In the given circuit, the ratio of charge stored in the capacitors $C, 2C, 3C, 4C, 5C$ is

In the circuit shown below,the switch $S$ is connected to position $P$ for a long time so that the charge on the capacitor becomes $q_1 \mu C$. Then $S$ is switched to position $Q$. After a long time,the charge on the capacitor is $q_2 \mu C$.
$(1)$ The magnitude of $q_1$ is
$(2)$ The magnitude of $q_2$ is
Give the answer of question $(1)$ and $(2)$

$A$ 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 electrician requires a capacitance of $6 \mu F$ in a circuit across a potential difference of $1.5 kV$. $A$ large number of $2 \mu F$ capacitors which can withstand a potential difference of not more than $500 V$ are available. The minimum number of capacitors required for the purpose is

To establish an instantaneous current of $2\,A$ through a $1\,\mu F$ capacitor,the potential difference across the capacitor plates should be changed at the rate of:

Seven capacitors,each of capacitance $2\ \mu F$,are connected in such a way that the total equivalent capacitance is $\frac{10}{11}\ \mu F$. Which of the following circuit diagrams represents this arrangement?