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Multiple choice question for engineering

Set 1

1. The open circuit impedance of the transmission line is given by
a) ZOC = j Zo tan βl
b) ZOC = – j Zo tan βl
c) ZOC = j Zo cot βl
d) ZOC = -j Zo cot βl

View Answer

Answer: d [Reason:] The open circuit in a transmission line refers to the load side open circuited. In this case, the load impedance will be infinite. Thus the transmission line equation will be ZOC = -j Zo cot βl.

2. The short circuit impedance of the transmission line is given by
a) ZSC = j Zo tan βl
b) ZSC = -j Zo tan βl
c) ZSC = j Zo cot βl
d) ZSC = -j Zo cot βl

View Answer

Answer: a [Reason:] The short circuit in a transmission line refers to the load side shorted. In this case, the load impedance will be zero. Thus the transmission line equation will be ZSC = j Zo tan βl.

3. In a shorted line, the reflection coefficient will be
a) 0
b) 1
c) -1
d) ∞

View Answer

Answer: c [Reason:] The shorted line will absorb more power than any other line. Thus the reflection coefficient is considered to be negative.

4. The open circuit line will have a reflection coefficient of
a) 0
b) 1
c) -1
d) ∞

View Answer

Answer: b [Reason:] An open circuit line has infinite output impedance. Any wave incident at the output will be completely reflected. Thus the reflection coefficient is unity.

5. The standing wave ratio in short and open circuit transmission lines will be
a) 0
b) -1
c) 1
d) ∞

View Answer

Answer: d [Reason:] The reflection coefficient is 1 and -1 in open and shorted lines respectively. This value of reflection coefficient will yield infinite standing wave ratio.

6. The characteristic impedance of a line having open and short impedances of 20 and 5 respectively is
a) 20
b) 100
c) 25
d) 10

View Answer

Answer: d [Reason:] The characteristic impedance is the geometric mean of the short and open circuit impedance. It is given by Zo2 = Zsc Zoc. On substituting Zoc = 20 and Zsc = 5, we get Zo2 = 20 X 5 = 100. Thus Zo = 10 ohm.

7. The short circuit impedance is given by 18 ohm and the characteristic impedance is 50 ohm. Find the open circuit impedance.
a) 138.8
b) 188.3
c) 388.1
d) 838.1

View Answer

Answer: a [Reason:] The relation between characteristic impedance, open and short impedance is given by Zo2 = Zsc Zoc. For the given values Zo = 50 and Zsc = 18, we get Zoc = 502/18 = 138.8 units.

8. For maximum power transfer theorem to be applied to the transmission line, the reflection coefficient has to be
a) 1
b) -1
c) 0
d) ∞

View Answer

Answer: c [Reason:] Maximum power transfer between the load and source is possible, only when both are matched. This will lead to no reflections. Thus the reflection coefficient will be zero.

9. Find the transmission coefficient of a 75 ohm line with load impedance of 40 ohm.
a) 0.69
b) 0.96
c) 0.31
d) 0.13

View Answer

Answer: a [Reason:] The transmission coefficient in terms of the load impedance is given by T = ZL/Z0. On substituting for ZL = 40 and Zo = 75, we get T = 40/75 = 0.69.

10. The standing waves for open circuit voltage and short circuit current are the same. State true/false.
a) True
b) False

View Answer

Answer: a [Reason:] The open circuit voltage and short circuit current will be same for a transmission line. The phase difference is λ/8.

11. The standing waves for open circuit current and short circuit voltage are the same. State true/false.
a) true
b) false

View Answer

Answer: a [Reason:] The open circuit current and short circuit voltage will be same for a transmission line. The phase difference is λ/8.

12. The standing wave ratio for the maximum power transfer in a transmission line is
a) 1:2
b) 2:1
c) -1:1
d) 1:1

View Answer

Answer: d [Reason:] The load and the source has to be matched for maximum power transfer. This is indicated by the ratio of 1:1.

Set 2

1. The skin effect is a phenomenon observed in
a) Insulators
b) Dielectrics
c) Conductors
d) Semiconductors

View Answer

Answer: c [Reason:] The skin of the conductor allows a certain amount of electromagnetic power to pass through it. This phenomenon is called the skin effect. This is the reason why, electromagnetic waves cannot travel inside a conductor.

2. The skin depth is measured in
a) Meter
b) Millimetre
c) Centimetre
d) Micrometer

View Answer

Answer: d [Reason:] The depth to which the electromagnetic waves pass through the conductor is very small. It is measured in μm.

3. The skin depth is calculated from the amplitude of the wave. State true/false
a) True
b) False

View Answer

Answer: a [Reason:] The skin depth is the measure of the depth to which the amplitude of an EM wave will reduce to 36.8% of its initial value. Thus it can be calculated if the initial amplitude is known.

4. The attenuation constant is 0.5 units. The skin depth will be
a) 0.5
b) 0.25
c) 2
d) 4

View Answer

Answer: c [Reason:] The skin depth is the reciprocal of the attenuation constant. Thus δ = 1/α. On substituting for α = 0.5, we get δ = 1/0.5 = 2 units.

5. Calculate the skin depth of a conductor, having a conductivity of 200 units. The wave frequency is 10 GHz in air.
a) 355.8
b) 3.558
c) 35.58
d) 0.3558

View Answer

Answer: a [Reason:] The skin depth is calculated by δ = 1/√(πfμσ), where f is the frequency, μ is the permeability and σ is the conductivity. For the given data, f = 10 x 109, μ = 4π x 10-7 in air and σ = 200, we get δ = 355.8 μm.

6. The effective skin resistance of a material with conductivity 120 and skin depth of 2μm is
a) 4.16 kilo ohm
b) 4.16 mega ohm
c) 41.6 kilo ohm
d) 41.6 mega ohm

View Answer

Answer: a [Reason:] The effective skin resistance is given by Rs = 1/δσ, where δ is the skin depth and σ is the conductivity. For the given data, δ = 2 x 10-6 and σ = 120, we get Rs = 1/(120x2x10-6) = 4.16 kilo ohm.

7. The skin depth is used to find which parameter?
a) DC resistance
b) AC resistance
c) Permittivity
d) Potential

View Answer

Answer: b [Reason:] Since the skin depth varies for different frequencies, it can be used to calculate the varying AC resistance for a material.

8. The relation between the skin depth and frequency is given by
a) Skin depth α f
b) Skin depth α 1/f
c) Skin depth α √f
d) Skin depth α 1/√f

View Answer

Answer: d [Reason:] The skin depth is given by δ = 1/√(πfμσ). Thus the relation between the skin depth and the frequency is, Skin depth α 1/√f.

9. A perfect dielectric acts as a
a) Perfect transmitter
b) Perfect reflector
c) Bad transmitter
d) Bad reflector

View Answer

Answer: a [Reason:] A perfect dielectric acts as a perfect transmitter. In other words, a wave incident on a perfect dielectric will transmit completely through it.

10. A perfect conductor acts as a
a) Perfect transmitter
b) Perfect reflector
c) Bad transmitter
d) Bad reflector

View Answer

Answer: b [Reason:] A perfect conductor acts as a perfect reflector. In other words, a wave incident on a perfect conductor will be totally reflected back into the same medium. There will be no skin effect.

11. The resultant electric field of two components in the x and y direction having amplitudes 6 and 8 respectively is
a) 100
b) 36
c) 64
d) 10

View Answer

Answer: d [Reason:] The resultant electric field of two components is given by E = √(Ex2 + Ey2). For the given data, the electric field will be E = √(62+82) = 10 units.

12. The skin depth of the wave having a frequency of 3MHz and a velocity of 12 m/s is
a) 2
b) 3
c) 4
d) 6

View Answer

Answer: c [Reason:] The velocity of a wave is the product of the frequency and the skin depth. Thus v = f.δ. To get δ, put v = 12 and f = 3MHz, we get δ = 12/(3×106) = 4 μm.

Set 3

1. Find the value of Stoke’s theorem for y i + z j + x k.
a) i + j
b) j + k
c) i + j + k
d) –i – j – k

View Answer

Answer: d [Reason:] The curl of y i + z j + x k is i(0-1) – j(1-0) + k(0-1) = -i –j –k. Since the curl is zero, the value of Stoke’s theorem is zero. The function is said to be irrotational.

2. The Stoke’s theorem uses which of the following operation?
a) Divergence
b) Gradient
c) Curl
d) Laplacian

View Answer

Answer: c [Reason:] ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.

3. Which of the following theorem convert line integral to surface integral?
a) Gauss divergence and Stoke’s theorem
b) Stoke’s theorem only
c) Green’ s theorem only
d) Stoke’s and Green’s theorem

View Answer

Answer: d [Reason:] The Stoke’s theorem is given by ∫A.dl = ∫∫ Curl (A).ds. Green’s theorem is given by, ∫ F dx + G dy = ∫∫ (dG/dx – dF/dy) dx dy. It is clear that both the theorems convert line to surface integral.

4. Find the value of Stoke’s theorem for A = x i + y j + z k. The state of the function will be
a) Solenoidal
b) Divergent
c) Rotational
d) Curl free

View Answer

Answer: Since curl is required, we need not bother about divergence property. The curl of the function will be i(0-0) – j(0-0) + k(0-0) = 0. The curl is zero, thus the function is said to be irrotational or curl free.

5. The Stoke’s theorem can be used to find which of the following?
a) Area enclosed by a function in the given region
b) Volume enclosed by a function in the given region
c) Linear distance
d) Curl of the function

View Answer

Answer: a [Reason:] It states that the line integral of a function gives the surface area of the function enclosed by the given region. This is computed using the double integral of the curl of the function.

6. The energy stored in an inductor 2H and current 4A is
a) 4
b) 8
c) 12
d) 16

View Answer

Answer: d [Reason:] From Stoke’s theorem, we can calculate energy stored in an inductor as 0.5Li2. E = 0.5 X 2 X 42 = 16 units.

7. The voltage of a capacitor 12F with a rating of 2J energy is
a) 0.57
b) 5.7
c) 57
d) 570

View Answer

Answer: a [Reason:] We can compute the energy stored in a capacitor from Stoke’s theorem as 0.5Cv2. Thus given energy is 0.5 X 12 X v2. We get v = 0.57 volts.

8. Find the power, given energy E = 2J and current density J = x2 varies from x = 0 and x = 1.
a) 1/3
b) 2/3
c) 1
d) 4/3

View Answer

Answer: b [Reason:] From Stoke’s theorem, we can calculate P = E X I = ∫ E. J ds = 2∫ x2 dx as x = 0->1. We get P = 2/3 units.

9. The conductivity of a material with current density 1 unit and electric field 200 μV is
a) 2000
b) 3000
c) 4000
d) 5000

View Answer

Answer: d [Reason:] The current density is given by, J = σE. To find conductivity, σ = J/E = 1/200 X 10-6 = 5000.

10. The resistivity of a material with resistance 200 ohm, length 10m and area twice that of the length is
a) 200
b) 300
c) 400
d) 500

View Answer

Answer: c [Reason:] Resistance calculated from Ohm’s law and Stoke’s theorem will be R = ρL/A. To get resistivity, ρ = RA/L = 200 X 20/10 = 400.

Set 4

1. Gauss law for electric field uses surface integral. State True/False
a) True
b) False

View Answer

Answer: a [Reason:] Gauss law states that the electric flux passing through any closed surface is equal to the total charge enclosed by the surface. Thus the charge is defined as a surface integral.

2. Surface integral is used to compute
a) Surface
b) Area
c) Volume
d) density

View Answer

Answer: b [Reason:] Surface integral is used to compute area, which is the product of two quantities length and breadth. Thus it is two dimensional integral.

3. Coulomb’s law can be derived from Gauss law. State True/ False
a) True
b) False

View Answer

Answer: a [Reason:] Gauss law, Q = ∫∫D.ds By considering area of a sphere, ds = r2sin θ dθ dφ. On integrating, we get Q = 4πr2D and D = εE, where E = F/Q. Thus, we get Coulomb’s law F = Q1 x Q2/4∏εR2.

4. Evaluate Gauss law for D = 5r2/4 i in spherical coordinates with r = 4m and θ = π/2.
a) 600
b) 599.8
c) 588.9
d) 577.8

View Answer

Answer: c [Reason:] ∫∫ ( 5r2/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Put r = 4m and substitute θ = 0→ π/4 and φ = 0→ 2π, the integral evaluates to 588.9.

5. Compute the Gauss law for D= 10ρ3/4 i, in cylindrical coordinates with ρ= 4m, z=0 and z=5.
a) 6100 π
b) 6200 π
c) 6300 π
d) 6400 π

View Answer

Answer: d [Reason:] ∫∫ D.ds = ∫∫ (10ρ3/4).(ρ dφ dz), which is the integral to be evaluated. Put ρ = 4m, z = 0→5 and φ = 0→2π, the integral evaluates to 6400π.

6. Compute divergence theorem for D= 5r2/4 i in spherical coordinates between r=1 and r=2.
a) 80π
b) 5π
c) 75π
d) 85π

View Answer

Answer: c [Reason:] ∫∫ ( 5r2/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Since it is double integral, we need to keep only two variables and one constant compulsorily. Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas second integral gives -5π. On summing both integrals, we get 75π.

7. Find the value of divergence theorem for A = xy2 i + y3 j + y2z k for a cuboid given by 0<x<1, 0<y<1 and 0<z<1.
a) 1
b) 4/3
c) 5/3
d) 2

View Answer

Answer: c [Reason:] A cuboid has six faces. ∫∫A.ds = ∫∫Ax=0 dy dz + ∫∫Ax=1 dy dz + ∫∫Ay=0 dx dz + ∫∫Ay=1 dx dz + ∫∫Az=0 dy dx + ∫∫Az=1 dy dx. Substituting A and integrating we get (1/3) + 1 + (1/3) = 5/3.

8. The ultimate result of the divergence theorem evaluates which one of the following?
a) Field intensity
b) Field density
c) Potential
d) Charge and flux

View Answer

Answer: d [Reason:] Gauss law states that the electric flux passing through any closed surface is equal to the total charge enclosed by the surface. Thus, it is given by, ψ = ∫∫ D.ds= Q, where the divergence theorem computes the charge and flux, which are both the same.

9. Find the value of divergence theorem for the field D = 2xy i + x2 j for the rectangular parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.
a) 10
b) 12
c) 14
d) 16

View Answer

Answer: b [Reason:] While evaluating surface integral, there has to be two variables and one constant compulsorily. ∫∫D.ds = ∫∫Dx=0 dy dz + ∫∫Dx=1 dy dz + ∫∫Dy=0 dx dz + ∫∫Dy=2 dx dz + ∫∫Dz=0 dy dx + ∫∫Dz=3 dy dx. Put D in equation, the integral value we get is 12.

10. If D = 2xy i + 3yz j + 4xz k, how much flux passes through x = 3 plane for which -1<y<2 and 0<z<4?
a) 12
b) 24
c) 36
d) 48

View Answer

Answer: c [Reason:] By Gauss law, ψ = ∫∫ D.ds, where ds = dydz i at the x-plane. Put x = 3 and integrate at -1<y<2 and 0<z<4, we get 12 X 3 = 36.

Set 5

1. Which of the following is not an example of elemental solid dielectric?
a) Diamond
b) Sulphur
c) Silicon
d) Germanium

View Answer

Answer: c [Reason:] Elemental solid dielectrics are the materials consisting of single type of atoms. Such materials have neither ions nor permanent dipoles and possess only electronic polarisation. Its examples are diamond, sulphur and germanium.

2. Ionic non polar solid dielectrics contain more than one type of atoms but no permanent dipoles. State True/False
a) True
b) False

View Answer

Answer: a [Reason:] In ionic crystals, the total polarisation is electronic and ionic in nature. Thus, it implies that it contains more than one type of atom and no permanent dipoles.

3. Compute the refractive index when the dielectric constant is 256 in air.
a) 2562
b) 16
c) 256
d) 64

View Answer

Answer: b [Reason:] By Maxwell relation, εr = n2, where εro is the dielectric constant at optical frequencies and n is the refractive index.For the given dielectric constant we get n = 16.

4. Dielectric property impacts the behaviour of a material in the presence of electric field. State True/False.
a) True
b) False

View Answer

Answer: a [Reason:] Based on the dielectric property, a material can be classified as piezoelectric, ferroelectric, pyroelectric and anti-ferroelectric materials under the influence of electric field.

5. Curie-Weiss law is applicable to which of the following materials?
a) Piezoelectric
b) Ferroelectric
c) Pyroelectric
d) Anti-ferroelectric

View Answer

Answer: b [Reason:] Curie-Weiss law is given by χe = εr -1 = C/(T-θ), where C is the curie constant and θ is the characteristic temperature which is usually a few degrees higher than the curie temperature for ferromagnetic materials.

6. Curie-Weiss law is used to calculate which one of the following?
a) Permittivity
b) Permeability
c) Electric susceptibility
d) Magnetic susceptibility

View Answer

Answer: c [Reason:] Curie-Weiss law is given by χe = εr -1. Thus it is used to calculate the electric susceptibility of a material.

7. Calculate the loss tangent when the dielectric constant in AC field is given by 3 + 2j.
a) (2/3)
b) (3/2)
c) (-3/2)
d) (-2/3)

View Answer

Answer: d [Reason:] The AC dielectric constant is given by εr = ε` – jε“, where ε` is the real part of AC dielectric and ε“ is the imaginary part of AC dielectric. The loss tangent is given by tan δ = ε“/ε` = -2/3.

8. When a dielectric loses its dielectric property, the phenomenon is called
a) Dielectric loss
b) Dielectric breakdown
c) Polarisation
d) Magnetization

View Answer

Answer: b [Reason:] Due to various treatments performed on the dielectric, in order to make it conduct, the dielectric reaches a state, where it loses its dielectric property and starts to conduct. This phenomenon is called as dielectric breakdown.

9. Choose the best definition of dielectric loss.
a) Absorption of electric energy by dielectric in an AC field
b) Dissipation of electric energy by dielectric in a static field
c) Dissipation of heat by dielectric
d) Product of loss tangent and relative permittivity

View Answer

Answer: a [Reason:] In the scenario of an AC field, the absorption of electrical energy by a dielectric material is called as dielectric loss. This will result in dissipation of energy in the form of heat.

10. Compute the loss factor when the loss tangent is 0.88 and the real part of dielectric is 24.
a) 12.12
b) 12.21
c) 21.21
d) 21.12

View Answer

Answer: d [Reason:] The loss factor is nothing but the imaginary part of AC dielectric. It is given by, ε“ = ε` tan δ. We get loss factor as 24 x 0.88 = 21.12.