A parallel plate capacitor with plate area $$\mathrm{A}$$ and plate separation $$\mathrm{d}$$ is filled with a dielectric material of dielectric constant $$K=4$$. The thickness of the dielectric material is $$x$$, where $$x < d$$.
Let $$\mathrm{C}_{1}$$ and $$\mathrm{C}_{2}$$ be the capacitance of the system for $$\chi=\frac{1}{3} d$$ and $$\mathcal{X}=\frac{2 d}{3}$$, respectively. If $$\mathrm{C}_{1}=2 \mu \mathrm{F}$$ the value of $$\mathrm{C}_{2}$$ is __________ $$\mu \mathrm{F}$$
(Assuming Dielectric constant $=10$ )
A capacitor of capacitance $$900 \mu \mathrm{F}$$ is charged by a $$100 \mathrm{~V}$$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $$x \times 10^{-} { }^{2} \mathrm{~J}$$. The value of $$x$$ is _____________.