In $Millikan's$ oil drop experiment,a charge $Q$ is held stationary between two plates under a potential difference of $2400\, V$. If a second drop with half the radius is to be held stationary using a potential difference of $600\, V$,then the charge on the second drop is:

$A$ spherical drop of mercury having a potential of $2.5\, V$ is obtained as a result of merging $125$ droplets. The potential of constituent droplets would be........$V$

$A$ 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 . . . . . . .

Two capacitors $C_1 = 2\,\mu F$ and $C_2 = 6\,\mu F$ in series are connected in parallel to a third capacitor $C_3 = 4\,\mu F$. This arrangement is then connected to a battery of $e.m.f. = 2\,V$,as shown in the figure. How much energy is lost by the battery in charging the capacitors?

Three charged capacitors,$C_1 = 17 \ \mu F$,$C_2 = 34 \ \mu F$,$C_3 = 41 \ \mu F$ and two open switches,$S_1$ and $S_2$ are assembled into a network with initial voltages and polarities,as shown in the figure. The final status of the network is attained when the two switches,$S_1$ and $S_2$ are closed. In the figure,the final charge on capacitor $C_3$ in $mC$ is closest to:

$n$ identical droplets are charged to $V$ volt each. If they coalesce to form a single drop,then its potential will be