A bulb with a 12 V 50 W rating is designed to have a resistance of 12²/50 = 2.88 Ω when in operation (P=V²/R). Similarly, a bulb rated at 12 V 35 W rating is designed to have an operating resistance of 12²/35 = 4.11 Ω. The point to note is that a 50 W bulb has a smaller resistance than a 35 W bulb.

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At first both bulbs were individually connected across a 6 V battery. Since the potential differences across both bulbs were the same, to compare the power dissipated in the two bulbs, we should think V²/R. So the 50 W bulb, with a smaller resistance, shone brighter.

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Later the bulbs were connected in series across a 12 V battery. Since the current flowing through both bulbs was the same, to compare the power dissipated in the two bulbs, we should think I²R.  So the 35 W bulb, with larger resistance, shone brighter.

(Do note that when connected in series, the potential difference across each bulb was no longer 6 V each. By the potential divider principle, the 35 W bulb, with its larger resistance, ended up with more than 6 V of potential difference across, while the 50 W bulb had less than 6 V across)

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