What equal length of an iron wire and a copper-nickel alloy wire, each of $2 \; {mm}$ diameter connected parallel to give an equivalent resistance of $3 \Omega ?$
(Given resistivities of iron and copper-nickel alloy wire are $12 \;\mu \Omega {cm}$ and $51\; \mu \Omega {cm}$ respectively) (in ${m}$)
JEE MAIN 2021, Diffcult
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$\frac{{R}_{1} {R}_{2}}{{R}_{1}+{R}_{2}}=3$
$\frac{\left(12 \times 10^{-6} \times 10^{-2}\right) \ell \times 4}{\frac{\pi(2)^{2} \times 10^{-6}} \times \frac{\left(51 \times 10^{-6} \times 10^{-2}\right) \ell \times 4}{\pi(2)^{2} \times 10^{-6}}}{\frac{63 \times 10^{-6} \times 10^{-2} \times \ell \times 4}{\pi(2)^{2} \times 10^{-6}}}$
$\Rightarrow \ell=97 {m}$
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