A

Step 1: In a transistor configuration, the parameter \( \beta \) is defined as the current gain of the transistor. It is the ratio of the collector current (I_c) to the base current (I_b). This can be mathematically expressed as:
\( \beta = \frac{I_c}{I_b} \)

Step 2: The relationship can also be established using the lengths of the transistor sections, given that the currents are proportional to the corresponding lengths in this idealized scenario.
Step 3: From the options provided, the one that matches the relationship between the elements is:
\( A: \frac{l_b}{l_c} \)

Therefore, the correct answer is A.