A parallel plate capacitor with air between the plates has a capacitance of  $9\ pF$ . The separation between its plates is $ 'd'$ .The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$

The work done in placing a charge of $8 \times 10^{-18}$ coulomb on a condenser of capacity $100\, micro-farad$ is

A parallel plate capacitor has plates with area $A$ and separation $d$. A battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d$ is introduced. The ratio of energy stored in the capacitor before and after slab is introduced, is

As shown in the fig. charges $+\,q$ and $-\,q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

Calculate the work done in taking a charge $-2 \times 10^{-9} \,C$ from $A$ to $B$ via $C$ is ......... (in diagram)

The equivalent capacitance of the system of capacitors between $A$ and $B$ as shown in the figure