Two metal spheres,one of radius $R$ and the other of radius $2R$,both have the same surface charge density $\sigma$. They are brought in contact and then separated. What will be the new surface charge densities on them?

$A$ part of a circuit is shown in the figure. If $V_A - V_B = 4 \, V$,then find the charge on the $4 \, \mu F$ capacitor connected to point $A$. (in $, \mu C$)

$A$ parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to a potential $V$ and then the battery is disconnected. $A$ slab of dielectric constant $k$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q$,$E$,and $W$ denote respectively the magnitude of charge on each plate,the electric field between the plates (after the slab is inserted),and the work done on the system in the process of inserting the slab,then state the incorrect relation from the following:

The following figure shows a $9 \ V$ battery and $3$ uncharged capacitors of capacitances $C_1 = C_2 = C_3 = 1 \ \mu F$. The switch is thrown to the right side until capacitor $C_1$ is fully charged,then the switch is thrown to the left. The final charge on capacitor $C_2$ is (in $\mu C$)

In the figure, a potential of $+1200\, V$ is applied to point $A$ and point $B$ is earthed. What is the potential at point $P$ in volts?

Calculate the amount of heat liberated in the circuit after closing the switch $S$.