I’m a bit confused on how to find the resistance of a purely 2d conductor. I tried just taking the formula for a 3d conductor and assuming that the “thickness” in the z-direction is constant, but this does not give the correct answer (that resistance does not depend on size.) I get that the resistance is proportional to the lenght l and to 1/h, where h is the thickness of the conductor in the direction perpendicular to the current. Where does this argument go wrong?
How do you judge that you did not get the correct answer?
When I asked what the answers to the warm-up exercises of the drude model are, anton-akhmerov said:
I take this to mean that the resistance of a purely 2d material does not depend on its size, and thus also not on its length or thickness. Maybe I misread this, but I don’t see how else to interpret this.
Not exactly. The thickness of a 2D material doesn’t vary. So another way to view the question is to ask by which factor does resistance of a 2D material change if we increase both its length and width by 2x.
Aha then I misread the question. I also get that the resistance is proportional to l/w, so if you double both then the resistance is the same. Thanks!
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