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 = 8 × 10⁻⁶ × 50 = 4 × 10⁻⁴ C . Total capacitance: 8 + 8 = 16 μF . Final voltage: V = (Q/C) = (4 × 10⁻⁴/16 × 10⁻⁶) = 25 V . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V² and common potential V = Q_total/C_total,