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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?
Verified Answer
Calculate the phase constant of a dielectric with frequency 6 x 106in ...
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.
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.
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Calculate the phase constant of a dielectric with frequency 6 x 106in ...
Calculation of Phase Constant of Dielectric in Air
Given: Frequency = 6 x 106 Hz
We know that the phase constant of a dielectric can be calculated using the formula:
β = ω√(με)
Where,
β = Phase constant
ω = Angular frequency = 2πf
μ = Permeability of air = 4π x 10^-7 H/m
ε = Permittivity of the dielectric
Substituting the given values, we get:
ω = 2π x 6 x 10^6 = 37.7 x 10^6 rad/s
μ = 4π x 10^-7 H/m
ε = Permittivity of the dielectric (unknown)
To find ε, we can use the relation between permittivity and the speed of light in vacuum and the speed of light in the dielectric:
ε = (c0/c)^2
Where,
c0 = Speed of light in vacuum = 3 x 10^8 m/s
c = Speed of light in the dielectric
Substituting the given frequency, we get:
c = fλ = (3 x 10^8)/(6 x 10^6) = 50 m
Hence, the permittivity of the dielectric is:
ε = (c0/c)^2 = (3 x 10^8/50)^2 = 3.6 x 10^13 F/m
Substituting the values of ω, μ, and ε in the formula of phase constant, we get:
β = ω√(με) = 37.7 x 10^6 √(4π x 10^-7 x 3.6 x 10^13) = 0.02 m^-1
Therefore, the phase constant of the dielectric in air with a frequency of 6 x 10^6 Hz is 0.02 m^-1.
Given: Frequency = 6 x 106 Hz
We know that the phase constant of a dielectric can be calculated using the formula:
β = ω√(με)
Where,
β = Phase constant
ω = Angular frequency = 2πf
μ = Permeability of air = 4π x 10^-7 H/m
ε = Permittivity of the dielectric
Substituting the given values, we get:
ω = 2π x 6 x 10^6 = 37.7 x 10^6 rad/s
μ = 4π x 10^-7 H/m
ε = Permittivity of the dielectric (unknown)
To find ε, we can use the relation between permittivity and the speed of light in vacuum and the speed of light in the dielectric:
ε = (c0/c)^2
Where,
c0 = Speed of light in vacuum = 3 x 10^8 m/s
c = Speed of light in the dielectric
Substituting the given frequency, we get:
c = fλ = (3 x 10^8)/(6 x 10^6) = 50 m
Hence, the permittivity of the dielectric is:
ε = (c0/c)^2 = (3 x 10^8/50)^2 = 3.6 x 10^13 F/m
Substituting the values of ω, μ, and ε in the formula of phase constant, we get:
β = ω√(με) = 37.7 x 10^6 √(4π x 10^-7 x 3.6 x 10^13) = 0.02 m^-1
Therefore, the phase constant of the dielectric in air with a frequency of 6 x 10^6 Hz is 0.02 m^-1.
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Calculate the phase constant of a dielectric with frequency 6 x 106in air.a)2b)0.2c)0.02d)0.002Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Calculate the phase constant of a dielectric with frequency 6 x 106in air.a)2b)0.2c)0.02d)0.002Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the phase constant of a dielectric with frequency 6 x 106in air.a)2b)0.2c)0.02d)0.002Correct answer is option 'C'. Can you explain this answer?.
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