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

$A$ conducting sphere $A$ of radius $a$,with charge $Q$,is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed. $C$ is the common centre of the $A$ and $B$.

$N$ identical spherical drops,each charged to the same potential $V$,are combined to form a single big drop. What will be the potential of the new big drop?

$A$ parallel plate capacitor $A$ is filled with a dielectric whose dielectric constant varies with applied voltage as $K = V$. An identical capacitor $B$ of capacitance $C_0$ with air as dielectric is connected to a voltage source $V_0 = 30\,V$ and then connected to the first capacitor $A$ after disconnecting the voltage source. Find the charge and voltage on capacitor $A$.

Three capacitors are connected to a battery as shown in the figure. The ratio of charge on capacitors $C_3$ and $C_1$ is (in $.5$)

Determine the charge on the capacitor in the following circuit ................ $\mu C$.