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All questions of Refraction of Plane Waves for UPSC CSE Exam

The conductivity in free space medium is
  • a)
    Infinity
  • b)
    Unity
  • c)
    Zero
  • d)
    Negative
Correct answer is option 'C'. Can you explain this answer?

Yash Patel answered
Answer: c
Explanation: As the charge carriers are not available in free space, the conductivity will be very low. For ideal cases, the conductivity can be taken as zero.

In free space, which parameter will be unity?
  • a)
    Permittivity
  • b)
    Absolute permittivity
  • c)
    Relative permittivity
  • d)
    Permeability
Correct answer is option 'C'. Can you explain this answer?

Ravi Singh answered
Answer: c
Explanation: The relative permittivity is a constant for a particular material. It is unity for free space or air. The absolute permittivity is a constant given by 8.854 x 10-12 C/m2.

The permeability of a dielectric material in air medium will be
  • a)
    Absolute permeability
  • b)
    Relative permeability
  • c)
    Product of absolute and relative permeability
  • d)
    Unity
Correct answer is option 'A'. Can you explain this answer?

Zoya Sharma answered
Answer: a
Explanation: The total permeability is the product of the absolute and the relative permeability. In air medium, the relative permeability will be unity. Thus the total permeability is equal to the absolute permeability given by 4π x 10-7 units.

The frequency in rad/sec of a wave with velocity of that of light and phase constant of 20 units is (in GHz)
  • a)
    6
  • b)
    60
  • c)
    600
  • d)
    0.6
Correct answer is option 'A'. Can you explain this answer?

Poulomi Ahuja answered
Given information:
Velocity of wave = Velocity of light = c
Phase constant = 20 units

Formula used:
Frequency of wave = (2π/λ) * Velocity of wave
Where,
λ = wavelength of wave

Calculation:
As per the formula, we know that
wavelength of wave = 2π/phase constant
= 2π/20
= π/10

Now,
Frequency of wave = (2π/λ) * Velocity of wave
= (2π/(π/10)) * c
= 20c rad/sec

To convert rad/sec to GHz, we know that
1 GHz = 10^9 Hz
1 Hz = 2π rad/sec

Therefore,
20c rad/sec = (20c/2π) * (1/10^9) GHz
= 10 GHz * c/π

Substituting the value of c = velocity of light = 3 * 10^8 m/s
= 10 GHz * 3 * 10^8/π
= 9.549 GHz

Hence, the correct option is A) 6 GHz.

In free space, the charge carriers will be
  • a)
    0
  • b)
    1
  • c)
    100
  • d)
    Infinity
Correct answer is option 'A'. Can you explain this answer?

Rounak Rane answered
Answer: a
Explanation: Free space is not a conductor. Thus the charge carrier in free space is assumed to be zero. But the free space consists of particles or ions that get ionized during conduction.

EM waves do not travel inside metals. State True/False. 
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?

Debanshi Iyer answered
Answer: a
Explanation: The conductors or metals do not support EM wave propagation onto them due the skin effect. This is the reason why mobile phones cannot be used inside lifts.

The expression for velocity of a wave in the conductor is
  • a)
    V = √(2ω/μσ)
  • b)
    V = √(2ωμσ)
  • c)
    V = (2ω/μσ)
  • d)
    V = (2ωμσ)
Correct answer is option 'A'. Can you explain this answer?

Nayanika Kaur answered
Answer: a
Explanation: The velocity is the ratio of the frequency to the phase constant. In conductors, the phase constant is given by √(ωμσ/2). On substituting for β,ω in v, we get v = √(2ω/μσ) units

The phase shift in the electric and magnetic fields in an EM wave is given by which parameter?
  • a)
    phase constant
  • b)
    attenuation constant
  • c)
    propagation constant
  • d)
    intrinsic impedance
Correct answer is option 'D'. Can you explain this answer?

Answer: d
Explanation: The intrinsic impedance in a conductor is given by η = √(ωμ/2σ) x (1+j). The phase shift is represented by the 1+j term. In polar form it indicates 45 degree phase shift.

Zero permeability/permittivity implies which state?
  • a)
    No ions are allowed in the medium
  • b)
    No current is generated in the medium
  • c)
    No magnetic or electric energy is permitted in the medium
  • d)
    No resistivity
Correct answer is option 'C'. Can you explain this answer?

Poulomi Chopra answered
Answer: c
Explanation: The zero permittivity in an electric field refers to the ability of the field/medium to permit electric charges in it. Similarly, zero permeability in a magnetic field refers to the ability of the field/medium to permit the magnetic energy into the field.

In free space, the condition that holds good is
  • a)
    Minimum attenuation and propagation
  • b)
    Minimum attenuation and maximum propagation
  • c)
    Maximum attenuation and minimum propagation
  • d)
    Maximum attenuation and propagation
Correct answer is option 'B'. Can you explain this answer?

Megha Datta answered
Answer: b
Explanation: The free space does not have any barrier for attenuation. Thus it enables minimum attenuation and maximum propagation. This technique is employed in line of sight communication

In metals, the total permittivity is
  • a)
    Absolute permittivity
  • b)
    Relative permittivity
  • c)
    Product of absolute and relative permittivity
  • d)
    Unity
Correct answer is option 'A'. Can you explain this answer?

Avantika Kaur answered
Answer: a
Explanation: The total permittivity is the product of the absolute and the relative permittivity. For metals or conductors, the relative permittivity is unity. Thus the permittivity is simply the absolute permittivity.

The phase constant of a wave with wavelength 2 units is
  • a)
    6.28
  • b)
    3.14
  • c)
    0.5
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?

Niti Tiwari answered
Answer: b
Explanation: The phase constant is given by β = 2π/λ. On substituting λ = 2 units, we get β = 2π/2 = π = 3.14 units.

The total permittivity of a dielectric transformer oil (relative permittivity is 2.2) will be (in order 10-11
  • a)
    1.94
  • b)
    19.4
  • c)
    0.194
  • d)
    194
Correct answer is option 'A'. Can you explain this answer?

Jaya Rane answered
Answer: a
Explanation: The total permittivity is the product of the absolute and the relative permittivity. The absolute permittivity is 8.854 x 10-12 and the relative permittivity(in this case for transformer oil) is 2.2. Thus the total permittivity is 8.854 x 10-12 x 2.2 = 1.94 x 10-11 units.

The propagation constant of the wave in a conductor with air as medium is
  • a)
    √(ωμσ)
  • b)
    ωμσ
  • c)
    √(ω/μσ)
  • d)
    ω/μσ
Correct answer is option 'A'. Can you explain this answer?

Malavika Nair answered
Answer: a
Explanation: The propagation constant is the sum of the attenuation constant and the phase constant. In conductors, the attenuation and phase constant both are same and it is given by √(ωμσ/2). Their sum will be √(ωμσ), is the propagation constant.

In free space, the ratio of frequency to the velocity of light gives the phase constant. State True/False. 
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?

Aman Datta answered
Answer: a
Explanation: The phase constant is given by the ratio of the frequency in radian/sec to the velocity of the wave propagating. In free space, the velocity is considered to be the velocity of light. Thus the statement is true.

Calculate the phase constant of a dielectric with frequency 6 x 106 in air. 
  • a)
    2
  • b)
    0.2
  • c)
    0.02
  • d)
    0.002
Correct answer is option 'C'. Can you explain this answer?

Pankaj Mehta answered
Answer: c
Explanation: The phase constant of a dielectric is given by β = ω√(με). On substituting for ω = 6 x 106 , μ = 4π x 10-7, ε = 8.854 x 10-12 in air medium, we get the phase constant as 0.02 units.

For conductors, the loss tangent will be
  • a)
    Zero
  • b)
    Unity
  • c)
    Maximum
  • d)
    Minimum
Correct answer is option 'C'. Can you explain this answer?

Answer: c
Explanation: In conductors, the conductivity will be more. Thus the loss tangent σ/ωε will be maximum.

In conductors, the E and H vary by a phase difference of
  • a)
    0
  • b)
    30
  • c)
    45
  • d)
    60
Correct answer is option 'C'. Can you explain this answer?

Sanjana Chopra answered
Answer: c
Explanation: The electric and magnetic component, E and H respectively have a phase difference of 45 degrees. This is due to the wave propagation in conductors in the air medium.

Calculate the attenuation constant of a conductor of conductivity 200 units, frequency 1M radian/s in air.
  • a)
    11.2
  • b)
    1.12
  • c)
    56.23
  • d)
    5.62
Correct answer is option 'A'. Can you explain this answer?

Pallavi Nair answered
Answer: a
Explanation: The attenuation constant of a conductor is given by α = √(ωμσ/2). On substituting ω = 106, σ = 200 and μ = 4π x 10-7, we get α = 11.2 units.

The attenuation in a good dielectric will be non- zero. State True/False. 
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?

Arshiya Basu answered
Answer: a
Explanation: Good dielectrics attenuate the electromagnetic waves than any other material. Thus the attenuation constant of the dielectric will be non-zero, positive and large.

The vectors of the electromagnetic wave propagation can be expressed in
  • a)
    Dot product
  • b)
    Cross product
  • c)
    Unit vector
  • d)
    Perpendicular vector
Correct answer is option 'B'. Can you explain this answer?

Answer: b
Explanation: In an EM wave, the electric and the magnetic fields will be perpendicular to each other and with the direction of the propagation. Thus it can be expressed in cross product where iE x iH = iw. Here iE is the electric vector component, iH is the magnetic vector component and iw is the vector of the wave propagating.

The relation between the speed of light, permeability and permittivity is
  • a)
    C = 1/√(με)
  • b)
    C = με
  • c)
    C = μ/ε
  • d)
    C = 1/με
Correct answer is option 'A'. Can you explain this answer?

Nayanika Kaur answered
Answer: a
Explanation: The standard relation between speed of light, permeability and permittivity is given by c = 1/√(με). The value in air medium is 3 x 108 m/s.

The skin depth of a wave with phase constant of 12 units inside a conductor is
  • a)
    12
  • b)
    1/12
  • c)
    24
  • d)
    1/24
Correct answer is option 'B'. Can you explain this answer?

Answer: b
Explanation: The skin depth is the reciprocal of the phase constant. On substituting for β = 12, we get δ = 1/β = 1/12 units.

An example for electromagnetic wave propagation is
  • a)
    refrigerator
  • b)
    electric fan
  • c)
    mobile transponder
  • d)
    relays in actuators
Correct answer is option 'C'. Can you explain this answer?

Answer: c
Explanation: The refrigerator, electric fan and relays are electrical devices. They do not use electromagnetic energy as medium of energy transfer. The mobile transponder is an antenna, which uses the EM waves for communication with the satellites.

In pure dielectrics, the parameter that is zero is
  • a)
    Attenuation
  • b)
    Propagation
  • c)
    Conductivity
  • d)
    Resistivity
Correct answer is option 'C'. Can you explain this answer?

Manoj Mehra answered
Answer: c
Explanation: There are no free charge carriers available in a dielectric. In other words, the charge carriers are present in the valence band, which is very difficult to start to conduct. Thus conduction is low in dielectrics. For pure dielectrics, the conductivity is assumed to be zero.

Which parameter is unity in air medium?
  • a)
    Permittivity
  • b)
    Absolute permeability
  • c)
    Relative permeability
  • d)
    Permeability
Correct answer is option 'C'. Can you explain this answer?

Ishan Saini answered
Answer: c
Explanation: In free space or air medium, the relative permeability is also unity, like relative permittivity. The absolute permeability is given by 4π x 10-7 units.

The velocity of a wave travelling in the air medium without transmission lines or waveguides(wireless) is 
  • a)
    6 x 108
  • b)
    3 x 108
  • c)
    1.5 x 108
  • d)
    9 x 108
Correct answer is option 'B'. Can you explain this answer?

Rajesh Saha answered
Answer: b
Explanation: In free space or air medium, the velocity of the wave propagating will be same as that of the light. Thus the velocity is the speed of light, V = c. It is given by 3 x 108m/s

The intrinsic impedance of free space is
  • a)
    489
  • b)
    265
  • c)
    192
  • d)
    377
Correct answer is option 'D'. Can you explain this answer?

Answer: d
Explanation: The intrinsic impedance is the square root of ratio of the permeability to the permittivity. In free space, the permeability and the permittivity is same as the absolute permeability and permittivity respectively. This is due to unity permeability and permittivity in free space. Thus η = √(μ/ε), where absolute permeability is given by 4π x 10-7 and absolute permittivity is given by 8.854 x 10-12. The intrinsic impedance will be 377 ohms.

The total permeability in a conductor is
  • a)
    Absolute permeability
  • b)
    Relative permeability
  • c)
    Product of absolute and relative permeability
  • d)
    Unity
Correct answer is option 'C'. Can you explain this answer?

Sravya Khanna answered
Answer: c
Explanation: The total permeability is the product of the absolute and the relative permeability. For metals or conductors, the relative permittivity is not unity. Thus the permittivity is the product of absolute and relative permeability.

The skin depth of a conductor with attenuation constant of 7 neper/m is
  • a)
    14
  • b)
    49
  • c)
    7
  • d)
    1/7
Correct answer is option 'D'. Can you explain this answer?

Raj Singh answered
Answer: d
Explanation: The skin depth is the measure of the depth upto which an EM wave can penetrate through the conductor surface. It is the reciprocal of the attenuation constant. On substituting for α = 7, we get δ = 1/α = 1/7 units.

The expression for intrinsic impedance is given by
  • a)
    √(με)
  • b)
    (με)
  • c)
    √(μ/ε)
  • d)
    (μ/ε)
Correct answer is option 'C'. Can you explain this answer?

Aman Jain answered
 The intrinsic impedance is given by the ratio of square root of the permittivity to the permeability. Thus η = √(μ/ε) is the intrinsic impedance. In free space or air medium, the intrinsic impedance will be 120π or 377 ohms.

Calculate the phase constant of a conductor with attenuation constant given by 0.04 units.
  • a)
    0.02
  • b)
    0.08
  • c)
    0.0016
  • d)
    0.04
Correct answer is option 'D'. Can you explain this answer?

Answer: d
Explanation: The phase constant and the attenuation constant are both the same in the case of conductors. Given that the attenuation constant is 0.04, implies that the phase constant is also 0.04.

The electric and magnetic field components in the electromagnetic wave propagation are in phase. State True/False. 
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?

Hiral Kulkarni answered
Answer: a
Explanation: In dielectrics, the electric and magnetic fields will be in phase or the phase difference between them is zero. This is due to the large attenuation which leads to increase in phase shift.

The loss tangent of a perfect dielectric will be
  • a)
    Zero
  • b)
    Unity
  • c)
    Maximum
  • d)
    Minimum
Correct answer is option 'D'. Can you explain this answer?

Suyash Joshi answered
Answer: d
Explanation: Dielectrics have poor conductivity. The loss tangent σ/ωε will be low in dielectrics. For perfect dielectrics, the loss tangent will be minimum.

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