$A$ $4\,\mu F$ capacitor is connected in parallel to another capacitor of $8\,\mu F$. Both the capacitors are then connected in series with a $12\,\mu F$ capacitor and charged to $20\;V$. The charge on the plate of the $4\,\mu F$ capacitor is......$\mu C$.

Find the charge on capacitor $C_3$. Given that $C_1 = C_2 = C$ and $C_3 = C_4 = 3C$.

$A$ 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 . . . . . . .

Assertion: Charges are given to plates of two plane parallel plate capacitors $C_1$ and $C_2$ (such that $C_2 = 2C_1$) as shown in the figure. Then the key $K$ is pressed to complete the circuit. Finally,the net charge on the upper plate and the net charge on the lower plate of capacitor $C_1$ is positive.
Reason: In a parallel plate capacitor,both plates always carry equal and opposite charge.

As shown in the figure,four capacitors each of capacitance $25 \, \mu F$ are connected. The voltmeter reads $200 \, V$. Find the charge on each plate of the capacitors.

The values of charges $q_1, q_2$ and $q_3$ as shown in the figure are: