Two capacitors, $C_1 = 2 \text{ mF}$ and $C_2 = 8 \text{ mF}$, are connected in series across a $300 \text{ V}$ source. Then:

If the initial charge on all the capacitors was zero,the work done by the battery in the circuit shown is ........... $mJ$.

$A$ capacitor of capacitance $1 \ \mu F$ withstands a maximum voltage of $6 \ kV$,while a capacitor of $2 \ \mu F$ withstands a maximum voltage of $4 \ kV$. What maximum voltage will the system of these two capacitors withstand if they are connected in series? (in $kV$)

$A$ finite ladder is constructed by connecting several sections of $2\,\mu F$ and $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between? (in $\mu F$)

Five capacitors are connected to a $DC$ potential of $100\,V$ as shown in the figure. Find the charge in the $10\,\mu F$ capacitor (in $\mu C$).

$A$ capacitance of $2\ \mu F$ is required in an electrical circuit across a potential difference of $1.0\ kV$. $A$ large number of $1\ \mu F$ capacitors are available which can withstand a potential difference of not more than $300\ V$. The minimum number of capacitors required to achieve this is