A 25-W light bulb and a 60-W light bulb both operate at the same voltage. Which bulb has the lower resistance?

1. Both bulbs operate at the same voltage V, so compare them using P = V^2 / R. 2. Rearranged for resistance, this gives R = V^2 / P. 3. With V fixed and the same for both bulbs, resistance R is inversely proportional to power P. 4. The 60-W bulb has the higher power rating, so by this inverse relationship it must have the lower resistance of the two. 5. This is a trap worth naming: it is tempting to assume a 'bigger', more powerful bulb has more resistance, but at fixed voltage higher power actually means lower resistance, since it draws more current. 6. The option claiming the 25-W bulb has the lower resistance reverses this inverse relationship. 7. The option claiming equal resistance ignores that the two bulbs have different power ratings at the same voltage. 8. The voltage value itself is not needed to answer which bulb has lower resistance, only that it is the same for both, so 'cannot be determined' is incorrect. _Source: OpenStax Physics (CC BY 4.0), Ch 19 "Electrical Circuits", section 19.4 Electric Power_