Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectrics ($k_1$ and $k_2$) in the following fashion. Which of the following is true? $(k_1 > k_2)$

An air-filled parallel plate capacitor has capacity $C$. If the distance between the plates is doubled and it is immersed in a liquid,the capacity becomes twice. The dielectric constant of the liquid is:

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant $4$,the capacitance is $C_1$. If one third of the space between the plates of the capacitor is filled with the medium of dielectric constant $4$,the capacitance is $C_2$. If in both cases,the dielectric is placed parallel to the plates of the capacitor,then $C_1: C_2=$

$A$ parallel plate capacitor is connected to a battery. The quantities charge,voltage,electric field,and energy associated with the capacitor are given by $Q_0, V_0, E_0$,and $U_0$ respectively. $A$ dielectric slab is introduced between the plates of the capacitor,but the battery remains connected. The corresponding quantities now given by $Q, V, E$,and $U$ related to the previous ones are:

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \ pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has a dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$,while the other one has a dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. The capacitance of the capacitor is now ......... $pF$.

The electrostatic force between two charges kept in air is $F$. If $30 \%$ of the space between the charges is filled with a medium,then the electrostatic force between the charges becomes $\frac{F}{2.56}$. The dielectric constant of the medium is