The fundamental radio antenna is a metal rod which has a length equal to

Options

A. `lamdba` in free space at the frequency of operation
B. `omega//2` in free space at the frequency of operation
C. `lambda//4` in free space at the frequency of operation
D. `3 lambda//4` in free space at the frequency of operation

Answer

To determine the length of the fundamental radio antenna, we need to understand the relationship between the length of the antenna and the wavelength of the signal it is designed to transmit or receive. The fundamental radio antenna is typically a metal rod, and its effective length is crucial for efficient operation.

### Step-by-Step Solution:

1. **Understanding the Wavelength (λ)**:
The wavelength (λ) is the distance over which the wave's shape repeats. It is inversely related to the frequency (ν) of the wave. The relationship can be given by the equation:
\[ v = \lambda \nu \]
where \(v\) is the speed of light in free space (approximately \(3 \times 10^8 \, m/s\)).

2. **Antenna Length**:
The length of the fundamental radio antenna is typically a fraction of the wavelength. Commonly, antennas are designed to be:
- \( \frac{\lambda}{2} \) (half-wave dipole)
- \( \frac{\lambda}{4} \) (quarter-wave monopole)
- \( \frac{3\lambda}{4} \) (three-quarter wave)

3. **Resonance Condition**:
For maximum power transmission, the antenna must resonate at the frequency of operation. The resonance condition is achieved when the length of the antenna matches a specific fraction of the wavelength. In this case, the length of the antenna is chosen to be \( \frac{\lambda}{4} \).

4. **Impedance Matching**:
At resonance, the impedance of the antenna matches the impedance of the LCR circuit connected to it. This matching is crucial for efficient power transfer. The \( \frac{\lambda}{4} \) length allows for this impedance matching to occur effectively.

5. **Conclusion**:
Therefore, the length of the fundamental radio antenna in free space at the frequency of operation is:
\[ L = \frac{\lambda}{4} \]

### Final Answer:
The length of the fundamental radio antenna is \( \frac{\lambda}{4} \).