If R1 and R2 are the resistances of filaments of a 400 W and a 200 W lamp, designed to operate on the same voltage, then find the relationship between R1 and R2.

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# If R1 and R2 are the resistances of filaments of a 400 W and a 200 W lamp, designed to operate on the same voltage, then find the relationship between R1 and R2.

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## Kashyap abhishek

For R_{1}, P_{1}= 400 WFor R_{2}, P_{2}= 200 WUsing, P =^{V²}/_{R}(V_{1})^{2}= P_{1}x R_{1}= 400R_{1}and (V_{2})^{2}= P_{2}x R_{2}= 200R_{2}Since, both filaments operate on the same voltage.So, (V_{1})^{2}= (V_{2})^{2}⇒ 400R_{1}= 200R_{2}⇒ 2R_{1}= R_{2}