Can I use Djikstra's algorithm to solve this problem?

[iknownothing]

Note, this is not an assignment. Just something that I came across online. 

Say I wanted to determine if a path exists that will allow an electrical car to travel to every single city on an undirected, weighted graph, given a limited number of recharges. Note, it is not stipulated that the car ever returns to its original city (which I believe disqualifies this problem as a case of the traveling salesman). However, I do need to determine path, and path cost. Can Djikstra's algorithm be modified in order to solve this problem, and how?