Two insulated metallic spheres of $3\,\mu F$ and $5\,\mu F$ capacitances are charged to $300\, V$ and $500\, V$ respectively. The energy loss, when they are connected by a wire is

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A,$ the energy stored in the capacitor is 

The capacity of a condenser is $4 \times {10^{ - 6}}$ farad and its potential is $100\,\,volts$. The energy released on discharging it fully will be.......$Joule$

A $10\, micro-farad$ capacitor is charged to $500\, V$ and then its plates are joined together through a resistance of $10\, ohm$. The heat produced in the resistance is........$J$

A parallel plate capacitor is made of two square parallel plates of area $A$ , and separated by a distance $d <  < \sqrt A $ . The capacitor is connected to a battery with potential $V$ and allowed to fully charge. The battery is then disconnected.  A square metal conducting slab also with area $A$ but thickness $\frac {d}{2}$ is then fully inserted between the plates, so that it is always parallel to the plates. How much work has been done on the metal slab by external agent while it is being inserted?

A parallel plate capacitor of capacity ${C_0}$ is charged to a potential ${V_0}$

$(i)$ The energy stored in the capacitor when the battery is disconnected and the separation is doubled ${E_1}$

$(ii)$ The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is ${E_2}.$

Then ${E_1}/{E_2}$ value is