Practice question

**Sharing of charges** when charged capacitor C₁ at V₁ connected to uncharged C₂, total charge Q = C₁ V₁ conserved, common potential V_common = Q/(C₁+C₂) = C₁ V₁/(C₁+C₂), final charges Q₁' = C₁ V_common, Q₂' = C₂ V_common. For 4 μF at 100 V (Q=4×10⁻⁴ C) connected to 4 μF uncharged, V_common=4×10⁻⁴/8×10⁻⁶=50 V. Initial energy: U_i = (1/2) × 4 × 10⁻⁶ × (300)² = 0.18 J . Charge: Q = 4 × 10⁻⁶ × 300 = 1.2 × 10⁻³ C . Total C = 4 + 8 = 12 μF , V = (1.2 × 10⁻³/12 × 10⁻⁶) = 100 V . Final energy: