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

Q: 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 ${m}$)

b $\frac{{R}_{1} {R}_{2}}{{R}_{1}+{R}_{2}}=3$ $\frac{\left(12 \times 10^{-6} \times 10^{-2}\right) \ell \times 4}{\frac{\pi(2)^{2} \times 10^{-6}} \times \frac{\left(51 \times 10^{-6} \times 10^{-2}\right) \ell \times 4}{\pi(2)^{2} \times 10^{-6}}}{\frac{63 \times 10^{-6} \times 10^{-2} \times \ell \times 4}{\pi(2)^{2} \times 10^{-6}}}$ $\Rightarrow \ell=97 {m}$

SECTION - A [PHYSICS - MCQ]

GSEB - English 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) (in ${m}$)

A$82$
B$97$
C$110$
D$90$

JEE MAIN 2021, Diffcult

STD 11 Science
NEET
STD 12 - 3. current electricity
Physics

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