In the given circuit,the charge $Q_2$ on the $2 \ \mu F$ capacitor changes as $C$ is varied from $1 \ \mu F$ to $3 \ \mu F$. $Q_2$ as a function of '$C$' is given properly by:

$A$ 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 of capacitances $25 \mu F, 30 \mu F$ and $45 \mu F$ are connected in parallel to a supply of $100 \ V$. Energy stored in the above combination is $E$. When these capacitors are connected in series to the same supply,the stored energy is $\frac{9}{x} E$. The value of $x$ is . . . . . . .

$A$ conducting sphere of radius $a$ has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a$. Find the electrostatic energy of the system.

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$. $(i)$ The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is $E_1$. (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$. Then,the value of $E_1 / E_2$ is:

In the given figure,three capacitors $C_1, C_2$ and $C_3$ are connected to a battery. With symbols having their usual meanings,the correct conditions are: