A part of a circuit is in steady state along with the current flowing in the branches. Value of each resistance is shown in figure. Calculate the energy stored in the capacitor $\mathrm{C}\left(4\mathrm{\mu F}\right)$is $\mathrm{K}\times {10}^{-4}\mathrm{J}$ then K is ___

Applying Kirchhoff’s first law at junction M. we get the current I₁ = 3A. 

Applying Kirchhoff’s first law at junction P. we get the current I₂ =1A

Moving the loop from MNOP, we get
${\mathrm{V}}_{\mathrm{M}}-5{\mathrm{I}}_1-{\mathrm{I}}_1-2{\mathrm{I}}_2={\mathrm{V}}_{\mathrm{P}}\text{ or }{\mathrm{V}}_{\mathrm{M}}-{\mathrm{V}}_{\mathrm{P}}=6{\mathrm{I}}_1+2{\mathrm{I}}_2=20\mathrm{V}$
Energy stored in the capacitor is $\frac{1}{2}{\mathrm{CV}}^2=\frac{1}{2}\times 4\times {10}^{-6}\times 20\times 20=8\times {10}^{-4}\mathrm{J}$