If the size of the electrode is doubled, then internal resistance becomes
The resistivity (ρ) of the liquid, the distance (l) between the electrodes, and the cross-sectional area (A) of the electrodes all affect the cell's internal resistance (r). This is how it's shown:
r = ρ A
In the case that the electrode doubles in size, its cross-sectional area (A) also doubles. Since resistance goes down as area goes up, the internal resistance will be cut in half.
So, when you double the size of the wire, the internal resistance goes down by two times.