$A$ $2\,\mu F$ capacitor is charged to $100\,V$ and then its plates are connected by a conducting wire. The heat produced is........$J$.

The energy stored in the electric field produced by a metal sphere is $4.5\, J$. If the sphere contains $4\,\mu C$ charge,its radius will be.......$mm$. [Take: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\, N\cdot m^2/C^2$]

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.

$A$ fully charged capacitor has a capacitance $C$. It is discharged through a small coil of resistance wire,embedded in a block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$,the potential difference $V$ across the capacitor initially is

$A$ $6\,\mu F$ capacitor is charged from $10\,V$ to $20\,V$. The increase in energy will be:

$A$ capacitor of capacitance $5 \mu F$ is charged by a battery of emf $10 \text{ V}$. At an instant of time,the potential difference across the capacitor is $4 \text{ V}$ and the time rate of change of potential difference across the capacitor is $0.6 \text{ Vs}^{-1}$. Then,the time rate at which energy is stored in the capacitor at that instant is: