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: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 80 [1 + 1.7 × 10⁻⁴ (225 - 25)] . Calculate: R_t = 80 [1 + 1.7 × 10⁻⁴ × 200] = 80 [1 + 0.034] = 80 × 1.034 = 82.72 Ω . 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,