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Can someone explain the different coils to me?

Pretty much all of the above answers are correct in one way or another - but all of them neglect to mention that if the two coils in a dual coil build are not matched in resistance then the result will be that one coil will get hotter than the other, creating no end of issues with the vape experience. It's important to use coils of very closely matching resistance in dual coil builds (I'd be looking for less than 0.05 variance between the two coils). In which case it is safe to say that the final build resistance will be half of whatever value of coil you are using - ie: for 1 ohm coils the final resitance would be 0.5 ohms.
However the correct formula for determining TOTAL parallel resistances is 1/Rt = 1/R1 + 1/R2 + 1/R3 + ..., this is horribly complicated for the average vaper - and even I need to use a calculator to do it. So since most people only use single and dual coil setups it's better to stick with one of the shortcut type calculations. The (R1+R2)/4 is fine for most people - as is the "Half whatever your single coil value is" rule - Even Quad coil builds can be broken into two pairs and the value worked out for each pair, then the pair values taken together for the total resistance, after that you'll just have to bite the bullet and get out the calculator.

Getting back to the OP's question -
Each of those coils is a different combination of Wire types and sizes, wound, twisted or woven together in various ways, The simplest to explain are the Clapton - basically a thick central core wire with an outer thinner wire wtapped around it to give an apperance similar to a guitar string, Fused Claptons use two cores next to each other with the outer wrap covering both continuously, Staple fused is similar but the outer wire is actually two wires (IIRC) and are woven in and out of the cores to give a look similar to a row of staples.
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[QUOTE="Tubbyengineer, post: 1532047, "The (R1+R2)/4 is fine for most people"

Yeah, that's why I use that as a simple explanation to new builders.
The reason I used the imbalanced example of 3 ohm & 2 ohm was to demonstrate that half the vale of a single coil is not correct, as in which coil would you halve the value of ? either answer in that case would be wide of the mark.

I have to congratulate you on the images of various coils, are these all yours ?
 
[QUOTE="Tubbyengineer, post: 1532047, "The (R1+R2)/4 is fine for most people"

Yeah, that's why I use that as a simple explanation to new builders.
The reason I used the imbalanced example of 3 ohm & 2 ohm was to demonstrate that half the vale of a single coil is not correct, as in which coil would you halve the value of ? either answer in that case would be wide of the mark.

I have to congratulate you on the images of various coils, are these all yours ?
Nah, I'm not that patient - they're just from google...
 
Pretty much all of the above answers are correct in one way or another - but all of them neglect to mention that if the two coils in a dual coil build are not matched in resistance then the result will be that one coil will get hotter than the other, creating no end of issues with the vape experience. It's important to use coils of very closely matching resistance in dual coil builds (I'd be looking for less than 0.05 variance between the two coils). In which case it is safe to say that the final build resistance will be half of whatever value of coil you are using - ie: for 1 ohm coils the final resitance would be 0.5 ohms.
However the correct formula for determining TOTAL parallel resistances is 1/Rt = 1/R1 + 1/R2 + 1/R3 + ..., this is horribly complicated for the average vaper - and even I need to use a calculator to do it. So since most people only use single and dual coil setups it's better to stick with one of the shortcut type calculations. The (R1+R2)/4 is fine for most people - as is the "Half whatever your single coil value is" rule - Even Quad coil builds can be broken into two pairs and the value worked out for each pair, then the pair values taken together for the total resistance, after that you'll just have to bite the bullet and get out the calculator.

Getting back to the OP's question -
Each of those coils is a different combination of Wire types and sizes, wound, twisted or woven together in various ways, The simplest to explain are the Clapton - basically a thick central core wire with an outer thinner wire wtapped around it to give an apperance similar to a guitar string, Fused Claptons use two cores next to each other with the outer wrap covering both continuously, Staple fused is similar but the outer wire is actually two wires (IIRC) and are woven in and out of the cores to give a look similar to a row of staples.
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@Tubbyengineer and @Badboybez. Thank you your absolutely spot on as always. Sometimes in haste its easy to neglect the whole of the story. Thanks guy's for a thorough and clear explanation.
Tubby has the idea of the top ten section moved any further forward. We have a fine record of excellent ideas being forgotten between all the discussions.
It looked like you where coming up with a great framework.
 
Nah, I'm not that patient - they're just from google...

Aw, now you have disappointed me.

I was thinking that come the revolution in this green, and festering country, once I was president, I was going to have you appointed as Master Coil Builder to El Presidente badboybez............................

On a serious note though, out of all those build patterns, which one do you think creates the best flavour level ?
 
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