Two electric bulbs marked 25W-220V and 100W-220V are connected in series to a 440V supply. Which of the bulbs will fuse?

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Both

100W

25W

Neither

answer is C.

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Detailed Solution

$\begin{array}{l} The current upto which bulb of marked 25 W - 220 V, will not fuse \\ I_{1} = \frac{P_{1}}{V_{1}} = \frac{25}{220} Amp \\ {Similarly, I}_{2} = \frac{P_{2}}{V_{2}} = \frac{100}{220} Amp \\ The current flowing through the circuit \\ I = \frac{440}{R_{e f f}} \\ R_{eff} = R_{1} + R_{2} \\ R_{1} = \frac{V_{1}^{2}}{P_{1}} = \frac{{(220)}^{2}}{25}; R_{2} = \frac{V_{2}^{2}}{P_{2}} = \frac{{(220)}^{2}}{100} \\ \Rightarrow I = \frac{440}{\frac{{(220)}^{2}}{25} + \frac{{(220)}^{2}}{100}} = \frac{440}{{(220)}^{2} [\frac{1}{25} + \frac{1}{100}]} \\ \Rightarrow I = \frac{40}{220} Amp \\ ∵ I_{1} (= \frac{25}{220} A) < I (= \frac{40}{220} A) < I_{2} (= \frac{100}{200} A) \\ Thus the bulb marked 25 W - 220 will fuse. \end{array}$