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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?
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Calculate the attenuation constant of a conductor of conductivity 200 ...
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.
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.
Most Upvoted Answer
Calculate the attenuation constant of a conductor of conductivity 200 ...
To calculate the attenuation constant of a conductor, we need to use the formula:
α = √(jωμσ)
Where:
α = attenuation constant (in neper/m)
j = imaginary unit (√(-1))
ω = angular frequency (in radian/s)
μ = permeability of the medium (in H/m)
σ = conductivity of the conductor (in S/m)
Given:
ω = 1M radian/s
σ = 200 units (S/m)
Assuming the conductor is in air, the permeability can be considered as the permeability of free space, μ0, which is approximately 4π × 10^-7 H/m.
Now, let's calculate the attenuation constant step by step.
1. Calculate ωμσ:
ωμσ = (1M radian/s) * (4π × 10^-7 H/m) * (200 S/m)
= 8π × 10^-1 radian/m
2. Take the square root of ωμσ:
√(8π × 10^-1) ≈ 2.824
Therefore, the attenuation constant (α) is approximately 2.824 neper/m.
However, the given options do not include this exact value. So, we need to convert neper to decibel (dB) using the conversion factor:
1 neper = 8.686 dB
3. Convert the attenuation constant to decibel:
α (dB) = 2.824 * 8.686
≈ 24.514 dB/m
Rounding off to one decimal place, the attenuation constant is approximately 24.5 dB/m.
None of the given options match this value, so unfortunately, none of the options are correct.
α = √(jωμσ)
Where:
α = attenuation constant (in neper/m)
j = imaginary unit (√(-1))
ω = angular frequency (in radian/s)
μ = permeability of the medium (in H/m)
σ = conductivity of the conductor (in S/m)
Given:
ω = 1M radian/s
σ = 200 units (S/m)
Assuming the conductor is in air, the permeability can be considered as the permeability of free space, μ0, which is approximately 4π × 10^-7 H/m.
Now, let's calculate the attenuation constant step by step.
1. Calculate ωμσ:
ωμσ = (1M radian/s) * (4π × 10^-7 H/m) * (200 S/m)
= 8π × 10^-1 radian/m
2. Take the square root of ωμσ:
√(8π × 10^-1) ≈ 2.824
Therefore, the attenuation constant (α) is approximately 2.824 neper/m.
However, the given options do not include this exact value. So, we need to convert neper to decibel (dB) using the conversion factor:
1 neper = 8.686 dB
3. Convert the attenuation constant to decibel:
α (dB) = 2.824 * 8.686
≈ 24.514 dB/m
Rounding off to one decimal place, the attenuation constant is approximately 24.5 dB/m.
None of the given options match this value, so unfortunately, none of the options are correct.
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