Two conducting wires A and B are made of same material. If the length of B is twice that of A and the radius of circular cross-section of A is twice that of B, then their resistances RA and RB Eire in the ratio

The resistance (R) of a conductor is determined by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. For a circular cross-section, the area is A = πr², where r is the radius. Since both wires are made of the same material, their resistivity (ρ) is identical. Let the length and radius of wire A be L_A and r_A. For wire B, the length L_B = 2L_A and the radius r_B = r_A/2 (since r_A = 2r_B). Calculating the resistances: R_A = ρL_A / (πr_A²) and R_B = ρ(2L_A) / (π(r_A/2)²) = ρ(2L_A) / (πr_A²/4) = 8ρL_A / (πr_A²). Comparing the two, R_B = 8R_A. Therefore, the ratio R_A: R_B is 1: 8.

Sources

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