Do larger caps age better then small ones?

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First of all, if the cap has been sitting around unused for years (even after being iinstalled in equipment) I'd want to "reform" them. Put about a 1k-10k resistor (higher resistance for a higher voltage rating)in series with the cap and put the cap's rated voltage across the series combination. A new or reformed cap will charge up in a few seconds. A cap needing reforming will take longer, and pull current for a while, but should eventually (a few minutes) charge up to rated voltage.

Things (equipment) that use electrolytic capacitors should be powered up at least once a year for a few minutes to make sure the electrolytic capacitors stay formed.

Once the cap is reforned, you should measure the capacitance to make sure it's got at least 80 percent of its rated capacitance. That's probably the tolerance spec (-20 percent), and I'd toss it if it's below that.

The temperature thing appears to be a separate issue. I wasn't aware of the info in post #19, but I've been under the impression that the lifetime goes up exponentially with lower temperature. If it last 4,000 hours at 85, it should last twice (or ten times?) that or 8,000 at 75, and twice again at 65. Panasonic has a lot of capacitor info online.

Here it is - read especially "long term storage" on the last page here - it essentially says what I said above about reforming:
http://industrial.panasonic.com/www-data/pdf/ABA0000/ABA0000PE26.pdf
and there's a lot of interesting info in the PDF's on this page, though I haven't read it in a few years:
Aluminum Electrolytic Capacitor | Passive & Electromechanical | Panasonic Industrial Solutions Global

I've heard of those Black Gate caps as if they were Something Special but I don't know anything about them.
 
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