Um, kinda all of it. What I thought I understood, I am now completely confused about.... But yeah, mainly about regulated devices, I thought I understood that of course the resistance of the coil changes the amps drawn, or doesn't it?
No, it doesn't. People will usually use higher wattages with lower resistances and that changes the amps, but at the same wattage different resistances would still use the same amps -
on a regulated mod.
I have no explanation at all about why my batteries will be used up quicker with lower resistance coils than higher ones at the exact same wattage.
They shouldn't. At the same wattage, you should get the same battery life.
I thought that was WHY the mod even read the resistance, but goodness at this point? I'm almost thinking of going to radioshack and getting some rechargeable regular batteries.
Anna
No, the mod needs to know the resistance so the board can do its job and provide the correct voltage to the coil. The battery doesn't see the coil and couldn't care less what its resistance is (on a regulated mod).
I'm going to have a go at explaining things another way. If I screw this up, someone please correct me.
Watts = volts x amps
Battery <---> Board <----> Coil
The board takes electricity from the batteries. You pick the wattage of this electricity. The voltage is determined by the state of the batteries' charge and the number of batteries, and it drops as the batteries discharge. To keep the wattage the same (i.e. where you set it), the board pulls more amps as the batteries discharge and the voltage drops. Only the batteries' voltage and your wattage settings matter in determining the amps drawn from the batteries.
The board now has a given wattage of electricity - what it got from the batteries. Unfortunately, it's at the wrong voltage for the coil. So it changes the voltage - that's its reason for being, to adjust the electricity into a form that works for the coil. (This is where Ohm's law comes in - the board uses the coil resistance to decide what voltage it needs, but it does all the calculations so you don't need to.) Remember that watts = volts x amps. The wattage has to stay the same, because you've only got the wattage you pulled from the battery. So, when the board changes the volts it changes the amps too to keep the wattage the same. That's why the volts and the amps you might see on your screen are irrelevant to the battery - they're what the board changed things to, not what it got from the battery.
Short version: Your battery doesn't care what your resistance is. Your board does.