$64$ identical mercury drops,each charged to a potential of $10\, V$,are combined to form a single larger drop. The potential of the new larger drop is........$V$.

In the circuit shown in the figure,for section $AB$,$C_1 = 1\ \mu F$,$C_2 = 2\ \mu F$,$E = 10\ V$,and the potential difference $V_A - V_B = -10\ V$. Find the charge on capacitor $C_1$.

Two capacitors of $6 \, pF$ are connected in series and a potential difference of $5000 \, V$ is applied across the combination. If the combination is disconnected and then reconnected in parallel, what will be the potential difference between the plates?

Initially $n$ identical capacitors are joined in parallel and are charged to potential $V$. Now they are separated and joined in series. Then

$A$ radioactive substance in the form of a metallic sphere of diameter $10^{-3} \ m$ emits particles at a constant rate of $6.25 \times 10^{10}$ particles per second. If the sphere is electrically isolated,how long will it take for its potential to increase by $1.0 \ V$? Assume that $80\%$ of the emitted particles escape from the surface. The time taken is $... \mu s$.

Three capacitors $C_1, C_2$ and $C_3$ are connected as shown in the figure to a battery of $V$ volt. If the capacitor $C_3$ breaks down electrically,the change in total charge on the combination of capacitors is