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. Equivalent resistance of cube network: Rₑq = (5/6) R = (5/6) × 2 = (10/6) = (5/3) Ω . Total current: I = (V/Rₑq) = (20/(5/3)) = 20 × (3/5) = 12 A . 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 12 A,