If what you mean by voltage is 'potential difference', the wires are assumed to have zero voltage across them. You need to clear up the terminology first. Refer another one of anorlunda's great insights for this issue. https://www.physicsforums.com/threads/tiny-tweak-in-teaching-basic-circuits.908496/ If you mean 'potential' by the term voltage, I believe tbe answer is already given by delta2 in #13. Wires are assumed to have zero resistance, so no electric field is required to maintain the current. No field, no potential 'difference', hence, 'constant' potential throughout the wire. Edit: Sorry, the thread I linked was a 'featured thread' and not an insights article.