The charge on each capacitor when a voltage source of $15 \ V$ is connected in the circuit as shown,is (in $\mu C$)

In the given circuit,a charge of $+80 \ \mu C$ is given to the upper plate of the $4 \ \mu F$ capacitor. Find the charge on the upper plate of the $3 \ \mu F$ capacitor in the steady state in $\mu C$.

$A$ 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 $A$.

Two identical capacitors are joined in parallel,charged to potential $V$,separated and then connected in series,$i.e.$,the positive plate of one is connected to the negative plate of the other. Then

Two positive charges of magnitude $q$ are placed at the ends of one side of a square of side $2a$. Two negative charges of the same magnitude are kept at the other two corners. Starting from rest,if a charge $Q$ moves from the midpoint of the side with positive charges to the centre of the square,its kinetic energy at the centre of the square is

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