Two uniform wires A and B are made of different materials but have the same length

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

Two uniform wires A and B are made of different materials but have the same length. Their respective resistivities are ρA\rho_A and ρB\rho_B, and their resistances are equal. (i) Show that the ratio of their cross-sectional areas is AAAB=ρAρB\dfrac{A_A}{A_B}=\dfrac{\rho_A}{\rho_B}. (ii) Wire A is of nichrome with resistivity 1.1×10−6  Ω m1.1\times10^{-6}\;\Omega\,\text{m}, while wire B is of copper with resistivity 1.7×10−8  Ω m1.7\times10^{-8}\;\Omega\,\text{m}. If their common length is 2.0 m2.0\,\text{m} and their common resistance is 2.0 Ω2.0\,\Omega, calculate the individual cross-sectional areas of A and B. (iii) When the same current passes through both wires for the same time, which wire will produce more heat? Support your answer with suitable reasoning and calculation.

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