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. Drift speed: v_d = (I/n e A) . Substitute: v_d = (0.9/8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 3 × 10⁻⁷) . Calculate: v_d = (0.9/4.08 × 10³) ≈ 2.21 × 10⁻⁴ m/s . 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 = ε - I r and P = I²R, evaluation yields 2.21