What would make the resistance change like this?
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Does metal increase resistance (talking the actual wire and metal it is made of), the answer is yes in these instances.
1) This first mainly is seen and used with Temperature Control Mode. All metals, that I know of, as power and heat are applied, the resistance in the metal increases with that heat, TC mode capable mods read this increase, and based on that increase, calculate and guess the temperature of the coil. This heat vs resistance increases and is compounded upon each successive hit until you set the mod aside and let the metal of the coil cool back down to lower its resistance. Nickel Ni200, Titanium T1, and SS316L this heat to resistance value can be read in real time with some decent accuracy, as their TCR values are readily know, Kanthal and NiChrome being they have such high resistance to begin with and the heat to resistance increase is so slight it barely detectable is the reason they are not used for TC mode.
2) Aging of the wire metal. More power you apply to a coil wire, the more heat it is abused with, basic physics here, things get hot, they expand, things get cold they shrink. This constant expansion and contraction, ages the metal, crystalizing it and making it more brittle. That crystalization increases the resistance of the metal, so you see a gradual increase over time of a coil head.
3) Over time of #1 and #2, also the coil connection legs can lengthen and shrink, this works those leads out of original position, which can lead to higher or lower resistance readings, laying the mod on its side like in your first post, could have lead to a coil shift, may have been just a nano-meter in distance, but enough to throw off a reading.
4) Tank/Coil Head/Coil Posts - where the wire connects on the atomizer device. #1 and #2 Strike again, mainly #1 here, the post screws, rubber insulator grommets, what ever hold the wire leads in place, RDA/RDTA/RTA rebuildables screws loosen over time due to expansion and contraction, rubber and insulator grommets on drop in coils deteriorates and shrinks from the wire, both instances resistance can increase.