Are there any measurable characteristics that would allow one to discern the size of a conductive medium?
Say I apply the same voltage to a two foot long wire and a four foot long wire. Is there anything I could physically measure to determine the difference in relative size of the mediums?
Thanks!
If you know something about what is surrounding your wire (like it's very far from any other conductors or it's a known distance above a ground plane) you could determine its length from its rf resonances. This would most readily be done with a network analyzer, although a more primitive setup with just a synthesizer and a vector voltmeter or an SWR meter or even a Wien bridge could be used.
If you restrict the discussion to a wire above a ground plane, (or in another structure that forms a transmission line), then time domain reflectometry could be used to find the length. This technique involves sending a pulse along the wire and using an oscilloscope to measure the time it takes for a reflected pulse to return to the launch point.
Couldn't you measure the current? Resistance has the equation $R = p \dfrac{l}{A}$ where $p$ is the electrical resistivity, $l$ is the length and $A$ is the cross-sectional area. This formula shows resistance is directly proportional to the length of the resistor, and inversely proportional to the cross-sectional area. By hooking a known voltage across resistors of different sizes and utilising an ammeter, (and the equation $V = IR$) knowledge can be gained on the length and cross sectional areas of the resistors you are measuring.
