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I have been reading in pretty much all the books that in a LC circuit when you switch on the circuit, Capacitor starts to discharge. It will take some time for current to be maximum in an inductor which is understandable. And then they say, after the current has reached maximum, it starts to charge the capacitor ( with opposite polarity).

Why doesn't capacitor start to get charged (in opposite polarity) when current is building up in inductor.? why it has to wait till current reaches maximum in inductor.?

user31058
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3 Answers3

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You seem to have implied that the capacitor is both simultaneously discharging and charging.

With the capacitor fully charged an inductor is connected across the capacitor thus completing an electrical circuit.

The capacitor starts to discharge and a current starts to flow but its rate of increase is hindered by the back emf produced by the inductor.
So basically you have electrons moving from the negative plate of the capacitor to the positive plate of the capacitor thus the capacitor starts to discharge.

This continues and it so happens that when the current in the circuit reaches a maximum the capacitor is completely discharged.

Even though the capacitor is fully discharged there are electrons in motion in the circuit and these electrons cannot stop instantaneously as they have a mass and that would require an infinite force to act on them.

So the current continues to flow in the same direction and the capacitor start to charge with the opposite polarity.
This continues until the capacitor has the same charge but opposite polarity as at the start.

Then the sequence starts all over again with the current now flowing in the opposite direction.

In terms of energy you can think of it as an oscillation of the energy stored in the electric field of the capacitor and the energy stored in the magnetic field of the inductor.

Here is a diagrammatic representation also showing the more familiar oscillation of a spring and mass system.

enter image description here

You can think of the inductor as the mass and the capacitor as the spring in this analogy.

Farcher
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Electrical energy oscillates between the capacitor and the inductor.

The energy stored in the capacitor is a maximum when the charge stored on it is a maximum, and zero when it is discharged. The energy stored in the inductor is a maximum when the current flowing through it is a maximum and zero when there is no current flowing. At other times there is energy stored in both the capacitor and the inductor. The polarity of the charge and the direction of the current have no effect on how much energy is stored.

There is a fixed total amount of energy stored in the circuit. When the energy stored in the capacitor is decreasing the energy stored in the inductor must be increasing. And vice versa.

If the current through the inductor is increasing while the charge on the capacitor is also increasing then the total energy stored in the circuit is increasing. This cannot happen : there is nowhere for the extra energy to come from.

See also
Where does the extra energy come from in an LC circuit?
Why does the current increase in an LC circuit while the capacitor is being discharged?

sammy gerbil
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It does. Charges migrates from one plate to the other, working to reverse the polarity, but this is gradual and it takes time for the polarity to actually flip. Further, it happens that the current reaches its maximum exactly when the capacitor is fully discharged and after that point the charge continues to flow, now building up on the opposite side. Incidentally, I say "it happens" above but this is not a coincidence. It is the charge separation on the plates that drives the current. Once the polarity of the plates flipped, those charges are now providing an EMF working against the instantaneous current.

MarkP
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