A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF . The space between the plates is now filled with two dielectrics, the first having $\mathrm{K}_1=3$ and thickness $\mathrm{d}_1=\mathrm{d} / 3$, while the $2^{\text {nd }}$ has $\mathrm{K}_2=6$ and thickness $d_2=2 \mathrm{~d} / 3$. The capacitance of the new capacitor is :

A parallel plate capacitor has plate area $40 \mathrm{~cm}^2$ and plate separation 2 mm . The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5 . The capacitance of the system is ( $\varepsilon_0=$ permittivity of vacuum)

A parallel plate capacitor is charged and then isolated. If the separation between the plates is increased, which one of the following statement is NOT correct?

Two circular metal plates each of radius ' $r$ ' are kept parallel to each other distance ' $d$ ' apart. The capacitance of the capacitor formed is ' $\mathrm{C}_1$ '. If the radius of each of the plates is increased to $\sqrt{2}$ times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ' $\mathrm{C}_2$ '. The ratio of the capacitances $\mathrm{C}_1: \mathrm{C}_2$ is