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Q39 (CDS-I/2018) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

A wire of copper having length I 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

Result
Your answer: —  ·  Correct: C
Explanation

The power dissipated in a wire is given by the formula P = I²R, where I is the current and R is the resistance [1]. Resistance is determined by the material's resistivity (ρ), length (l), and cross-sectional area (A) using the formula R = ρ(l/A) [2]. In this scenario, both the copper and aluminium wires have the same dimensions (l and A) and carry the same current (I). Therefore, the power dissipation depends solely on the resistivity of the material. Copper has a lower electrical resistivity (approximately 1.72 × 10⁻⁸ Ωm) compared to aluminium (approximately 2.65 × 10⁻⁸ Ωm). Since aluminium has a higher resistivity, its resistance (R_al) is greater than that of copper (R_cu). Consequently, for the same current, the power dissipated in the aluminium wire (P_al = I²R_al) will be greater than the power dissipated in the copper wire (P).

Sources

  1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192
  2. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
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