The insulated spheres of radii ${R_1}$ and ${R_2}$ having charges ${Q_1}$and ${Q_2}$ respectively are connected to each other. There is

The lower plate of a parallel plate capacitor is supported on a rigid rod. The upper plate is suspended from one end of a balance. The two plates are joined together by a thin wire and subsequently disconnected. The balance is then counterpoised. Now a voltage $V = 5000\, volt$ is applied between the plates. The distance between the plates is $d =5\, mm$ and the area of each plate is $A = 100 cm^2.$ Then find out the additional mass placed to maintain balance.......$g$ [All the elements other than plates are massless and nonconducting] :-

A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference $V =12\, V$ between its plates. The charging battery is now disconnected and a porcelin plate with $k =7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of $..........pJ$. (Assume no friction)

The energy of a charged capacitor is given by the expression ($q$= charge on the conductor and $C$ = its capacity)

In an electrical circuit drawn below the amount of charge stored in the capacitor is___ $\mu \mathrm{C}$.

If initial charge on all the capacitors were zero, work done by the battery in the circuit shown is ........... $mJ$