At distances of $5 \ cm$ and $10 \ cm$ outwards from the surface of a uniformly charged solid sphere,the potentials are $100 \ V$ and $75 \ V$ respectively. Then:

$(a)$ $A$ $900 \; pF$ capacitor is charged by a $100 \; V$ battery [Figure $(a)$]. How much electrostatic energy is stored by the capacitor?
$(b)$ The capacitor is disconnected from the battery and connected to another $900 \; pF$ capacitor [Figure $(b)$]. What is the electrostatic energy stored by the system?

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 . . . . . $\mu C$.

Three uncharged capacitors of capacitance $C_1$,$C_2$ and $C_3$ are connected as shown in the figure to one another and to points $A$,$B$ and $D$ at potentials $V_A$,$V_B$ and $V_D$. Then the potential at point $O$ will be

$A$ 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 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:

$A$ parallel plate capacitor of capacitance $2\; F$ is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The ratio $E_2 / E_1$ is