Two identical capacitors have the same capacitance $C$. One of them is charged to potential $V_1$ and the other to $V_2$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

A capacitor of capacitance $C$ is charged to potential difference $V$ and then disconnected from the battery. The air dielectric of capacitor is replaced by another dielectric of dielectric constant $k$. The fractional decrease in energy of the capacitor is

If a $4 \mu \mathrm{F}$ capacitor is charged to $1 \mathrm{kV}$, then energy stored in conductor is

A parallel plate capacitor carries a charge $Q$. If a dielectric slab with dielectric constant $k=2$ is dipped between the plates, then

A capacitor of capacity $4 \mathrm{\mu F}$ charged to $50 \mathrm{V}$ is connected parallel to another capacitor of $2 \mathrm{\mu F}$ charged to $100 \mathrm{V}$ with plates of like charges connected together. What is the total energy before and after connection respectively?

A parallel plate capacitor is connected to a battery. The plates are pulled apart with uniform speed $v$. If $x$ is separation between plates, then the rate of change of the electrostatic energy of the condenser is proportional to

Assertion: A parallel plate capacitor is charged by connecting it across a battery. The battery is then disconnected and separation between the plates is decreased as a result of which the energy stored in the capacitor decreases.

Reason: Energy stored in the capacitor is equal to the work done in charging the capacitor.

A piece of cloud is having area $25\times {10}^6 {\mathrm{m}}^2$ and electric potential of $10^{5}$ $\mathrm{V}$. If the height of cloud is $0.75 \mathrm{km}$, the energy of electric field between earth and cloud will be,

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be