If I stuck two earth rods in a uniform field (e.g. a big flat area with grass or whatever) at ever increasing distances (e.g. 10m, 20m, 30m ..., 1000m etc) how would the result vary as a function of distance? An obvious answer would be linear (i.e. of the form R = AL + B where B is the resistance of the rods themselves). But a field isn't a wire, it's a plane - and that's a bit beyond my intuition, and beyond any easy maths.
The distance between the earth rods is unimportant. The accepted view is that the general mass of earth has zero resistance and that the measured resistances are in fact a CONTACT resistance due to the limited area of contact.
Or put another way, the resistance between two earth rods would be the same if they are 100 yards apart or thousands of miles apart. (presuming similar sized rods and ground conditions in each case)
Earth return telegraph systems worked fine over thousands of miles, this not only saved the cost of a second wire, but gave half the circuit resistance of a two wire circuit.
Earth return power circuits are used in some places and give a lower resistance than two wires.
The cross channel power link normally operates as a two wire system with well insulated positive and negative cables. In the event of a cable fault, it may be operated at half capacity via the sound cable and an earth return.
Yep I reeckon Broadage has given the essence here. Good answer.
The earth is not a big thick highly conductive metal plate.
Is is composed of tiny lumps of soil, rock etc.
Each lump in itself is quite resistive.
However your rods are attached to loads of lumps. Each one is connected to a few other lumps.
Imagine each lump as a tiny ball-bearing of high resistance in a container all pressing on each other.
From any two points you`d have lots of series parallel and parallel series connections. Therefore the further away you get the resistance becomes nearer to zero.
Very near each rod etc the rods have the highest resistance.
If you draw a diagram with say two standard 4` rods say 8` apart and then draw a triangle about the length of each rods with curved sides you`d see the "resistance mountain" as a graph. Draw a second diagram with the rods 1 mile or 10 miles or 1000 miles or more apart and the resistance between the rods would be substantially the same in all cases.
It may help to visualise that (on regions of the earth small and uniform enough to be thought of as flat anyway )the cross-section of the resistor is approximately the shape of a rugby ball sliced longways, with the electrodes at the 'points' .
Then imagine slicing it into thick semi circles and looking at the resistance of a stack of half disks.
Increasing the length of the mid-section, also increases the diameter and so the area of that slice, which lowers the resistance faster then increasing the length raises it. Assuming the expanding region of influence it is not truncated by rock formations or caves, then as such the actual resistance is as others have said, almost independent of the bit in the middle, and dominated by what is happening where the current is converging or diverging very steeply, near the electrodes.
If you are brave (or well insulated, or use a lower voltage) you can see this, by livening up an electrode, and looking at the contours of surface voltage as you move away from it, nearly all the voltage drop is in the first couple of rod lengths - hence the assumption that rods 2 rod lengths apart can be considered as independent connections to the plate at the end of the universe, and even if they are only 1 rod length apart they are becoming fairly independent..
