A capacitor of capacitance $\mathrm{C}$ and potential $\mathrm{V}$ has energy $E$. It is connected to another capacitor of capacitance $2 \mathrm{C}$ and potential $2 \mathrm{~V}$. Then the loss of energy is $\frac{x}{3} E$, where $\mathrm{x}$ is____________.

An uncharged capacitor is connected to a battery. On charging the capacitor

Two identical capacitors are connected in parallel across a potenial difference $V$. After they are fully charged, the positive plate of first capacitor is connected to negative plate of second and negative plate of first is connected to positive plate of other. The loss of energy will be

The energy of a charged capacitor is given by the expression ($q$= charge on the conductor and $C$ = its capacity)

A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If $x$ is the separation between the plates, the time rate of change of electrostatic energy of capacitor is proportional to

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path of radius $r$, the work done will be equal to