Current Electricity

JEE Main level, single correct, medium

73 of 380

Question 73 of 380

What equal length of an iron wire and a copper-nickel alloy wire, each of 2mm2mm diameter connected parallel to give an equivalent resistance of 3Ω3\Omega?
(Given resistivities of iron and copper-nickel alloy wire are 12μΩcm12\mu \Omega cm and 51μΩcm51\mu \Omega cm respectively)

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Answer: (A) 97m97m

R1R2R1+R2=3Ω\dfrac{{R}_{1}{R}_{2}}{{R}_{1}+{R}_{2}}=3\Omega
ρ1ρ2ρ1+ρ2×ℓA=3Ωℓ=3×A×(ρ1+ρ2)ρ1ρ2=3×[π(10−3)2]×(63×10−8)(12×10−8)(51×10−8)ℓ≈97m\dfrac{{\rho }_{1}{\rho }_{2}}{{\rho }_{1}+{\rho }_{2}}\times \dfrac{\ell }{A}=3\Omega \ell =3\times A\times \dfrac{\left({\rho }_{1}+{\rho }_{2}\right)}{{\rho }_{1}{\rho }_{2}}=\dfrac{3\times \left[\pi {\left({10}^{-3}\right)}^{2}\right]\times \left(63\times {10}^{-8}\right)}{\left(12\times {10}^{-8}\right)\left(51\times {10}^{-8}\right)} \ell \approx 97m

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