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. Resistance ( R = rho l / A ) depends on resistivity ( rho ), which is rho = m / (n e² tau) . As temperature increases, the average time between collisions ( tau ) decreases due to increased lattice vibrations, leading to higher rho and thus higher R . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0,