Current is not controlled here, resistance (aka the soldering iron) and voltage are.
Power = Voltage ^ 2 / Resistance. Double the voltage, that quadruples the power. So you only want to plug in 25% of the time to get the equivalent power of 120V.
But it might not melt at double power? Maybe the extra heat helps, I can't find a resistance/temperature curve for a soldering iron...
Ok. I was acountless on lemmy for a long time, your comment made me finally register. Thanks!
So, yeah, with double the voltage you get 4x the power.
But you you put 4 times the power at 50% of the time, you get only 2x the power. And the other half of the time, you get 0 power. On the average you get the same power output.
I imagine this is more or less what it felt like to be in the room at the time. A whole group of people discussing electrical theory and optimal soldering techniques and meanwhile the one guy standing there holding the actual device notices the power cord is a little loose and pushed it in another 1/8" without mentioning it because everyone is so involved in their nerdy conversation.
I had to think about it too, lol. This is an equation for DC/instantaneous power, and if you want to get into AC math, this is more like a square wave. Averaging the power out over time doesn’t necessarily work with the equation, as you figured out, as it doesn’t when you try to measure AC (sinusoidal) power by average voltage or whatever.