A wire of copper having length l and area of cross-section A is taken and a current I is flown through it. The power dissipated in the wire is P. If we take an aluminium wire having same dimensions and pass the same current through it, the power dissipated will be
- A.P
- B.< P
- C.> P
- D.2P
Correct answer
Explanation
The correct answer is C, > P. The power turned into heat in a wire carrying a current I is P = I²R, and the resistance of a wire is R = ρl/A, where ρ is the resistivity of its material. With the same length, the same cross-section and the same current, the power depends only on ρ. Aluminium has a resistivity of about 2.8 × 10⁻⁸ ohm metre, roughly 1.6 times that of copper, about 1.7 × 10⁻⁸ ohm metre. So the aluminium wire has more resistance and dissipates more power than P. Option A is wrong because equal power would need equal resistivity. Option B is wrong because only a better conductor than copper, such as silver, would give less heat. Option D is wrong because the ratio of the two resistivities is about 1.6, not 2. Exam tip: same current, more resistance, more heat (P = I²R); silver, copper, gold and aluminium are the best conductors in that order.
Practice Questions
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- B.2 and 4
- C.1 and 3 only
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