Two metallic wires A and B are of same material and have equal length. If the cross-sectional area of B is double that of A, then which one among the following is the electrical resistance of B?

The electrical resistance (R) of a uniform metallic conductor is determined by the formula R = ρ(L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area [2]. According to this relationship, resistance is directly proportional to the length of the wire and inversely proportional to its cross-sectional area [2]. In this scenario, wires A and B are made of the same material and have equal lengths, meaning ρ and L are constants for both. Since the cross-sectional area of wire B is double that of wire A (A_B = 2A_A), the resistance of B will be inversely affected. Mathematically, R_B = ρL / (2A_A) = 1/2 (ρL / A_A) = 1/2 R_A. Therefore, doubling the cross-sectional area results in halving the resistance, making the resistance of B one-half that of A.

Sources

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