Why can I put an electrolytic capacitor on AC?
"Can" and "should" are two things. Should you do this? No: this use is outside the specified operating parameters of ordinary electrolytic capacitors. You seem to understand this already. Can you do it? Yes, as the video demonstrates. To understand why requires some understanding of what's inside the capacitor.
A capacitor is two conductors (usually plates) separated by an insulator. The more surface area, and the closer together they are, the higher the capacitance. Electrolytic capacitors have a thin film rolled up in the can. This film is covered in a thin oxide layer, and the thinness of this layer is what gives electrolytic capacitors their high capacitance relative to their size.
This oxide layer is created by the chemistry of the materials in the capacitor, and the polarity of the voltage applied to each side of the film. A voltage applied in the correct direction builds and maintains the oxide layer. If the polarity is reversed, the oxide layer dissolves.
If the oxide layer dissolves, you no longer have an insulator between the two plates of the capacitor. Instead of two plates separated by an insulator, you have two plates separated by a conductor. Instead of a device that blocks DC, you have a device that conducts it. Basically, you have a wire in a can.
Usually, when you encounter this failure mode, a large current flows, rapidly heating the internals of the capacitor. The expanding fluid and gas ruptures the safety vent or the can explodes.
Why then, does the capacitor in this example not explode?
The reverse polarity voltage is never applied for very long, and never without a correct polarity voltage applied soon after to repair whatever damage was done.
The oxide layer doesn't dissolve instantly when a reverse voltage is applied; it takes time. The time depends on the voltage applied, the size of the capacitor, the chemistry, etc, but half a cycle of 50 Hz AC is probably not long enough to cause serious damage. When the other half of the cycle comes around, the oxide layer is restored.
Any fault current is significantly limited by the series resistors.
With those resistors in series, the power available to heat the capacitor is small. There simply isn't enough power available to catastrophically destroy the capacitor because most of the available energy goes into the resistors. Perhaps you just warm the capacitor slightly. When the voltage reverses direction, the oxide layer can reform.
Probably you still damage the capacitor eventually, to some extent, but it is operational enough for the demonstration.
Most likely you are not noticing that the capacitor has a DC bias and that the lowest peaks of the voltage accross it don't go negative.
In the only example you provided, there is a LED in the circuit. Remember that a LED is also a diode. When he put the capacitor in series with the LED, it should have prevented significant reverse voltage accross the capacitor. When the capacitor was put parallel to the LED, the LED would have shunted anything more than a couple of volts reverse polarity around the capacitor.
More importantly however, this was just some video from some guy on the internet doing a demo and not trying to be rigorous. He may well have been aware the capacitor was being abused somewhat and didn't care. We also don't know whether the capacitor eventually suffered some damage.
So in summary, the reasons you are seeing electrolytic capacitors apparenly being reverse voltaged are:
- They aren't. There is a DC bias that you didn't notice.
- They are, and maybe getting damaged, but whoever is doing it doesn't realize this or doesn't care.
- You can't believe everything you see on the internet.
There are a couple of possible answers.
The most common application of electrolytics in AC applications is as coupling capacitors in AC amplifiers. In this case, there is usually a clear DC bias across the capacitor (as a result of how the individual amplifier stages are biased), so even though it's passing an AC current, the voltage across the capacitor itself never actually reverses.
Second, there is such a thing as a non-polarized electrolytic capacitor that is sometimes used in powerline-frequency applications. It has oxide layers on both plates.