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 charge: Q = 4 × 10⁻⁶ × 50 = 2 × 10⁻⁴ C . Total capacitance: 4 + 2 = 6 μF . Final voltage: V = (Q/C) = (2 × 10⁻⁴/6 × 10⁻⁶) = 33.33 V . Final energy: U = (1/2) C V² = (1/2) × 6 × 10⁻⁶ × (33.33)² = 3.33 × 10⁻³ J . Using V = kQ/r, U = k q₁q₂/r, E =