It's been a long time since I did these things in school, but I like writing up stuff, so here I go. Correct me wherever you see fit.
OHM`S LAW FOR VAPERS & WHY RESISTANCE MATTERS
Once an electric circuitry is closed, a battery will deliver a certain "amount" (ampere) of electricity with a certain "speed" (voltage). While the battery's output voltage is determined by its internal charging status, it's ampere output is determined by the electric resistance of the closed circuitry (ohm).
This resistance is the ratio of voltage to ampere, R=U/I, meaning the amount of current that can flow with a certain voltage at any given time, and it is determined by the properties the material which electricity travels through. The higher the resistance, the less amperes flow, and the lower the resistance, the more amperes will flow, I=U/R.
If a circuit consists of elements with different resistances, for example wires (which have their own resistance) leading to a consumer element (e.g. a light bulb, which also has its own resistance), the element with the highest resistance acts as a bottleneck and determines the resistance of the entire chain.
The lower the resistance of the circuitry gets, the closer it gets to becoming a "short circuit", which is simply an expression for a circuitry with (virtually) no resistance. When that zero ohm circuitry is closed, amperes flow with no (only the battery's internal) restrictions. If this flow exceeds what the battery can deliver (meaning that it can take the heat the voltage × ampere output produces), it will least vent, quickly and heftily, or simply explode. Discharge accomplished.
When a regulated mod works correcty, it does the following:
It sees your desired watt output, meaning [voltage × ampere]. It then looks at the coil's resistance (e.g. 0.5ohms), meaning its given ratio of U/R, and with that, by the rule of three, calculates which voltage would draw what ampere current, in order to produce your desired Watts, W=I×U. It then uses its in-built electronics to convert the battery's given voltage to the voltage it has calculated to be the right one, and therefor draw the right amount of amperage.
What happens with a mechanical mod or a mod whose electronics are broken?
If a coil's resistance isnot/cannot be determined, no calculation takes place to reach a desired Watts number. The battery's voltage is used as it comes, and depending on the defacto-resistance of the coil, a certain amperage will be drawn from the battery.
Example1: Your battery is fully charged to 4.2V, the coil's resistance is 1.0Ω, then the ampere flow will be I=U/R, 4.2V/1.0Ω = 4.2A. The wattage output will then be I×U=4.2V×4.2A=17,64W. Easy sailing.
Example2: Your battery is fully charged to 4.2V, the coil's resistance is 0.25Ω, then the ampere flow will be 4.2V/0.25Ω=16.8A. The wattage output is 4.2V×16.8A=70.56W. That's already something.
Example3: Your battery is fully charged to 4.2V, the coil's resistance is 0.15Ω, then 4.2/0.15Ω=28A. That already exceeds what most vaping batteries can take even for only a short while. Theoretical final power output = 4.2V*28A = 117.6W. Cloud chaser territory.
Example4: Your battery is fully loaded to 4.2V, your DIY coil is shorted, therefor the circuitry has only a resistance of the wire it travels through, respectively the inner resistance of the battery, which is MUCH MUCH lower than what a coil's resistance would be.
A Sony VTC6 for example, has an internal resistance of 20 mΩ, which is 0,02Ω. Now let's calculate I=U/R. 4.2V/0,02Ω = 210AMPS, or in other words: The battery will open its flood gates and try to discharge itself with all the might it can muster. In a fraction of a second, it will get extremely hot, and it will go on to vent heavily, if not outright explode, depending only on the battery's internal protection mechanisms. If you're a vaper, and you use "unprotected" batteries, you don't want to press the fire button on this configuration.
The calculations in the examples are idealised/simplified, leaving other minor factors out of the equation, but basically, that's what happens if you don't pay attention to Ohm's law.
Generally, I trust my mod to work as advertised, and protect me from, for example, a too low resistance/short circuit, but I freely admit that I always look at the resistance reading on the screen after I change coils, just to be on the safe side. DIY/mech mod users should pay even more attention to this than I do. They haven't got any protection mechanisms between them and an accidental over-discharge of their batteries.
