How does a circuit regulate current in response to a lower voltage?

Question

Brief background, I studied physics in college and am learning EE on-the-job through Art of Electronics and this wonderful website.

So this is a follow up to a previous question I submitted here yesterday. I was trying to see what could have gone wrong when I wired a bunch of devices in parallel and then ran them under-voltage. In the comments, I was informed that I should pay attention to P = IV in that the devices I'm using will try to maintain a fixed power rather than respond according to V = IZ.

I'm not entirely clear on this so I was hoping someone could enlighten me as to what kind of circuit could be drawing more current in response to less voltage. I always understood current and voltage to be proportional on a fundamental level, regardless of the load, since the voltage is the energy source. But, if we take the fluid flow analogy, perhaps there's some sort of "thinning of pipes" when a lower voltage is applied.

How does a circuit pull more current when it doesn't get the voltage it wants with respect to a constant minimum power?

What kind of circuit keeps a constant power?

Answer 1

Imagine a universal power supply that works in multiple countries that have different mains voltages, just like the one that is used to charge a mobile phone. Let's assume the phone requires 5V at 1A so it draws 5 watts of power when charging. Let's also assume the power supply is made of unobtainable ideal components so it does not consume power itself, so it will always take 5 watts from the mains socket when charging. So as power drawn by the supply is constant, it means it draws double the current from a 110V mains socket than it would from a 220V socket.