Two coils have a combined resistance of `9 Omega` when connected in series and `2 Omega` when connected in parallel. Find the resistance of each coil.

Two coils have a combined resistance of `9 Omega` when connected in se

1.	Two coils have a combined resistance of `9 Omega` when connected in series and `2 Omega` when connected in parallel. Find the resistance of each coil.
Answer» Let `R_(1)` and `R_(2)` be the resistance of two coils When coils are in series, then `R_(s)=R_(1) +R_(2)=9` When coils are in paralle, then `R_(p) =(R_(1)R_(2))/(R_(1)+R_(2))= 2` or `R_(1) R_(2)=2(R_(1) +R_(2))=2 xx 9 =18` From (i), `R_(1) =9 -R_(2)` Putting this value in (ii), we get `(9 -R_(2))R_(2)=18` or `9 R_(2) - R_(2)^(2) =18` or `R_(2)^(2)-9R_(2) +18=0` On solving, we get `R_(2)=3Omega` or `6 Omega` and `R_(1)=6 Omega` or `3 Omega`

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Two coils have a combined resistance of `9 Omega` when connected in series and `2 Omega` when connected in parallel. Find the resistance of each coil.

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