Question E9D10:
How does radiation resistance of a base-fed whip antenna change below its resonant frequency?  

Choices:  
A: Radiation resistance increases  
B: Radiation resistance decreases  
C: Radiation resistance becomes imaginary  
D: Radiation resistance does not depend on frequency    

Correct Answer is  B: Radiation resistance decreases  

Correct answer: B — Radiation resistance decreases.

Why B is correct:
- A base-fed whip (monopole) shorter than its resonant length (about $\lambda/4$) is “electrically short.” For electrically short antennas, radiation resistance scales with the square of electrical length:
  $$R_r \approx 20\pi^2\left(\frac{l}{\lambda}\right)^2 \text{ (ohms, short monopole over ground)}$$
  As frequency goes down, $\lambda$ increases, so $l/\lambda$ gets smaller and $R_r$ decreases.

Why the other choices are incorrect:
- A: Increases — Incorrect. From the formula above, decreasing frequency (increasing $\lambda$) reduces $l/\lambda$, so $R_r$ drops, it doesn’t rise.
- C: Becomes imaginary — Incorrect. Radiation resistance is, by definition, the real part of the input impedance associated with radiated power. Below resonance the antenna’s input reactance becomes capacitive ($-jX$), but $R_r$ itself remains real.
- D: Does not depend on frequency — Incorrect. $R_r$ depends on $l/\lambda$, so it varies with frequency.

Useful rules of thumb and reference values:
- Short monopole (over ground): 
  $$R_r \approx 20\pi^2\left(\frac{l}{\lambda}\right)^2$$
- Short dipole (free space): 
  $$R_r \approx 80\pi^2\left(\frac{l}{\lambda}\right)^2$$
- Quarter-wave monopole at resonance (ideal ground): 
  $$R_r \approx 36.5\ \Omega$$
- Below resonance, input impedance looks like:
  $$Z_{in} \approx R_r + R_{loss} - jX \quad\text{(capacitive reactance dominates)}$$

Practical takeaway: As you tune lower in frequency with a fixed whip, $R_r$ falls rapidly, hurting efficiency unless you use loading coils and minimize losses.