When charge flows energy is shifting
So, to summarise the main points:
In a circuit that has been complete for some time, charged particles (usually electrons), already everywhere around the circuit, are kept in motion by the battery.
In this steady state, the filament of the bulb is shifting energy as the charged particles pass through it. This energy is dissipated in the surroundings.
A partial model
In this way you might imagine the circuit continuously shifting energy, with the battery's store of energy steadily emptying on one one side of the loop as energy is dissipated to the surroundings in many thermal stores in other parts of the same loop. The circuit connects these changes of the energy in the stores.
Note that for the first tiny fractions of a second, when the loop is first completed, the filament will be warming up, so the energy description will be modified.
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