Electromagnetism - Capacitor

The capacitor in the circuit shown above is initially charged. After closing the switch, how much time elapses until one-half of the capacitor’s initial stored energy is dissipated?

A. RC
B. RC/2
C. RC/4
D. RC ln 2
E. ½ RC ln 2

(GR9277 #11)

Solution:

U_t  = ½U₀ , t = ?
Energy of capacitor:  U = ½CV² 

U_t  = ½U₀ → ½CV_t ²  = ½ × ½CV₀2
V_t ²  = ½ V₀2

Potential difference of capacitor: V_t = V₀e^−t/RC
V_t ² = V₀2e^−2t/RC
 ½ V₀2 = V₀2e^−2t/RC → ½  = e^−2t/RC
ln ½ = − 2t/RC →  ln 2 = 2t/RC 
t =  ½ RC ln 2

Answer: E