What happens to the voltage of a series circuit as you add bulbs to the circuit?

For any lamp to operate at its rated power, it must be subject to its rated voltage. If you connect, say, three identical 120-V rated lamps across a 120-V supply, then each lamp will be subject to one-third of its rated voltage. As a result each lamp will not be able to achieve its rated power. If the lamps have different power ratings, then it is rather more complicated, with the most powerful lamp becoming the dimmest while the least powerful lamp becoming the brightest.