Two insulated spheres of radii $R_1$ and $R_2$ having charges $Q_1$ and $Q_2$ respectively are connected to each other. There is:

Two spheres $A$ and $B$ of radii $4 \text{ cm}$ and $6 \text{ cm}$ are given charges of $80 \mu\text{C}$ and $40 \mu\text{C}$ respectively. If they are connected by a fine wire,the amount of charge flowing from one to the other is

$A$ conducting sphere $S_1$ of radius $r_1 = 3 \text{ cm}$ is connected by a conducting wire to another conducting sphere $S_2$ of radius $r_2 = 2 \text{ cm}$. Before they are connected,$S_1$ carries a charge of $10 \text{ units}$. The electric potential at a point which is at a distance $4 \text{ cm}$ from the centre of $S_1$ and a distance $3 \text{ cm}$ from the centre of $S_2$ is:

An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air-cored parallel capacitor charged to a potential $V$. The two share the charge and the common potential is $V'$. The dielectric constant $K$ is

Two metallic spheres of radii $1\,cm$ and $2\,cm$ are given charges $10^{-2}\,C$ and $5 \times 10^{-2}\,C$ respectively. If they are connected by a conducting wire,the final charge on the smaller sphere is

$A$ capacitor is charged with a battery and the energy stored is $U$. After disconnecting the battery,another capacitor of the same capacity is connected in parallel to the first capacitor. Then the energy stored in each capacitor is