In the circuit shown, a potential difference of $30\, V$ is applied across $AB$ . The potential difference between the points $M$ and $N$ is....$V$

Half of the space between parallel plate capacitor is filled with a medium of dielectric constant $K$ parallel to the plates . If initially the capacity is $C$, then the new capacity will be

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 $P$....$V$

The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$ where $r$ is the distance from the centre $a,\,b$ are constants. Then the charge density inside the ball is

A finite ladder is constructed by connecting several sections of $2\,\mu F$ , $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between.......$\mu F$

Two capacitors $C_1$ and $C_2 = 2\,C_1$ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state, the charge on capacitors will be