Resistance Variations: Effect's on battery drain rate (regulated mod)

I've heard and seen supporting evidence of two opposing theories on whether or not battery life is conserved at low resistance and in an opposing theory that low resistance correlates to faster battery drainage. From my interpretation of Ohms law V=I*R in conjunction with P=(V^2)/R or P=I*V. Where P is power (watts), I denotes current (A), V for voltage (V), and R resistance (Ohms). I personally believe that with lower resistance correlates to shorter battery life in a regulated mod where power is a constant, along with voltage to some extent being constant. As your left with your amps and your resistance as your variables. So if we look at P=(V^2)/R you can tell as you raise your power output for a constant voltage (Just say 3.7V) your resistance must be at a lower resistance. Then if you raise your resistance the load or power consumption is lower. the power output decreases in value. This correlation can also be made for P=I*V, as your power increases your current rises or your voltage decrease. Looking from only a current load stand point it goes to reason in my opinion that the lower the resistance your going to experience a greater current draw which therefore drains your battery faster. But I have heard reports that a low ohm coil such as the TF-V4 (0.15Ohms) is conserving more battery than a 0.5ohm coil. Can someone explain the correlation between battery life and resistance levels and explain how, if any, voltage plays a role in factoring battery life. I assumed voltage was closely related to remaining volume of battery life while current was the leading cause for battery duration. Correct me if I'm wrong in my assumptions as I do know voltage doesn't remain a true constant in a regulated mods. So if you know the role in which voltage plays in regards to equating variations in battery duration that that would be a bonus piece of information that perhaps I'm neglecting to account for.

The DC - DC voltage conversion performed in the regulated mod does not operate at the same efficiency throughout it's entire voltage/current output range.
This will vary from manufacturer to manufacturer.

While Robert's answer is correct, I think it's one step beyond the op's understanding of how variable wattage mods work. If the output wattage stays the same, the required input wattage (power) stays the same. If you change the resistance of the coil you change the output voltage required to hit your set watts, but the total output power is still the same. If output power is constant, input power is constant. In short, coil resistance has nothing to do with battery current in a variable wattage mod. Any minor differences in chip efficiency at different points of it's range is nothing you'll notice.

Sorry for sounding like a novice at all this but I suppose I am in the sense I cannot draw any correlations to what you can and cannot calculate in variable wattage devices that aren't set to bypass. So patience is a virtue here if you will.... okay so strictly from a variable wattage device are there any calculations I can use to determine a rough estimate of battery life based on coil resistance? I believe I'm getting lost within the understanding what you mean by "if you change the resistance of the coil you change your output voltage required to hit your set watts". does this mean you can think of a regulated mod as a chip with an input power from the battery to the regulating chip and an output power from the chip to the atomizer? where the power you denoted remains your constant wile your variables, in relation to battery discharge rate, are your input voltage and its inversely proportional current draw on the batteries. So correct me if I'm wrong, but in a simple example if you wanted to know the amp draw on your input power source you simply would take your desired wattage, e.g. 80Watts, utilize the P=IV formula where P is constant. V is your resultant voltage from your battery configuration; in this example lets use say... 2 series 3000mAh, 4.0 volt 18650's: while neglecting battery sag, voltage drops, any and all impedances for simplicity. So your current draw on your battery would be I=80/(4+4) or 10 amps. So this 10 amps is then proprietary to your input power source and doesn't have and relation to the output current if I'm understanding this? Then depending on the limiting factors for voltage set on the chip, using ohms law in conjunction with P=V^2/(R) it will manipulate the optimal voltage to achieve output power of 75 watts as you vary your coils resistance. So I may still be a bit confused but what your saying, Boomstick, as well as Robert vaguely put it; you may have the same input/output power though are derived independently from each other? then that would mean your only factor in battery life is dependent on the level of desired wattage one wants to fire at, despite his/her sub ohm coil vs ultra ohm coil?

if the theory is correct as I previously stated above, is there a rough estimate of battery duration one can denote, using the input/output power and input current in conjunction with the battery's capacity using simple dimensional analysis? 3000mAh*(1A/1000mA)= 3Ah's. Assuming continuous 10amp battery draw (3Ah/10A)(3600Sec/1hr) = 1080seconds/(average of 5 second puffs)= 216puffs.... could you theoretically determine, just by a set constant power value on a regulated mod without accounting for size of tank or type of build, a rough estimate of puffs per battery discharge? If so I know I can find these estimates for voltage drop and current addition adjustment factors, but if someone could list off the standardized variables i should considered in a problem similar to this and their reduction coefficient's if I wanted to try this in a real life example. for example what should I assume the "standard" continuous input voltage to be on an regulated 18650 3500mAh 35amp LG hg2, can I multiply the voltage capacity of identical batteries' but the total number or some fraction of the (mAh) summation if their in series. What is battery sag and how should I adjust for it? if I parallel can I multiply the number of batteries in parallel by the total number of batteries, should I account for voltage drop through the battery cathode to the positive post of the atomizer, the impedance (what is impedance referring to in vaping mods?), etc. sorry I know that's a lot of questions I'm just now getting into vaping and I'm just trying to learn it all at once. I have an Engineering degree in CVEN, so I've taken these basic classes before I just need a refresher.

Watt setting divided by total battery voltage get you battery current. Watts in equals watts out. The load on the batteries is the chip. The load on the chip is the coil. The only thing that affects the rate at which the batteries drain (battery current) is the watt setting. The combination of volts and amps that hit the coil to achieve the set watts isn't the same as the combination of volts and amps that the batteries supply to the chip, but the input watts equals the output watts. That of course ignores the approximate 5% power loss of the chip. Also, when talking about runtime with multiple battery, variable wattage mods, use the batteries total watt hours. Not the individual mah of each cell. However, trying to calculate how many puffs per charge you're gonna get is a waste of time unless you perform a bunch of measurements first. If you really want to know, leave the textbook in the classroom for a minute and head to the lab.

Thanks for the terminology correction's, as for the concept I'm able to grasp it a bit more thanks to your previous post, I appreciate that. As for your batteries voltage, when doing calculations, should its max rating be used? I've heard in some cases is just a good rule of thumb to use 3.7V for an 18650 like the Samsung 25R. Also should you completely double the batteries capacity when in series or just multiply by a factor of 1.5 or fully double it when you have 2+ batteries?

When calculating max battery current you use the mods cutoff voltage (usually around 3.2) for variable wattage mods as that's where the battery current is highest. Use the cells max voltage (4.2) for unregulated mods as that's where the battery current is highest. For runtime calculations use the nominal voltage (3.7) as that's where the cells spend the most time during a discharge cycle. Also, the capacity doesn't fully double when a cell is added. Some people say to consider it to increase by 50%, but I think it's more than that. Again, measuring your gear would be required to know for sure.