Practice question

**Temperature dependence** of resistance R_t = R₀[1+α(T-T₀)], α temperature coefficient (per °C), R₀ resistance at T₀ (Ω). For metals α positive ≈10⁻³ /°C, resistance increases with temperature because τ decreases due to increased phonon scattering, n nearly constant. Use: rho_t = rho₀ [1 + α (T - T₀)] . Substitute: rho_t = 7 × 10⁻⁸ [1 + 4 × 10⁻³ (85 - 25)] . Calculate: rho_t = 7 × 10⁻⁸ [1 + 0.24] = 7 × 10⁻⁸ × 1.24 = 8.68 × 10⁻⁸ Ω m . 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,