Phantom Circuit

Copyright ©1997 by Paul Niquette.  All rights reserved.

 

The sophisticated solver of this puzzle knows that the resistance of a conductor depends on the "resistivity" of the material out of which it is made and is furthermore directly proportional to the length of the conductor and inversely proportional to its crossectional area.

Now, a conventional conductor, like a wire, has a constant crossectional area, so the resistance varies with its length. The earth forms what is called a "sheet resistor"...
 

Assuming a rather constant conducting depth, the space between any two points on the surface offers countless pathways via which current can flow, an effective crossectional area proportional to the surface area, which is in turn proportional to the distance between the two points. The effect of widening tends to cancel out the effect of lengthening, giving a nearly constant resistance.

The engineering unit for sheet resistance is "ohms per square."  Hey, ohms per square what?

 


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