Final answer:
We cannot determine the currents through resistors A (2Ω) and B (3Ω) without additional information such as the total voltage of the circuit or whether the resistors are arranged in series or parallel.
Step-by-step explanation:
To find the currents through resistors A and B, we would typically need more context such as the total voltage supplied and the specific configuration of the circuit to calculate it using Ohm's law or other circuit analysis methods. However, based on the provided information alone, we do not have sufficient details to ascertain the currents through A (2Ω) and B (3Ω). If resistors A and B were part of a series circuit, we could use the given resistances alongside the total voltage of the circuit to calculate the current using Ohm's law (V = IR), but this is impossible without knowing either the total current or total voltage.
If the circuit is parallel, the current would divide among the paths and we would need to know the total current entering the parallel combination to calculate the individual currents through A and B. Even with the additional provided information about currents through other resistors in various scenarios or the annotations related to Ampère's Law, we cannot infer the specific currents through resistors A and B without further details regarding the entire circuit.