It’s that series config that doesn’t sit well with me.
I’m at 3.18v divided by .22ohms = 14.45 amps running 46 watts.
But what I’m really doing is 23 watts divided by 3.2 = 7.18 amps per battery. Minus .9.
Where are those numbers from? I think you're confusing what's happening on either side of the circuit board.
Let's say you're running a .3 ohm coil at 50 watts on a dual battery mod.
Coil Side
First, we'll look at what's happening on the coil side of the circuit board (not that it matters with a regulated mod, but as you want to understand what's happening we'll work it out).
We know resistance, which is 0.3 ohms, and power, which is 50 watts. We don't know voltage or current.
First, we'll find the voltage. That will be the square root of resistance times power.
Square root of (0.3 ohms)(50 watts) = square root of 15 = 3.9 volts
This means that the circuit board must provide electricity to the coil at 3.9 volts to meet the 50 watt setting. (Note that this does not say anything about the batteries' voltage. That's a completely different issue.) Not also that if your mod displays voltage, this is the voltage it will usually display.
Now that we have the voltage, we can also find the current. Current = v/r = 3.9 / 0.3 = 13 amps.
This current is irrelevant to your batteries, because they will provide energy in a different form!
Now, what do the batteries care about? To find out, we look at the battery side of the circuit board.
Battery Side
First, a note about circuit boards. They can change the form, but not the overall amount, of the electricity that passes through them. Amount = power, a.k.a. wattage. Wattage in will always equal wattage out, but voltage and current (amperage) can change. That's the point of the circuit board.
The battery side of the circuit board couldn't care less that your resistance is 0.3 ohms. It only matters that the power is 50 watts. Whether 50 watts is applied to 0.3 ohms or 0.5 ohms, it's still 50 watts.
The batteries themselves have their own voltage. It's 4.2 volts at the beginning of the charge and 3.2 volts when the batteries need to be recharged. In a dual battery mod, the voltage available to the circuit board from the batteries depends on their connection. With a serial mod, the available voltage will range from 6.4 v to 8.4 v. With a parallel mod, it will range from 3.2 v to 4.2 v.
Now, we know that the circuit board needs to provide the coil with 13 amps of current at 3.9 volts, and we know that 13 amps @ 3.9 volts is equal to 50 watts. What the circuit board has access to may be anything between 3.2 v and 8.4 v. The circuit board therefore has to pull enough current (amperage) at whatever volts the batteries happen to provide at the moment to equal 50 watts.
Since we want to know what the highest demand on the batteries will be, we use the lowest voltage in our calculations (It will take more amps to make 50 watts at 3.2 volts than it will at 4.2 volts, and we want to know how high the amps can get).
For a parallel setup:
We know the cutoff (e.g. lowest) voltage is 3.2 volts. We know that we need to end up with 50 watts. Current is power divided by voltage, so:
50 watts / 3.2 volts = 15.6 amps (from the batteries together)
For a serial setup:
Now, the cutoff is 6.4 volts (two batteries at 3.2 volts in series, which doubles voltage). We still need the same 50 watts, so:
50 watts / 6.4 volts = 7.8 amps (from the batteries together)
You'll notice that you need twice as many amps to get your 50 watts if the batteries are connected in parallel as you do if they're in series. Fortunately, you'll remember that when batteries are connected in parallel you double the current, so the CDR is twice what it would be if they were series.
The reason the calculation is the same for series and parallel is because:
- In series, you have more volts so you don't need as many amps
- In parallel, you have fewer volts so you need more amps.