What is energy density ? Writes its formula.

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $\mathrm{V}$ and other to the potential $2 \mathrm{~V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference $4\, V.$ When another parallel combination of $n_2$ capacitors, each of value $C_2,$ is charged by a source of potential difference $V$, it has the same (total) energy stored in it, as the first combination has. The value of $C_2,$ in terms of $C_1$ is then

Two capacitors each of $1\,\mu F$ capacitance are connected in parallel and are then charged by $200\;volts$ $d.c.$ supply. The total energy of their charges (in $joules$) is

Effective capacitance of parallel combination of two capacitors $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ is $10\; \mu \mathrm{F}$. When these capacitors are individually connected to a voltage source of $1\; \mathrm{V},$ the energy stored in the capacitor $\mathrm{C}_{2}$ is $4$ times that of $\mathrm{C}_{1}$. If these capacitors are connected in series, their effective capacitance will be

A battery does $200 \,J$ of work in charging a capacitor. The energy stored in the capacitor is ......... $J$