The potential difference between the plates of a parallel plate capacitor is $10 V$ and separation is $5 \mathrm{cm}\mathit{.}$ Find the energy density between plates. $\left({\epsilon }_0={10}^{-11} \mathrm{F} {\mathrm{m}}^{-1}\right)$

In the circuit given below, the capacitor $C$ is charged by closing the switch $S_1$ and opening the switch $S_2$. After charging, the switch $S_1$ is opened and $S_2$ is closed, then the maximum current in the circuit

The potential differences that must be applied across the parallel and series combination of $3$ identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

A capacitor of capacitance $C$ is connected in series with a resistance $R$ and $DC$ source of emf $E$ through a key. The capacitor starts charging when the key is closed. By the time the capacitor has been fully charged, what amount of energy is dissipated in the resistance $R?$

A parallel plate capacitor whose capacitance $C$ is $14 \mathrm{pF}$ is charged by a battery to a potential difference $V=12 \mathrm{V}$ between its plates. The charging battery is now disconnected and a porcelain plate with $k=7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _______ $\mathrm{pJ}.$

(Assume no friction)