"since the length of a conductor is the same distance that the charge will travel,they are the same thing.."

Are you sure about it? So, you mean to say that each electron actually travels the length of the conductor?

I visualised it something like a pipe filled with fluid..as soon as there is an increased pressure of electrons at any point, this is transmitted instantaneously in all directions based on the resistance of the paths. The electron 'x' doesn't actually travel the whole distance of the path instantaneously.

Where is LP??