Find the amount by which the total energy stored in the capacitor (in $\mu \mathrm{J}$) will increase in the circuit shown in the figure after the switch $K$ is closed. Consider all capacitors are of capacitance $3 \mathrm{\mu F}$ and battery voltage is $10 \mathrm{V}$.

The plate separation in a parallel plate condenser is $d$ and plate area is $A$. If it is charged to $V$ volt & battery is disconnected then the work done in increasing the plate separation to $2d$ will be

The equivalent capacitance between the points $a$ and $b$ is $KC$ ($K$ is a constant). Find the value of $K$.

In the figure, a capacitor is filled with dielectrics. The resultant capacitance is

The effective capacity in the following figure between the points $P$ and $Q$ will be