(A) : For transmitting a signal, the antenna should have a size comparable to wave length of the signal at least `lamda//4` in dimension
(R) : The antenna properly senses the time variation of the signal

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'.
C. A' is true abd 'R' false
D. A' is false and 'R' is false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that for transmitting a signal, the antenna should have a size comparable to the wavelength of the signal, at least \( \frac{\lambda}{4} \) in dimension.
- This means that the antenna must be at least one-fourth the wavelength of the signal it is intended to transmit or receive.

2. **Understanding the Reason (R)**:
- The reason states that the antenna properly senses the time variation of the signal.
- An antenna's ability to sense the time variation of a signal is crucial for effective transmission and reception. If the antenna is too small compared to the wavelength, it may not be able to accurately detect the variations in the signal.

3. **Analyzing the Relationship**:
- The assertion is based on the principle that antennas need to be of a certain size to effectively transmit or receive electromagnetic waves.
- The reason supports the assertion by explaining why the size is important: it allows the antenna to properly sense the time variations of the signal.

4. **Conclusion**:
- Both the assertion (A) and the reason (R) are true.
- Additionally, the reason (R) correctly explains the assertion (A).
- Therefore, we can conclude that both statements are true, and the reason is the correct explanation of the assertion.

### Final Answer:
Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).