Two wires are made having same length l and area of cross-section A. W

Two wires are made having same length l and area of cross-section A. Wire 1 is made of copper and wire 2 is made of aluminium. It is given that the electrical conductivity of copper is more than that of aluminium. In this context, which one of the following statements is correct?

[amp_mcq option1=”The resistance of wire 1 will be higher than that of wire 2.” option2=”The resistance of wire 2 will be higher than that of wire 1.” option3=”The resistance of both the wires will be the same.” option4=”If same current is flown through both the wires, the power dissipated in both the wires will be the same.” correct=”option2″]

This question was previously asked in
UPSC CDS-2 – 2017
The resistance of wire 2 will be higher than that of wire 1.
The resistance (R) of a wire is inversely proportional to its electrical conductivity (σ) for a given length (l) and area of cross-section (A). The formula is R = (1/σ) * (l/A). Since both wires have the same length and area of cross-section, their resistances are directly proportional to their resistivities (ρ = 1/σ). We are given that the electrical conductivity of copper (wire 1) is more than that of aluminium (wire 2), i.e., σ_Cu > σ_Al. This implies that the resistivity of copper is less than that of aluminium (ρ_Cu < ρ_Al).
Since R = ρ * (l/A) and l and A are the same for both wires, R is proportional to ρ. As ρ_Cu < ρ_Al, it follows that R_1 (copper) < R_2 (aluminium). Therefore, the resistance of wire 2 (aluminium) is higher than that of wire 1 (copper). Power dissipated is given by P = I²R or P = V²/R. If the same current flows, power dissipated is proportional to resistance. If the same voltage is applied, power dissipated is inversely proportional to resistance.
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