The variation of the electric field between the plates of a capacitor is shown in the figure. Find the relation between $K_1$,$K_2$,and $K_3$,if $2x = y$.

If a capacitor with air,a capacitor with a dielectric,and a capacitor with a conducting slab have capacitances $C_1$,$C_2$,and $C_3$ respectively,then:

Three parallel plate capacitors $C_1, C_2$ and $C_3$ each of capacitance $5 \mu F$ are connected as shown in the figure. The effective capacitance between points $A$ and $B$,when the space between the parallel plates of $C_1$ capacitor is filled with a dielectric medium having a dielectric constant of $4$,is (in $\mu F$)

While a capacitor remains connected to a battery and a dielectric slab is inserted between the plates,then:

$A$ parallel plate capacitor with square plates of side $L$ is filled with four dielectrics of dielectric constants $K_1, K_2, K_3, K_4$ arranged as shown in the figure. The effective dielectric constant $K$ will be

$A$ capacitor is charged by a battery and the energy stored is $U$. Now,the battery is removed and the distance between the plates is increased to four times its original value. The new energy stored becomes: