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Question:

A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length l of the antenna and effective power radiated Peff will be given respectively as :(K is a constant of proportionality)

λ/6, Peff=K(1/λ)3

λ/8, Peff=K(1/λ)

λ/5, Peff=K(1/λ)12

λ, Peff=K(1/λ)2

Solution:

Power radiated by antenna, Pr ∝ (L/λ)2 ⇒ Pr ∝ (1/λ2) ⇒ Pr = K(1/λ)2
⇒ Length of Antenna, L ∝ λ (Usually L = λ/4, where power peaks)
Therefore, option 2.