1.) AC power output Vout*2/speaker ohms =
2.) Gain for transitor or OP-amp stages Vout/Vin =
3.) RC= time constants
4.) To convert frequency into Time formula
I can't really use ohms law because there is to many resistors and capacitors in series/parallel networks so it would be hard to verify that
What do you mean by formula? That one does not resonate.
If the device does not work the way it should, you look for the problem. Totally dead is great, as that is usually a power problem. The rest depends on how the device is failing to do what it's supposed to.
Obscure case in point. I worked for a couple of hours on a old Univac 1206 computer (CP-642A in the Navy's terminology). It failed memory tests. I could make more errors come and go by adjusting X and Y driveline currents, but could not get rid of a failure at one address.
Diagnosis - a ferrite core had cracked and failed. So we chucked about a zillion dollars of memory chassis and got a replacement.
Had another computer - a 1208, or CP-642B. The multiply/divide timing chain would start to run erratically. We could relate the onset of the problem to the uppermost bit setting in the instruction register.
Neither flip flop was in any way related, yet when one set, so did the other. The common element was the neon indicator driver card that handled both flip flops.
The cure was a kludge. We swapped both flip flops (A14 & B12 in chassis 4) with aother pair of flip flop cards in the computer. The problem went away for several months. It did come back, but we just made up a chart of swapped cards and kept swapping. We weren't about to chase any wiring problems (had that experience in another computer. Found out how handy a crochet hook can be).
You don't need a formula, but you do need to understand how to read a schematic and predict what things should look like if they are working.
To give you feel when something isn't right. Troubleshooting is a catalog of skills, not just one big skill set. The more you know, the easier it is (but sometimes it will never be easy). There have been times I needed theory to argue an engineer into acknowledging his design had a flaw. Not often, but it happens. You need to be able to speak the language before you can communicate.
Yes, there are a nice set of equations! For now, these are built in my head and programmed. I don't even think of them as formulas anymore, as long with many others. They become second nature when you are using them all the time, kind of analogous to calling multiplication a formula. I am sure many will agree on this.