Final answer:
In a series circuit, the 60 W bulb will be brighter than the 100 W bulb because it has a lower resistance, allowing it to dissipate more power at the same current, which is limited by the bulb with the higher resistance, in this case, the 100 W bulb.
Step-by-step explanation:
When two household lightbulbs with different power ratings, 60 W and 100 W, are connected in series to household power, the 60 W bulb will be brighter. This is because, under a series connection, the same current flows through both bulbs. The power rating of a bulb, when connected in a standard parallel circuit in a household (at a fixed voltage), indicates how much current it draws: a 60 W bulb draws more current than a 100 W bulb at the same voltage. This implies that the 60 W bulb has a lower resistance than the 100 W bulb.
When connected in series, the current that flows through the bulbs will be limited by the bulb with higher resistance, which is the 100 W bulb. However, since the 60 W bulb has a lower resistance, it will drop less voltage across it and thus convert more of the available electric power into light, making it brighter than the 100 W bulb. In simpler terms, the brightness depends on how much power (P = I^2 * R) each bulb dissipates, and with a constant current in a series circuit, the bulb with the lower resistance dissipates more power, thus, the 60 W bulb is brighter in the series configuration.