$A$ capacitor is charged with a battery and the energy stored is $U$. After disconnecting the battery,another identical uncharged capacitor is connected in parallel with it. The total energy of the system of capacitors is . . . . . . .

The circuit shows two capacitors $A$ and $B$ of capacitances $C$ and $2C$ respectively. When they are fully charged,the cell is removed and the capacitors are connected with their plates of opposite polarities touching each other. Then:
$(a)$ Charge on $A$ is $\frac{4CE}{9}$
$(b)$ Charge on $B$ is $\frac{8CE}{9}$
$(c)$ Loss of energy in this process is $\frac{CE^2}{3}$
The correct statement$(s)$ is/are:

$A$ $3\ \mu F$ capacitor is charged to a potential of $300\ V$ and a $2\ \mu F$ capacitor is charged to $200\ V$. They are then connected in parallel with plates of opposite polarity joined together. What is the amount of charge (in $\mu C$) that flows through the connecting wires?

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 spheres of radii $1 \, cm$ and $2 \, cm$ are charged with $1.5 \times 10^{-8} \, C$ and $0.3 \times 10^{-7} \, C$ of positive charge,respectively. When they are connected by a wire,the charge will flow:

An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air-cored parallel plate capacitor charged to a potential $V$. The two capacitors share charges and the common potential becomes $V^{\prime}$. The dielectric constant $K$ is