what is the total work done by the battery during charging of capicator ? how energy is lost
Answers
Explanation:
At the moment the circuit is completed, the capacitor has zero voltage, while the supply has V. This voltage difference creates an electric field that accelerates charges. This acceleration sets up a current.
As the current flows, the capacitor charges until the voltage reaches V as well. At this point there is no voltage difference. But the accelerated charges are still moving. So half the energy has gone into the capacitor and (discounting losses) half has gone into the current in the wire. The current will continue to flow, charging the capacitor above V until the current stops. This is overshoot. Then since a potential difference exists, current will flow back the other way. The current and voltage oscillate for a period. This oscillation behavior in the circuit is ringing. Resistance in the circuit will eventually remove this extra energy, leaving only the charged capacitor.
This is very similar to suspending a ball from a spring and releasing it. It can be slowly lowered to the new equilibrium point, or it can be dropped and it will oscillate above and below the new equilibrium until frictional losses remove the extra energy