One of the two identical capacitors having the same capacitance $C$ is charged to a potential $V_1$ and the other is charged to a potential $V_2$. If they are connected with their like plates together,then the decrease in the electrostatic potential energy of the combined system is

$A$ capacitor of capacitance $900\,\mu F$ is charged by a $100\,V$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of the uncharged capacitor is connected to the positive plate and the other plate of the uncharged capacitor is connected to the negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}\,J$. The value of $x$ is $..............$

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

Two charged spheres of radii $a$ and $b$ are connected by a wire. The ratio of the electric fields on their surfaces $E_a/E_b$ is:

$A$ capacitor of capacitance $C_1 = 10 \mu F$ is charged using a $9 \text{ V}$ battery. It is then removed from the battery and connected to another uncharged capacitor $C_2 = 20 \mu F$ as shown in the figure. The charge on $C_2$ after equilibrium is reached 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