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19. Unit wise Quiz Questions and long answer questions
UNIT – 1
(a). Objective Questions
1. Electric field intensity and electric flux density are related by the equation------
2. Coulomb’s force law equation is given by-------
3. According to gauss law flux passing through the closed surface φ = -------
4. According to divergence theorem surface integral is related to------
5. Maxwell’s first equation in electro static fields is derived from------
6. Maxwell‘s first equation in integral form is given by-----------
7. Maxwell‘s first equation in point form is given by-----------
8. Electrostatic field is conservative. TRUE/FALSE
9. Azimuthal angle varies from---to-----
10. Limits of elevation angle are------
11. Work done in moving a charge from one point to other point on equipotential
surface is
a) zero b) infinity c) depends on the charge d) none
12. Work done in moving a charge around the closed path is
a) zero b) infinity c) depends on the charge d) none
13. At every point in space aФ . aθ = 1 TRUE/FALSE
14. a unit vector normal to the cone θ = 300 is
a) aФ b) aθ c) ar d) none
15. which of these is not valid at (0,4,0)
a) aФ = - a x b) aθ = - a z c) a r = 4 ay
16. where surfaces ρ = 2 and z = 1 intersect is
a) cone b) circle c) cylinder
17. Relation between E and V is given by----------
18. Curl of gradient of a scalar is equal to--------------
19. Divergence of curl of any vector is given by------------
20. Maxwell‘s second equation in point form is given by-----------
(b). Descriptive Questions
1. Derive the equation for electric field intensity at any point due to infinitely long line charge.
2. Write a short notes on stream lines.
3. Derive the equation of a field due to infinite sheet of charge.
4. What is flux density? Explain Gauss law and divergence theorem.
5. What is coulombs law of force? Define and distinguish the terms electric field intensity, electric flux density.
6. Write a short notes on poisson’s and laplace equation.
7. Four 10 nc positive charges are located in the z=0 plane at the corners of a square 8 cm
on a side. A fifth 10 nc positive charge is located at a point 8 cm distant from each of the
other charges. Calculate the magnitude of the total force on the fifth charge for Є=Є.
8. The volume charge density ρv = exists over all free space. Calculate the total
charge present.
9. A uniform surface charge density of 5nC/m^2 is at y=0 , z=2m in free space, while -
5nC/m is located at y=0 , z=-2m. A uniform surface charge density of 0.3 nC/m^2 is at
y=0.2 m , and -0.3nC/m^2 is at y = - 0.2m. Find |E| at the origin.
10. Surface charge density is positioned in free space as follows : 20nC/m^2 at x= -3 , -
30nC/m^2 at y=4, and 40 nC/m2 at z= 2. Find the magnitude of E at (a) Pa(4,3,-2);
(b)Pb(-2,5,-1); (c) Pc(0,0,0).
11. If , find the total electric flux leaving the surface of the cube, .
12. Two uniform line charges, each 20nC/m are located at y=1, z= ±1m. Find the total
electric flux leaving the surface of a sphere having a radius of 2m , if it is centered at : (a)
A(3,1,0): (b) B(3,2,0).
13. The cylindrical surfaces ρ = 1,2, and 3 cm carry uniform surface charge densities of 20,-8
and 5 nC/m2, respectively. How much electric flux passes through the closed surface
ρ=5xm , 0<z<1m? Find D at P(1cm,2cm,3cm).
14. If C/m^2 , evaluate both sides of the divergence
theorem for the region : 1<r<2m , 1<θ<2rad , 1<Ø<2rad.
15. Let a uniform surface charge density of 5nC/m^2 be present at the z=0 plane , a uniform
line charge density of 8nC/m be located at x=0 , z=4, and a point charge of 2µC be
present at P(2,0,0). If V=0 at M(0,0,5) find V at N(1,2,3).
16. Find the energy stored in free space for the region 2mm<r<3mm, 0<θ<90° , 0<Ø<90°,
given the potential field V= :
17. A charge =-20µC is located at A(-6,4,7) and a charge =50µC is at B(5,-8,-2) in free
space. If distances are given in meters, Find : (a) ; (b) Determine the vector force
exerted on by if .
18. Infinite uniform line charges of 5nC/m lie along the (positive and negative) x and y axes
in free space . Find E at: (a) (0,0,4); (b) (0,3,4).
19. Three infinite uniform sheets of charge are located in free space as follows : 3nC/ at
z=-4, 6nC/ at z=1, and -8nC/ at z=4. Find E at the point: (a) (2,5,-5); (b)
(4,2,-3) (c) (-1,-5,2) (d) (-2,4,5).
20. Two identical uniform line charges , with , are located in the x=0 plane at y=±0.4m .
What force per unit length does each line charge exert on the other.
21. Given the surface charge density, in the region ρ<0.2m,z=0, and is zero
elsewhere, find E at (a) (ρ=0,z=0.5) (b) (ρ=0,z=-0.5).
22. Uniform line charges of 120nC.m lie along the entire extent of the three coordinate axes.
Assuming free space conditions , find E at : (a) P(-3,2,-1).
23. A uniform line charge of 2 µC/m is located on the z axis. Find E in Cartesian coordinates
at P(1,2,3) if the charge extends from : (a) Z = -∞ to Z = ∞ ; (b) Z=-4 to Z=4.
24. Volume charge density is located in free space as for 0<r<1mm, and
=o elsewhere. (a) Find the total Charge enclosed by the spherical surface r =1mm. (b)
By using Gauss’s law, calculate the value of Dr on the surface r=1mm.
25. Given the field , , find : (a) the volume charge density ; (b) the
total charge contained in the region r < 2m ; (c) the value of D at the surface r = 2 ; (d)
the total electric flux leaving the surface r = 2 .
26. Let the surface y=0 be a perfect conductor in free space. Locate a point charge of 4nC at
P1(7,1,-2) , and a point charge of -3nC at p2(4,2,1) (a) Find E at A(5,0,0) (b) Find | | at
B(3,0,0).
27. Two concentric spherical shells separated by a dielectric €p = 4 have radius r = 10 cm
(inner) and R = 12 cm (outer). A potential difference of 1000 volt exists between them.
Calculate the energy stored between the shells.
28. Eight 25 n c point charges in free space are located symmetrically on a circle of radius
0.2 m centered at the origin in the z = 0 plane. at what point on the z axis is E maximum?
What is the value of E max?
29. The portion of the z axis for which -2,z,2 m carries a non uniform charge density of z 2 +
1 n c/m in free space Find E at (1,0,0).
30. Find E at (1,5,2) in free space if a point charge of 6 uc is located at (0,0,1), a uniform
line charge of 180nc/m lies along the X axis, and a uniform surface charge of 25nc/m2
lies in the z = 1 plane.
31. If E = -8xy ax – 4x2 ay + az v/m Find the work done in moving 6 c charge from( 1,8,5) to
(2,18,6) along the path y = 3x2 + z, z = x+4.
UNIT II
(a). Objective Questions
1. Magnetic field is produced due to static charges TRUE/FALSE.
2. Magnetic flux line are continuous around the closed path
a) true b) false
3. According to biotsavert’s law dH is given by-----
4. Ampere’s circuital law in integral form is given by-----
5. Maxwell’s equation based on ampere’s law is
a) Div D = ρv b) curl of H = J
6. Maxwell’s equation based on non existence of magnetic monopole is given by------
7. Match the following
A. Electric field 1. Amp/meter2
B. Magnetic flux density 2. Coulombs/meter2
C. Current density. 3. Tesla
D. Magnetic field strength 4.volt/meter
5. amp/meter
8. Relation between vector potential and magnetic flux density is -----
9. Magnetic vector potential equation in integral form---------
10. Two Maxwell’s equations in integral form are given by---------
11. Magnetic flux lines are closed loops due to------------
12. one of the following is not a source of magnetic field.
a) an accelerated charge b) a dc current in a wire.
13. Which of these statements is not a characteristic of of a static magnetic field
a)it has no sinks or source b) it is conservative.
14. According to Maxwell . D = --------
15. According to Maxwell X H = ------------
16. According to Maxwell . B= --------
17. According to Maxwell XE = -----------
18. Units of surface charge density is--------
19. Units of magnetic field intensity is--------
20. Unit of magnetic flux is ---------
(b). Descriptive Questions
1. Define and explain the Biot-Savart's Law. Hence obtain the field due to a straight current
carrying filamentary conductor of finite length.
2. Explain the terms “Conduction current” and “Displatement Current”. Deduce the
equation of continuity of current.
3. Derive boundary conditions to be satisfied at the boundary surface of two different
magnetic media.
4. Write a short notes on ampere circuital law?
5. Derive the equations for the internal and external inductance of a co axial cable.
6. Derive the equation of inductance for the solenoid and toroid.
7. A current filament of 3 A lies along the x axis. Find H in Cartesian components at P(-
1,3,2).
8. An infinite filament on the z axis carries 20 П mA in the direction. Three uniform
cylindrical current sheets are also present: 400 mA/m at ρ=1 cm , -250 mA/m at ρ=1 cm ,
-250 mA/m at ρ=2 cm, and -300 mA/m at ρ=3 cm . Calculate at ρ=0.5, 1.5, 2.5 and
3.5 cm.
9. Evaluate both sides of stokes’ theorem for the field G=10sinθ and the surface r=3,
0≤θ≤ 90° , 0≤Ø≤ 90°. Let the surface have the direction.
10. The magnetization in a magnetic material for which Xm=8 is given in a certain region as
a. 150 . At z=4cm , find the magnitude of : (a) ; (b) J; (c)
11. A conducting filament at z=0 carries 12 A in the direction. Let =1 for ρ<1 cm,
=6 for 1<ρ<2 cm , =1 for ρ<2 cm . Find (a) H everywhere; (b) B everywhere
12. A toroidal core has a rectangular cross section defined by the surfaces ρ=2 cm, ρ=3 cm,
z=4cm , z=4.5 cm. The core material has a relative permeability of 80. If the core is
wound with a coil containing 8000 turns of wire, find its inductance.
13. Find the magnetization in a magnetic material where: (a) µ = 1.8 × H/m and H=120
A/m; (b) , there are 8.3 × atoms/ , and each atom has a dipole moment
of 4.5 × A. ; (c) B=300µT and =15.
14. Given a ferrite material which we shall specify to be operating in a linear mode with
B=0.05T, let us assume , and calculate values for , M , and H.
15. A current filament carrying 15 A in the direction lies along the entire z axis. Find H in
Cartesian coordinates at : (a) (b) (2,-4,4).
16. Let the permittivity be 5µH/m in region A where x<0, and 20µH/m in region B where
x>0. If there is a surface current density K=150 -200 A/m at x=0, and if =300
-400 +500 A/m, find: (a) | | (b) | |(c)| | (d) | |.
17. A solenoid is 50-cm long , 2cm in diameter, and contains 1500 turns . The cylindrical
core has a diameter of 2 cm and a relative permeability of 75. This coil is coaxial with a
second solenoid, also 50 cm long , but with a 3-cm diameter and 1200 turns. Calculate :
i. L for the inner solenoid; (b) L for the outer solenoid;(c) M between the
two solenoids.
18. Two infinitely long parallel filaments each carry 50 A in the direction. If the filaments
lie in the plane y=0 and x=5mm, find the vector force per meter length on the filament
passing through the origin.
19. Calculate the self-inductances of and the mutual inductances between two coaxial
solenoids of radius and , < , carrying currents I1 and I2 with n1 and n2
turns/m, respectively.
20. The cylindrical shell, 2mm < ρ< 3mm, carries a uniformly distributed total current of 8 A
in the - direction, and a filament on the z axis carries 8 A in the direction. Find H
everywhere.
21. Let a filamentary current of 5mA be directed from infinity to the origin on the positive z
axis and then back out of infinity on the positive x axis, Find H at P(0,1,0).
22. Evaluate both sides of the strokes’ theorem for the field H=6xy -3 A/m and the
rectangular path around the region, 2≤x≤5, -1≤y≤1,z=0. Let the positive direction of dS
be
23. A solid nonmagnetic conductor of circular cross section has a radius of 2mm. The
conductor is in homogenous, with . If the conductor is 1m in
length and has a voltage of 1mV between its ends, find: (a)H;(b) the total magnetic flux
inside the conductor .
24. Use an expansion in Cartesian coordinates to show that the curl of the gradient of any
scalar field G is identically equal to zero.
25. The free-space region defined by 1<z<4cm and 2<ρ<3cm is a toroid of rectangular cross
section. Let the surface at ρ=3cm carry a surface current K=2 kA/m. (a) Specify the
currents on the surfaces at ρ=2cm , z=1cm , and z=4 cm. (b) Find H everywhere. (c)
Calculate the total flux within the toroid.
26. A filamentary conductor on the z axis carries a current of 16 A in the direction, a
conducting shell at ρ=6 carries a total current of 12 A in the - direction, and another
shell at ρ=10 carries a total current of 4 A in the - direction. (a) Find H for 0<ρ<12. (b)
Plot versus ρ . (c) Find the total flux Ø crossing the surface 1<ρ<7, 0<z<1.
27. Determine the flux density at the center of a semi-circular current ring of radius ρ.
28. A long conductor carries steady current along the z-axis. Integrate H along a square loop
(X-Y plane) boundary of one meter side around the conductor. Verify Ampere's circuital
law.
29. Two long parallel wires separated 3 m apart carry currents of 50 A and 100 A
respectively in the same direction. Determine the magnitude and direction of the force
between them per unit length.
30. Find the H in Cartesian system at (1.5,2,3) caused by a current filament of 24 A in the az
direction on the Z axis extending from z= 0 to z = 6. and z= - ∞ to ∞.
31. A filamentary current of 10 A is directed from ∞ to the origin on the positive X axis
and then back to ∞ along the positive y axis. Use biot savert’s law to find H at (0,0,1).
UNIT – III
(a) Objective Questions
1.Which of these is not a correct form of the wave Ex = cos (wt-βz)?
a. cos (βz-wt) b. sin(βz-wt-900)
c.cos β( z-ut) d. none
2. Identify which of these functions do not satisfy the wave equation
(a) 50 e jw(t-3z) (b) sin w(10z + 5t)
(c) COS2(y +5t) (d) sin x cos t
3. Which of the following statements is not true of waves in general?
(a) It may be a function of time only.
(b) It may be sinusoidal or cosinusoidal.
(c) It must be a function of time and space.
(d) For practical reasons, it must be finite in extent.
4. The electric field component of a wave in free space is given by 10 cos(107t + kz) ay
V/m. It can be inferred that
(a) The wave propagates along ay.
(b) The wavelength = 188.5 m.
(c) The wave amplitude is 10 V/m.
(d) The wave number k = 0.33 rad/m.
(e) The wave attenuates as it travels.
5. Given that H = 0.5 e-O.lx sin (l06t - 2x) az A/m, which of these statements are incorrect?
(a) α = 0.1Np/m
(b) β = -2 rad/m
(c) w = 106 rad/s
(d) The wave travels along aX
6. What is the major factor for determining whether a medium is free space, lossless
dielectric, lossy dielectric, or good conductor?
(a) Attenuation constant
(b) Constitutive parameters (ε, σ, μ)
(c) Loss tangent
(d) Reflection coefficient
7. A certain medium, E = 10cos(l08t- 3y) axV/m. What type of medium is it?
(a) Free space
(b) Perfect dielectric
(c) Lossless dielectric
(d) Perfect conductor
8. Electromagnetic waves travel faster in conductors than in dielectrics.
(a) True
(b) False
9 . In a good conductor, E and H are in time phase.
(a) True.
(b) False
10. In a good conductor angle between E and H is-------
11. Relation between loss tangent and phase angle of E and H is -------
12. If σ / wЄ >> 1 , that material is a good-----------
13. If σ / wЄ << 1 , that material is a good-----------
14. Condition to be satisfied to locate the demarcation line between conductors and
dielectrics is -----------
15. Given that H = 0.5 e-O.5x sin (l06t - 2x) a z A/m, which of these statements are
incorrect?
(a) α = 0.1Np/m
(b) β = -2 rad/m
(c) w = 106 rad/s
(d) The wave travels along aX
16. Which of the following statements is true of waves in general?
(a) It may be a function of time only.
(b) It may be sinusoidal or cosinusoidal.
(c) It must be a function of time and space.
(d) For practical reasons, it must be finite in extent.
(e) b,c,d
17. Electro magnetic waves trvel faster in conductors than in dielectrics
a) TRUe b) FALSE
18. velocity of EM wave in terms of prmitivity and permeability is given by----------
19. Propagation constat interms of attenuation and phase shift constant is ----------
20. Propagation constant is a complex quantity. TRUE/FALSE.
21. The pointing vector physically denotes the power leaving or entering a given volume in a
time varying field
(a) True (b) False
22. Reflection co efficient is defined as-------
23. Transmission co efficient is defined as--------
24. Symbol of reflection co efficient is--------
25. Symbol of transmission co efficient is---------
26. Poyinting vector is given by---------
27. Average poyinting vector is given by---------
28. Complex poyinting vector is given by---------
29. Relation between Average poyinting vector & Complex poyinting vector is given by-----
30. Poyinting theorem is based on--------
31. Using pointing theorem we can calculate--------
32. Outward flow of power from a closed surface is given by-------
33. Inward flow of power from a closed surface is given by--------
34. Reflection co efficient in the case of reflection by a perfect conductor (normal
incidence) is----------
35. Reflection co efficient in the case of reflection by a perfect insulator (normal incidence)
is----------
36. Reflection co efficient in the case of reflection by a perfect insulator (oblique
incidence) is----------
37. Parallel polarization is defined as---------
38. Perpendicular polarization is defined as----------
39. Other name of parallel polarization is
a) Vertical polarization b) perpendicualr polarization
40. Other name of vertical polarization is
a) Horizontal Polarization b) Parallel polarization
(b). Descriptive Questions
1. What is meant by the polarization of wave. When the wave is linearly polarized and
circularly polarized.
2. Find all the relations between E & H in a uniform plain wave. Hence find the value of
intrinsic impedance of free space.
3. What is skin effect discuss the depth of penetration in dielectrics and conductors by
deriving necessary relations.
4. Distinguish between good conductors and good dielectrics. Explain the wave
propagation in good dielectrics.
5. Write a short notes on poynting theorem.
6. Let Find (a) E at
P(0,2,0.6) at t=25 ns (b) |E| at P at t=20ns (c) Es (d) Es at P.
7. An H field in free space is given as H (x,t) =10cos ( t – βx) A/m Find (a) β
(b) λ (c) E(x,t) at P(0.1,0.2,0.3) at t=1ns.
8. In phasor form , the electric field intensity of a uniform plane wave in free space is given
by V/m . Find (a) w (b) β (c) F (d)λ (e) Hs (f) H(z,t) at P(6,-
1,0.07) , t=71 ps
9. A 150 MHz uniform plane wave in free space is described by
A/m (a) Find numerical values for W, λ and β (b) Find
H(z,t) at t = 1.5ns , z=20 cm (c) What is ?
10. Let for the field E(z,t) = 1800 (a) Find w (b)
Determine the displacement current density Jd(z,t) (c) Find the total magnetic flux Ø
passing through the rectangle defined by 0<x<1, y=0,0<z<1, at t=0 .
11. A phasor magnetic field intensity for a 400 MHz uniform plane wave propagating in a
certain lossless material is A/m . Knowing that the maximum
amplitude of E is 1500 V/m , Find β , η , λ , and H(x,y,z,t).
12. A good conductor is planar in form , and it carries a uniform plane wave that has a
wavelength of 0.3mm and a velocity of 3× m/s Assuming the conductor is
nonmagnetic , determine the frequency and the conductivity .
13. A hollow tubular conductor is constructed from a type of brass having a conductivity of
1.2 × S/m . The inner and outer radii are 9 and 10 mm , respectively . Calculate the
resistance per meter length at a frequency of (a) dc (b) 20 MHz (c) 2 GHz
14. Given a wave for which V/m (a) Find Hy (b) determine the
average power density in W/ .
15. The electric field intensity of a uniform plane wave in free space is given by
(a) Determine the frequency f (b) find the magnetic field
phasor Hs (c) Describe the polarization of the wave .
16. A uniform plane wave in free space has electric field vector given by
(a) Describe the wave propagation (b) Find Hs (c)
Determine the average power density in the wave in W/ .
17. Let the fields , E(z,t) =1800 V/m and H(z,t) =3.8
A/m , represent a uniform plane wave propagating at a velocity of 1.4 × m/s . in a
perfect dielectric . Find (a) β (b) λ (c) η (d) (e)
18. A certain lossless material =4 and =9 . A 10 MHz uniform plane wave is
propagating in the direction with = 400 V/m and = = 0 at P(0.6,0.6,0.6)
at t = 60 ns . (a) Find β ,λ , η , and (b) Find E(t) (c) Find H(t) .
19. Given a 20 MHz uniform plane wave with Hs = A/m , assume
propagation in a lossless medium characterized by = 5 and an unknown (a) Find
,λ , η , and ( (b) Determine E at the origin at t = 20 ns.
20. A 2-GHz uniform plane wave has an amplitude = 1.4kV/m at (0,0,0,t=0) and is
propagating in the direction in a medium where F/m ,
F/m , and µ = 2.5 H/m . Find (a) Ey at P(0,0,1.8cm) at 0.2ns (b) Hx at P at 0.2 ns.
21. The plane wave Es = 300 V/m is propagating in a material for which µ = 2.25
µH/m, , and . If w=64 Mrad/s, find (a) λ ,β, η, α and (b)
Hs (c) E(3,2,4,10ns).
22. A 10 GHz radar signal may be represented as a uniform plane wave in a sufficiently
small region. Calculate the wavelength in centimeters and the attenuation in nepers per
meter if the wave is propagating in a mon magnetic material for which (a) and
(b) and (c) and .
23. The inner and outer dimensions of a coaxial copper transmission line are 2 and 7 mm ,
respectively . Bothe conductors have thickness much greater than δ. The dielectric is
lossless and the operating frequency is 400 MHz. Calculate the resistance per meter
length of the (a) inner conductor (b) outer conductor (c) transmission line.
24. Let jk = 0.2+j1.5 and η=450+j60Ω for a uniform plane propagating in the
direction. If w=300 Mrad/s , find є’ , є’’ and µ for the medium .
25. The cylindrical shell , 1cm<ρ<1.2 cm , is composed of a conducting material for which σ
= S/m. The external and internal regions are nonconducting . Let =2000 A/m at
ρ=1.2cm. (a) Find H everywhere (b) Find E everywhere (c) Find ρ everywhere.
26. If distilled water has μr = 1 Єr = 81 and power factor = 0.05 at 1GHz. Calculate the
depth of penetration.
27. What is the axial ratio.
28. What is the tilt angle of the major axis of the polarization ellipse.
29. What is the sense of rotation.
30. In a medium EZ = 16e-x/20 sin[108 t – 2x] V/m find the direction of propagation the
propagation constants, wave length, speed of the wave & skin depth.
31. An EM wave is propagated through a material having at μr = 5 Єr = 10. Determine
the velocity of propagation, intrinsic impedance of free space, wave length in free
space if f = 1GHz.
32. In a medium EZ = 10e-x/20 sin[2.108 t – 2x] V/m find the direction of propagation the
propagation constants, wave length, speed of the wave & skin depth
33.Derive the relation between E and H in free space.
34.Derive the relation between E and H for any general medium.
35.Discuss the wave propagation in good conductors.
36.Discuss the wave propagation in good dielectrics.
37.Write a short notes on
1. skin depth
2. Brewster angle.
38.Write about Reflection of Plane waves.
39.Write about Refraction of Plane waves.
40.What is Normal incidence for Perfect Conductors?
41.What is Normal incidence for Perfect Dielectrics?
42.What is Oblique incidence for Perfect Conductors?
43.What is Oblique incidence for Perfect Dielectrics?
44.When does total internal reflection takes place for plane waves?
45.Explain about Brewster angle?
46.What is Critical Angle?
47.What is Surface impedance?
48.What is the significance of Poynting Theorem?
49.Light is incident from air to glass at Brewster’s angle. Determine the incident and
transmitted angles.( Refractive index of glass is .
50. Write a short notes on Linear Polarization?
51.Write a short notes on Elliptical Polarization?
52.Write a short notes on Circular Polarization?
53.Determine the reflection coefficients for an electromagnetic wave incident normally on (a)
a sheet of copper (b) a sheet of iron . Use f = 1 MHz Assume σ=1× mhos/m , µ = 1000
for the iron.
54.A sheet of glass, having a relative dielectric constant of 8 and negligible conductivity, is
coated with a silver plate. Show that at a frequency of 100 MHz the surface impedance will
be less for a 0.0001 cm coating than it is for a 0.0002 cm coating, and explain why.
55.Write the equations for the power loss of Plane waves in a Plane conductor?
56.Determine the normal incidence reflection coefficients for sea, water, fresh water, and
“good” earth at frequencies of 60 Hz, 1 MHz, and 1 GHz . Use =80, σ = 4 mhos/m for sea
water; =80,
σ = 5 × mhos/m for fresh water; and = 15, σ = 10 × mhos/m for good earth.
57.A copper wire carries a conduction current of 1 amp. Determine the displacement current
in the wire at 100 MHz. (Assume that copper has about the same permittivity as free space ,
that is . For copper σ = 5.8 × mhos/m.
58.In free space z<=0, a plane wave with Hx = 10 cos (108t-βz) is incidenting normally on
aloss less medium with Є=2Є0 , μ=8μ0 in region z>0. determine the reflected wave and
transmitted wave.
59.A 5GHz uniform plane wave with E x = 10 e-jβz v/m is incident normally on a loss less
medium with Є=4Є0 , μ=μ0 in region z>0. determine the reflected wave and transmitted
wave.
60.A y-polarized uniform plane wave with fields (Ej, H) and a frequency of 100 MHz
propagates in air in the + x direction and impinges normally on a perfectly conducting
plane at x = 0, assuming the amplitude of Ej to be 6 mV/m, write the phasor and
instantaneous expressions for.
i. Ej and Hj of the incident wave
ii. E,.and Hr of the reflected wave.
61.For the above data
b. ET and HT of the total wave in air
c. Determine the location nearest to the conducting plane where ET and HT are
zero.
62.In free space z<=0, a plane wave with Hx = 20 cos (109t-βz) is incidenting normally on a
loss less medium with Є=3Є0 , μ=5μ0 in region z>0. determine the reflected wave and
transmitted wave.
UNIT – IV
(a). Objective Questions
1. Which of the following statements are not true of the line parameters R, L, G and C?
(a) Rand L are series elements.
(b) G and C are shunt elements.
I(c) G = 1/R (d) LC = με and RG =σε.
2. For a lossy transmission line, the characteristic impedance does not depend on
(a) The operating frequency of the line
(b) The length of the line
(c) The load terminating the line
(d) The conductivity of the conductors
(e) The conductivity of the dielectric separating the conductors
3. Which of the following conditions will not guarantee a distortionless transmission line ?
(a) R = 0 = G
(b) RC = GL
(c) Very low frequency range (R >>wL, G>>wC)
(d) Very high frequency range (R<<wL, G <<wC)
4. Which of these is not true of a lossless line?
(a) Zin = - jZ0 for a shorted line with l = χ / 8.
(b) Zin = joo for a shorted line with f = χ /4.
5. In air line adjacent maximum are found at 12.5 cm and 37.5 cm. The operating
frequency is------------
6. Which of these is not true for a lossless line
(a) Zin = jZo for an open line with € = 'A12.
(b) Zin = Zo for a matched line.
7. A lossless transmission line of length 50 cm with L = 10uHlm,C = 40 pF/m is
operated at 30 MHz. Its electrical length is
(a) 20χ
(b) 0.2 χ
(c) 108°
(d) None of the above
Write true (T) or false (F) for each of the following statements.
8. All r- and x-circles pass through point (Γr, Γi ) = (1, 0).
9. Any impedance repeats itself every χ/4on the Smith chart.
10. An s = 2 circle is the same as ׀ Γ 0.5 = ׀ circle on the Smith chart.
11. The basic principle of any matching scheme is to eliminate the reflected wave between
the source and the matching device.
12. The slotted line is used to determine ZL only.
13. At any point on a transmission line, the current reflection coefficient is the reciprocal of
the voltage reflection coefficient at that point.
14. In an air line, adjacent maxima are found at 12.5 cm and 37.5 cm. The operating
frequency is
(a) 1.5 GHz
(b) 600 MHz
(c) 300 MHz
(d) 1.2 GHz
15. Two identical pulses each of magnitude 12 V and width 2 us are incident at t = 0 on a
lossless transmission line of length 400 m terminated with a load. If the two pulses are
separated 3 us and u = 2 X 108 m/s, when does the contribution to VL(l, t) by the second pulse
start overlapping that of the first?
(a) t = 0.5 us
(b) t = 2 us
(c) t = 5 us
(d) t = 5.5 us
(e) t = 6 us
16. Condition for low loss ness on the transmission line is given by------------
17. Adding short stubs of inductors to the transmission line is known as---------
18. Input impedance of the infinite line is known as-----------------
19. Propagation constant equation is given by-------------
20. Propagation constant and characteristic impedance are known as---------
(b). Descriptive Questions
1. Define input impedance of a transmission line and derive the expression for it.
2. Explain how input impedance varies with frequency with neat sketches.
3. Define the terms
i. Propagation constant
ii. characteristic impedance
iii. phase velocity
iv. group velocity.
4. Explain the concept of infinite line.
5. Derive the condition for Distortionlessness and minimum attenuation.
6. Write a short notes on loading and types of loading.
7. Derive an expression for the characteristic impedance Zo, attenuation constant L,
Velocity of Propagation Vp and wavelength of a transmission line in terms of the primary
constants.
8. Define the following terms and their physical significance :
(i) Attenuation Function (ii) Characteristic Impedance
(iii) Propagation constant, and (iv) Phase velocity, as applied to transmission line
9. Prove that a line of a finite length and terminated by its characteristic impedance Zo is
equivalent to a line of an infinite length.
10. Calculate the characteristic impedance, attenuation constant and phase velocity on a 2 km
long line at 796 Hz, when the primary constants of the line are 42.9 Ω/km, m0.7 mH/km,
0.1 µF/km and 42.9Ω/km
11. The propagation constant of a line at 1000 Hz is 0.1855∟78.45°. Calculate the values of
(i) α (ii) β and (iii) Vp.
12. A telephone line has the following constants per loop km :
Series resistance 10.15 ohms
Series inductance 3.93 mH
Capacitance 0.008 mF
Conductance 0.92 micro-mho
Calculate the characteristic impedance, attenuation and phase constant at w = 5,000
rad/sec.
13. The propagation function at 1,000 Hz for a certain line is P = 0.008 + j0.0029. The
absolute value of the characteristic impedance is 700 ohm. Assuming that G=0, find R,L
and C
14. Derive the equations for voltage and current at any point on a simple transmission line.
Explain the meaning of the real and imaginary parts of the propagation constant.
15. Name of the types of transmission lines used in communication link state the factors
deciding primary constants of a line.
16. Derive the condition for distortionless transmission line.
17. How is transmission line made distortionless in practice.
18. Clearly explain the purpose of loading of telephone cables.
19. What are the reasons for the occurance of distortion during transmission of signals along
a transmission line? Derive the condition for the line to be distortionless.
20. For an unloaded cable in which R>> Lω and ωC<<G derive the expression for
attenuation constant , phase constant and velocity of propagation .
21. Obtain Cambell’s equation for a loaded cable.
22. Define frequency distortion and delay distortion with reference to a transmission line
23. What are the different ways of approaching the distortionless condition.
24. The primary constants of a transmission line are 42.9 Ω/km, 0.7mH/km , 0.1µF/km and
2.4µmho/km . Find the value of inductance to be placed every 0.6 km so that the line
becomes distortionless.
25. The transmission line has the following primary constants at angular frequency of 0.40
rad/sec :
i. R = 40 ohms/km
ii. L = 1mH/km
iii. C = 0.065µF/km
iv. G = 1.2 × 10^-6 mho/km.
26. If loading coil of inductance 0.32 mH and resistance 2.5 ohms are added at regular
intervals of 1.45 km calculate the secondary constants of the loaded lines.
27. Write short notes on :
i. (a) Transposed lines (b) Loaded lines (c) Loading coils
ii. (d) Lumped loading (e) Ocean Cable (f) Phantom circuits
28. The characteristic impedance of certain line is 710∟140 and γ = 0.007+j0.028 per
Km. The line is terminated in a 300ohm resistor. Calculate the input impedance if
its length is 100Km.
29. A lossy cable which has R = 2.25 ohm/m, L= 1uH/m, C= 1pf/m, G= 0 operates at
f = 0.5 Ghz. Find out the attenuation constant of the line.
30. A transmission line which has no distortion is present has the following parameters
Z0 = 50 ohms, α = 20 mNP/m v= 0.6v0. Determine the R,L,G,C and wavelength at
0.1 GHz.
31. A line 10 Km long has Z0 = 600 ohms α = 0.1NP/km β= 0.05 rad/km. Find the received
current and voltage when 200 ma current is sent down in to one end and receiving end is
shorted.
32. An open-wire transmission line having Z0= 650 ∟-12° ohms is terminated in Z0 at the
receiving end. If this line is supplied from a source of internal resistance ohms, calculate
the reflection factor and reflection loss at the sending end terminals.
UNIT – V
(a). Objective Questions
1. Characteristic impedance of a short circuit line is -------
2. Characteristic impedance of a open circuit line is -------
3. Input impedance of a short circuit line is -------
4. Input impedance of a open circuit line is -------
5. Finite line terminated with characteristic impedance acts as------------
6. Reflection co efficient is given by
a) Vr/Vi b) Vi / Vr c) Vi Vr d) none
7. Reflection co efficient of short circuit line is given by-----------
8. Reflection co efficient of open circuit line is given by-----------
9. Reflection co efficient of matched line is given by --------
10. Range of UHF is----------
11. UHF lines can be used as circuit elements. TRUE/FALSE
12. A SC line with length of 0< l < λ/4 acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
13. A SC line with length of λ/4 < l < λ/2 acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
14. A SC line with length of λ/2 < l < 3λ/4 acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
15. A SC line with length of 3λ/4 < l < λ acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
16. A OC line with length of 0< l < λ/4 acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
17. A OC line with length of λ/4 < l < λ/2 acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
18. A OC line with length of λ/2 < l < 3λ/4 acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
19. A OC line with length of 3λ/4 < l < λ acts as
a) capacitor b) inductor
c)series resonant circuit d) parallel resonant circuit
20. Single stub matching is advantageous over double stub matching. TRUE/FALSE
(b). Descriptive Questions
1. Derive the equation of input impedance for pen circuit and short circuit lines?
2. Write a short notes on the topic “UHF lines as circuit elements”.
3. Write a short notes on χ /4, χ/2, χ/8 lines.
4. Define the reflection coefficient and derive the the expression for the input impedance in
terms of reflection coefficient.
5. Explain clearly why short circuit stubs are preferred over open circuited stubs?
6. Derive the voltage and current variation along an open circuited and a short-circuited
line. Explain their nature.
7. Describe an experimental method of determining characteristic impedance of a line. What
are the important precautions in this method.
8. Derive expressions for the input impedance of a loss-free line of length l when the load
end is Short circuited.
9. Derive expressions for the input impedance of a loss-free line of length l when the load
end is Open circuited.
10. Mention the use of Short Circuited lines.
11. Mention the use of Open Circuited lines
12. Discuss the variation of voltages and currents on a lossy line short circuited at the far end.
13. Show that for any uniform transmission line the following relations are valid,
and .
14. Impedance measurements made on ¼ km length of the field quad cable at 1600
Hz under
Calculate Zo , α , β , R , C, L and G . Approximate velocity of propagation for a
field quad cable can be assumed to be 50,000 km/sec
15. A transmission line connects a transmitter of 1.2MHz to the antenna located 100 m away
from it. If Zo of the line equals 500 Ω , what is the input impedance of this line if
antenna end (i) open circuited , (ii) short circuited.
16. A 50 Ω short circuited line is 0.1 λ in length , at a frequency of 500 MHz. Calculate the
equivalent inductive reactance and the equivalent inductance. Find also the equivalent
capacitive reactance and the equivalent capacitance when the length of the line is 3λ/8.
17. In a smith chart plot the following normalized impedance.
(i) 2-j1 (ii) 1+j (iii) 1+2j (iv) matched load
18. A lossless transmission line in air has a characteristic impedance of 300 ohms and is
terminated by an unknown impedance. When the frequency is 200 MHz, the standing
wave ratio is 4.48 and first voltage minima is situated at 6 cm from the load. Determine
the complex reflection co-efficient and the terminating impedance of the line.
19. An UHF transmission line of is terminated in an unknown load. The VSWR
measured in the line is 3 and the position of current maxima nearest to the load is one-
fifth wavelength away(from the load). Calculate the value of the load impedance.
20. The Terminating load of UHF transmission line ( ) ohms working at 300 MHz
is 50 + j 50 ohms. Calculate VSWR and the position of the voltage minimum nearest the
load.
21. A certain low lossline has a characteristic impedance of 400 ohms. Determine the
standing wave ration with the following receiving end impedance.
a. (a) Zr=70+j0.0 ohms (b) Zr = 800 + j0.0 ohms (c) Zr = 650 – j 475
22. The VSWR measured on UHF transmission line, working at a frequency of 300 MHz is
found to be 2. If the distance between load and voltage minimum is 0.8 metre , calculate
the value of load impedance.
23. A low loss line with Zo = 70 ohms is terminates in an impedance Zr=115-j80 ohms. The
wavelength of the transmission is 2.5 metres ; using the given smith chart find the
following ,
i. Standing Wave Ratio.
ii. Maximum and minimum line impedance
iii. Distance between the load and first voltage maximum.
24. Find the sending end impedance of a line with negligible losses when Zo = 55 ohms and
the load impedance is 115+j75 ohms. Length of the line is 1.183 wavelengths.
25. A HF lossless transmission line of Zo=70 ohms is terminated in an open circuit.
Determine sending end impedance for the following lengths of the line (i) 3λ/8 (ii)
λ/2
26. A two wire line has a characteristic impedance of 300ohms and is to feed a 90ohm
resistor at 100 MHz. A Quarter wave line is to be used as a tube, 0.25 inch in diameter.
Find centre.-to-centre spacing in air?
27. The reflection co efficient at load is 0.5∟300. The characteristic impedance is 100Ω
at 200 MHz calculate
i. the position of V min nearest to the load
ii. the ratio of voltage to the current at the load
iii. The value of load , and VSWR.
28. A low loss transmission line of 100 ohm characteristic impedance is connected to a
load of 200 ohm. Calculate the reflection co efficient and standing wave ratio. Derive the
relationships used.
29. A 100 ohm loss less line connects a signal of 100 KHz to a load of 140 ohms. The
Load power is 100mW. Calculate Voltage reflection co efficient, VSWR,
position of Vmax, Vmin , Imax , Imin.
30. A loss less line of 100 ohms 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 the
load impedance.
