A solid conducting sphere of radius $a$ having a charge $q$ is surrounded by a concentric conducting spherical shell of inner radius $2a$ and outer radius $3a$ as shown in figure. Find the amount of heat produced when switch is closed.

$k=\frac{1}{4{\mathrm{\pi \epsilon }}_0}$

Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries charge $q$. Inner shell is neutral. Find the charge that will flow from inner shell to earth after the switch $S$ is closed.

A parallel plate capacitor with air as medium between the plates has a capacitance of $10 \mathrm{\mu F}$. The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant $K_1=2$ and $K_2=4$. The capacitance of the system will now be

Four condensers are joined as shown in the below figure. The capacity of each is $8\mathrm{\mu F}$. The equivalent capacity between the points $A$ and $B$ will be

The capacities and connection of five capacitors are shown in the below figure. The potential difference between the points $A$ and $B$ is $60 \mathrm{V}$. Then, the equivalent capacity between $A$ and $B$ and the charge on $5 \mathrm{\mu F}$ capacitance will be respectively

Three plates $A,B,C$ each of area $50 {\mathrm{cm}}^2$ have separation $3 \mathrm{mm}$ between $A$ and $B$ and $3 \mathrm{mm}$ between $B$ and $C$. The energy stored when the plates are fully charged is

Two capacitors $C_1$ and $C_2=2C_1$ 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 each capacitor will be

Five identical plates each of area $A$ are joined as shown in the figure. The distance between the plates is $d$. The plates are connected to a potential difference of $V$ volt. The charge on plates $1$ and $4$ will be

In the figure shown, what is the potential difference between the points $A$ and $B$ and between $B$ and $C$ respectively in steady state