Final answer:
The potential difference across the first resistor in a parallel circuit with two identical resistors and a 12 V battery is 12 V.
Step-by-step explanation:
In a circuit with a battery and two identical resistors connected in parallel, the potential difference across each resistor is the same as the emf (electromotive force) of the battery, provided the battery's internal resistance is negligible. Since the battery has an emf of 12 V, the potential difference across the first resistor is also 12 V.
Since the resistors are identical and in parallel, they both have the same potential difference across them as the total voltage supplied by the battery. This is because in a parallel circuit, voltage is the same across all components. Therefore, if the battery provides 12 V, each of the two parallel resistors will also have 12 V across them.