How does 'conservation of law of energy' work in an open circuit connected to a hydroelectric generator?

Question

I am trying to relearn high school physics and having trouble visualizing electricity in an 'open' circuit. I am going to use layman terms so i don't confuse myself! Apologies in advance if i am wording it wrong.

My assumptions:

I connect a battery to a copper wire circuit with a bulb. Chemical reaction happenss in the battery, The electrons circulate the wire and as they do, the bulb glows. open the circuit, and the resistance of air is too great, so the electrons stop flowing, and the chemical reaction inside the battery stops. (Is it possible to flow current in open circuit?)

Now instead of a battery, a hydroelectric generator is connected to the circuit. The bulb glows as long as the circuit is closed. When i open the circuit, the electrons stop flowing. However, unlike the chemical reaction in a battery, THE GENERATOR IS STILL SPINNING, and "energy" is being produced. But the electrons aren't going anywhere.

My question -

How do i reconcile this with 'conservation of law of energy'? No light / heat is being produced. i see the water spinning the generator as "input work". but i don't see where the "output work" is. (Sorry if i am not asking this right.)

My guess:

In an open circuit with a battery, I touch the copper wire and don't get electrocuted. In an open circuit with generator, I touch the copper wire and do get electrocuted. The "work" done by the generator is "used up" in keeping the electrons at an "excited state", as in a state that is not natural.

Would be a lot of help if you could point where exactly i'm wrong. I have been down the google rabbithole and nothing so far has 'clicked' for me.

Answer 1

If you open the circuit and the water flow is still doing work in the generator's turbine, the generator will speed up and its internal kinetic energy will increase. That is where the work done by the turbine will go.

The thing that is "invisible" is that when the generator is producing electricity, there is a mechanical force on the rotor which is trying to slow it down, and that is balanced by the force from the water turbine trying to speed it up. When you open the circuit, you remove the first force, and the rotor will speed up if nothing else changes.

In real life, there will be some device to restrict or divert the water flow so that it does less work in the turbine - i.e. when the electrical circuit is open the turbine only has to do enough work to overcome the mechanical friction in the generator and spin it at constant RPM.