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A short vertical grounded antenna is required to radiate at 1 MHz. The effective height of antenna is 302 meter then value of radiation resistance (approximately) is
- a)15.6 Ω
- b)31.6 Ω
- c)7.8 Ω
- d)73 Ω
Correct answer is option 'B'. Can you explain this answer?
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A short vertical grounded antenna is required to radiate at 1 MHz. The...
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Understanding the Problem
We are given a short vertical grounded antenna that needs to radiate at a frequency of 1 MHz. The effective height of the antenna is given as 302 meters. We are required to determine the value of the radiation resistance.
Explanation
To calculate the radiation resistance of the antenna, we can use the formula:
Rrad = (80 * π^2 * h^2) / λ^2
Where:
Rrad is the radiation resistance
h is the effective height of the antenna
λ is the wavelength of the signal
Calculating the Wavelength
The wavelength can be calculated using the formula:
λ = c / f
Where:
λ is the wavelength
c is the speed of light (approximately 3 x 10^8 meters per second)
f is the frequency (1 MHz = 1 x 10^6 Hz)
Substituting the values, we get:
λ = (3 x 10^8) / (1 x 10^6)
λ = 300 meters
Calculating the Radiation Resistance
Now we can substitute the values of h and λ into the formula for radiation resistance:
Rrad = (80 * π^2 * h^2) / λ^2
Rrad = (80 * π^2 * 302^2) / 300^2
Rrad ≈ 31.6 ohms
Therefore, the value of the radiation resistance (approximately) is 31.6 ohms.
Conclusion
The radiation resistance of the short vertical grounded antenna, given an effective height of 302 meters and operating at a frequency of 1 MHz, is approximately 31.6 ohms.
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A short vertical grounded antenna is required to radiate at 1 MHz. The effective height of antenna is 302 meter then value of radiation resistance (approximately) isa)15.6 Ωb)31.6 Ωc)7.8 Ωd)73 ΩCorrect answer is option 'B'. Can you explain this answer?
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