Discussion
The radiation resistance of a short dipole is \( 80\pi^{2}(dl/\lambda)^{2} \). What is it for dl = 0.05 lambda?
Answer: B
Substituting the length ratio directly:
\[ R_{r} = 80\pi^{2}(0.05)^{2} \approx 1.97 \]
giving about 1.97 ohms. Against a conductor and matching loss of even one ohm the efficiency would be barely two thirds, and at a tenth of this length the resistance falls a hundredfold. The square law is the quantitative reason electrically small antennas are inefficient, and it is worth being able to evaluate quickly.
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