Final answer:
The potential difference across each of two identical resistors connected in series to a battery with total potential V will be 0.5V. The voltage is divided equally between the two resistors, each taking half of the total voltage supplied by the battery.
Step-by-step explanation:
The question involves a battery connected to a combination of two identical resistors in series, and it asks for the potential difference (or voltage) across each resistor, given the total potential V across the battery. When resistors are in series, the total potential difference across them is the sum of each of their individual drops. Considering that the resistors are identical, the potential difference across each resistor will be the same and will therefore be half of the total potential difference supplied by the battery.
Using the formula Vbattery = V1 + V2 where V1 and V2 are the potential differences across the two resistors, we can say that for two identical resistors V = V1 + V1 (since they are identical, both potential differences are the same). Thus, each resistor in series has a potential difference of 0.5V, because V1 = V2 = 0.5 * Vbattery.
Therefore, the correct answer to the question is c. 0.5V, representing the potential difference across each resistor when two identical resistors are connected in series to a battery.