American power is actually 240V

My house had the center tap line break outside. Turning on the lights inside looked like flasbulbs going off. I pulled main circuit breaker and called electric company. Lineman knew right off what the problem cause and visually saw the break in wire.

This is called an open neutral. When that happens all the current flowing through the circuits connected to the positive 120V must match the current flowing in the circuits connected to the negative (well, 180° offset) 120V since the circuits are in series. This means the two sets of circuits are now in series with 240V in total across them. If they’re perfectly balanced (each circuit using same amount of power) all will be well since each will have 120V. However, if they’re imbalanced then more voltage will be offloaded onto the higher impedance (lower power draw) circuit so it has too much voltage and the higher power draw circuit has too little voltage, as this is what’s required to make their currents match. Additionally, the wire that should be neutral but is actually disconnected from the transformer will have a voltage on it which can be dangerous since a wire normally trusted to have no voltage on it will have voltage on it. Fortunately, I’ve had the luck to never have to experience this. Unfortunately, this means everything I’ve said is just theory, so reality may not match exactly.

My volunteer showed 220 volts at my 110 volt outlets when the neutral powerline broke outside. No known reason why it broke in middle of suspended air.

I assume that’s between the hot and neutral of the outlet? In that case, it sounds like one phase was experiencing much more power draw than the other phase. Almost like a short even. Because if a circuit on one phase was shorted that would bring the open neutral to that voltage meaning the outlets on the other phase would measure 220V between “neutral” and hot, because “neutral” was actually shorted to the other hot.

The 20Ω resistor feeds a lot of current into the base of the upper transistor making it conduct a ton of current. The middle transistor shifts some (or all, or none) of that current to the lower transistor. The middle transistor thus controls how much of the 20Ω resistor’s current goes into the base of the upper transistor and how much gets redirected to the lower transistor. This way, it controls how much current the output sinks/sources.

I just put stuff together until it works. No particular reason I chose one stage over another, except perhaps for simplicity. And I just tune the resistors until they give decent results. I don’t usually do math to determine the values for stuff.

Fine, but it's very time consuming that way, right?

Once again, I appreciate your efforts to help a noob.

Not usually. Just from playing with circuits for long enough I have a pretty good sense for how things should be constructed and what the component values should be so it usually works first time without much tweaking. And when I do need to tune a resistor or something I set it up with the scope so I have immediate feedback so I can tune it very quickly. Of course sometimes that’s not an option in which case I do either trial and error or math.