If ${R_1}$ and ${R_2}$ are respectively the filament resistances of a $200$ $watt$ bulb and $100$ $watt$ bulb designed to operate on the same voltage, then
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(b) $P \propto \frac{1}{R} \Rightarrow \frac{{{P_1}}}{{{P_2}}} = \frac{{{R_2}}}{{{R_1}}}$ $ \Rightarrow \frac{{200}}{{100}} = \frac{{{R_2}}}{{{R_1}}} \Rightarrow {R_2} = 2{R_1}$
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