Electronic – Polarity of capacitor on PCB

As clabacchio said, some capacitors are unpolarized, so it's perfectly fine to put positive and negative voltages on them.

However, it is still possible to put a AC signal thru a polarized capacitor. This is done by adding a DC bias of at least half the AC peak-peak voltage. The entire signal is then still positive, but AC-wise the capacitor acts on it normally.

Nowadays, polarized capacitors are mostly used for bulk storage on power supplies to reduce ripple and to provide short term high current. A nominal 12V supply, for example, may have 1Vpp AC ripple on it. That means the voltage is from 11.5V to 12.5V, which is fine for a electrolytic or other polarized cap. However, the large value of the cap will be applied to providing current to counter the 1Vpp AC voltage swing.

Put another way, polarized caps must always have a positive voltage on them, but there is no such restriction on current.

i would recommend repeating the experiments with fresh (unmolested) caps each time, applying only 1 stress at a time: (a) over-voltage, (b) reverse polarity, what happens when you (a) first then (b), then vice-versa. in your first experiment, the over-voltage may well have been the killer, but reverse-voltage on an electrolytic cap = instant heat death.

there is no perfect conditions to kill a cap, it depends on the type of cap, how long and how high the over-voltage is, what temp it reaches due to the abuse to further damage it, etc.

& as Meletis said, if you really want to see a bang, try some tantalum caps!

but PLEASE, wear protective eye cover when doing these tests, caps WILL explode violently and spray toxic chemicals, &/or molten metals, sometimes at high speed. this experimenting is not worth an eye. and do so with fire extinguishing apparatus handy too (fire blanket, extinguisher (of type apropriate to electric fires)).

your final question, not sure what you're really asking - but polarity is fundamental to electronics.