In the circuit shown in the figure,the ratio of charges on $5 \mu F$ and $4 \mu F$ capacitors is:

Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10 \mu F$ are individually charged by a $100 \, V$ $D.C.$ source. Capacitor $C_1$ is kept connected to the source and a dielectric slab is inserted between its plates. Capacitor $C_2$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards,the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be $......... \, V$. (Assuming dielectric constant $K = 10$)

In the circuit shown,initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1=10 \mu F$,$C_2=30 \mu F$,and $C_3=C_4=80 \mu F$.
Which of the statement$(s)$ is/are correct?
$(1)$ The key $S_1$ is kept closed for a long time such that capacitors are fully charged. Now key $S_2$ is closed. At this time,the instantaneous current across the $30 \Omega$ resistor (between points $P$ and $Q$) will be $0.2 A$.
$(2)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage difference between points $P$ and $Q$ will be $10 V$.
$(3)$ At time $t=0$,the key $S_1$ is closed,the instantaneous current in the closed circuit will be $25 mA$.
$(4)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage across the capacitor $C_1$ will be $4 V$.

Three identical capacitors $C_1, C_2$ and $C_3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity $\varepsilon_{r}$. The cell electromotive force (emf) $V_0=8 \,V$. First the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged,$S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium,the charge on $C_3$ is found to be $5 \mu C$. The value of $\varepsilon_{r}$ is:

$A$ parallel plate capacitor is charged and then disconnected from the source of steady $E.M.F.$ The plates are then drawn apart farther. Again it is connected to the same source. Then:

For what value of $C$ in $\mu F$ in the given figure,the equivalent capacitance between $A$ and $B$ becomes independent of the number of repeating sections?