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. For parallel: (1/rₑq) = (1/r₁) + (1/r₂) = (1/2) + (1/1) = (1 + 2/2) = (3/2) . rₑq = (2/3) ≈ 0.67 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, V = ε - I r and P = I²R, evaluation yields 0.67 Ω,