$A$ capacitor of capacitance $C = 900 \, pF$ is charged fully by a $100 \, V$ battery as shown in figure $(a)$. Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance $C = 900 \, pF$ as shown in figure $(b)$. The electrostatic energy stored by the system in figure $(b)$ is $\dots \times 10^{-6} \, J$.

$A$ particle of charge $Q$ and mass $M$ moves in a circular path of radius $R$ in a uniform magnetic field of magnitude $B$. The same particle now moves with the same speed in a circular path of same radius $R$ in the space between the cylindrical electrodes of a cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $3R/2$. Then the potential difference between the capacitor electrodes must be

The charge on the $4\,\mu F$ capacitor in the given circuit is .... in $\mu C$.

$A$ circuit is shown in the figure for which $C_1=(3 \pm 0.011) \mu F$,$C_2=(5 \pm 0.01) \mu F$,and $C_3=(1 \pm 0.01) \mu F$. If $C$ is the equivalent capacitance across $AB$,then $C$ is given by:

$27$ identical drops of mercury are charged simultaneously with the same potential of $10 \ V$. Assuming the drops to be spherical,if all the charged drops are made to combine to form one large drop,then its potential will be . . . . . . volt.

In the following circuit $C_1=12 \mu F, C_2=C_3=4 \mu F$ and $C_4=C_5=2 \mu F$. The charge stored in $C_3$ is . . . . . $\mu C$.