$27$ identical drops of mercury are charged simultaneously with the same potential of $10 \ V$. Assuming the drops to be spherical,if all the charged drops are made to combine to form one large drop,then its potential will be . . . . . . volt.

$STATEMENT-1$: For practical purposes,the Earth is used as a reference at zero potential in electrical circuits.
$STATEMENT-2$: The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\frac{Q}{4 \pi \varepsilon_0 R}$.

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

$A$ 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 $... \mu s$.

The figure shows a diagonal symmetric arrangement of capacitors and a battery. The potentials of the points $B$ and $D$ are:

In the steady state,what is the potential difference between points $A$ and $B$ in volts? (All capacitors are in $\mu F$.)