If you have an old computer that used to work, you probably expect it to work next time as well. But electronics parts age, and your 8-bit hardware is no exception. Read more on bad capacitors and what they can do to your machine below.
Capacitors are a necessary part in electronic circuits. They filter and even out voltages, which helps in getting a stable power supply for the actual electronics. There are different types of capacitors - and especially three of them can fail in vintage computers . Even modern PC main boards can suffer from this problem [2,3]. So it's no surprise that your vintage computer can fail to this as well.
Mostly it's electrolytic capacitors that fail with bad consequences. This is mainly due to their electrolyte, a more or less liquid material used to isolate the two sides from each other and store the electric energy in the electric field between the poles. Unfortunately, as this electrolyte is optimized for capacity, it turned out to be quite an agressive substance. So when the capacitor starts leaking - due to electrolyte evaporating in the heat, or mechanical break of the case due to age for example - the electrolyte can spill over the board and cause extensive damage. While electrolytic caps are usually high capacitance, smaller capacity caps can blow up as well.
One such particular culprit is the mains filter capacitor. It sits directly on the mains input, and filters out high frequency electronic "noise" from the computer, that would otherwise likely cause interference with other equipment. As it runs on AC mains, it only has a small capacity to just filter out the very high "digital" frequencies. When it fails, the machine still works, but does not pass regulations. See [4,5,6,7] for examples from the Apple II and Commodore PET. [8,9] show a video of the BBC power supply "blowing" up, basically blowing out nastily smelling smoke...
While the filter caps usually just "blow" without much damage (exceptions granted...), leaking electrolytic capacitors can create a much larger damage. The leaking electrolyte "eats" itself into the board and nearby electronic parts. This goes as far as completely eating away copper traces on the PCB or even chip pins! See [10,11] for examples of leaking caps and the damage they create deep within the Commodore 1M disk drives (8250LP, SFD1001).  shows the result of leaking caps on a C64.
The first machines had simple linear power supplies, which are easily repaired. But later machines, like the Commodore 8296-D or the Commodore 720 (or the Apple II and BBC) had switching power supplies, which are more difficult to understand and repair. And electrolytic capacitors can fail in that too. See  for a video on a leaking capacitor in the power supply.
So, as the author (André) has suffered from three blown power supplies, and five Commodore disk drives with leaking caps, and maybe more stuff waiting, we hope that this article helps you become aware of the problem and maybe check your vintage computer before it is too late. See [14,15] for more links - and don't forget the batteries in some of the machines... [16,17].
Did you already have problems with leaking or blown capacitors? Tell us about it in the comments!
3 of 4 common failures are bad caps...
Tezza's blog on restoring apple II, with blown power supplies
Apple II blown filter caps
Another Apple II power supply
Commodore PET filter cap
video of a BBC power supply blowing up
repair the BBC caps.
Commodore 8250 Matsushita drives with leaking caps
SFD1001 repair with pictures
A C64 with leaking electrolytic caps
CBM720 with blown power supply due to leaking caps (incl. video)
2 of the 3 power supply problems in the BBC are caps
types of capacitors
apple II GS battery leak
BBC master battery