A square plate of side $'a'$ is placed in $xy$ plane having centre at origin if charge density of square plate is $\sigma = xy$ then. Total charge on the plate will be.

The resultant capacitance between $A$ and $B$ in the fig. is.....$\mu F$

A network of four capacitors of capacity equal to $C_1 = C, C_2 = 2C, C_3 = 3C$ and $C_4=4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is

Four capacitors of capacitance $10\, \mu\, F$ and a battery of $200\,V$ are arranged as shown.  How much charge will flow through $AB$ after the switch $S$ is closed?

In the figure a potential of $+ 1200\, V$ is given to point $A$ and point $B$ is earthed, what is the potential at the point $P$....$V$

A $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$