What happens when a second battery is added to the circuit so that we now have two batteries and one bulb?
There are many equivalent ways of drawing this circuit—here we'll consistently prefer one, shown in the centre of the diagram. They are equivalent because the loop contains the same number of cells driving the current and the same number of bulbs impeding the current.
When the circuit is completed, the bulb lights up and it is now brighter than normal. How can we explain this observation using the electric circuit model?
The first effect is simply that there is a larger current, adding more batteries increases the current in every element in the loop.
Notice that the current is the same everywhere in the loop.