Given:
• C₁ charged to potential V₀, C₂ is uncharged.
• Switch S is closed → charges redistribute.

Step 1 — Energy Before Connection:
U₁ = ½ C₁V₀²

Step 2 — Common Potential After Connection:
Charge is conserved: Q = C₁V₀
V_common = C₁V₀ / (C₁ + C₂)

Step 3 — Energy After Connection:
U₂ = ½ (C₁ + C₂) × V_common²
= ½ (C₁ + C₂) × [C₁V₀/(C₁+C₂)]²
= ½ × C₁²V₀² / (C₁ + C₂)

Step 4 — Ratio of Energies:
U₁/U₂ = [½C₁V₀²] / [½C₁²V₀²/(C₁+C₂)]

┌───────────────────────────────┐
│ U₁/U₂ = (C₁ + C₂) / C₁ │
└───────────────────────────────┘

Note: U₂ < U₁ (Energy is lost as heat during charge redistribution)