Q 12-03-213JEE MainJEE Main 2021 (26 Aug, Shift 1)Medium
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)
Answer: (A) $97$ m
For equal $l$ and $A$, $R_{eq} = \dfrac{l}{A}\cdot\dfrac{\rho_1\rho_2}{\rho_1 + \rho_2}$.
$\dfrac{\rho_1\rho_2}{\rho_1+\rho_2} = \dfrac{12\times51}{63} = 9.71\ \mu\Omega$ cm $= 9.71\times10^{-8}\ \Omega$ m; $A = \pi(10^{-3})^2 = 3.14\times10^{-6}$ m$^2$.
$$l = \frac{3\times3.14\times10^{-6}}{9.71\times10^{-8}} \approx 97\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics