Four capacitors are connected to a battery as shown in the circuit. The ratio of charges on capacitors $C_2$ and $C_4$ is (Assume $C_1 = 1 \mu F, C_2 = 2 \mu F, C_3 = 3 \mu F, C_4 = 4 \mu F$ and the battery voltage $V = 10 \ V$ connected across the combination).

$A$ capacitor of $2\,\mu F$ capacitance is charged steadily from $0$ to $5\,C$. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the capacitor?

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

An automobile spring extends by $0.2\ m$ for a load of $5000\ N$. What is the ratio of the potential energy stored in the spring when it is compressed by $0.2\ m$ to the potential energy stored in a $10\ \mu F$ capacitor at a potential difference of $10000\ V$?

Two identical charged spherical drops,each at a potential $V$,coalesce to form a single larger drop. If the capacitance of each small drop is $C$,find the potential of the larger drop.

If the potential of $A$ is $10\,V$,then the potential of $B$ is