Practice question

**Resistivity** depends on material and temperature, not geometry. For metallic conductor, ρ ≈10⁻⁸ Ω·m for copper. Given ρ=4×10⁻⁸ Ω·m, l=2 m, A=π r², R calculation uses R=ρ l/A. Stretching wire conserves volume V = l A = l' A', so A' = A l/l', new R' = ρ l'²/V. Resistance: R = (rho l/A) . Rearrange: rho = (R A/l) . Given: R = 5 Ω , A = 3 × 10⁻⁶ m² , l = 3 m . Substitute: rho = (5 × 3 × 10⁻⁶/3) = 5 × 10⁻⁶ Ω m . Applying I = n e A v_d, R = ρ l/A,