Why does the resistance of a conductor increase when it is stretched to double its length, assuming volume remains const
**Resistivity temperature variation** ρ_t = ρ₀[1+α(T-T₀)], α ≈4×10⁻³ /°C for copper, 1.7×10⁻⁴ /°C for nichrome. Given R=60 Ω at 30°C, α=1.7×10⁻⁴ /°C, T=330°C, ΔT=300°C, R_t=60[1+1.7×10⁻⁴×300]=60×1.051=63.06 Ω, modest increase for nichrome due to small α. Resistance R = rho l / A . Doubling length ( l' = 2l ) halves area ( A' = A/2 ) due to constant volume. Thus, R' = rho (2l) / (A/2) = 4 rho l / A = 4R , due to both increased length and decreased cross-sectional area. Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V
Ref: NCERT > Physics Book > Current Electricity > Temperature Dependence of Resistance and Resistivity