This is good advice,
There are two types of capacitors commonly used. 1 is a combination cap with three terminals. It is a single large can that has both the compressor cap and the fan cal. Its usually marked something like 30uF and 5uf (Values vary depending on the unit). The three terminals are marked Com, HERM and Fan. Herm is the compressor since it is hermatically sealed.
You can also buy separate caps for the fan and herm and wire them together.
The "kickstarter" cap is typically optional and only needed in special situations. Did an AC tech add that during a service call? These are commonly a profit item for them.
The capacitors of old has PCBs (chemincal not electronics) in them that was banned in the late 90s. These caps lasted forever. The newer caps are eco friendly and have a higher failure rate over time at temperature.
I had the same thing happen to my 2003 Carrier. Around 2008 the unit stopped and the fan on top would not turn and the HERM would humm loudly. I killed the power at the breaker and took a look (I and an EE by the way). The AC cap had its top domed out like a beer can left in the sun and when I looked it up on the internet they showed it built up internal pressure and broke a fuse when the top swelled so it wouldn't explode.
https://www.youtube.com/watch?v=mB89knyysFE
Of course this was a Sunday on a weekend with a Monday holiday (Labor day). and it was in the high 90s. I limped by with a window unit in a single "cool room" until Tuesday.
I replaced it with a Dayton from Granger (only place I could get one that day) for ~$50 and was back in business for about a year and a half. Then it popped.
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I also bought a el-cheapo backup from ebay for $30 as a backup. So it went into service while I ordered a Genteq cap and the final backup.
The Genteq cap was swapped in when it arrived, and was in service until 2016 when the evaporator developed a hole and I upgraded to a higher efficiency unit. 16 seer vs 12. It showed a noticeable decrease in energy usage but not dramatically so. I think the previous unit was not "hurt" by sitting there humming for a few hours before I found the capacitor problem.
There is also one in your furnace fan. Its is also about 5uF. Mine had degraded down to 3uF and the fan was struggling to start. It has a loud hum on startup. AC tech said the cap was bad and they cost $150/each to replace + service fee. I bought a Genteq for $20 off amazon and figured out the two prongs myself.
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Note these are high (lethal) voltage capacitors and connected to high voltage service lines. If you don't know the safety aspects of dealing with a few hundred voltages and charge storing components like capacitors, you should have a qualified tech do it for you. Saving a few dollars is not worth your risking injury or death
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