Electromagnetism - Capacitor

Two real capacitors of equal capacitance (C₁ = C₂) are shown in the figure. Initially, while the switch S is open, one of the capacitors is uncharged and the other carries charge Q₀. The energy stored in the charged capacitor is U₀. Sometime after the switch is closed, the capacitors C₁ and C₂ carry charges Q₁ and Q₂, respectively; the voltages across the capacitors are V₁ and V₂; and the energies stored in the capacitors are U₁ and U₂.Which of the following statements is INCORRECT?

A. Q₀ = ½ (Q₁ + Q₂)
B. Q₁ = Q₂
C. V₁ = V₂
D. U₁ = U₂
E. U₀ = U₁ + U₂

(GR9677 #25)

Solution:

Initial charge: Q₀
Charge is conserved and distribute evenly
Q₀ = ½ (Q₁ + Q₂)
(A) CORRECT

C = Q/V
For parallel capacitor V = V₁ = V₂
Given C₁ = C₂ → Q₁ = Q₂
(B) and (C) CORRECT

U = ½QV
V₁ = V₂ and Q₁ = Q₂ 
→ U₁ = U₂
(D) CORRECT

U = ½QV → Q = 2U/V
From (A) Q₀ = ½ (Q₁ + Q₂),
2U₀/V₀ = ½ (2U₁/V₁ + 2U₂/V₂)
V₀ = V₁ = V₂ → 2U₀ = U₁ + U₂

(E) INCORRECT

Answer: E