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Combination of Resistances

Two electric ...

Question

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

A

Both

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B

100W

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C

25W

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D

neither

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Solution

The correct option is C 25W
$R_{1} = \frac{220}{25} \times 220, R_{2} = \frac{220}{100} \times 220$
$R = R_{1} + R_{2}$
$R = 220 \times 220 (\frac{1}{25} + \frac{1}{100})$
$R_{1} > R_{2}$
When connected in series, the voltages divide in them in the ratio of their resistances. The voltage of $440 V$ divides in such a way that voltage across $25 W$ bulb will be more than $220 V$ . Hence $25 W$ bulb will fuse.

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