Probably the most important bit of maths you need to know as a vaper!
There’s nothing mystical or magical about Ohm’s Law. It’s a few formulas, usually depicted inside of a triangle, and anyone can easily learn and use the formulas with any regular calculator.
The goal here is to show you the formulas behind Ohm’s Law and hopefully give you an understanding of the relationships between the different elements in a basic electronic circuit as related to vaping.
Inside the triangle you can see the three main elements in any electrical circuit, represented by the letters V, I, and R. I would vocalize the triangle as “V over I times R” with “times” being multiplication. The hardest part of this will be remembering what the letters represent, and that’s easy:
V = Voltage (your battery voltage) I = Current (the amperage drawn by your coil) R = Resistance (the resistance, in ohms, of your coil) So, how do we use the Ohm’s Law triangle? Again, simple – the triangle visually depicts the relationship between voltage, current, and resistance. In the following examples we’ll explore how to use the triangle and formulas to help you build coils targeting the current and wattage you desire.
If you want to determine the current draw through a resistance (your coil) the formula is:
I = V ÷ R (or I = V/R) How did we arrive at that? Look at the triangle and you will see that to solve for current (I) you must divide voltage (V) by resistance (R).
Let’s put the formula to work in a real life example. If you are using a mechanical mod, with a freshly charged battery you theoretically have 4.2 V available to power your coil. If your coil is 0.5Ω, you now have everything you need to determine current, in amps:
I = 4.2 V ÷ 0.5Ω (or 4.2/0.5) I = 8.4 A As you can see, with your 0.5-ohm coil and a freshly charged battery at 4.2 volts, the resulting max current draw will be 8.4 amps. If your battery has a 10-amp limit, you are well below the cap. Don’t forget that using a dual mechanical mod in series configuration will double your amp draw per battery, and you will have to build coils with twice as low resistance to be safe. Also note that as the battery depletes, the current will also tail off. For example, when the battery reaches 3.7 volts with the same load, current will drop to 7.4 amps (3.7 volts / 0.5 ohms)
Calculating power (wattage) The next thing you will probably want to know is the power generated at the coil, or wattage. It’s not shown in the triangle, but the formula is simple. Just multiply the current in your circuit by the voltage applied:
P = V x I In our original example, the formula would look like this:
P = 4.2 V x 8.4 A P = 35.3 W So that 0.5-ohm coil with a fully charged battery at 4.2 volts will pull a maximum of 8.4 amps and deliver 35.3 watts. You can see that as the resistance of your coil increases, current will drop and wattage will drop.
The second Ohm’s Law formula that can be of use to us is calculating resistance. Let’s say that you have a battery with a 10-amp current limit and you want to determine the lowest coil resistance that you can safely run without exceeding the CDR of the battery.
To calculate, you would use the following formula:
R = V ÷ I Since you know that the battery CDR is 10 amps, you might want to target 9 amps in your calculation, to give yourself 1 amp of headroom. You also know that your max voltage will be 4.2 volts on a single battery mod. So the calculation goes like this:
R = 4.2 V ÷ 9 A R = 0.47Ω The result tells you that your safe lower limit with the 10-amp battery is 0.47 ohms – anything lower and you risk exceeding the current limit of the battery. Of course, if you have a 25-amp battery, your low resistance drops to 0.17 ohms:
R = 4.2 V ÷ 25 A R = 0.17Ω Calculating voltage
Finally, and probably not as useful to us, using the triangle you can solve for voltage in a circuit, as long as you know the values of the other two variables.
To solve for voltage when current and resistance is known, the formula looks like this:
V = I x R
Important safety tips
Always assume the full battery voltage (4.2V) of a fully charged Li-Ion battery, even though resistance in the Mod will mean the coil will see a lower voltage!
Never use a battery at above its rated current draw! This can cause the battery to explode!
If the battery or the mod gets hot, something is wrong! Stop and find out what.
See also: Battery safety
Steam Engine ohm's law calculator
Youtube tutorial on ohms law in vaping