Two condensers, one of capacity $C$ and other of capacity $C/2$ are connected to a $V-$ volt battery, as shown in the figure. The work done in charging fully both the condensers is
$\frac{1}{4}\,C{V^2}$
$\;\frac{3}{4}\,C{V^2}$
$\;\frac{1}{2}\,C{V^2}$
$\;3\,C{V^2}$
Intially, switch $S$ is connected to position $1$ for a long time shown in figure. The net amount of heat generated in the circuit after it is shifted to position $2$ is
A parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, volt$ battery. Then the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ and the plates are maintained in connection with the battery, is
The insulated spheres of radii ${R_1}$ and ${R_2}$ having charges ${Q_1}$and ${Q_2}$ respectively are connected to each other. There is
A capacitor is charged to $200\, volt$ it has $0.1$ coulomb charge. When it is discharged, energy will be.....$J$
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 $E$.