Practice question

**Conductivity** σ=1/ρ decreases with temperature for metals, σ = n e² τ/m, τ ∝1/T due to lattice vibrations. For semiconductors, n increases exponentially with T, so σ increases, opposite to metals, explaining why metallic resistance rises with temperature. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 50 [1 + 1.7 × 10⁻⁴ (380 - 20)] . Calculate: R_t = 50 [1 + 1.7 × 10⁻⁴ × 360] = 50 [1 + 0.0612] = 50 × 1.0612 = 53.06 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,