A parallel plate capacitor of capacitance $2 \mathrm{F}$ is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The ratio $\frac{E_2}{E_1}$ 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 $R?$

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

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

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)