# Multiple choice question for engineering

## Set 1

1. The open circuit impedance of the transmission line is given by

a) Z_{OC} = j Zo tan βl

b) Z_{OC} = – j Zo tan βl

c) Z_{OC} = j Zo cot βl

d) Z_{OC} = -j Zo cot βl

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_{OC}= -j Zo cot βl.

2. The short circuit impedance of the transmission line is given by

a) Z_{SC} = j Zo tan βl

b) Z_{SC} = -j Zo tan βl

c) Z_{SC} = j Zo cot βl

d) Z_{SC} = -j Zo cot βl

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_{SC}= j Zo tan βl.

3. In a shorted line, the reflection coefficient will be

a) 0

b) 1

c) -1

d) ∞

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4. The open circuit line will have a reflection coefficient of

a) 0

b) 1

c) -1

d) ∞

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5. The standing wave ratio in short and open circuit transmission lines will be

a) 0

b) -1

c) 1

d) ∞

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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

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^{2}= Zsc Zoc. On substituting Zoc = 20 and Zsc = 5, we get Zo

^{2}= 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

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^{2}= Zsc Zoc. For the given values Zo = 50 and Zsc = 18, we get Zoc = 50

^{2}/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) ∞

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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

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_{L}/Z

_{0}. On substituting for Z

_{L}= 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

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

a) true

b) false

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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

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## Set 2

1. The skin effect is a phenomenon observed in

a) Insulators

b) Dielectrics

c) Conductors

d) Semiconductors

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2. The skin depth is measured in

a) Meter

b) Millimetre

c) Centimetre

d) Micrometer

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3. The skin depth is calculated from the amplitude of the wave. State true/false

a) True

b) False

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4. The attenuation constant is 0.5 units. The skin depth will be

a) 0.5

b) 0.25

c) 2

d) 4

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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

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^{9}, 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

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_{s}= 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

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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

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9. A perfect dielectric acts as a

a) Perfect transmitter

b) Perfect reflector

c) Bad transmitter

d) Bad reflector

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10. A perfect conductor acts as a

a) Perfect transmitter

b) Perfect reflector

c) Bad transmitter

d) Bad reflector

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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

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^{2}+ Ey

^{2}). For the given data, the electric field will be E = √(6

^{2}+8

^{2}) = 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

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^{6}) = 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

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2. The Stoke’s theorem uses which of the following operation?

a) Divergence

b) Gradient

c) Curl

d) Laplacian

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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

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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

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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

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6. The energy stored in an inductor 2H and current 4A is

a) 4

b) 8

c) 12

d) 16

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^{2}. E = 0.5 X 2 X 4

^{2}= 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

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^{2}. Thus given energy is 0.5 X 12 X v

^{2}. We get v = 0.57 volts.

8. Find the power, given energy E = 2J and current density J = x^{2} varies from x = 0 and x = 1.

a) 1/3

b) 2/3

c) 1

d) 4/3

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^{2}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

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^{-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

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## Set 4

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

a) True

b) False

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2. Surface integral is used to compute

a) Surface

b) Area

c) Volume

d) density

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

a) True

b) False

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^{2}sin θ dθ dφ. On integrating, we get Q = 4πr

^{2}D and D = εE, where E = F/Q. Thus, we get Coulomb’s law F = Q1 x Q2/4∏εR

^{2}.

4. Evaluate Gauss law for D = 5r^{2}/4 i in spherical coordinates with r = 4m and θ = π/2.

a) 600

b) 599.8

c) 588.9

d) 577.8

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^{2}/4) . (r

^{2}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= 10ρ^{3}/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

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^{3}/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= 5r^{2}/4 i in spherical coordinates between r=1 and r=2.

a) 80π

b) 5π

c) 75π

d) 85π

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^{2}/4) . (r

^{2}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 = xy^{2} i + y^{3} j + y^{2}z 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

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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

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9. Find the value of divergence theorem for the field D = 2xy i + x^{2} 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

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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

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## Set 5

1. Which of the following is not an example of elemental solid dielectric?

a) Diamond

b) Sulphur

c) Silicon

d) Germanium

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

a) True

b) False

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3. Compute the refractive index when the dielectric constant is 256 in air.

a) 2562

b) 16

c) 256

d) 64

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^{2}, 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

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5. Curie-Weiss law is applicable to which of the following materials?

a) Piezoelectric

b) Ferroelectric

c) Pyroelectric

d) Anti-ferroelectric

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6. Curie-Weiss law is used to calculate which one of the following?

a) Permittivity

b) Permeability

c) Electric susceptibility

d) Magnetic susceptibility

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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)

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8. When a dielectric loses its dielectric property, the phenomenon is called

a) Dielectric loss

b) Dielectric breakdown

c) Polarisation

d) Magnetization

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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

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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