When the potential difference and current across a circuit are both doubled, the circuit's resistance:

We know that according to Ohm's law:

Current flowing through a circuit is directly proportional to the potential difference across the circuit. It can be expressed as:

$\mathrm{V}= \mathrm{IR}$

Therefore, R can e written as:

$\mathrm{R}= \frac{\mathrm{V}}{\mathrm{I}}$

In the given problem both potential and current are doubled:

$\mathrm{R}= \frac{2\mathrm{V}}{2\mathrm{I}}= \frac{\mathrm{V}}{\mathrm{I}}$

We can see that the resistance will remain the same.