Four capacitors of capacitances $2 \mu F$,$3 \mu F$,$4 \mu F$,and $x \mu F$ are connected to a battery of emf $6 \text{ V}$ and of negligible internal resistance,as shown in the figure. If the ratio of the charges on $x \mu F$ and $4 \mu F$ capacitances is $\frac{3}{8}$,then the value of $x$ is

$A$ parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to a potential $V$ and then the battery is disconnected. $A$ slab of dielectric constant $k$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q$,$E$,and $W$ denote respectively the magnitude of charge on each plate,the electric field between the plates (after the slab is inserted),and the work done on the system in the process of inserting the slab,then state the incorrect relation from the following:

$A$ circuit shown in the figure consists of a battery of $emf$ $10\,V$ and two capacitors $C_1$ and $C_2$ of capacitances $1.0\,\mu F$ and $2.0\,\mu F$ respectively. The potential difference $V_A - V_B$ is $5\,V$. Which of the following statements is correct?

$A$ parallel plate capacitor is charged fully by using a battery. Then,without disconnecting the battery,the plates are moved further apart. Then,

In the circuit shown in the figure,for section $AB$,$C_1 = 1\ \mu F$,$C_2 = 2\ \mu F$,$E = 10\ V$,and the potential difference $V_A - V_B = -10\ V$. Find the charge on capacitor $C_1$.

Three capacitors $A, B$ and $C$ are connected to a battery of $25 \text{ V}$ as shown in the figure. The ratio of charges on capacitors $A, B$ and $C$ will be $-$