Finding the voltage drop along a tapered wire

[bob012345]

It could be a lot more complicated than that.
If we assume the current density is the same everywhere then the twisting has increased the path length and the effective cross section (normal to the current) has reduced.
If not, it's really messy.

In the truncated conical resistor problem above we calculated the total resistance under the assumption that a simple integration over the geometry yields the correct formula and answered the OP's question of where the formula came from.

But here is a paper that examines the physics of current flow and potential in such a resistor by authors Romano and Price from the University of Utah. Enjoy. The introduction reads;

ABSTRACT
A truncated cone, made of material of uniform resistivity, is given in many introductory physics texts as a nontrivial problem in the computation of resistance. The intended method and answer are incorrect and the problem cannot be solved by elementary means. In this paper, we (i) discuss the physics of current flow in a non-constant cross‐section conductor, (ii) examine the flaws in the ‘‘standard’’ solution for the truncated cone, (iii) present a computed resistance found from a numerically generated solution for the electrical potential in the truncated cone, and (iv) consider whether any problem exists to which the standard solution applies.

1. © 1996 American Association of Physics Teachers.

https://www.researchgate.net/publication/252273146_The_conical_resistor_conundrum_A_potential_solution