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Your question reveals fundamental misunderstandings about the nature of electricity.

'Voltage' is simply another word for 'potential difference', and a potential difference appears across opposite ends of the resistor; it doesn't 'travel through' that resistor! Current, on the other hand, DOES 'travel through' the resistor and is caused by the potential difference across the resistor.

Resistance is the ratio of potential difference to current. So if the resistance remians unchanged when the current through it doubles, then it has happened because the potential difference has doubled.

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