What is the current - voltage relation in a wire?
Every wire has a resistor which increase with the length. Since it's very small, we normally ignore it. Thanks to Ohm law, we can calculate the dropping voltage due to a resistor : \$U = RI\$, \$I = U * \frac{1}{R}\$. As you can see, the current is proportional to the volage drop by a factor of \$\frac{1}{R}\$