Two capacitors,one of capacitance $C$ and the other of capacitance $C/2$,are connected in parallel to a battery of potential difference $V$. Calculate the heat produced in the connecting wires.

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 $.5$)

$A$ capacitor of capacitance $C$ is charged to a potential difference $V$ from a cell and then disconnected from it. $A$ charge $+Q$ is now given to its positive plate. The potential difference across the capacitor is now:

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

$A$ parallel plate capacitor of capacitance $2\; F$ is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The ratio $E_2 / E_1$ is

$A$ parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant,then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$,where $\alpha$ is . . . . . . .