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This is incorrect. I need to increase gauge for voltage drop. Overloading the cable via length can only happen if I have a motor or other magnetic load at the end. A motor will try to draw it's designed wattage regardless of voltage. A wire of a given ampacity will handle that many amps regardless of the length of the conductor. The relationship is power = voltage x current and voltage = current x resistance for single phase. The fire concern on extension cords tied together indoors is you have 100% strung that shit through a doorway or window, which is a code violation. You are going to pinch it and burn your shit down. all outdoor plugs are gfci these days and on site i can have 4 or 5 extension cords tied together. i only get 109 volts at the end but a heater is a resistive load. Doesnt matter for that application.
It's obvious you know more or less all there is to know about this topic. So much so that I suspect you have trouble explaining it to laypersons like me because it's difficult for you to determine which parts of your knowledge are obvious common knowledge and which parts are specialist knowledge.
The super simple explanation is that the wires are too small. The water hose analogy breaks down fairly quickly, but I'll try using it. Imagine a garden hose, with a regular nozzle on the end. But it's not a perfect world, and our hose doesn't transfer all the water that goes into it. Think of this as ten pinprick holes along every meter of hose. If we have ten meters of hose, that's fine, we only need to turn on the tap a little bit to get a decent spray out of the nozzle, and a little bit will dribble out these holes. Now let's join another hose on. We lose more water to leakage, so to get the same amount of water out of our nozzle, we have to turn on the tap more, giving it a bit more water flow. Now, our pinprick holes are not just dribbling, they're flowing freely. Now let's take it to the extreme- we join a thousand garden hoses together, all leaking a little bit. We have to turn the tap on A Lot More, and suddenly our pinpricks are spraying a serious amount of water everywhere. Now imagine we use a bigger hose. Let's take it to the extreme again and say it's a big stormwater pipe. But the key part here is that it has the same amount of holes, ten pinpricks per meter. This way, we can get heaps more water down that pipe, more than enough to give that water nozzle everything it wants. Also, because our pressure can remain low, those pinpricks are only leaking a little bit, not spraying everywhere. This is getting pretty wordy and unwieldy to type out on my phone, so I'll try and bring it into the real world a bit more. An electrical load, like a motor (say a compressor in a fridge, a circular saw, etc) is like to our nozzle. It will pull more current (amps, or water flow) to maintain the same amount of power output (water coming out of the nozzle). As we get a longer conductor, the voltage drop (pressure reduction due to water lost to the pinpricks) gets larger, and our voltage at the end of a conductor gets lower. Power = voltage * current, so if that voltage is lower, to get the same power we need more current. More current means more heating. More heat in a small cable means melting. Physics has a way out for us, thankfully! The thicker a cable is, the less voltage drop it has, kind of like our stormwater pipe. So the voltage remains at a normal level at the motor, and consequently the motor draws a normal amount of current. This is why longer extensions are generally a lot thicker than shorter ones. If you're interested in the math, let me know, it's actually pretty fascinating, and ties into why long distance power lines are all super high voltage, among many other things. The basic equations are also not too hard to work with.
This is junior highschool level stuff. Not a vector or phasor in sight.
Your school taught anything at all about electricity? Mine sure didn't.
My high school had a lot of vocational courses. I took auto shop, construction, welding, and small engine mechanics. Several of those covered electricity.
We had small level building, like a coffee table size thing but smaller.
That was kinda it.
Do you mean inductive load rather than magnetic load? Or are all inductive loads attributed to electromagnets?
Edit: also, don't like... a lot of appliances create inductive loads?
Most inductive loads are motors. I used the term magnetic rather than inductive in the Hope of making my response less jargon filled and more intelligible. Very generally speaking inductance is the magnetic portion of the circuit or more technically it would the contribution to the circuit that causes the wave form to lag. That is specific to an AC circuit.