Two parallel plate air capacitors of same capacity ' C ' are connected in series to a battery of emf ' $E$ '. Then one of the capacitors is completely filled with dielectric material of constant ' K '. The change in the effective capacity of the series combination is

Seven capacitors each of capacitance $2 \mu \mathrm{~F}$ are connected in a configuration to obtain an effective capacitance $\frac{6}{13} \mu \mathrm{~F}$. The combination which will achieve this will have

Two identical capacitors have the same capacitance ' $C$ '. One of them is charged to potential $\mathrm{V}_1$ and other to $\mathrm{V}_2$. The negative ends of capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is

The potential difference that must be applied across the series and parallel combination of 4 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is