Change $Q$ on a capacitor varies with voltage $V$ as shown in the figure, where $Q$ is taken along the $X$-axis and $V$ along the $Y$-axis. The area of triangle $OAB$ represents

A $700\,pF$ capacitor is charged by a $50\,V$ battery. The electrostatic energy stored by it is

As in figure shown, if a capacitor $C$ is charged by connecting it with resistance $R$, then energy is given by the battery will be

If the charge on a capacitor is increased by $2C$, the energy stored in it increases by $44 \%$. The original charge on the capacitor is (in $C$ )

Two positively charged particles $X$ and $Y$ are initially far away from each other and at rest. $X$ begins to move towards $Y$ with some initial velocity. The total momentum and energy of the system are $p$ and $E$.

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