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. In parallel, the reciprocal of total resistance is the sum of reciprocals of individual resistances ( 1/Rtₒtₐl = 1/R₁ + 1/R₂ + ·s ). This adds more paths for current, reducing the effective resistance below the smallest individual value. 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 =