Two metal spheres of radii $0.01 \ m$ and $0.02 \ m$ are given a charge of $15 \ mC$ and $45 \ mC$ respectively. They are then connected by a wire. The final charge on the first sphere is $\ldots \ldots \ldots \times 10^{-3} \ C$.

The energy of a charged capacitor is $U$. It is removed from the battery and then connected in parallel to another uncharged capacitor having capacitance twice that of the first one. The energy of the first and second capacitors respectively is . . . . . . .

$A$ $10 \ \mu F$ capacitor is charged to a potential difference of $50 \ V$ and connected in parallel to another uncharged capacitor. The common potential difference becomes $20 \ V$. The capacitance of the second capacitor is ........ $\mu F$.

$A$ sphere of radius $4 \ cm$ has a charge of $80 \ \mu C$ and a sphere of radius $6 \ cm$ has a charge of $40 \ \mu C$. If they are connected by a conducting wire,how much charge will flow from the $4 \ cm$ sphere to the $6 \ cm$ sphere?

Two identical capacitors have the same capacitance $C$. One of them is charged to potential $V_1$ and the other to $V_2$. The negative ends of the capacitors are connected together. When positive ends are also connected,the decrease in energy of the combined system is

$A$ capacitor of capacity $4 \, \mu F$ is charged to $80 \, V$ and another capacitor of capacity $6 \, \mu F$ is charged to $30 \, V$. When they are connected, the energy lost by the $4 \, \mu F$ capacitor is: (in $ \, mJ$)