The resistance of a wire is 10 fi. If it is stretched ten times, the resistance will be

The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A), expressed as R = ρL/A [1]. When a wire is stretched, its volume (V = A × L) remains constant. If the wire is stretched ten times its original length (L' = 10L), the cross-sectional area must decrease by the same factor (A' = A/10) to maintain constant volume. Substituting these new values into the resistance formula, the new resistance R' = ρ(10L)/(A/10) = 100 × (ρL/A) = 100R. Given the initial resistance is 10 Ω, the new resistance becomes 100 × 10 Ω = 1000 Ω. This demonstrates that for a stretched wire, resistance increases by the square of the stretching factor (n²), where n is the factor by which the length increases.

Sources

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