An antenna behaves as resonant circuit only when its length is

Options

A. `(lamda)/(2)`
B. `(lamda)/(4)`
C. `lamda`
D. `(lamda)/(2)` or integral multiple of `(lamda)/(2)`

Answer

To solve the question regarding when an antenna behaves as a resonant circuit, we need to understand the conditions for resonance in antennas. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Resonance
An antenna behaves as a resonant circuit when it can efficiently radiate or receive electromagnetic waves. This occurs when the physical length of the antenna is related to the wavelength of the signal it is intended to transmit or receive.

**Hint:** Recall that resonance occurs when the length of the antenna matches specific fractions of the wavelength.

### Step 2: Identify the Relationship Between Length and Wavelength
The condition for resonance in antennas is that the length of the antenna should correspond to specific fractions of the wavelength (λ). The common fractions are:
- λ/2 (half wavelength)
- λ/4 (quarter wavelength)
- λ (full wavelength)

**Hint:** Think about how waves behave in terms of nodes and anti-nodes.

### Step 3: Determine the Condition for Resonance
For an antenna to resonate, it should have a length that is an integral multiple of λ/2. This means:
- The length (L) can be expressed as:
\[ L = n \cdot \frac{\lambda}{2} \]
where \( n \) is an integer (0, 1, 2, ...).

**Hint:** Consider how the number of nodes and anti-nodes relates to the length of the antenna.

### Step 4: Analyze the Options Given in the Question
The options provided in the question are:
1. λ/2
2. λ/4
3. λ
4. Integral multiple of λ/2

From our analysis, we see that the correct condition for resonance is that the length of the antenna must be an integral multiple of λ/2.

**Hint:** Compare the derived condition with the options to identify the correct answer.

### Step 5: Conclusion
The correct answer is that an antenna behaves as a resonant circuit only when its length is an integral multiple of λ/2.

Therefore, the answer to the question is:
**Option D: Integral multiple of λ/2.**