Find the ratio of energy stored in $5\,\mu F$ and $4\,\mu F$ capacitor in the given circuit in steady state

A $400\, pF$ capacitor is charged with a $100\, V$ battery. After disconnecting battery this capacitor is connected with another $400\, pF$ capacitor. Then find out energy loss.

A fully charged capacitor has a capacitance $‘C’$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $‘s’$ and mass $‘m’$. If the temperature of the block is raised by ‘$\Delta T$’, the potential difference $‘V’$ across the capacitance is

If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

The plates of a parallel plate capacitor have an area of $90 \,cm ^{2}$ each and are separated by $2.5\; mm .$ The capacitor is charged by connecting it to a $400\; V$ supply.

$(a)$ How much electrostatic energy is stored by the capacitor?

$(b)$ View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume $u$. Hence arrive at a relation between $u$ and the magnitude of electric field $E$ between the plates.

$100$ capacitors each having a capacity of $10\,\mu F$ are connected in parallel and are charged by a potential difference of $100\,kV$. The energy stored in the capacitors and the cost of charging them, if electrical energy costs $108\;paise\;per\;kWh$, will be