In the circuit shown,$q_2$ and $q_3$ are respectively (Initially all capacitors are uncharged).

In the circuit shown in the figure,the charge stored in the capacitor of capacity $5 \ \mu F$ is......$ \mu C$.

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is:

The diagram shows four capacitors with capacitances and breakdown voltages as mentioned. What should be the maximum value of the external emf source such that no capacitor breaks down? (in $kV$)

$A$ composite parallel plate capacitor is made up of two different dielectric materials with different thicknesses ($t_{1} = 0.5 \text{ mm}$ and $t_{2} = 1 \text{ mm}$) and dielectric constants ($\epsilon_{r1} = 3$ and $\epsilon_{r2} = 4$) as shown in the figure. The two dielectric materials are separated by a conducting foil $F$. The voltage of the conducting foil is $.....V$.

Four capacitors are connected as shown in the figure. Their capacities are indicated in the figure. The effective capacitance between points $x$ and $y$ is (in $\mu F$)