Practice question

**Common potential** after connection is weighted average of initial potentials by capacitances. Energy loss ΔU = ½ C₁ C₂ (V₁-V₂)²/(C₁+C₂) dissipated as heat and spark, always positive unless V₁=V₂, explaining why energy reduces after sharing. Initial energy: U_i = (1/2) × 5 × 10⁻⁶ × (120)² = 0.036 J . Charge: Q = 5 × 10⁻⁶ × 120 = 6 × 10⁻⁴ C . Total C = 5 + 15 = 20 μF , V = (6 × 10⁻⁴/20 × 10⁻⁶) = 30 V . Final energy: U_f = (1/2) × 20 × 10⁻⁶ × (30)² = 0.009 J . Loss: U_i - U_f =