*Question T9A05:
Which of the following increases the resonant frequency of a dipole antenna?*  

*Correct Answer is  C: Shortening it*  

### AI Response: (may contain errors)  

To understand how to increase the resonant frequency of a dipole antenna, let's analyze the options provided:

### Correct Answer: C - Shortening it

- **Explanation**: The resonant frequency of a dipole antenna is inversely related to its length. As you shorten the length of the dipole, the resonant frequency increases. This is because a shorter antenna will resonate at a higher frequency due to the relationship between length and frequency.

### Why the Other Choices are Incorrect:

- **A: Lengthening it**  
  - Lengthening the dipole antenna decreases the resonant frequency. A longer antenna will resonate at a lower frequency because it takes a longer wavelength to match the physical length of the antenna.

- **B: Inserting coils in series with radiating wires**  
  - Inserting coils (inductors) in series with the antenna increases the inductance, which lowers the resonant frequency. This is because the added inductance requires a longer wavelength to resonate, thus decreasing the frequency.

- **D: Adding capacitive loading to the ends of the radiating wires**  
  - Adding capacitive loading effectively shortens the electrical length of the antenna, which can also lower the resonant frequency. Capacitive loading introduces a capacitive reactance that counteracts the inductive reactance, leading to a lower resonant frequency.

### Useful Formulas and Rules of Thumb:

- The resonant frequency ($f_r$) of a dipole antenna can be approximated by the formula:

$$
f_r = \frac{c}{\lambda}
$$

where:
- $c$ = speed of light in meters per second (approximately $3 \times 10^8$ m/s)
- $\lambda$ = wavelength in meters

- The length of a half-wave dipole antenna ($L$) is given by:

$$
L = \frac{\lambda}{2}
$$

Thus, if you decrease $L$, you increase $f_r$. 

In summary, shortening the dipole antenna increases its resonant frequency, while the other options either decrease the frequency or do not affect it in the desired way.