This implies to me that you're using a regulated VW or "variable-wattage"
device. Ohm's law is more important on an unregulated, mechanical
mod. Ohm's law states that the current (amperage) through an electrical conductor between two points is directly proportional to the voltage, and
inversely proportional to the resistance (ohms). The equation is as follows:
I = V/R, where I = current, V = voltage, and R = resistance.
This says that Amps = Volts / Ohms. The power equation (sometimes referred to as "Watt's Law") is a related concept, which states that power (wattage) is directly proportional to the
square of the voltage, and still, like with the amps, inversely proportional to the resistance:
P = V^2 / R, or Watts = Volts * Volts / Ohms.
As these are mathematical equations, you can rearrange the terms and they will still hold true. For example, Ohm's law (I=V/R) could also be stated as V=IR or R=V/I. It just depends on which are the knowns, and which are the unknowns.
Ohm's law is important in a mechanical mod because it tells you how many amps you are drawing from the battery. Try to pull too many amps, and the battery goes *BANG!* (Or, more likely, it goes "pfffFFFFFFFTSSSSSSSSSSSSSSSHHHHHHHH" as it vents hot gases and flames -- it's not likely to actually
explode unless it's confined inside a rigid container like a metal tube without adequate venting, aka certain mechanical mods that do not have vent holes. Regulated devices too, I guess. Anything with a battery in it should have adequate venting, even your laptop and cell phone use the same kind of batteries we use and can vent if abused.) Ohm's law calculations should always be done assuming 4.2v, as with a fully-charged battery.
With a mechanical mod, the battery voltage is applied directly to the atomizer, and so the wattage (and amperage) will vary along with the battery charge state. With a regulated device, however, the wattage is held constant by the circuitry inside. Let's take another look at Watt's Law:
Watts = Volts * Volts / Ohms
Note that "volts / ohms" makes up a part of the equation. But "volts / ohms" is also equal to another value we have already discussed, the current (amps). So you could also state it as Watts = Volts * Amps. If you know the watts (determined by user setting) and volts (battery charge state), but not the amps, just divide both sides by volts to end up with Amps = Watts / Volts. If your device is set at 60 watts, for example, and the battery has 3.7v charge remaining, then you are drawing 60 / 3.7 = 16.216 amps. Note that I didn't mention ohms. That's because
ohms don't matter on a wattage-regulated device. All that matters are the wattage setting, and the battery charge state. If your battery can safely push 60 watts, then it doesn't matter if it's pushing them through two ohms, or two-tenths of an ohm -- the amp draw is the same in either case. Since the amp draw is highest on a
weak battery (as opposed to a mechanical mod, where it is highest when the battery is at full charge), Watt's law calculations should always be done assuming 3.2v or whatever the low-voltage cutoff is on your particular device, since that's when the battery will be worked the hardest at a given wattage setting.
Note that we are talking about the
output voltage (charge state) of the battery which is often represented only by a "fuel gauge"-type icon on the device's interface, and not the
applied voltage delivered to the atomizer, which may be displayed as a numerical value. These are not the same value (not usually, anyway, but even a broken clock is right twice a day.) If you want to know the output voltage more precisely than "well it looks to be about two-thirds full, or so" then you will need to check it with a multimeter. Some chargers, and a few (but not very many) devices also show the battery voltage as a number, but usually it's just the not-very-precise battery bar on the device, or a blinking red/green light on the charger.