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?

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The resistance of wire 1 will be higher than that of wire 2.

The resistance of wire 2 will be higher than that of wire 1.

The resistance of both the wires will be the same.

If same current is flown through both the wires, the power dissipated in both the wires will be the same.

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CDS-2 – 2017

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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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