A parallel plate capacitor has plates of area $0.4 \pi \mathrm{~m}^2$ and spacing of 0.5 mm . If a slab of thickness 0.5 mm and dielectric constant 4.5 is introduced in between the plates of the capacitor, then the capacitance of the capacitor is

In the given circuit, the potential difference across the plates of the capacitor $C$ in steady state is

One of the two identical capacitors having the same capacitance $C$, is charged to a potential $V_1$ and the other is charged to a potential $V_2$. If they are connected with their like plates together, then the decrease in the electrostatic potential energy of the combined system is

If 27 indentical charged conducting spheres each of capacitance $10 \mu \mathrm{~F}$ combine to form a big sphere, then the capacitance of the big sphere is