# Electric potential and length of wire?

The formula of electric potential is $$V=\frac{kQ}{r}$$ and the voltage across two points is $a$ and $b$ that determines the work of the electric field on a charge $q_1$ from $a$ to $b$.

If, say, we have short wire and make a circuit with a power source, then there would be some voltage. Now if we use a long wire instead of short wire, isn't now the distance increased between $a$ and $b$? So why does the voltage remain same if we consider the wire conductivity 100%? If we use the above formula then it means that the voltage must decrease. So how does all this happen?

Outside of a static spherically symmetric charge distribution with total charge $Q$, the electric potential is indeed given by the formula you quote.
Your formulae $$V=\frac{kQ}{r}$$ is for the potential of a point charge in an infinite non-conductive medium. Simply put,it doesn't apply to the case within an electric wire which in the ideal case is what is known as a equipotential i.e. "at the same voltage". Of course in the real world you can have a voltage drop along the length of the wire when current flows.