A parallel plate capacitor is charged to a potential difference of $100\,V$ and disconnected from the source of $emf$. A slab of dielectric is then inserted between the plates. Which of the following three quantities change?

$(i)$ The potential difference    $(ii)$ The capacitance    $(iii)$ The charge on the plates

Side length of equilateral triangle is $d. P$ is mid of side then potential at point $P, V_P$ is

Four metallic plates, each with a surface area of one side $A$, are placed at a distance $d$ from each other. The plates are connected as shown in the figure. The capacitance of  the system between $a$ and $b$ is

Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

A hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in figure. Let $V_A, V_B, V_C$ be the potentials at points $A, B$ and $C$ respectively. Then

In steady state heat conduction, the equations that determine the heat current $j ( r )$ [heat flowing per unit time per unit area] and temperature $T( r )$ in space are exactly the same as those governing the electric field $E ( r )$ and electrostatic potential $V( r )$ with the equivalence given in the table below.

We exploit this equivalence to predict the rate $Q$ of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If $\dot{Q} \propto R^{n}$, where $R$ is the radius, then the value of $n$ is