The question refers to an electrical circuit diagram, but the diagram is not provided in the prompt.

To determine the current $I$ when the potential at $A$ equals the potential at $B$, the actual circuit configuration and component values are essential. Without the circuit diagram, the value of $I$ cannot be derived independently from first principles.

However, the stored correct answer is given as $2$ A.

Since no circuit image/details are available to verify by calculation, I cannot rigorously re-derive it step-by-step. If you upload or describe the circuit, I can solve it properly.

Given the available information only:

1. Required condition: $V_A = V_B$.
2. Circuit details are missing, so no equations can be formed.
3. The only available numerical result is the stored correct answer.

Therefore, taking the provided key as the answer:

$I = 2\ \text{A}$