Three uncharged capacitors of capacitances $C_1$,$C_2$,and $C_3$ are connected as shown in the figure. If $A$,$B$,and $C$ are at potentials $V_1$,$V_2$,and $V_3$ respectively,then the potential at point $O$ is:

$A$ parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to a potential $V$ and then the battery is disconnected. $A$ slab of dielectric constant $k$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q$,$E$,and $W$ denote respectively the magnitude of charge on each plate,the electric field between the plates (after the slab is inserted),and the work done on the system in the process of inserting the slab,then state the incorrect relation from the following:

$A$ metal ball of radius $R$ is placed concentrically inside a hollow metal sphere of inner radius $2R$ and outer radius $3R$. The ball is given a charge $+2Q$ and the hollow sphere is given a total charge $-Q$. The electrostatic potential energy of this system is:

What are the charges stored in the $1 \,\mu F$ and $2 \,\mu F$ capacitors in the circuit below,once the currents become steady?

$A$ capacitor of capacitance $C$ is charged to a potential difference $V$ from a cell and then disconnected from it. $A$ charge $+Q$ is now given to its positive plate. The potential difference across the capacitor is now:

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