A condenser having a capacity $2.0$ micro farad is charged to $200\;volts$ and then the plates of the capacitor are connected to a resistance wire. The heat produced in joules will be
$4 \times {10^4}\,J$
$4 \times {10^{10}}\,J$
$4 \times {10^{ - 2}}\,J$
$2 \times {10^{ - 2}}\,J$
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
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
A capacitor is charged with a battery and energy stored is $U$. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is
A $16\ \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ battery with internal resistance $1\ \Omega$ is connected across one of its sides. If a $4\ \mu \mathrm{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \ \mu \mathrm{J}$. where $x=$________.
The energy stored in a condenser of capacity $C$ which has been raised to a potential $V$ is given by