A $100\, watt$ bulb working on $200 \,volt$ and a $200\, watt$ bulb working on $100\, volt$ have
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(b) $R = \frac{{{V^2}}}{P}$ $ \Rightarrow $ ${R_1} = \frac{{200 \times 200}}{{100}} = 400\,\Omega $ and
${R_2} = \frac{{100 \times 100}}{{200}} = 50\,\Omega .$ Maximum current rating $i = \frac{P}{V}$
So ${i_1} = \frac{{100}}{{200}}$ and ${i_2} = \frac{{200}}{{100}}$$ \Rightarrow $ $\frac{{{i_1}}}{{{i_2}}} = \frac{1}{4}$.
${R_2} = \frac{{100 \times 100}}{{200}} = 50\,\Omega .$ Maximum current rating $i = \frac{P}{V}$
So ${i_1} = \frac{{100}}{{200}}$ and ${i_2} = \frac{{200}}{{100}}$$ \Rightarrow $ $\frac{{{i_1}}}{{{i_2}}} = \frac{1}{4}$.
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