Generated electron flow

I am not sure if I am answering the correct question.

1. If nothing is connected to the generator the circuit is open (i.e. not connected), the electrons won't flow. No electricity will be generated. The generator will run at the idle speed (and will use the minimum amount of fuel). The energy from the fuel will be turned to heat... but since no electricity is being generated it will be a limited amount of heat that dissipates safely.

Your image of the electrons piling up is incorrect. Electricity doesn't work that way. A slightly better metaphor is when you turn off a faucet there is still water pressure, but the water doesn't flow. The water pressure running the faucet stays the same... it doesn't go up continually just because the water isn't running.

2. If you short the circuit, it could be dangerous. This means you connect one pin of the the generator to the other allowing the electrons to flow in the circuit with no load. Generators generally have a fuse or circuit breaker to break the circuit when this happens. If you didn't have this type of safety feature, it would overheat in a dangerous way.

To answer a possible follow up question... the more load you put on the generator, the harder the generator is to turn (this is Lenz's law). The generator will burn more fuel the greater load you put on it.

Research 'Dipole'.

Electric power system: Power systems in practice: Residential power systems

Residential dwellings almost always take supply from the low voltage distribution lines or cables that run past the dwelling. These operate at voltages of between 110 and 260 volts (phase-to-earth) depending upon national standards. A few decades ago small dwellings would be fed a single phase using a dedicated two-core service cable (one core for the active phase and one core for the neutral return). The active line would then be run through a main isolating switch in the fuse box and then split into one or more circuits to feed lighting and appliances inside the house. By convention, the lighting and appliance circuits are kept separate so the failure of an appliance does not leave the dwelling's occupants in the dark. All circuits would be fused with an appropriate fuse based upon the wire size used for that circuit. Circuits would have both an active and neutral wire with both the lighting and power sockets being connected in parallel. Sockets would also be provided with a protective earth. This would be made available to appliances to connect to any metallic casing. If this casing were to become live, the theory is the connection to earth would cause an RCD or fuse to trip - thus preventing the future electrocution of an occupant handling the appliance. Earthing systems vary between regions, but in countries

Generators do not produce current, they produce voltage that will allow current to flow when a load is applied. The amount of current that the generator can allow to flow is determined by the size of the windings in the generator. The amount of current that flows from your generator changes as each load is applied because with the additon of each load the circuit resistance decreases, allowing more current to flow. The maximum current the generator could allow to flow would be when there was a short circuit and almost zero resistance. There are breakers and or fuses as mentioned to prevent this. A good example of varing the load on your generator to see the effect would be to plug in drill motor with the generator at idle there is no current flow, pull the trigger and you will hear the generator start to work harder to supply the current your load is requesting based on its resistance. Take your finger off the trigger and the generator goes back to idle with no current production based on the infinate resistance of the open circuit.