V = voltage, the output of a battery. R = resistance of the cartomizer or atomizer.
I = the current drawn by the atomizer/cartomizer. I = V/R (Ohm's Law)
A battery is a constant voltage device (not really, but close). Put a resistor across its terminals and the resistor will draw as much current out of the battery as needed so that the voltage drop across the resistor = the battery voltage.
Battery capacity, mAh, milliamp hours, is the total quantity of current that the battery can deliver. A 380 mAh battery could drive 380 mA for one hour before being discharged. A higher mAh rating means longer vaping time compared to a smaller mAh. When running a PV, the current draw (mA) is almost always larger than the capacity (mAh) -- our little PV batteries are typically pushing out 1.5 - 2 amps, but would not maintain that output for a full hour before needing a recharge. You can think of it mAh as being like how many gallons of water a barrel can hold, while the current, the amps, is like how fast the water is flowing out a hole in the barrel, the gallons-per-minute.
Power, P = VxI = VxV/R, measured in Watts. More power = hotter, more "hit", more vapor production, often more flavor (though if you go too high the eliquid may lose some flavor or have a burnt taste).
If you have a higher voltage, then you have higher power for a given resistance. Conversely, for a given desired power, the higher voltage device generally gives longer run time, since the current draw is lower.
Two batteries, KR808D-1 at 3.8V, 510 at 3.3V. Take a 2.5 ohm cartomizer.
Power: 3.8x3.8/2.5 = 5.8W for the 808, while 3.3x3.3/2.5 = 4.4W for the 510. The 510 will be noticeably cooler.
Say you want the 5.8W on a 510, what does it take? 5.8 = 3.3x3.3/R. R= 1.9 ohms.
What's the current look like? 808: 5.8 = 3.8xI, I = 1.5A. 510: 5.8 = 3.3xI, I = 1.8A. The 510 battery has to supply 20% more amperes than the 808 battery to get the given power level. Even if the batteries have the same mAh, the 510 battery is draining, using up the mAh, faster than the 808 battery.
Hopefully the above helps
