Answer
The potential difference across the series arrangement is equal to that across the parallel arrangement.
Work Step by Step
Let $\Delta V$ be the potential difference across the battery.
When the resistors are in series, the potential difference across each resistor is $\frac{\Delta V}{3}$. When the resistors are in series, we add the potential differences across each resistor to find the total potential difference across the arrangement of resistors. The total potential difference across the series arrangement is $\Delta V$
When the resistors are in parallel, the potential difference across each resistor is $\Delta V$. The potential difference across the parallel arrangement is $\Delta V$
The potential difference across the series arrangement is equal to that across the parallel arrangement.
