 Reg.)

    18. Using Gausss law derive expressions for electric field intensity and electric flux density due to an infinite sheet of conductor of charge density C/cm (Set No. 4 Apr/May 2008 Reg.)

    19. A parallel plate capacitance has 500mm side plates of square shape separated by 10mm distance. A sulphur slab of 6mm thickness with r = 4 is kept on the lower plate find the capacitance of the setup. If a voltage of 100 volts is applied across the capacitor, calculate the voltages at both the regions of the capacitor between the plates.

    (Set No. 4 Apr/May 2008 Reg.) 20. In a cylindrical conductor of radius 2mm, the current density varies with distance from the axis according to J =

    103e400rA/m2. Find the total current I. (Set No. 1 Aug / Sep 2 0 0 8 Supply) 21. Apply Gausss law to derive the boundary conditions at a conductor-dielectric interface. (Set No. 4 Aug / Sep 2 0 0 8 Supply) 22. In a cylindrical conductor of radius 2mm, the current density varies with distance from the axis according to J =

    103e400rA/m2. Find the total current I. (Set No. 4 Aug / Sep 2 0 0 8 Supply)

  • H+H

    Unit II Syllabus: Convection and Conduction Currents, Dielectric Constant, Isotropic and Homogeneous Dielectrics, Continuity Equation, Relaxation Time, Poissons and Laplaces Equations; Capacitance Parallel Plate, Coaxial, Spherical Capacitors

    1. Derive Poissons and Laplaces equations starting from Gausss law. (Set No. 2 Apr/May 2008 Reg.) 2. An infinitely long straight conducting rod of radius a carries a current of I in +Z direction. Using Amperes

    Circuital Law, find H in all regions and sketch the variation of H as a function of radial distance. If I = 3 mA. and a = 2 cm., find and at ( 0, 1cm., 0) and (0, 4cm., 0). (Set No. 1 Apr/May 2008 Supply)

    3. Define Amperes Force Law and establish the associated relations. (Set No. 2 Apr/May 2008 Supply) 4. A long coaxial cable has an inner conductor carrying a current of 1 mA. Along Z direction , its axis coinciding with Z-

    axis. Its inner conductor diameter is 6 mm. If its outer conductor has an inside diameter of 12 mm. and a thicknessof 2

    mm., determine at (0, 0, 0), (0, 1.5 mm, 0), (0, 4.5 mm, 0) and (0, 1cm, 0). (No derivations) (Set No. 2 Apr/May 2008 Supply)

    5. Find the field at the centre of a circular loop of radius a, carrying a current I along in z = 0 plane.

    (Set No. 3 Apr/May 2008 Supply) 6. Determine the magnetic flux , for the surface described by

    i. = 1m., 0 ./2, 0 z 2m.,

    ii. a sphere of radius 2 m., if the magnetic field is of the form ( Set No. 3 Apr/May 2008 Supply)

    7. A conducting plane at y = 1 carries a surface current of 10 Zb mA/m. Find H and B at (0, 0, 0) and at (2, 2, 2). (Set No. 4 Apr/May 2008 Supply)

    8. State Maxwells equations for magneto static fields. (Set No. 1 Apr/May 2008 Reg)

    9. Show that the magnetic field due to a finite current element along Z axis at a point P, r distance away along y- axis is given by H = (I /4pir)(sin 1 sin 2).b a where I is the current through the conductor , 1 and 2 are the angles made by the tips of the conductor element at P?. (Set No. 1 Apr/May 2008 Reg)

    10. State Amperes circuital law. Specify the conditions to be met for determining magnetic field strength, H, based on Amperes circuital law (Set No. 2 Apr/May 2008 Reg)

    11. A long straight conductor with radius a has a magnetic field strength H = (I r/2pia2) a within the conductor (r < a) and H = (I /2pir) a outside the conductor (r > a) Find the current density J in both the regions (r < a and r > a (Set No. 2 Apr/May 2008 Reg)

    12. Define Magnetic flux density and vector magnetic potential. (Set No. 2 Apr/May 2008 Reg) (Set No. 1 Aug/Sep 2008 Supply)

    13. Derive equation of continuity for static magnetic fields.(Set No. 3 Apr/May 2008 Reg) 14. Derive an expression for magnetic field strength, H, due to a current carrying conductor of finite length placed along

    the y- axis, at a point P in x-z plane and r distant from the origin. Hence deduce expressions for H due to semi- infinite length of the conductor. (Set No. 2 Apr/May 2008 Reg)

    15. A long straight conductor with radius a has a magnetic field strength H = (Ir/2pia2) a_ within the conductor (r < a) and H = (I/2pir) a_ outside the conductor (r > a) Find the current density J in both the regions (r < and r > a) (Set No. 1 Aug/Sep 2007 Supply)

    16. State Amperes circuital law. Specify the conditions to be met for determining magnetic field strength, H, based on Amperes circuital law (Set No. 1 Aug/Sep 2007 Supply)

    17. State Biot- Savart law (Set No. 4 Aug/Sep 2007 Supply) 18. Derive an expression for magnetic field strength, H, due to a finite filamentary conductor carrying a curent I and placed

    along Z- axis at a point P on y- axis. Hence deduce the magnetic field strength for the length of the conductor extending from - 1 to + 1. (Set No. 4 Aug/Sep 2007 Supply)

    19. Obtain an expression for differential magnetic field strength dH due to differential current element I dl at the origin in the positive Z- direction. (Set No. 2, 3 Aug/Sep 2007 Supply)

    20. Find the magnetic field strength, H at the centre of a square conducting loop of side 2a in Z=0 plane if the loop is carrying a current, I, in anti clock wise direction. (Set No. 2, 3 Aug/Sep 2007 Supply)

    Unit III Syllabus:

    Biot-Savart Law, Amperes Circuital Law and Applications, Magnetic Flux Density, Maxwells Two Equations for Magneto static Fields, Magnetic Scalar and Vector Potentials, Forces due to Magnetic Fields, Amperes Force Law, Inductances and Magnetic Energy

    1. In free space D = Dm Sin (wt + z)ax. Determine B and displacement current density. (Set No. 1 Apr/May 2008 Supply)

  • 2. Region 1, for which r1 = 3 is defined by X < 0 and region 2, X < 0 has r2 = 5 given H1 = 4 ax + 3ay 6 az (A/m). Determine H2 for X > 0 and the angles that H1 and H2 make with the interface. (Set No. 1 Apr/May 2008 Supply)

    3. In a perfect dielectric medium, the EM wave has maximum value for E of 10 V/m with r = 1 and r = 4. Find the velocity of the wave, peak poynting vector, average poynting vector, impedance of the medium and peak value of the magnetic field (Set No. 2 Apr/May 2008 Supply)

    4. What is the inconsistency in Amperes Law? How it is rectified by Maxwell? (Set No. 2 Apr/May 2008 Supply

    5. Show that the total displacement current between the condenser plates con- nected to an alternating voltage sources is exactly the same as the value of charging current (conduction current).

    (Set No. 3 Apr/May 2008 Supply) 6. In a perfect dielectric medium, the EM wave has maximum value for E of 10V/m with r = 1 and r = 4. Find

    the velocity of the wave, peak poynting vector, average poynting vector, impedance of the medium and peak value of the magnetic field. (Set No. 3 Apr/May 2008 Supply)

    7. What is the inconsistency in Amperes Law? How it is rectified by Maxwell? (Set No. 3 Apr/May 2008 Supply)

    8. Show that the total displacement current between the condenser plates connected to an alternating voltage sources is exactly the same as the value of charging current (conduction current). (Set No. 4 Apr/May 2008 Supply)

    9. Derive Maxwells equations in integral form and differential form for time varying fields. (Set No. 4 Apr/May 2008 Supply

    10. Explain how the concept of Displacement current was introduced by Maxwell to account for the production of Magnetic fields in the empty space. (Set No. 4 Apr/May 2008 Supply)

    11. The electric field intensity in the region 0 < x < 5, 0 < y < pi/12, 0 < z < 0.06m in free space is given by E=c sin12y sin az cos2 10 t ax v/m. Beginning with the xE relationship, use Maxwells equations to find a numerical value for a , if it is known that a is greater than0. ( Set No. 1 Apr/May 2008 Regular)

    12. Write down the Maxwells equations for Harmonically varying fields.(b) A certain material has = 0and R = 1if H = 4sin(106t 0.01z)ay A/m. make use of Maxwells equations to find r ( Set No. 1 Apr/May 2008 Regular)

    13. In figure 3 let B=0-2cos 120pi t T, and assume that the conductor joining the two ends of the resistor is perfect. It may be assumed that the magnetic field produced by I(t) is negligible find (a) Vab (t)

    (b) I(t) ( Set No. 2 Apr/May 2008 Regular)

    Figure 3

    14. What is the inconsistency of Amperes law? ( Set No. 2 Apr/May 2008 Regular)

    15. A circular loop conductor of radius 0.1m lies in the z=0plane and has a resistance of 5 given B=0.20 sin 103taz T. Determine the current ( Set No. 3 Apr/May 2008 Regular)

    16. Derive the equation of continuity for time varying fields ( Set No. 3 Apr/May 2008 Regular) 17. A Parallel plate capacitor with a plate area of 5cm2 and plate separation of 3mm has a voltage 50 Sin 103t V applied to its

    plates. Calculate the displacement current assuming 2= 2 20 (Set No. 4 Apr/May 2008 Regular)

    Unit IV Syllabus: Faradays Law and Transformer emf, Inconsistency of Amperes Law and Displacement Current Density, Maxwells Equations in Different Final Forms and Word Statements, Conditions at a Boundary Surface: Dielectric-Dielectric and Dielectric-Conductor Interfaces.

  • 1. Prove that under the condition of no reflection at an interface, the sum of the Brewster angle and the angle of refraction is pi/2 for parallel polarization for the case of reflection by a perfect conductor under oblique incident, with neat sketches.

    (Set No. 1 Apr/May 2008 Supply) 2. 3. Prove that uniform plane wave does not have field components in the direction of the propagation.

    (Set No. 2 Apr/May 2008 Supply) 4. Determine the intrinsic impedance of free space. (Set No. 2 Apr/May 2008 Supply) 5. What is polarization of an EM wave? Distinguish between different types of polarizations? Prove that the

    polarization is circular when the two components of electric field are equal and are 90o apart. (Set No. 3 Apr/May 2008 Supply)

    6. A plane EM wave is normally incident on the boundary between two di- electrics. What must be the ratio of refractive indices of the two media in order that the reflected and transmitted waves may have average Power of equal magnitude? (Set No. 3 Apr/May 2008 Supply)

    7. Derive the expression for attenuation and phase constants of uniform plane wave. (Set No. 4 Apr/May 2008 Supply)

    8. If r = 9, = 0 for the medium in which a wave with frequency f = 0.3 GHz is propagating, determine propagation constant and intrinsic impedance of the medium when

    i. = 0 and ii. = 10 mho/m. (Set No. 4 Apr/May 2008 Supply)

    9. For good dielectrics derive the expressions for , , and . (Set No. 1 Apr/May 2008 Reg)

    10. Find , , and . for Ferrite at 10GHz r = 9, r = 4, = 10ms/m. (Set No. 1 Apr/May 2008 Reg)

    11. For a conducting medium derive expressions for and. (Set No. 1 Apr/May 2008 Reg) 12. Determine the phase velocity of propagation, attenuation constant, phase con- stant and intrinsic impedance for a

    forward travelling wave in a large block of copper at 1 MHz ( = 5.8 107, r = r = 1) determine the distance that the wave must travel to be attenuated by a factor of 100 (40 dB)

    (Set No. 1 Apr/May 2008 Reg) 13. A plane sinusoidal electromagnetic wave travelling in space has Emax = 1500v/m i. Find the accompanying Hmax

    ii. The average power transmitted (Set No. 1 Apr/May 2008 Reg)

    14. The electric field intensity associated with a plane wave travelling in a perfect dielectric medium is given by Ex (z, t) = 10 cos (2pi x 107 t - 0.1 piz)v/m

    i. What is the velocity of propagation ii. Write down an expression for the magnetic field intesity associated with the wave if = 0

    (Set No. 1 Apr/May 2008 Reg) 15. A large copper conductor ( = 5.8 107s/m, r = r = 1)support a uniform plane wave at 60 Hz. Determine the

    ratio of conduction current to displace- ment current compute the attenuation constant. Propagation constant, in- trinsic impedance, wave length and phase velocity of propagation. (Set No. 1 Apr/May 2008 Reg)

    16. A 3 GHz uniform plane wave propagates through rexolite in the positive Z-direction the E-field at Z = 0 is 100 6 00v/m

    (Set No. 1 Apr/May 2008 Reg) 17. Calculate the RMS value and phase of E at Z=4 cm (Set No. 1 Apr/May 2008 Reg) 18. Calculate the total attenuation in dB over a distance of 6 wave lengths. For rexolite 2r=2.54 and tan =0.0005

    (Set No. 1 Apr/May 2008 Reg) Unit V Syllabus

    Wave Equations for Conducting and Perfect Dielectric Media, Uniform Plane Waves Definition, All Relations between E & H. Sinusoidal Variations. Wave Propagtion in Lossless and Conducting Media. Conductors & Dielectrics Characterization, Wave Propagation in Good Conductors and Good Dielectrics. Polarization. Related Problems.

    1. Define uniform plane wave. (Set No. 1 Apr/May 2008 Supply) 2. Define and distinguish between the terms perpendicular polarization, parallel polarization, for the case of reflection by

    a perfect conductor under oblique incidence. 3. A plane wave of frequency 2MHz is incident upon a copper conductor normally. The wave has an electric field amplitude of

    E= 2mV/m. The copper has r = 1, r = 1 and = 5.8 107 mho/m. Find out average power density absorbed by the copper. (Set No. 1 Aug/Sep 2008 Supply)

  • 4. A plane wave traveling in a medium of r = 1, r = 1 has an electric field intensity of 100ppi. Determine the energy density in the magnetic field and also the total energy density. (Set No. 3 Aug/Sep 2008 Supply)

    5. A uniform plane wave is normally incident from air on a perfect conductor. Determine the resulting E and H fields. Sketch their variations. (Set No. 4 Aug/Sep 2008 Supply)

    6. A plane EM wave is normally incident on the boundary between two dielectrics. What must be the ratio of the refractive indices of the two media in order that the reflected and transmitted waves may have equal magnitudes of average power (Set No. 4 Aug/Sep 2008 Supply)

    7. Explain wave propagation in a conducting medium. (Set No. 1 Apr/May 2008 Reg)

    Unit VI Reflection and Refraction of Plane Waves Normal and Oblique Incidences, for both Perfect Conductor and Perfect

    Dielectrics, Brewster Angle, Critical Angle and Total Internal Reflection, Surface Impedance. Poynting Vector, Poynting Theorem Applications, Power Loss in a Plane Conductor.

    1. Define and differentiate between the terms: Instantaneous average and complex poynting vectors, giving their mathematical expressions. ( Set No. 1 Apr/May 2008 Supply)

    2. State and Prove Poynting Theorem. ( Set No. 2, 3 Apr/May 2008 Supply) 3. Derive expression for Reflection and Transmission coefficients of an EM wave when it is incident normally on a

    dielectric. ( Set No. 4 Apr/May 2008 Supply)

    4. For an incident wave under oblique incident from medium of 1 to medium of 2with parallel polarization ( Set No. 4 Apr/May 2008 Supply)

    5. Explain the significances of Poynting theorem and Poynting vector. (Set No. 2 Aug/Sep 2008 Supply) 6. A Plane wave traveling in a free space has an average poynting vector of 5 watts/m2. Find the average energy

    density. ( Set No. 2, 3 Apr/May 2008 Supply) 7. Plot C and Br versus the ratio of 1/2 8. Write short notes on the following

  • (a) Surface Impedance (b) Brewster angle (c) Total Internal Reflection 9. Explain the difference between the Intrinsic Impedance and the Surface Impedance of a conductor. Show that for a good

    conductor, the surface impedance is equal to the intrinsic impedance. 10. Define surface impedance and explain how it exists. (Set No. 4 Apr/May 2008 Supply) 11. Define and establish the relations for the critical angle C and Brewster angle Br for non-magnetic media with neat

    sketches.

    12. Define Complex Poynting vector and explain how to obtain an average power. (Set No. 1 Aug/Sep 2008 Supply) 13. Prove that under the condition of no reflection at an interface, the sum of the Brewster angle and the angle of refraction is 90

    degrees for parallel polarization for the case of reflection by a perfect conductor under oblique incidence, with neat sketches. (Set No. 2 Aug/Sep 2008 Supply)

    Unit VII Syllabus: Types, Parameters, Transmission Line Equations, Primary & Secondary Constants, Expressions for Characteristic Impedance, Propagation Constant, Phase and Group Velocities, Infinite Line Concepts, Loss less ness/Low Loss Characterization, Distortion, Condition for Distortion less and Minimum Attenuation, Loading - Types of Loading.

    1. Derive a relation between reflection coefficient and characteristic impedance. (Set No. 1 Apr/May 2008 Supply)

    2. Determine the reflection coefficients when (Set No. 1 Apr/May 2008 Supply) i. ZL = Z0

    ii. ZL = short circuit iii. ZL = open circuit. iv. Also find out the magnitude of reflection coefficient when ZL is purely reactive.

    3. List out types of transmission lines and draw their schematic diagrams. (Set No. 2 Apr/May 2008 Supply)

    4. Draw the directions of electric and magnetic fields in parallel plate and coaxial lines. (Set No. 2 Apr/May 2008 Supply)

    5. A transmission line in which no distortion is present has the following parameters Z0= 50, = 20mNP/m, = 0.60. Determine R, L, G, C and wavelength at 0.1 GHz.

    (Set No. 2 Apr/May 2008 Supply) 6. List out types of transmission lines and draw their schematic diagrams.

    (Set No. 3 Apr/May 2008 Supply) 7. Draw the directions of electric and magnetic fields in parallel plate and coaxial lines.

    (Set No. 3 Apr/May 2008 Supply) 8. A transmission line in which no distortion is present has the following parameters Z0= 50, = 20mNP/m, = 0.60.

    Determine R, L, G, C and wavelength at 0.1 GHz. (Set No. 3 Apr/May 2008 Supply)

    9. What are the salient aspects of primary constants of a two wire transmission line (Set No. 4 Apr/May 2008 Supply)

    10. A lossless transmission line used in a TV receiver has a capacitance of 50 PF/m and an inductance of 200 nH/m. Find out the characteristic impedance for 10 meter long section of the line and 500 meter section. (Set No. 4 Apr/May 2008 Supply)

    11. Explain the different types of transmission lines. What are limitations to the maximum power that they can handle (Set No. 1 Apr/May 2008 Reg.)

    (Set No. 1 Aug/Sep 2008 Supply) 12. A coaxial limes with an outer diameter of 8 mm has 50 ohm characteristic impedance. If the dielectric constant of the

    insulation is 1.60, calculate the inner diameter. (Set No. 1 Apr/May 2008 Reg.) (Set No. 1 Aug/Sep 2008 Supply)

    13. Describe the losses in transmission lines (Set No. 1 Apr/May 2008 Reg.) (Set No. 1 Aug/Sep 2008 Supply)

    14. Definite following terms and explain their physical significance. i. Attenuation function ii. Characteristic impedance iii. Phase function, and iv. Phase velocity as applied to a transmission line. (Set No. 2 Apr/May 2008 Reg.)

  • 15. At 8 MHz the characteristic impedance of transmission line is (40-j2) and the propagation constant is (0.01+j0.18 ) per meter. Find the primary constants. (Set No. 2 Apr/May 2008 Reg.)

    16. Define the following i. Infinite line ii. Insertion loss iii. Lossy and loss less lines iv. Phase and group velocities (Set No. 3 Apr/May 2008 Reg.)

    17. Derive the characteristic impedance of a transmission line in terms of its line constants (Set No. 3 Apr/May 2008 Reg.)

    18. Explain the meaning of the terms characteristic impedance and propagation constant of a uniform transmission line and obtain the expressions for them in terms of Parameters of line?

    (Set No. 4 Apr/May 2008 Reg.) 19. A telephone wire 20 km long has the following constants per loop km resistance 90 , capacitance 0.062 F , inductance

    0.001H and leakage = 1.5 x 106 mhos. The line is terminated in its characteristic impedance and a potential difference of 2.1 V having a frequency of 1000 Hz is applied at the sending end. Calculate :

    i . The characteristic impedance ii. Wavelength iii. The velocity of propagation (Set No. 4 Apr/May 2008 Reg.)

    19. Sketch the voltage and current distribution along matched, open and short circuited transmission lines. (Set No. 1, 4 Aug/Sep 2007 Supply)

    20. A line 10 km long has the following line constants: Z0= 600 |0 0 = 0.1neper/km = 0.05radians/km Find the received current and voltage when 200 mA are sent down into one end, and the receiving end is shorted.

    (Set No. 1, 4 Aug/Sep 2007 Supply) 21. Define the i/p impedance of a transmission line and derive the expression for it.

    (Set No. 2, 3 Aug/Sep 2007 Supply) (Set No. 2 Aug/Sep 2008 Supply)

    22. The characteristic impedance of a certain line is 710 |140 and = 0.007 + j0.028 per km. The line is terminated in a 300Ohm resistor. Calculate the i/p impedance of the line if its length is 100 km.

    (Set No. 2, 3 Aug/Sep 2007 Supply) (Set No. 2 Aug/Sep 2008 Supply)

    23. Show that for any uniform transmission line the following relations are valid. Z0 = (Zoc.Zsc)1/2 TanhP1 = (Zsc/Zoc)1/2 What will be their modifications for loss less lines? (Set No. 3 Aug/Sep 2008 Supply)

    24. Short-circuited and open ?circuited measurements at frequency of 5000 Hz on a line length 100 km yields the following results: Zoc = 570? 480 Zsc = 720, 340 Find the characteristic impedance and propagation constant of the line. (Set No. 3 Aug/Sep 2008 Supply)

    25. List out types of transmission lines and draw their schematic diagrams. (Set No. 4 Aug/Sep 2008 Supply) 26. Draw the directions of electric and magnetic fields in parallel plate and coaxial lines.

    (Set No. 4 Aug/Sep 2008 Supply) 27. A transmission lines in which no distortion is present has the following parameters Z0 = 50 , = 20 mNP/m = 0.60.

    Determine R, L, G, C and wavelength at 0.2 GHz (Set No. 4 Aug/Sep 2008 Supply)

    Unit VIII Syllabus: Input Impedance Relations, SC and OC Lines, VSWR. UHF Lines as Circuit Elements; /4, /2, /8 Lines Impedance Transformations, Smith Chart Configuration and Applications, Single and Double Stub Matching.

    1. An EM wave of 3 W/m2 Power density is incident normally from air on a perfect dielectric boundary. If the resulting VSWR is 2.2, find the reflected and transmitted powers. ( Set No. 1 Apr/May 2008 Supply)

    2. Explain how UHF lines can be treated as circuit elements, giving the necessary equivalent circuits. (Set No. 1Apr/May 2008 Supply)

    3. A loss less line of 100 is terminated by a load which produces SWR = 3. The first Maxima is found to be occurring at 320 cm. If f = 300 MHz, determine load impedance. (Set No. 1Apr/May 2008 Supply) Draw the equivalent circuits of a transmission lines when

    i. length of the transmission line, 1

  • ii. when 1
  • the load voltage to be 10 V, calculate the r.m.s voltage and current at intervals of one fourth wave length from the load up to a distance 5 cm.

    (Set No. 1 Aug/Sep 2008 Supply) 29. A 75 line is terminated by a load of 120 + j80. Find the maximum and minimum impedances on the line.

    (Set No. 1 Aug/Sep 2008 Supply)