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?
- A.The resistance of wire 1 will be higher than that of wire 2.
- B.The resistance of wire 2 will be higher than that of wire 1.
- C.The resistance of both the wires will be the same.
- D.If same current is flown through both the wires, the power dissipated in both the wires will be the same.
Correct answer
Explanation
The correct answer is B, The resistance of wire 2 will be higher than that of wire 1. With equal length and area, the wire of lower conductivity, aluminium, has the higher resistance.
Resistance is R = ρl/A, where ρ is resistivity, and resistivity is the reciprocal of conductivity (ρ = 1/σ). Since l and A are the same for both wires, resistance depends only on the material. Copper conducts better, so its resistivity is lower (about 1.7 × 10⁻⁸ Ω m against about 2.8 × 10⁻⁸ Ω m for aluminium), and the copper wire has less resistance. Aluminium is still used in overhead power lines because it is much lighter and cheaper.
A is wrong: copper has the lower resistivity, so wire 1 has the lower resistance, not the higher.
C is wrong: different materials have different resistivities, so the resistances cannot be equal.
D is wrong: power dissipated is P = I²R; with equal current and unequal resistance the power differs, and is greater in the aluminium wire.
Exam tip: R = ρl/A and ρ = 1/σ; silver is the best conductor, then copper, gold and aluminium.
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