$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and charged to a potential difference $V$. Another capacitor of capacitance $3C$ is similarly charged to a potential difference $3V$. The charging battery is then disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

When a number of charged liquid drops coalesce,which of the following quantities does not change?

In the given circuit,$C_1=2\,\mu F, C_2=0.2\,\mu F, C_3=2\,\mu F, C_4=4\,\mu F, C_5=2\,\mu F, C_6=2\,\mu F$. The charge stored on capacitor $C_4$ is $.....\mu C$.

Sixty-four conducting drops,each of radius $0.02 \ m$ and each carrying a charge of $5 \ \mu C$,are combined to form a bigger drop. The ratio of the surface charge density of the bigger drop to that of the smaller drop will be ............

$A$ particle of mass $0.2 \ gm$ and charge $1 \ \mu C$ is held at a distance of $1 \ m$ from a fixed charge of $1 \ \mu C$. If the particle is released,it will be repelled. The speed of the particle when it is at a distance of $10 \ m$ from the fixed charge is $.... \ m/s$.

Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10 \mu F$ are individually charged by a $100 \, V$ $D.C.$ source. Capacitor $C_1$ is kept connected to the source and a dielectric slab is inserted between its plates. Capacitor $C_2$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards,the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be $......... \, V$. (Assuming dielectric constant $K = 10$)