A layer (1) single free standing copper track (a micro-strip) of 0.40 mm width will have an impedance of 50 ohms with respect to a solid copper ground plane on layer (2).
You may have a top pcb 20mil trace 5 mm long, shorted to bottom's ground plane via a single via, and its impedance could be 80ohm (at few GHz for example).Z = 0.0000001 + j80So the impedance is "inductive" - it means the "via" behaves as a small inductor - that is important when you want to ground a decoupling capacitor though a single via for example, thus you must consider the physical sizes and material properties as well..
Nope, if the resistance or conductance per unit length are non zero
There's a lot of very informative theory being described here. Makes me want to read Heaviside's biography, :-). But what are the practical implications for OP laying out a PCB? When should he worry about the effective impedance of his traces? Probably not of major concern on boards with Arduino chips. ?