I failed and succeeded to repair a large number of electrical/electronic equipment since my childhood days (after I used to destroy all my electric toys to see what was inside), and never got paid in cash for the work... Only the sense of fulfillment and a lot of money saved that would otherwise go to the repairman.
Just like everything that involves practice, you are right in saying that it takes some time to get a sense of the size and source of the problems when they present themselves. You are also right to say that luck is involved, as I learned over the years that most failures have an easy repair: blown fuses, faulty or rusted power switches, broken or failing power cords, bad or scratchy contacts in rheostats, etc.
Obviously that over time you feel braver and start venturing yourself inside of the equipment's housings. In this case I still found that most of the failures are easily
diagnosed with a voltmeter as they are usually related to the power supply circuitry - to have an idea, I still have some old radio books that mention the majority of issues can be diagnosed with a simple 120V light bulb probing voltages inside the tube radios!
However, as Dave's video shows, the process of pinpoint the culprit is a different story, as the symptom may reveal itself in a specific part of the circuit but the faulty device is in a complete separate area. Performing a careful trace of the signals will get closer to the source, but sometimes it really becomes a matter of chance and patience. I recall having an amplifier that was doing a loud pop in one of the channels, and some signal tracing revealed an entire board full of "candidates" that needed replacement (old capacitors). The fix? Replaced all of them (~15) after trying to do a one-by-one replace-test (the pop was really loud!).
The most disheartening situations happen when you diagnose, find a faulty device and, when replacing it, it fails again. That shows the problem is being caused by a third element and the diagnosis is a lot harder. These cases are way more involving and they usually involve not only an analysis of the schematics but also a round robin process of replacing the faulty device and trying to trace the signals during blowup - in these cases the ohmmeter helps as it can identify short circuits where they shouldn't exist (just like the video). Another great way is the "blow-whatever-is-in-the-way" method used in the video (which works wonders but you have to be careful not to blow the PCB).
Another disheartening scenario is when the faulty device is replaced and another problem shows up. This is more common when the original issue is located in the power supply (or some high power circuitry) and, during the failure, another device gets blown by overvoltage or overcurrent.
The only scenario where you are 100% reliant on luck is when the issue is intermittent. In this scenario absolutely all bets are off; you have to try your best to find a way to make the problem reveal itself consistently, but you need to be prepared to never find the actual source of the problem.
Suggestion: keep finding nice equipment around the house to fix or even from friends and family - be careful with these last two: either get whatever they would throw them away anyways or only promise you will "take a look". If you fix some, you will find yourself invited to stay for dinner or to a nice and cold beer... (at least that is what happened during my high school and university years!
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