Discussion
High frequency resistance of an antenna of length 'l', cross-section 'A', conductivity '\(\sigma\)', perimeter 'P' (\(\mu_{0}\) is free space permeability, \(\omega\) is operating frequency) is given by :
Answer: A
The resistance is \(l/P \sqrt{\omega \mu_{0}/2\sigma}\) ohms.
At high frequency the current flows only in a thin skin of depth \(\delta\), so the effective cross-section is the perimeter times the skin depth:
\[ \begin{aligned} \delta &= \sqrt{\frac{2}{\omega \mu_{0} \sigma}} \\ R &= \frac{l}{\sigma P \delta} = \frac{l}{P}\sqrt{\frac{\omega \mu_{0}}{2\sigma}} \end{aligned} \]
The cross-sectional area A no longer matters, which is why it does not appear. The other options put σ in the numerator, which would make a better conductor more resistive, or misplace the factor 2 and the perimeter.
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