Understanding the relationship between power and coil resistance
A much asked question amoung new users specifically of regulated devices (variable wattage) is "what coil do I need" or "what resistance is best for wattage X, and what wire should I use?".
The answer to the first question is, whatever coil works best for you as long as your device can supply enough power to get it up to heat. The answer to the second, is that that coil resistance is essentially unimportant on a regulated device, use whatever you like.
The key to understanding this is to think of the chosen power level dictating the wire guage and end resistance, rather than the other way around.
If you want to use a lot of wattage, then you need a heavier gauge of wire to be able handle this power. Heavier wire, more mass, with an intrinsically lower electrical resistance.
If you want to use a far lower power level, then you need a much thinner wire with less mass, or your power level will not be sufficient to light it up. Thinner wire, less mass, with an intrinsically higher electrical resistance.
On a unregulated device this takes care of itself, as the relationship between resistance and power is fixed. Using thicker wire produces lower resistance coils, which draw more amps and produce more wattage as per Ohms law - P=V²/R
There are practical limits to how low a resistance coil you can due to battery voltage sag, and voltage drop within the mod which increases exponentially as amp draw increases. Also very high mass coils have undesirably long ramp/down times. There are also safety issues with using extremely low resistance builds.
On a regulated device the relationship between resistance and power is not fixed, you can apply any power level you like to any coil regardless of it's resistance. Coils can be chosen to suit the desired power level, not the other way around.
The resistance of the coil becomes irrelevant, other than limitations set by the mod's own regulator chip. Now the important factors become the relationship between coil mass, surface area and the selected power level. Generally for maximum vapor production and battery efficiency one should choose a coil with the greatest surface area and the least possible mass.
Karl puts 12 watts through a 0.25 ohm dual 24AWG coil. He gets barely any vapor and the ramp up time of his coils is measured in hours.
Frank puts 70 watts through a single 6 wrap 30AWG 1.8 ohm coil. The vape is hideously harsh and his coil turns to a pool of molten slag in the bottom of his atomizer.
Understanding the relationship between wire thickness, surface area and mass
If you have two lengths of wire with one twice the thickness of the other, the thicker wire will have twice the surface area but four times the mass.
Once you understand this it's easy to see that coils made from lots of wraps of thin wire will be exponentially more efficient.
This equates to either less power used for the same vapor production, or the same power for more vapor production.
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