Capacitors: Practice Problem & Solution

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Capacitors. Understanding the underlying formula is key to arriving at the correct answer below:

Initial energy $U = \frac{1}{2}CV^{2}$. Common potential after sharing charge is $V' = \frac{CV}{C+C} = \frac{V}{2}$. Energy in each capacitor is $U' = \frac{1}{2}C(V')^{2} = \frac{1}{2}C(\frac{V}{2})^{2} = \frac{1}{4}(\frac{1}{2}CV^{2}) = \frac{U}{4}$.