• # question_answer 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 [NCERT 1980; CPMT 1991, 97] A)            ${{R}_{1}}$ is two times ${{R}_{2}}$                          B)            ${{R}_{2}}$ is two times ${{R}_{1}}$ C)            ${{R}_{2}}$ is four times ${{R}_{1}}$                          D)            ${{R}_{1}}$ is four times ${{R}_{2}}$

$P\propto \frac{1}{R}\Rightarrow \frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}$ $\Rightarrow \frac{200}{100}=\frac{{{R}_{2}}}{{{R}_{1}}}\Rightarrow {{R}_{2}}=2{{R}_{1}}$