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An antenna can be modeled as an electric dipole of length 4 m at 3 MHz. If current is uniform over its length, then radiation resistance of the antenna is
  • a)
    1.974 Ω
  • b)
    1.263 Ω
  • c)
    2.186 Ω
  • d)
    2.693 Ω
Correct answer is option 'B'. Can you explain this answer?
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An antenna can be modeled as an electric dipole of length 4 m at 3 MHz...
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An antenna can be modeled as an electric dipole of length 4 m at 3 MHz...
Given:
- Length of the antenna: 4 m
- Frequency of operation: 3 MHz

To find:
The radiation resistance of the antenna

Solution:
Step 1: Calculate the wavelength
The wavelength (λ) of the signal can be calculated using the formula:
λ = c/f
where c is the speed of light (3 x 10^8 m/s) and f is the frequency of operation (3 MHz = 3 x 10^6 Hz).

Substituting the values, we get:
λ = 3 x 10^8 / (3 x 10^6)
λ = 100 m

Step 2: Calculate the effective length of the antenna
The effective length (Leff) of the antenna is given by the formula:
Leff = λ/2

Substituting the value of λ, we get:
Leff = 100/2
Leff = 50 m

Step 3: Calculate the radiation resistance
The radiation resistance (Rr) of a half-wave dipole antenna is given by the formula:
Rr = (80π^2 x (Leff^2))/(λ^2)
where π is a constant (approximately 3.14).

Substituting the values, we get:
Rr = (80 x 3.14^2 x (50^2))/(100^2)
Rr = (80 x 9.8596 x 2500)/(10000)
Rr = 19659.2/10000
Rr ≈ 1.966 Ω

Step 4: Answer
The radiation resistance of the antenna is approximately 1.966 Ω, which is closest to the given option 'B' (1.263 Ω).
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An antenna can be modeled as an electric dipole of length 4 m at 3 MHz. If current is uniform over its length, then radiation resistance of the antenna isa)1.974 Ωb)1.263 Ωc)2.186 Ωd)2.693 ΩCorrect answer is option 'B'. Can you explain this answer?
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