Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l/2 then the resistance of this wire will be

The resistance (R) of a 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]. For a wire with radius r, the area A is πr². In the first case, R = ρ(l/πr²). For the second copper wire, the material remains the same (constant ρ), but the length becomes l/2 and the radius becomes 2r. The new cross-sectional area A' is π(2r)² = 4πr², which is four times the original area [1]. Substituting these new values into the resistance formula, the new resistance R' = ρ(l/2) / (4πr²) = (1/8) * ρ(l/πr²). Since the original resistance R was ρ(l/πr²), the new resistance is R/8 [1]. Thus, doubling the radius and halving the length reduces the resistance to one-eighth of its original value.

Sources

1. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
2. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Example 11.6 > p. 180