Lamps in series: the electric circuit model
Physics Narrative for 5-11 11-14
Two equal resistances: equal energy dissipated in each
Given that there are now two equal resistances in the circuit, and bearing in mind that energy is shifted wherever there is an electric current in a resistance you should focus on the resistances. These are equal, so the forces on the charged particles in these resistances will be equal. What else could they be? So the same amount of energy is shifted at each resistor: same push and pull on each charge; same number of charged particles passing through each resistor.
There is no difference: the resistors or bulbs are identical, so what other possibilities need we consider?
The bulbs are dimmer because adding the extra bulb increases the resistance and reduces the current everywhere in the whole circuit.
As a result fewer charged particles per second pass through each bulb and each charge shifts less energy as it passes through the filament.