In electrical circuits, the behavior of potential difference (voltage), current, and resistance varies depending on whether the components are connected in series or parallel. In this question, we are considering a situation where resistors are connected in a parallel configuration.

Let's explore what happens in a parallel combination of resistors:

• Current (I): In parallel, the total current flowing into the parallel branches is the sum of the currents through each branch. Therefore, the current is not the same across each resistor but is instead divided proportionally according to their resistances due to \(I = \frac{V}{R}\).
• Potential Difference (V): In a parallel circuit, each resistor is directly connected across the same two points, meaning that the potential difference across each resistor is the same. Thus, the correct statement is that the potential difference remains constant across all resistors in a parallel combination.
• Equivalent Resistance (Req): The equivalent resistance of resistors in parallel can be calculated using the formula \(\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}\). The equivalent resistance is not the same as the individual resistances but is actually less than the smallest individual resistance in the combination.
• Power Consumed (P): The power consumed by each resistor depends on the current through and voltage across it, calculated individually as \(P = IV\). Because the current differs, the power consumed is not uniform across all resistors.

Therefore, the only quantity that remains the same across all resistors in a parallel combination is the potential difference (V).

Conclusion: The correct answer is The potential difference (V).