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