Two copper wires A and B of length I and 21 respectively, have the same area of cross-section. The ratio of the resistivity of wire A to the resistivi ty of wi re B is

The electrical resistivity (ρ) of a material is an intrinsic property that depends solely on the nature of the material and its temperature, rather than its physical dimensions [c2][t3]. While the resistance (R) of a conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A) as per the formula R = ρl/A, the resistivity remains constant for a specific material [c2][t4]. In this case, both wires A and B are made of copper. Since they are composed of the same material, their resistivity is identical regardless of the fact that wire B is twice as long as wire A [t2][t6]. Therefore, the ratio of the resistivity of wire A to the resistivity of wire B is 1:1, which simplifies to 1.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178