Ohm's law is stated at-
I X R = E over I times R
Where E= Energy, voltage
I= Current, anperage
R= Resistance, Ohms of.
A much better explanation is here, this breaks it down in terms most can understand in a useful way. Ohm's Law - The basics - Ohms Law Formulas Explained to save you time
So say you have a 4.2V battery and a 1.5ohm carto, you take 4.2v divided by 1.5ohms to get 2.8amps.
A 4.2v at 3.0ohms gives 1.4amps.
Wattage is another measurement of power/work, it's a function of voltage and amperage. Volts times amps gives watts. Watts divided by amps gives volts. Watts divided by volts gives amps.
In the instances above, 4.2v times 2.8amps, you get 11.76 watts.
4.2v times 1.4amps you get 1.88watts.
Now what does any of this have to do with personal vapors? A LOT!!! With all the influx of new variable voltage and variable wattage mods hitting the market I think it's a good idea for users to understand the basics of what and why they are made this way and how to use them. It seems a general conciseness that around 12watts is the sweet spot for most juices, much over that and it's burnt. I also don't understand the fad for VW units, some basic calculations can do the same, and you are going to experiment/play with them to find a sweet spot anyway.
But this will show you a way to monitor battery life, 2.8amps is twice as much as 1.4amps, therefore you should get close to double the battery life out of the lower amperage. I say "should" as there are too many other factors involved to get exact, battery output, usage, age of battery, internal resistance of the PV or otherwise, used, temperature, it goes on.
I'm sure Morandir will add as he see's fit (feel free to edit this post if needed) to get more information, as basic as we can keep it. All in an attempt to help you understand how these units work, and why "it does this or that" when you "do this or that".
I hope it helps some of you understand this a little better.