Two spherical conductors of capacities $$3 \mu \mathrm{F}$$ and $$2 \mu \mathrm{F}$$ are charged to same potential having radii $$3 \mathrm{~cm}$$ and $$2 \mathrm{~cm}$$ respectively. If '$$\sigma_1$$' and '$$\sigma_2$$' represent surface density of charge on respective conductors then $$\frac{\sigma_1}{\sigma_2}$$ is

Three identical capacitors of capacitance '$$\mathrm{C}$$' each are connected in series and this connection is connected in parallel with one more such identical capacitor. Then the capacitance of whole combination is

A parallel plate capacitor is charged by a battery and battery remains connected. The dielectric slab of constant '$$\mathrm{K}$$' is inserted between the plates and then taken out. Then electric field between the plates

Two identical capacitors have the same capacitance '$$C$$'. One of them is charged to a 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