Find the energy stored in the capacitor using Kirchhoff's Laws.

Strategy `:` Step-1 `:` Take the current from the batter of highest EMF
Step -2` :` Divide the total current into branch currents, keeping in mind that no current flows through capacitor.
Step-3 `:` Apply KVL to 3 loops shown in the figure.
Step -4 `:` Find the voltage across the capacitor using KVL
Step -5 ` :` Apply the formula `E = (1)/(2) CV^(2)` to find energy

Explanation

(1) Applying KVL to loop 2.
`-4i_(1)+ 6 =0implies i_(1) = 1.5 A `
(2) Applying KVL to loop -3.
`= (i-i_(1)) xx 3-3-(i-i_(1)) xx 2 + i_(1) xx 4 =0`
i.e., `- 5i + 9 i_(1) =5`
` :. I = ( 9)/(5) i_(1) -1`
`I = 1.7 A ( :' i_(1) = (3)/(2) A )`
(3) Applying KVL to loop C , during steady state capacitor acts as a open circuit having voltage across it.
`:. 2+ ( 1.7 - 1.5) xx + V = 0`
`:. V= - 2.4 ` volts.
(4) Energy stored in the capacitor
`E = (1)/(2) CV^(2) = (1)/(2) xx 5 xx 10^(-6) xx ( 2.4 )^(2)`
`:. E = 14.4 xx 10^(-6) J `