BATTERY after charging, the charge stored in eke capacitor remains constant. When a capacitor is CHARGED by connecting a battery across its plates, the initial energy stored, \[U=\frac{{{q}^{2}}}{2C}\] When the battery is DISCONNECTED, then the charge remains constant i.e., \[q=\]constant. Now another identical capacitor is connected across it i.e., the capacitors are connected in PARALLEL, so the equivalent capacitance \[{{C}_{eq}}={{C}_{1}}+{{C}_{2}}=C+C=2C\] Thus, final energy stored by the system of capacitors, \[U'=\frac{{{q}^{2}}}{2{{C}_{eq}}}\] \[=\frac{{{q}^{2}}}{2(2C)}=\frac{1}{2}U\] \[\THEREFORE \] \[U'=\frac{U}{2}\]