As shown in the figure, two parallel plate capacitors having equal plate area of $$200 \mathrm{~cm}^{2}$$ are joined in such a way that $$a \neq b$$. The equivalent capacitance of the combination is $$x \in_{0} \mathrm{~F}$$. The value of $$x$$ is ____________.

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 __________ $$\mu \mathrm{F}$$

For the given circuit, in the steady state, $\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=$ ________ V.

Two parallel plate capacitors $C_{1}$ and $C_{2}$ each having capacitance of $10 \mu \mathrm{F}$ are individually charged by a 100 V D.C. source. Capacitor $C_{1}$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor $\mathrm{C}_{2}$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $C_{1}$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ________ V.

(Assuming Dielectric constant $=10$ )