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MCQ · Q1

Q.You are given four bulbs of 25 W, 40 W, 60 W and 100 W of power, all operating at 230 V. Which of them has the lowest resistance? (A) 25 W (B) 40 W (C) 60 W (D) 100 W

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All four bulbs operate at the SAME voltage, V=230 V, since they are described as 'all operating at 230 V'. Using P=IV=V^2/R (Eq. 11.21 combined with Ohm's law), the resistance of each bulb is R=V2PR=\frac{V^2}{P}. Since VV is the same constant for all four bulbs, RR is INVERSELY proportional to PP: the bulb with the HIGHEST power rating draws the most current and therefore has the LOWEST resistance. Ranking by power (25 W, 40 W, 60 W, 100 W), the 100 W bulb has the lowest resistance: R100W=2302100=529 ΩR_{100W}=\frac{230^2}{100}=529\,\Omega, compared with R25W=230225=2116 ΩR_{25W}=\frac{230^2}{25}=2116\,\Omega, which is more than four times larger. [!ANSWER] (D) 100 W

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