Q 12-03-129JEE MainJEE Main 2023 (25 Jan, Shift 1)Medium
A uniform metallic wire carries a current $2\ \text{A}$, when $3.4\ \text{V}$ battery is connected across it. The mass of uniform metallic wire is $8.92\times10^{-3}\ \text{kg}$, density is $8.92\times10^3\ \text{kg m}^{-3}$ and resistivity is $1.7\times10^{-8}\ \Omega\,\text{m}$. The length of wire is
Answer: (B) $l=10\ \text{m}$
$R=\dfrac{3.4}{2}=1.7\ \Omega$; volume $V=\dfrac{m}{d}=10^{-6}\ \text{m}^3$.
$R=\dfrac{\rho l}{A}=\dfrac{\rho l^2}{V}\Rightarrow l^2=\dfrac{1.7\times10^{-6}}{1.7\times10^{-8}}=100\Rightarrow l=10\ \text{m}$.
Solution by Sreeraj P, M.Sc Physics