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!!!!!CHECK HERE FOR BATTERY AND ATTY/CARTO COMBOS!!!!
Acceptable battery/carto combos are highlighted in green. 

Others may work but there is a risk of damage.
FWIW, the math, IMO states that there is really no completely safe, or happy resistance for 180mAh (510) batteries. Yet they manage to work albeit on the weaksauce side.. 


A good friend here at little shop of vapors, Jason IRL and mendnwngs at ecf , put together this information regarding ohms, volts, resistances, and the variables that determine which atomizer or cartomizer is appropriate for which battery at what voltage.

It is a lot of info but important info to consider when deciding on your purchases.
In each product description is a very basic break down ie: this carto is recommended for devices running at such and such volts or more. It may work on higher voltage devices/batteries but will drain the battery quicker.
For your reading enjoyment:
Styles, and marketable differences aside, I'm focusing on the usability of given atty/ carto on given battery.
This may, or may not make sense but I'm basing my recommendation on standard LiIon chemistry that doesn't have any “specialness” built into it.
It all boils down to the draw on the battery, this is measured in “C” If you have a 500mAh battery, and draw 500mA from it, it should last 1 hour (500mA/Hour) 
This is 1C.
If you draw 1,000mA from it, it would, in theory live 30 minutes, (This would be 2C, or ½ an hour)
At 4,000mA that 500mAh battery would last 7 minutes, or 8C discharge (1/8th of an hour) 

In the real world we never see these numbers.. 
The faster you discharge a LiIon, the unhappier it gets, and the more inefficient it gets.. 
The 2C example might actually only live 25, or 20 minutes, and the 8C example might only go 4 minutes before the cell is drained. 
 I'm basing my suggestions on the “4C” golden number we've found to be the magic toggle point where a regular Li Ion battery gets unhappy, and results in significantly shortened charge/discharge cycle life. This has a lot to do with “Duty cycle” or time on Vs Time off, and other significant variables.. 
Frankly, its hard to come up with “Hard and fast” rules here.. For the brief time we actually engage the battery while taking a drag, 6, 7, even 8C are okay, but will result in long-term damage to the battery. 

Higher xC = unhappier battery, Lower xC = happier battery. 
“Batteries will be 510 in 180/280/340 eGos in 650/800/1000” - those sold at little shop of vapors when this doc was created in Jan of 2012.
We can reduce this.. Mods, battery styles, etc.. It all boils down to voltage, and mAh.. 
So were seeing 180, 280, 340, 650, 800, and 1000mAh batteries. 
All of this is figuring for the 3.3V regulated output of 510 / eGo batteries.

@3.3V:
1.5ohm: 2,200mA, 7.6Watts
1.7ohm: 1,940mA, 6.41Watts
2.0ohm: 1,650mA, 5.45Watts
2.3ohm: 1,430mA, 4.3Watts 

So, from this, we can tell the maximum “Happy” factor from batteries for various attys /cartos 
Now, I'm just repeating myself  :) 
Again, this is all figuring on a 3.3V regulated system (510s and eGos are regulated down to 3.2-3.3V, as I understand) 
As the voltage gets higher (say 3.7V, but the mAh of the battery, and resistance of the atty stay the same, there will be more wattage, and a higher C on the battery.






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