In the adjoining figure are shown three capacitors $C_1, C_2$ and $C_3$ joined to a battery. The correct condition will be (symbols have their usual meanings)

  

 

$A\mathit{,}\mathit{ }B\mathit{,}\mathit{ }C$ and $D$ are large conducting plates kept parallel to each other. $A$ and $D$ are fixed. Plates $B$ and $C$, connected to each other by a rigid conducting rod, can slide over frictionless rails as shown. Initially, the distance between plates $A$ and $B$ is the same as that between plates $C$ and $D$. If now, the rod (along with plates $B$ and $C$) is slightly moved towards the right, the capacitance between the terminals $1$ and $2$

Four plates of equal area $A$ are separated by equal distances $d$ and are arranged as shown in the figure. The equivalent capacity is

A parallel plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constants $k_1,k_2$ and $k_3$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by,

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

Consider a parallel plate capacitor of $10 \mu \mathrm{F}$ with air filled in the gap between the plates. Now one-half of the space between the plates is filled with a dielectric of dielectric constant $4$ as shown in the figure. The capacity of the capacitor changes to