In the circuit shown in the figure,four capacitors are connected to a battery. The charge on the $5 \ \mu\text{F}$ capacitor is ....... $\mu\text{C}$.

$A$ parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is . . . . . . .

Three capacitors are connected to a battery as shown in the figure. The ratio of charge on capacitors $C_3$ and $C_1$ is (in $.5$)

$A$ capacitor is made of two circular plates of radius $R$ each,separated by a distance $d \ll R$. The capacitor is connected to a constant voltage $V$. $A$ thin conducting disc of radius $r \ll R$ and thickness $t \ll r$ is placed at the center of the bottom plate. Find the minimum voltage required to lift the disc if the mass of the disc is $m$.

The potential of point $A$ is greater than that of point $B$ by $19 \, V$. What is the potential difference in volts across the $3 \, \mu F$ capacitor?

Five capacitors of $10\,\mu F$ capacity each are connected to a $d.c.$ potential of $100\;V$ as shown in the figure. The equivalent capacitance between the points $A$ and $B$ will be equal to..........$\mu F$.