Two thin conducting plates (very large) parallel to each other carrying total charges $\sigma A$ and $-2\sigma A$, respectively (where $A$ is the area of each plate), are placed in a uniform external electric field $E$ as shown. Find the surface charge on each surface.

A parallel plate capacitor of capacitance $C$ is as shown. A thin metal plate $A$ is placed between the plates of the given capacitor in such a way that its edges touch the two plates as shown. The capacity a cross $P$ and $Q$now becomes

Two spherical conductors $A_1$ and $A_2$ of radii $r_1$ and $r_2$ are placed concentrically in the air. The two are connected by a copper wire as shown in the figure. Then the equivalent capacitance of the system is

There are two conducting spheres of radius $a$ and $b$ $(b>a)$ carrying equal and opposite charges. They are placed at a separation $d(>>>a\mathit{ }\mathit{\&} b).$ The capacitance of the system is

A network of uncharged capacitors and resistances is as shown.

Current through the battery immediately after the key, $K$ is closed and after a long time interval is: