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. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: 31.5 = 30 [1 + α (75 - 25)] . Solve: 31.5 = 30 + 1500α ⇒ 1500α = 1.5 ⇒ α = (1.5/1500) = 1.0 × 10⁻³ °C⁻¹ . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT],