I really like this one. I common with most excellent investigation it's a simple idea but it turns out complex. On the face of it it's a too simple. What is the relationship between the resistance and length of a conductor. But this conductor is wide, does the whole width of the conductor carry current? The not electric field lines don't go up into the corners so maybe the current doesn't either. Using this conducting paper it is possible to plot the field lines by using voltmeter to determine the direction of maximum potential gradient. The first run of this experiment gave a proportional relationship with a very large Y intercept. Could this be due to the leads, I think not, the resistance of the paper is several megaohms and the resistance of the leads it's maybe just a few Ohms or less. It is more likely to be the connection between crocodile clip and the paper. This is a big problem when welding on a car, the connection between the Earth and the body is sometimes poor, to improve this a piece of copper is sandwiched between the jaws of the clip so we tried this with the paper with excellent result. The next stage is to extend the copper to the edges of the paper. It will be interesting to see if the results are more in line with the theory.