An aluminium wire `7.5 m` long is connected in parallel with a copper wire `6 m` long. When a current of `5 A` is passed through the combination, it is found that the current in the aluminium wire is `3 A`. The diameter of the aluminium wire is `1 mm`. Determine the diameter of the copper wire. Resistivity of copper is `0.017 muOmega-m` and that of the aluminium is `0.028 muOmega-m`.

An aluminium wire `7.5 m` long is connected in parallel with a copper

1.	An aluminium wire `7.5 m` long is connected in parallel with a copper wire `6 m` long. When a current of `5 A` is passed through the combination, it is found that the current in the aluminium wire is `3 A`. The diameter of the aluminium wire is `1 mm`. Determine the diameter of the copper wire. Resistivity of copper is `0.017 muOmega-m` and that of the aluminium is `0.028 muOmega-m`.
Answer» In parallel current distributes in inverse ratio of resistance `1rarr "Aluminimum" 2rarr Copper` `R_1/R_2=i_2/i_1` `(rho_1l_1//A_1)/(rho_2l_2//A_2)=2/3 ` `:. (rhi_1l_1d_2^2)/(rho_2l_2d_1^2)=2/3` `:. D_2=(sqrt((2rho_2l_2)/(3rho_1l_1)))d_1` `=(sqrt((2xx0.017xx6)/(3xx0.028xx7.5)))(1mm)`

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