Two conducting spheres of radii $5\, cm$ and $10\, cm$ are given a charge of $15\,\mu C$ each. After the two spheres are joined by a conducting wire, the charge on the smaller sphere is.......$\mu C$.

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 the positive ends are also connected,the decrease in energy of the combined system is

Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

In the following figure,$C_1=5 \mu F$,$C_2=C_3=10 \mu F$ and $\varepsilon=20 \text{ V}$. Initially,the switch $S$ is connected to point $A$ until capacitor $C_1$ is fully charged. Afterwards,the switch is thrown to the left side and connected to point $B$. The charge on capacitor $C_3$ after equilibrium is reached will be (in $\mu C$)

$A$ $10\,\mu F$ capacitor and a $20\,\mu F$ capacitor are connected in series across a $200\,V$ supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together,and no external voltage is applied. What is the potential difference across each capacitor?

Two capacitors of capacitances $C$ and $2C$ are charged to potential differences $V$ and $2V$,respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is $.....CV^2$.