Two conducting shells of radius $a$ and $b$ are connected by a conducting wire as shown in the figure. The larger shell is grounded. The capacitance of the system is:

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).

$A$ particle of charge $Q$ and mass $M$ moves in a circular path of radius $R$ in a uniform magnetic field of magnitude $B$. The same particle now moves with the same speed in a circular path of same radius $R$ in the space between the cylindrical electrodes of a cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $3R/2$. Then the potential difference between the capacitor electrodes must be

Find $V_A - V_B$ for the following given circuit in volts.

In the figure,the area of each plate is $A$ and the distance between consecutive plates is $d$. What is the effective capacitance between points $A$ and $B$?

$1000$ small drops,each of radius $r$ and charge $q$,coalesce to form a single large drop. How many times greater is the potential of the large drop compared to the potential of a small drop?